IAEA-135

HEAT AND MASS TRANSFERIN NUCLEAR POWER PLANTS

REPORT OF A PANELSPONSORED BY THE

INTERNATIONAL ATOMIC ENERGY AGENCYAND HELD IN VIENNA14-17 SEPTEMBER 1970

A TECHNICAL REPORT PUBLISHED BY THEINTERNATIONAL ATOMIC ENERGY AGENCY, VIENNA, 1971

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FOREWORD

A panel on "Heat and Mass Transfer in Nuclear Power Plants" was held "bythe International Atomic Energy Agency on 14 to 17 September 1970 at AgencyHeadquarters. A total of 19 specialists representing 13 countries and oneinternational organization participated in the discussions.

At present large nuclear power stations are competitive with large fossilfuel plants in most countries of the world. An improvement in the economicposition of nuclear power stations to permit them to become even more widelycompetitive, especially in medium sized units, is an important need today.Better knowledge and understanding of the heat and mass transfer processeswhich take place in nuclear power reactors, particularly in the core, willpermif an improvement in their performance and economics as well as in theirsafety. Continuing research and development in heat and mass transfer ofnuclear steam supply systems will permit more accurate analytical methodsto be developed for predicting the real behaviour of heat and mass flow inreactors and for achieving optimum designs.

The objective of the panel was to review the heat and mass transferproblems involved with different reactor types as well as the state of theart in heat and mass transfer research and technology with special referenceto the possible application in nuclear power plants. The panel was alsoasked to advise the Agency on its future programme of activities in this field.

It ie hoped, that this collection of nineteen papers, together with theconclusions and recommendations which were developed by the Panel Meeting,will be of interest to reactor designers and to persons working in researchand development. The teqrts of these papers have been supplied by the Panelmembers and no editing has been done by the Agency.

The Agency is grateful to the authors of the papers and to all the 'participants of the Panel for their contributions and it would particularlylike to express its thanks to the Chairman of the Panel, Dr. E.R.G. Eckert,of the University of Minnesota, for his guidance of the discussions in themost productive manner.

TABLE OP CONTENTSPage

FOREWORD

EXCERPTS PROM OPENING PVü&VTKSby Sir. C.A. Hennie I

SUMMARY REPORT"introductionSub-Committee PeportsT?ecomffleTví«yí 8«»"«i<?.r>cb Project?Panel Jteef

PAPERS

AUSTRIAPL-410/1 Prof. Dipl.-Ing. Dr.-techn. P.V. GILLI

Review of Problems Governing the DesignOptimization of Heat Exchangers in NuclearPower Plant. 15CANADA

/2 Dr. G.D. NcPHERSONThe Status of Heat and Mass Transfer ResearchRelated to the CANDU Power Reactor Program. 47GERMANY

/3 Prof. Dr. D. SMIDTProblems of Cooling Disturbances and SodiumBoiling in Fast Reactors. 67

/4 Prof. Dr.-Ing. P. MAYINGER, D. HEIN, W. KOEHLERBubble Formation and Departure with Sub-ccoledBoiling in Water-cooled Channels of High HeatFlux Density. 87

/5 Prof. Dr.-Ing. P. MAYIUGSRReview of Heat and Mass Transfer Studies Relatedto Nuclear Power Plant in Progress in theFederal Republic of Germany. 109

PageSWEDEN

/6 Dr. B. KJELLSTROEM, Ing. 0. NYLUNDHeat and Mass Transfer in Nuclear Power.Research Activities in Sweden. 121U.K.

/7 Dr. B.E. LAUNDER. Prof. D.B. SPALDJNGThe Problem of Predicting Heat and MomentumTransfer in Gas-cooled Nuclear Reactors.Current Status and Future Prospects» 125CSSR

/8 Dr. V. KRETTHeat and Mass Transfer in HWGCR Type A-lFuel Assemblies. 191POLAND

/9 Prof. J. MADEJSKIReport on Activities of the Institute ofNuclear Research in the Field of Heat andMass Transfer. 225

/10/Prof. J. KAB&JSKISome Basic Therraophysical Problems ofNucleate Pool Boiling. 231YUGOSLAVIA

/11/Prof. Z. 2ARICInternational Centre for Heat and Mass :Transfer and Cooperative Research. 247INDIA

/12/Kr. S.K. MEHTA, Mr. S.R. SASTRYBasic Research and Development Work in Heatand Mass Transfer in Nuclear Power Plants. 255

/13/Dr. B. KJELLSTROEMLateral Heat Transport for Turbulent Flowof a Gas in a Rod Bundle. 27?ITALY

/14/Prof. M. CUMOPost Burnout Heat Transfer. 303YUGOSLAVIA

/15/Prof. P. ANASTASIJEVICYugoslav Activities in the Field of Heat andMass Transfer Research in Nuclear Power ReactorSystems. 327

fegeCASABA

/16 Dr* G*3>. McPHERSOHThe Recommendation of Correlations and ComputerProgrames for use in the Design of NuclearPower Reactora.Suanary of Canadian Heat Transfer Studies 1970-71* 337

SPAIff/17 Dr. P. LDIS T LOIS

Actividades en España, sobre Transmisión deCalor y Transferencia de Materia en el Caapode Reactores Vadeares y Aplicaciones de laEnergía Suelear* 345

/l8 Prof. Dipl.-Ing. Dr.-teohn. P.V* aiLLIReview of Austrian Activities in the Field ofHeat and Mass Transfer in Nuclear Power* 353U.S.A.

/19 Prof. Dr, S.E*0* ECKEBTThe Present Status of Analysis Ijy Calculation ofLaminar and: Turbulent Heat Transfer «

CONCLUDING COMMENTSby Prof. Dr. E.R.Q. EekertGeneral Problems in Heat and Mass Transfer inNuclear Power Reactors. 367

ANNEX I Programme 371ANNEX II List of Participants

EXCERPTS FROM OPENING REMARKS

C.A. RennieDirectorDivision of Nuclear Power and ReactorsInternational Atomic Energy Agency, Vienna, Austria

We are very pleased to have a gathering of experts in the field heré¿particularly as this is the first formal Agency meeting on this subject.Earlier activities of the Agency in this field have been restricted to

. :'J •-•supporting rather small research projects.

One reason for this was that it mis thought that the probJLcms^n heatand mass transfer «ere not basically "nuclear" and that anyway. they, -were,being sufficiently covered by the work done outside the nuclear fie W.,,Another reason was the complex nature of the phenomena involved in heattransfer which seemed to indicate that it would be difficult to makegeneralised or analytical approaches. So, in order to find answers to"€•' 'practical problems in nuclear reactors y it was necessary to resort to semi-'•it- ••empirical methods involving the use of large and probably expensive experi-mental facilities for simulating the actual operating c'bhditi'olfe. finally,there was the historical fact that in the early stages of vïévetopraont ofnuclear energy scientists and engineers were much more' if ami liar with theproblems of heat and mass transfer than with the problems of nuclear andreactor physics. So, in the early days the reactor' physics aspects wererelatively more important than the heat and mass transfer problems.

Recently there have been some opinions expressed that the situationhas changed to a certain extent. For instance, some people believe thatthere are some problems today in the field of heat and mass transfer whichcan really be considered as specifically "nuclear". Similarity it seemsto be true that even some general heat and mass transfer problems are neithersufficiently understood nor adequately discussed on the internationalscientific level. There is also a danger that the work may tend to divergein two separate directions, one the purely academic or theoretical approachand the other semi empirical or industrial studies. It would clearly be anadvantage if these two approaches could be closely integrated.

It is worth keeping in mind that one of the biggest safety marginsinvolved in reactor core design is that which concerns the heat transfermechanism, as in «any cases it is necessary to adopt rather conservativedesign limite because of inadequate knowledge of the heat and mass transferprocesses. It is important to try and obtain practical and theoreticalresults which enable these margins to be narrowed. In fact, I think itis true to say today that the earlier position is now reversed, in thatour knowledge of reactor physics is probably more complete than our know-ledge of heat and mass transfer. This is mainly because of the largeeffort put into solving the reactor physics problems, and perhaps thisindicates that more effort could and should be put into solving the problemsof heat and mass transfer. The Agency has another interest in work on heatand mass transfer and that is advising Member States who wish to undertakework in this field, but very often with rather limited resources.

The following questions seem relevant and are suggested for consider-ation by the Panel. One is the problem of identifying the important shortterm and long term problems in the field of heat and mass transfer in nuclearpower engineering. A second is the identification of problems which could besuccessfully dealt with in smaller laboratories or in developing countrieswhich will probably not be equipped with extensive or expensive experimentalfacilities. A third is consideration of the possibilities of internationalcooperation in the heat and mass transfer field for nuclear power applicationswith particular emphasis on what role the IAEA could play.

SUMMARY REPORT

1. íyPROPÜCTION

In the initial phase of the development of nuclear reactors a great dealof emphasis was placed on fundamental research to demonstrate the technicalfeasibility of nuclear power reactors. For example, the problems related toreactor physics were the subject of extensive research over a long period oftine in several laboratories in different countries. This has led to theoptimisation of the physics design of the proven types of reactor systemsand to a narrowing down of the uncertainties* . ,

•' • •• • . • • . • ; • • . • ' . • • . " . . . ,';,• • ; ' . • : •The technical and economic feasibility of nuclear power reactors hasbeen clearly demonstrated and nuclear plants are being built in largenumbers. Farther improvements will depend largely on advances in materialstechnology and in systems engineering. In particular the subject of heat

~ • • " " • wi1 j '!•! , <• ;•;.and mass transfer should receive more attention. Most of the reactor designf\ - , : •> -tif :development to date has been based on empirical methods. Although these

designs have proved to be satisfactory there is now a need to make them moreeconomic to permit the benefits of low. cost nuclear power to be made avail-able to a larger number of users to meet their ever increasing demand forenergy. . . . .

The field of heat and mass transfer, which includes both conventionaland nuclear systems activities, is very broad in scope and the overall workiife not well coordinated at present. Several types of nuclear reactor systemsare in operation or under development involving different coolants, materialsand temperature and pressure conditions. There is a real need to improve theexchange of information among research and development workers engaged intheoretical, in experimental and in reactor design areas. This wouldaccelerate the flow of information from one group to another and lead toimproved designs in a shorter time.

Por these reasons the Agency organised fh«s Panel on Heat and Mass Trans-fer in Suelear Power Plants. The Panel meeting was requested to reviewsin general, the state of the art of the heat and mass transfer field with

particular emphasis on the application of recent developments in nuclearpower engineering; specific heat and mass transfer problems involved withparticular reactor types; specific heat and mass transfer problems involvedwith the new applications or concepts of use to nuclear power; equipment,components and instrumentation problems. The Panel was also asked to makerecommendations for further activities, including the identification ofalready existing activities which should be coordinated in order to meetspecific requirements, and to list problems and areas of work requiringfurther research.

It is worth noting that at the present time a number of new approachesare available to improve the experimental techniquest which along with bettercalculational techniques, (especially through the use of new tools such asmore sophisticated computer codes,) could allow a greater volume of in-formation to be analysed, and better predictions to be made, based on modelswhich would incorporate available experimental data which would otherwisebe too difficult to handle. The object of such work is to reduce over-designmargins, without reducing the operating safety, through a more precise under-standing of the heat and mass transfer phenomena.

The Panel discussions covered a wide range of topics, including status1reports of national heat and mass transfer activities and reviews of somedetailed studies, such as problems of predicting heat and momentum transferin gas-cooled nuclear reactors, and bubble formation and departure with sub-cooled boiling in water-cooled channels with high flux density. While thediscussions were by no means comprehensive and while not enough time wasavailable to cover all items thoroughly, it was, nevertheless, a most valuablefirst step and served to provide a better idea of the major problems and ofthe steps needed to resolve them*

There were 19 papers presented at the Panel, and each of the papers wasfollowed by a discussion. At the conclusion of the presentation of thepapers and discussions, the panelists were divided into three committees,each of which was given a specific task to review. Summaries of the committeereports are given below. The Panel as a whole reviewed the committee reports,came to some conclusions, and presented a number of recommendations for theconsideration of the Agency.

4

Hie Panel participants «ere unanimous in-their feeling tha* it would beappropriate for the Agency to play a co-ordinating role in futur* in thefield of heat and mass transfer associated with nuclear power, in particularby bringing together those activities related to system design and those

• . ' * , " . . ' -;n' . . " _ 'related to basic research work in the Member States. It recommended thatthe Agency should establish a Working Group of experts to meet periodicallyto review the development in the field, exchange information and advise theAgency on its programme*

2. SUB-COMMITTEE REPORTS

Following the presentation of papers, three Sub-committees of panelistswere formed to prepare Summary Reports which could serve as the basis of the1 ' . • i ' ""• "! iPanel's Recommendations.

4.

These Sub-committees were:Sub-committee Ko« 1. (Chairman B.E. Launder) to deal with heat and mass

•r\"f.: ' ' ~transfer problems in nuclear reactor technology;

» ' !t! " • •

Sub-oommittee So. 2. (Chairman D. Smidt) to deal with topics suitable forresearch and development in heat and mass transfer for small laboratories or• rin developing countries; andSub-committee Ho, j, (Chairman G.D. McPherson) to deal with the possibilitiesof international cooperation in the heat and mass transfer field ..for,.nuclearpower application with particular emphasis on the role of the:-IAEA..,. /,r

• • • •••''Vu.--; -.»•,'•The reports prepared by the Sub-committees were subsequently considered'• .'VI - • . ••- -.'•:.'

in detail during the final Panel discussion and a number of additionalcontributions were made. Finally, the Agency Secretariat was authorized tocombine these reports and contributions into & single document. The high»

' \ > f ' ' ' j ''

lights of these Sub-committee reports are presented below followed by therecommendations of the Panel.

PROJECTS

fhe following list of possible research projects, presented for theconsideration of the IAEA or other professional organizations, is basedon the proposals made by the Sub-committees or by individual Panel members*

3*1 Computational techniques for the solution of laminar and turbulentheat and mass transfer problems have been developed to a point«here they can be used for a wide variety of situations occuringin nuclear reactors as long as no change of phase occurs. Theyare, however« dependant on experimental verification, especiallyon the determination of turbulent transfer parameters. The requiredexperiments should be carried out at laboratories which have experiencein the required techniques and should be planned in close cooperationwith the institutions which develop the computations.

The organization of this cooperation could be considered as anappropriate activity of the IAEA since geometries and boundaryconditions are often specific to nuclear reactor applications»

3*2 The rapid expansion in the nuclear reactor field during the last20 years has forced the designers of nuclear power plants to carryout applied research and development work to a very large extent.Often, in doing so, little use has been made of existing basicresearch information and activity. This gap is especially widedue to the fact that the research work is expensive and needslarge facilities. The IAEA could consider that one of its tasksshould be to build a bridge between the basic and applied researchgroups. This can be done through the exchange of information orby arranging working sessions in which experts in the basic andthe applied research fields can discuss the possibilities ofcollaboration and can agree on specific tasks and programmes forfuture work as well as on possibilities for their solution.

3.3 There are often many correlations and computer programmes in existencewhich can be used to predict given heat transfer and fluid dynamics

phenomena. It is, therefore, difficult for a reactor designer to knowwhich particular one is the most accurate and suitable for his purpose*'The Agency could help greatly in clarifying the situation Toy sponsoringa Panel io discuss the comparison of correlations and programmes and laypublishing the recommendations of such a Panel*

3*4 The measurement of ihermodynamic and transport properties of fluidsis undertaken at various research laboratories, and internationalorganizations arrange for the coordination of this work. It couldbe a task of thft IAEA to aasure th$t subsistes which occur in nuclear'.reactor work, (and ranges of their rstates) are included in thisresearch, and to provide for a wide dissemination of the resultinginformation and formulât] cms for use in computers. . . . . .

. . - • * ' • • ' ' " t

3«5 There exists today a considerable amount of experimental data of afundamental as well as of an applied nature. The development ofnuclear reactors has been based on a large number of experimentsranging from basic ones up to the set tins: up of full-scale modelsof the proposed fuel elements* Such experiments have helped resolvemost of the problems to a degree of accuracy acceptable from the.engineering point of view. It is suggested that the IAEA encouragea re-analysis of the results of many of these experiments with aview to explaining and correlating the data, based on the new andimproved knowledge of the fundamental mechanisms, and thereby permitlearning more from these valuable experiments.

3*6 Safe reactor operation and the consequences of reactor accidents areof wide international interest. The Agency could, therefore, emphasizeits support of research work which leads to improved reactor designsafety standards and which relates particularly to heat and mass transfer,

3*7 $h* flow passages between rod bundles are of a very complex shape andthe surface texture of the boundaries may be non-uniform. These circum-stances combine tc jnake it very important in certain types of reactorto provide a rather detailed model of the way in which heat andmomentum is transferred laterally between one sub-channel and the next.

This is a problem where fundamental experimental and theoreticalresearch needs to proceed in parallel» A. turbulence model capable oftaking accurate account of these processes would need to abandon or,at least, substantially modify the traditional notion of "effective"turbulent exchange coefficients* The most promising route appears tobe to develop transport equations for the turbulent fluxes of heat andmomentum. Such a model would be capable of predicting turbulence-driven secondary flows and of recognizing the fact that momentum andheat may sometimes be transferred in the direction of increasingvelocity and temperature respectively.

Experimental research should aim at providing detailed measurementsof mean-flow and of turbulence quantities, including secondary flowvelocities and surface distributions of temperature and shear stress.A major outcome of this research would be that it would become possibleto design from a sound theoretical basis the optimum distribution ofrods within the cluster to provide as uniform surface temperaturedistributions as possible.

3.8 Over the past 20 years, a great deal of research has been done on theexperimental determination of the performance of various types ofroughened surfaces. Many shapes of roughness have been consideredand it does not appear especially urgent to undertake further testingprogrammes of this type. It is probable that roughness shapes ofsomewhat better performance could be determined by such means but themargin of improvement would probably not be great considering theexpense involved.

It is recommended, however, that consideration be given to a morefundamental and potentially much less costly approach to theseresearch problems. New computational procedures based on the numericalsolution of the governing fluid transport equation could be employedto predict the performance of the turbulence promoter* Some researchwould be necessary to refine the turbulence model to be used but thiscould proceed efficiently in parallel with the research described in recom-mendation 3.1 above. Moreover, because there is much experimental

8

• data available on existing roughened surfaces, -these could be used, - • • ? • . • J n •to verify the turbulence model adopted.Such a theoretical approach could be used, to assess very quickly theperformance of many shapes of surface* The effect of erosion or. damage

\to the turbulence promoter also could be covered in the calculations*

3«9 la high-temperature reactors, large variations in temperature mayoccur close to the wall and thus may substantially affect the locally , .prevailing- wall-temperature distributions. This is a problem whichtheoretically is a little easier to resolve than the two previous ones.Existing models of turbulence need but a small refinement to bring thenM % ". "- , *'ii'- <•"»••'-*^ •• :^ w

into satisfactory accord with the data. However* the viscous-affected.—>-jj •'••'.. .-. > . • • < • - • •region is very thin and to obtain accurate' profiles?, even of mean

;". ; . ..• '.v '" £ - . - . . . •velocity and temperature near the surface, requires great precision.-'-.;...-• M .. - • • vrnyr'1- • • ' "A useful outcome of this research would be the provision of computer-generated deuign correlations for heat-transfer rates in pipes andannuli.

/ ** *3*10. Up to now, measurements of sub-cooled boiling have been confined to

global effects. Investigators have been concerned with the....measurement .of- wean.vo?-d- fractions without examining" the processesof bubble growth and-decayf '.Corresponding theoretical approaches haveot .inooirporated the influence of bubble dynamics and thermodynamies»It ie 'important to isaie such fundaHiental experimental studies parti-i >•',•cularly concerning the temperature distribution in the superheatedboundary layer and the heat .and mass transfer processes during Igubble

r ~ , ' . ' *•'' '• ~ ' •condensation, fhese measurements will provide the data for guidingtheoretical models of the ncneqnilibrium process.

3.11 The very extensive existing measurements.of dry-out under steadystate using simple geometries dc.- not provide sufficient informationfor assessing the behaviour in complex .geometries — especially intransient conditions which may occurf for example, through pump failure.Great importance should, therefore, be placed on the experimentalmeasurement of dry-out under transient conditions. Simple jceqaetries

should be considered first to gain fundamental insight into theprocesses involved, including the question of whether thermodynamionon-equilibrium effects are important.More fundamental research on the mechanism of dry-out is also calledfor. Moreover, from the point of view of emergency cooling, thepost-dryout regime deserves careful experimental work and considerationneeds to be given to the problem of cooling a core after melt-down»

3*12 In BUR's, the turbulent mixing process is severely complicated bythe two-phase nature of the flow. Until now, measurements of mixingin two-phase flows has been restricted to geometrically simpleconfigurations. It seems desirable to conduct further careful anddetailed experimental research into the inter-subchannel mixingprocesses at low and high quality. These measurements would provideat least a starting point for constructing a general theoreticalmodel of two-phase flow transport.

3.13 A high degree of thermodynamic non-equilibrium is associated withmany of the severe transient conditions which may arise in BHR's.Although some research has been done on these problems there is stillonly a very limited knowledge of dynamic behaviour in orifices or ofthe density distribution in a reactor vessel during severe dépress-urisât i on. Moreover, further fundamental research should beconsidered on pressure-suppression problems, especially on bubblecondensation in water pools and vapour condensation on ice and onthe containment structures.

3*14 Experimental test work on two-phase flows is extremely expensive.In order to reduce the cost of research it would be desirable tomodel the flow conditions by using a fluid with a smaller enthalpyof vaporization than that of water. However, the problem of carryingput such simulations accurately is a challenging one, sincesimilarity laws are almost unknown. Further experimental andtheoretical work is called for to refine and verify the scalinglaws between, say, freon, and water to enable the modelling ofsuch phenomena as dryout, flow instabilities and the pressure dropthrough the reactor.

10

3.15 Using the criteria that in choosing the work in smaller laboratories,preference should be given to problems which are basic in nature and

; "' 'related to safety, the following topics are recommended for theselaboratories)

a) Experimental proof of general theoriesffor instance the one of Launder arid Spalding);

b) Development of particular measuring techniques;c) Analysis of existing data.

3.16 The IAEA could provide help to researchers at small laboratorieswhereby they could work for certain periods at related facilitiesof larger laboratories, obtain advisors for topics of interest tothem, and find larger programmes or organizations with which theycan associate.

3«17 The Agency could promote the. exchange of information and sponsormeetings of experts, preferably involving working groups.

4. PAHEL HBCOMBBrPATIONS

4,1 Heat and mass transfer problems in nuclear reactor technology4.1.1 Great emphasis should be placed upon fundamental research,

drawing, where possible» upon the recent advances intheoretical computational procedures for single-phase flow.

4.1.2 Keeping in mind that there will be a continuing need formore development and design-oriented research and that, asusual, large sums of money have to be spent on suchdevelopment research, it is recommended that a portion ofthie activity should be re-channelled towards a more basic

-• approach to the heat and mass transfer problems which arisein nuclear power technology.

4.1.3 In gas-cooled reactors three areas can be identified it»further fundamental research is neededt (l) turbulenprocesses in rod clusters, (2) the performance of sixrfaceturbulence promoters, and (3) the influence of severe property

H

gradients upon the structure of the viscous sublayer.(Much of the fundamental research proposed for gas-cooledreactors would be of relevance to liquid-metal systems aswell).

4.1.4 There has been an iimnense amount of research in the pasttwo decades inte the problems of boiling and two-phaseflow. In spite of this effort, there remain many unresolvedproblems concerning layout and safety calculations. Emphasisshould be placed on the five most important areas for furtherresearch: (l) sub-cooled boiling, (2) dry-out and burnoutin complex geometries in both steady-state and transientconditions, (3) two-phase mixing processes, (4) fluiddynamics problems in transiont conditions, and (5) modellinglaws for two-phase problems.

4»2 Topics for research and development in heat and mass transferfor small laboratories or in developing countries.4.2.1 The research effort of small laboratories, especially those

in developing countries, could be most fruitful if it werecoordinated with that of a larger programme, through bilateralor multilateral arrangements. The work could be moreproductive if carried out in close cooperation with a largergroup with greater experience.

4.2.2 For defining the most promising tasks it is important toconsider that one of the main reasons for doing researchin small laboratories is the training and education ofpersonnel. This leads to the conclusion that basic researchis preferable.

4*2.3 Another general conclusion is that research on safety problemslends itself to international cooperation between smaller andlarger groups. Whereas development problems sometimes involveindustrial interests, competition and patent regulations,safety research and international agreement on safety problemsare of common interest to all parties and ideal for unre-stricted exchange of information.

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4.3 The possibilities of interfflatlonal coopérât ion in the heat andmass transfer field, for nuclear power application with ;particularemphasis on the role of the IAEAIt is "believed that the coordination of research programmes in thefield of heat and mase transfer would reduce the redundancy andincrease the amount of research in progress while stimulating1 theexchange of ideas and results among the interested countries. Avast amount of research is required in this field and it would servethe needs of nuclear power reactor development io have the IAEAcarry out the follctdng functions:

4.3.1 Organize joint projects, to bring together those researchinstitutions looking for pertinent areas of applied and

•>; • fundamental research and tho.se organizations which are activein the field and willing to recommend useful work. In orderto aid laboratories in developing countries the IAEA might

1 ' consider offering technical assistance in such forms as• sending experts and supplying essential equipment.4«3«2 Identify ma.lor research projects within the Member States

and help in their coordination. Some, of these major projectsmight also be proposed to other organizations, such as theInternational Centre for Heat and Maás transfer, which mightbe in a position to divide the project into work sub-projectsto be distributed among laboratories according to theircapability and interest. It is emphasized that theselaboratories should attempt to achieve resuJt.s which constitutea real advancement in the state of knowledge,

4.3.3 Initiate and sponsor scientific Biefttings to discuss theresults obtained by (a) and (b) and. thereafter, publishthe proceedings.

4.3.4 Encourage exchangee of information in tbi« field by sponsoringor organizing such activities as panels and internationalseminars on specialized topi en of interest jn nuclear powertand advanced courses (in which members of leading rerearchteam» deliver lectures'- to members of new research teams).

13

In large international or national conferences and meetingssome sessions could be devoted very usefully to nuclearapplications.

4*3*5 Establish working groups to study and recommend correlationsand computer programmes, such as outlined in Panel PaperPL-410/16, and publish relevant monograms.

4.3.6 Gather and disseminate relevant information which is notreadily available. In particular, the Agency could serve asa bank for data which is often omitted from the usual publishedliterature and as a depository of computer programs. (Much couldbe obtained from the Argonne Computer Programme Library.)It could collect uncirculated literature and regularly distributean acquisition list and publish bibliographies in specializedareas. (This might be done through INIS.)

4*3*7 Support training courses. In regions where a serious lack ofadequately trained personnel exists, the Agency could considersupporting regional courses to upgrade the level of heat andmass transfer knowledge and research*

4*3*8 Cooperate with other international bodies. The Agency shouldcooperate with existing international organizations - such asthe Assembly for International Heat Transfer Conferences andthe International Centre for Heat and Mass Transfer. Such co-operation would permit the most efficient use of the Agency'sresources for activities in heat and mass transfer.

4.3.9 The Agency should sat up under its auspices a permanent workinggroup of approximately six members which could act as an advisorybody on heat and mass transfer, help in carrying out the tasksdescribed above, provide liaison with appropriate internationaland national bodies, and facilitate exchange of experience amonginterested countries. This group should meet annually and atother convenient times and, when possible, the meetings shouldbe held at important centres of heat and mass transfer research.

14

REVIEW OF PROBLEMS GOVERNING THE DESIGN OPTIMIZATION OFHEAT EXCHANGERS IN NUCLEAR POWER PLANT

by

P.V. GILLIHead, Institute of Heat and Power Engineering,University of Technology, Graz, Austria

Abstract

,TJie importance of the so-called "conventional" parts of nuclear powerplants has sometimes been underestimated. Particularly the main heatexchangers exert a considerable influence on lay-out, static and dynamicbehaviour, optimization, reliability, availability, and cost of a nuclear powerplant. They work under rather unconventional conditions regarding perior -manee , space restriction, power density, safety requirements, accessibility,leak tightness and cleanliness. The problems governing the design and thedesign optimization of heat exchange equipment - ranging from steam generators,intermediate heat exchangers or regenerative heat exchangers in the primarycycle to condensers in the cold portion of the steam cycle- are reviewed fortypes of reactors and nuclear power plants currently, being built or underdevelopment

The steam generator design is largely governed by the overall design >of the primary circuit. The integrated system of the gas-cooled reactor haslead to the removable pod boiler concept, whereas present, water-cooled re-actors still, are non-integrated. The once-through boiler system,, generallywith direct reheat, is now employed fqr gas-cooled and most of liquid metalcooled reactors* Live steam data are about 17C bar, 540°C. Power densitiesin the tube bundle of up to about 10 MW/m3 have been achieved. Safety consi-derations are mainly concerned with loss of coolant and ingress of secondarysystem water into the primary circuit, leading to adverse chemical reactions.Apart from carbon mass transfer, the most serious material problem is still•stress corrosion cracking of austeniticsteel. It is overcome by using nickelalloys for the tubes of the steam generators in the PWR, HTGR and LMFBR,-Identified problems with regard to structural integrity and presently incompleteknowledge in the field of heat transfer are mainly connected with fluid flow:flow instability, e. g. pulsations, or oscillations, particularly in downhill boiling,two-phas.e pressure drop (especially in helical tubes), flow distribution, in-complete flow mixing, phase separation, vortex shedding frequency, trans-ient thermal behaviour.

In view of growing emphasis on increased performance, compactness,accessibility for repair, and at the same time reduction in costs, heat exchan-gers and particularly steam generators should receive special attention. Inaddition, promotion of information and further exchange and dissemination ofexperience in this important field is required. It is suggested that the IAEAshould act as a focus for activities of this kind.

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1. INTRODUCTION ' • • » * '

Although problems of nuclear physics and of heat and mass transferin the core have attracted interest from the very beginning of nuclear powerdevelopment, the design problems of heat exchangers in nuclear power planthave only recently begun to receive a similar degree of attention [1 - 9].The importance of these "conventional"items clearly has been underestimated.This is borne out by the fact that the vast majority of breakdowns of nuclearpower plants had their reason in the conventional part and in a good many ofcases in the main heat exchanger.

Furthermore, it is a fact that today the nuclear behaviour of a core• at least, as far as thermal reactors are concerned - may be predicted toa much higher degree of accuracy than the behaviour of the heat exchangersin terms of heat transfer and fluid flow (particularly under transient conditions)»vibration, stress analysis etc. *

This lack of knowledge is partly due to the fact that even in conventionalsteam power plants the corresponding problems are not known very well» butthere experience on the one hand and lower ratings on the other hand have leadto an acceptable even if not fully satisfactory state of the art. Another reasonfor the lack of knowledge are the rather unconventional conditions of the so-called "conventional" parts of nuclear power plants such as heat exchangerswith regard to performance, space restriction, power density safety require-ments, accessibility, leak tightness and cleanliness.

The heat exchanger thus has a considerable andhitherto sometimesunderestimated influence on lay-out, optimization, reliability, availabilityand cost of a nuclear power plant, hi this paper, the problems that governthe design and the design optimization of heat exchangers in nuclear power plantare reviewed.

Reactor types being as divers as they are, it is understandable thatheat exchangers in nuclear power plant exhibit rather different featuresalthough many problems are common for at least some of the reactor types.After a short discission of types of reactors and associated heat exchangers,the common problems are reviewed first, with discussions of the problemsspecific to individual reactor types as appropriate.

2. TYPES OF REACTORS AND HEATOf the many theoretically possible reactor types, i. e. combinations

of fuel,cladding, moderator (if any), and heat transfer medium, only a feware presently being built as economic power reactors or prototypes and se-veral others -mainly the fast breeder reactor types - are being developedwith some or major effort. They are listed in Table I where a classificationis made according to the heat transfer medium used and according to thenumber of cycles employed. Only closed cycles are considered whereas theopen cooling cycle at the cold end of the process - the cooling water and/orair cooling cycle transferring part of the heat to the environment • has not 'been counted.

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A single cycle means that the reactor coolant is at the same time theworking medium. This is the case in the reactor types generating steamdirectly in the core: the Boiling Water Reactor (BWR), the Steam GeneratingHeavy Water Reactor (SGHWR), the C/H2O reactor of the Beloyarsk type, andthe Steam Cooled Fast Breeder Reactor (SCFBR). There is no main heat ex-changer other than the condenser at the cold end of the process. What iscalled the nuclear steam generator or the nuclear steam supply system (NSSS)consists only of the reactor as such plus equipment for water circulation andfor phase separation - cyclone-type separators and steam driers - and, inthe SCFBR, a Loeffler arum. In such a nuclear power plant there will, ofcourse, be regenerative feed water heaters, where bled steam is condensed,and a variety of auxiliary heat exchangers. There may also be, in additionto moisture* extracting buckets of the saturated steam turbine, a mechanicalsteam dryer and a live steam heated reheater at an intermediate pressure ofthe steam cycle in order to avoid unduly high wetness in the last turbinestages.

The medium acting as reactor coolant and working medium in direct-cycle systems niay also be gaseous as in nuclear gas turbine plants witheither High Temperature Gas-cooled Reactor (HTGR+GT) or Gas-CooledFast Reactor (GCFR*GT)* in' possible future nuclear MHD plants, and in theUltra- High Temperature Reactor being developed foi* the nuclear rocket(NERVA). m.the Brayton cycle of the nuclear gas turbine plants, the precoolerbefore the compressor and the intercooler between the compressor stages takethe place of the condenser in the steam plant as main heat sink. In addition,

there will be a rather voluminous regenerative heat exchanger (RHX) trans- .ferring heat from the gas leaving the gas turbine before entering the compressorto the gas leaving the compressor before entering the core (10, 11, 12].

In indirect cycle reactor types - the Pressurized Water Reactor (PWR),the Canadian pressure tube heavy water reactor (CANDU), the PressurizedHeavy Water Reactor of the pressure vessel type (PHWR), the Advanced Gas-cooled Reactor (AGR), the D2

O/CC>2 reactor, the IITGR,the space ship orspace base reactor SNAP-8, "the GCFR, and other indirect cycle reactors -heat transfer cycle and working cycle are separated. The heat transfer mediumin the closed primary cycle is now chosen according to the requirements of thecore, the working medium being steam as in conventional power plants (mercuryvapor in the SNAP -8). Both cycles meet at the main heat exchanger - steamgenerator (SG), steam rising unit, boiler - which, together with the wholeprimary cycle, forms the NSSS.

There are further reactor types employing three cycles: the Liquid Metal.cooled Fast Breeder Reactor (LMFBR), and the Molten Salt Breeder Reactor(MSBR). There, for safety reasons, an additional cycle is introduced betweenthe active primary cycle removing heat from the core and the steam cycle.This intermediate cycle consists of non-active sodium in the LMFBR whereasa eutecUc mixture of sodium fluorobate and sodium fluoride (NaBF. - NaF) is .envisaged for the MSBR. For these two reactor types an intermediate heat ex-changer (IHX) transferring heat from the primary to the secondary cycle becomestherefore necessary. The nuclear steam generator thus consists of primary andsecondary cycle and includes HOC and SG. .

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The future fusion reactor may also employ three cycles. It is envisagedto use lithium as heat transfer medium in a primary cycle» and a binary Rantdneworking cycle consisting of a NaK vapor cycle and a subsequent Ü2O steam cycle113J.

3. HEAT EXCHANGER DESIGN

3.1 Steam generator design philosophy

There are two basically different design principles of the steam generatorin nuclear power plant. In indirect cycle water reactors (PWR, PHWR, CANDÜ),the temperature of the primary water and therefore its pressure has to be higherthan the saturation temperature on the secondary side of the SG. Heat is trans-ferred from a high pressure primary cycle to a medium pressure, saturatedsteam secondary cycle (Fig. 1). In a non-integrated design, that is with externalSG units as usually employed in present PWR power plants, the primary fluidwill therefore be applied to the inside of the SG tubes, steam will be produced outsideof the tubes, similar to a conventional shell boiler. An integrated design has,however, been chosen for the SG of the German nuclear ship Otto Hahn [14];The SG tubes being located inside the pressure vessel that encloses both thereactor and the whole primary circuit, the obvious choice in this case was toapply the secondary water to the inside of the SG tubes which are now to bedesigned for outside pressure.

la steam generators of reactors with liquid metal or molten salt as heattransfer medium, conditions are reversed: Pressures in the primary cyclemay be medium or low even at high temperatures, for the primary fluid iseither a gas and thus above the saturation temperature or a liquid with veryhigh boiling point Pressure and temperature on the secondary'side may bechosen freely. Even supercritical pressures are possible. The only restrictionis that the SG inlet temperature of the primary fluid is somewhat higher thanthe temperature of the superheated steam on the secondary side. Heat is trans-ferred from a low or medium pressure high temperature primary fluid to ahigh pressure, superheated (and often reheated)steam secondary cycle. Theprimary fluid will therefore be applied to the outside of the SG tubes, steamwill be produced and superheated at the inside of the tube much in the sameway as in the conventional water-tube boiler.

Steam water flow is the next consideration (Table H). In water reactors,the simplest and cheapest way at the limited pressure is natural circulation.Por the SG of the PWR and the PHWR, the U-tube design (Fig. 2) has becomecustomary [15, 16, 171; for the CANDU, the U-tube, U-shell type withexternal drum has been used, one leg of the U-shell serving as counter-currenteconomizer, thus increasing the steam pressure obtainable and/or reducing theheat transfer area required [18]. The same effect is obtained by the integratedhelical coil design of the aforementioned SG in the German nuclear ship [14].There, with steam generators in relatively long and almost horizontal tubeswinding around the core, a once-through system was chosen. In this way slightlysuperheated steam is produced (Fig. 1). A similar solution may be adopted forfuture land-based integrated PWR or PHWR systems in prestressed concretereactor vessels.

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la high-pressure, high-temperature steam generators for gas or liquidmetal cooled reactors, recirculation or once-through designs are feasible inprinciple. Of the gas-cooled reactors, -.early non-integrated Magnox reactor;steam generators had used natural or forced recirculation designs. The U-tube,U-shell modular design (Fig. 3) is being used for the forced recirculation boilerof the Czechoslovak nuclear power station A-l [19]. Modern gas-cooled re-actors feature integrated systems in prestressed concrete reactor vessels(PCRV). Regarding the boiler units, there is a strong tendency to the so-calledpod boiler concept [20 - 26] which consists of a number of SG units arrangedin cylindrical holes in the wall of the PCRV (Fig. 4 and 5). As the SG unitsare to be removable, closures of the double-barrier type are required andthe penetration of the feed water, live steam and cold and hot reheat linesthrough the PCRV becomes a meta design problem. The once-through boilerrequires the minimum number of penetrations and is the clear choice for thisreactor type {20 - 32]. Since the possibility of plugging individual tubes orgroups of tubes in case of a tube failure is usually required in addition to theremovability of the complete pod boiler unit,there must be no intermediate hea-ders between water inlet and superheater outlet. By the same token, internalspray attemperators for fast-response control of the superheater temperatureare not feasible. Contrary to conventional once-through boilers, steam tempera-ture control has therefore to rely on the control of feed water mass flow and/or primary cycle mass flow.

Turning to liquid metal cooled reactors. Table II shows that no clearpicture has yet emerged regarding the flow scheme for future large commercialLMFBR plants [2; 33-37]. Forced recirculation as well as the once-throughprinciple have been .employed for LMFBR prototypes {2,38, 39,40]: recircu-lation for the British PFR, genuine once-through without any intermediateheaders between feed water inlet and superheated steam outlet for the EnricoFermi Nuclear Power Plant (EFNPP) and a modified once-through design featu-ring a once-through evaporator with slightly superheated outlet and separatesuperheater and reheater units for EBR-H. This latter .design has the advan-tage that sodium streams from 1he superheater and reheater may easily becombined and pass through the evaporator as is shown in the heat transferplot (Fig. 1). .

For the sake of completeness, the direct cycle reactor systems--BWR,SGHWR, C/H2O and SCFBR - have been included in Table IL

3. 2 Safety considerations' :

The steam generator in a double-cycle system is part of the primarycycle and as such a main item in investigating normal and accidental transientbehaviour of the plant, after-heat removal,and other overall safety analyses.More specific safety considerations are:(a) Consequences of the failure of one or more SG tubes in terms of reactivityincrease of undermoderated thermal or of fast gas-cooled reactor cores;(b) Consequences of tube failures in terms of corrosion (mass transfer) of ..graphite-moderaxed cores due to C-HoO reactions;

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(c) Consequences of penetration cover shell failures on primary circuit pres-sures , mass flow and shut-down heat removal capacity of gas-cooled reactors,particularly gas-cooled fast reactores;(d) Consequences of tube failures in terms of Na-I^O reactions in single-wall steam generator units of liquid metal cooled reactors.

Small bore tubes will help to reduce the problems connected with tuberupture (a, b). Gas flow restrictions or double shell designs will be used tolimit or avoid the loss-of-coolant problem (c). Regarding (d), thermal shieldingof critical parts such as tube plates or nozzles by their location in an inertgas filled space above the sodium level will minimize transient thermal stressesand thermal fatigue. The inert gas space will also act as a shock-surge cushion.Besides, rupture disks on the shell are provided in order to reduce the effectsof a large reaction. Unfortunately, very small leaks that would be tolerablein terms of the Na-H2O reaction, lead to localized corrosion. Stringent leaktesting and sensitive, fast acting leak detection by hydrogen monitoring isrequired [40]. Although the double-wall SG design with a narrow NaK or Hginterspace might greatly alleviate the problem, todays effort is mainly on iheless expensive single-wall designs.

3.3 General steam generator design features

One of the basic design alternatives- of the. SG is the choice between themadule concept and the concept of maximum unit performance. The moduleconcept has been followed in the development of: theU-tube, U-shell SG unitsfor CANDU [18]; the helical coil tube steam generator for the early Frenchgas-graphite natural uranium stations; the SG for the Czechoslovak D2O/CO2power station [19]; early French designs for LMFBR steam generators [34];*and of the pod boilers for modern gas-cooled reactors, although in this casethe number of units has become rather small recently, when it turned out thatremarkably large openings in. the PCRV wall could be designed. The advantagesof the module concept are easier testing and handling of the smaller units, thepossibility of assembly-line production, smaller PCRV penetration diameter»«nd easier replacement of a faulty unit. The large unit, on the other hand, hasthe advantage of the law of decreasing specific cost with increasing unit size.

Another design alternative is the choice between straight or U-shapedtubes on the one hand and helical or involute tubes on the other (Table II).Steam generators of water-cooled reactors mainly use U-tubes with the ex-ception of the integrated design for ship reactors where helices are employed[14]. In steam generators of early gas-cooled reactors, straight tube nqnean-ders in cylindrical shells or involute tube meanders in annular geometry wereemployed [25], whereas in the pod boiler units helical tubes are used. InLMFBR steam generators, straight tubes with a sine wave to accomodatethermal expansion, involutes (EFNPP), and helical coils [33] are being usedor proposed.

Experience has shown that almost absolute leak tightness (zero leakage)can be achieved even for intricate tube bundles with many hundreds of welds[41]. A high standard of welding is required and automatic welding techniquesare preferred. During manufacture, stringent inspection and non-destructivetesting methods are applied. Leak tests are performed by means of the heliummass spectrometer»

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3. 4 Steam generator lay-out data

Typical data for steam generators of large power reactors are given inTable ItL For comparison, data of a large conventional boiler have been in-cluded. Since space is at a premium at the, generally, high pressures of theprimary cycle, there is a strong tendency to high power densities in the steamgenerator tube bundle [42]. For the cases considered, power densities rangefrom about 4 to more than 10 MW/m3 for modern reactor types as comparedto about 0.1 MW/m3 in a conventional boiler. These high power densities arethe result of an increase in the heat transfer area density by about an orderof magnitude due to smaller tubes and smaller tube spacings which in turn be-come possible in the clean, ash-and soot-free medium; in addition, the meanflux is increased by almost one order of magnitude as a result of heat transfercoefficients which are more than one order of magnitude higher and meantemperature differences which are somewhat lower than in conventional boilers.(Peak heat fluxes are, however, of a magnitude comparable to the ones in thefurnace chamber of conventional boilers).

It is interesting to compare the SG of the water, helium and liquid metalcooled reactors. Table III demonstrates that their power densities are almostequal. This is achieved in the PWR by a rather low temperature difference buta very large heat transfer coefficient due to high-velocity water in the tubesand boiling water on the outside; in the LMFBR by a medium temperaturedifference and an equally medium heat transfer coefficient (despite the very highcoefficient on the sodium side its mean value is considerably lower than inthe SG of the PWR because of the steam-side limitations in superheater andparticularly reheater); and in the HTGR and GCFR by a relatively high tem-perature difference but a relatively moderate heat transfer coefficient due togas-side limitations.

Deviations from the standard subcritical steam parameters - 170 bar,540/5400C (about 2400 psia, 1000/1000°F) - take place for the PWR (saturatedsteam), for the GCFR (where a non-reheat cycle has been assumed in Table IH),for the LMFBR (where, for present sodium technology, an upper primarysodium temperature of 600°C and a superheat and reheat of 500/500°C wasassumed). Feed water temperatures are generally somewhat lower in gas-cooled reactors than in conventional boilers with comparable steam para-meters since SG heat transfer surface as well as reactor inlet temperatureand circulator power are rather sensitive to this parameter [42]. As isshown in Fig.l, enthalpy rise per unit mass of live steam is, of course,smallest in the PWR; it is largest in the AGR with its low feed water tempe -rature. The specific live steam rate varies thus by a factor of 2.

Because of the generally low temperature difference between primaryand secondary side (compared to the conventional boiler), extensive use ismade of the counter-current principle (Fig. 1). Other arrangements of super-heater and reheater have, however, been suggested Í23].

3. 5 Specific steam generator design features

'From Table III it may be taken that the U-tube steam generator of thePWR (Fig. 2) today is built for steam rates of up to about 2400 tonnes/h per

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unit, that is of about 4800 tonnes/h for an 800 MWe reactor with 2 SG units,or about 6600 tormes/h for an 1100 MWe reactor with 3 SG units. The numberof tubes (about 22 r.:m o. d., 1. 2mm wall thickness) per SG unit exceeds 5000,their length 16m, their haat transfer area 6000m2. The shell diameter in thetube bundle section ranges up to about 4 m, in the steam dryer section up toabout 6 m, the tube plate thickness up to about 700 mm, and the unit weight upto about 450 tonnes (15-17].

The inner (primary) surface of the hemispherical headers is clad withnickel alley by an c.uton?atic weJ.d deposit method or explosively. For connectingthe tubes to the cladding of tba tube plate, automatic welding guns are used.The tubes are given a mechanical roll to minimise the crevice between tubecr¿d tubssheet thereby excluding las collection of solids from the secondaryv<T*er, Alterantivsly, the so-called explosive-expansion (Explansion) methodxaay be used. Thin consists oí tube expansion by the detonation of a carefullycontrolled explosive in c. plastic plu«f inserted in a tube through the thicknessof the tube sheets.

After the first helix steam generator had been built for the Dragon HTGR[41], this tube configuration - which fits very v/eU. to the cylindrical geometrycf the pod boiler concept - is used o.r to be used in steam generators for gas-ccoled reactors of the E^O/CC^, AGR, HTGR and GCFBR type and even forrât orated F7/R systcras"snd the LMFBR (Fig. 4, 5, 6). The straight tube orinvolute tube'near. 1er configuration, of shell-type or annular boilers of Magnoxend earlier AGR plants h<is been largely abandoned. It req'iires a large numberof tv'bc bcncb vhicj. ?.?3 expensive to rr^anuíacture, le?.ds to additional steam-\7t.tor cioe precnvro <¿ ..-o?, rcqvircs .larger longitudinal tube spacings than thefcelL: tlssisn and is therefore not very v/cll edited to the pod boiler concept.

The onca-thvrough boiler tubes usually are fitted with inlet orfices whichminimise maldistribution cf flov^ and restrict water ingress into the primarycircuit in caso of a tube failure.

As hs.s already been mentioned, the helix tube configuration has greatpromiGS also for the steam generator of tho LTjETBR. In this application, itspossibility to anally e;:pand or contract virtually v/ithout any thermal stressis an advantage. However, other cscign concepts - a hockey-stick configura-tion with ene 90° bend to ailov/ for thermal expansion; and U-tubes - are beingpursued, too(Fig. 7).

Tube support i cruotur-ss require special attention in the pure non-o-ïydizing hslium environment of thfi HTGR or GCFR. Fretting may thereforeoccur v;here parto in contoct xnuergo repeated relative motion withoutspecial protection. A sleeve end v3-*!ge ccmbûiation has, for instance, beenprovided for the ste^m generator 'abes of &. large HTGR v/here they are incontact with their support structure [32], The design principle involved is thatthe sleeve material which is in contact vdth the support must have a higherv/ear resistance than tLo support ¡material, aid the v/edge material which isin contact with the tube must bs similar to the tube material. To avoid a loosefit between tube and sleeve undsi- thermal expansion the sleeve material musthave a coefficient of thermal expansion leso than that of the tube material.

In addition.hocit transfer tubing that is subject to relative motion and incontact with bsfiles or thermal shields has been flame-sprayed with chromiumcarbide, snd structural parts that are in sliding contact with each other areprotected by a weld-overlay of cobalt-base alloy in appropriate areas.

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S. 6 Design features of heat exchangers other than SG

The intermediate heat exchanger of a LMFBR plant is usually of thestraight tube type with sine waves to allow for thermal expansion or of theIJ-tube type [38Î.

Regenerative heat exchangers of nuclear gas turbine plants (Fig. 8) orfuture MHD plants present design problems due to their size and due to thenecessity of integrating them into the PCRV [10, 11, 12, 43],

For the live steam heated reheater of nuclear power plants with water-cooled reactors, an interesting design solution has been found by combiningit with the steam dryer [44]. Fig, 9 shows one of the two combined units for aSOCMWe station.

3.7 Materials

The following are some of the criteria for the selection of materials forheat exchangers in nuclear power plant:- adequate strength (tensile strength, yield strength, creep resistance) at

design condition to avoid unduly thick walls which may cause large steadystate and transient thermal stresses;

- adequate ductility;- acceptable thermal conductivity to limit thermal stresses;- adequate fatigue properties at design temperatures and at the temperatures

where load changes occur;- adequate resistance to corrosion caused by the primary fluid (CC^; Na);- resistance to mass transfer such as carburization or decarburization;- adequate resistance to chloride, caustic, and oxygen-assisted corrosion

(SG tubes);- workability and weldability;» reasonable cost and cost/strength ratio.

In Table IV, some of the materials used in recent installations orproposed for use are listed, whereas in Table V the chemical compositionof the materials and approximate cost figures are given. Inspection, accep-tance testing and clean condition requirements are more severe for tubes innuclear service than for conventional plants. This puts an economic burdenon the material but the percentage cost increase due to nuclear standards isnow much smaller for expensive materials, .reducing the cost multiplier forhigh-alloy materials.

In the somewhat radioactive steam circuit of a BWR it is customary touse Monel for the feed water heaters. In steam generators there is a strongtendency to avoid the use of austenitic stainless steel due to its susceptibilityto stress corrosion if, for instance, traces of chlorides from a condenserleakage are present. For PWR steam generator s, nickel-alloy s are thereforeused in more recent plants for the tubes and the cladding of the tube plate.In addition, the tuble bundle is always kept flooded on the secondary side; con-sequently there is no dry-out on the tube surface and, therefore, no concentrat-ion of solids which could lead to stress corrosion.

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The same tendency to the use of nickel alloys can be observed with steamgenerators for HTGR or LMFBR plants. An alternative for these types ofreactors is the use of ferritic alloyed steels. This is relatively easy for theLMFBR where optimized steam temperatures are of the order of only 500°C(900 F); for reasons of high temperature strenght it is difficult to achieve inah HTGR with steam temperatures of the order of 540 C (1000°F) or more •where it may necessitate the use of 12% C-Steel which is somewhat difficultto manufacture and for which only limited operational experience in conven-tional plant is available.

A nickel alloy has also been proposed for the heat exchangers of theMolten Salt Breeder Reactor [45].

For the AGR steam generator, so far, austenitic steel has been used forthe superheater tubes but its use is limited to the portion where under all oper-ational conditions a superheat of at least 50 degree C above saturation will pre-vail [25]. A 9% Cr-1% Mo alloy steel is used in the evaporator and primarysuperheater section. This is dictated by the CC^ coolant.

The tendency to the use of nickel alloys has no counterpart in conventio -nal plants, although the stress corrosion problem is the same. The reason isan economic one: As may be taken from Table III, the heat flux in a PWR,HTGR or LMFBR is about 8 to 10 times higher, and the required heat trans-fer area correspondingly lower than in a conventional plant. In addition thebreakdown of a steam generator of a nuclear plant due to stress corrosionmay cause longer shutdown of a more expensive plant. Thus, if a certain riskof stress corrosion is assumed, there are sound economic reasons for the useof nickel alloys in the steam generator of a nuclear plant whereas it may notbe economical in a conventional plant.

4. HEAT TRANSFER AND FLUID FLOWContrary to the mechanism of heat transfer in the furnace chamber of a

conventional boiler, heat transfer in the core as well as in the steam genera-tor of a nuclear power plant is almost entirely by convection-Even in CCXjsystems radiation play s only a minor role due to the moderate fluid temperatureand the magnitude of the convective heat transfer.

Fluid flow conditions are therefore of paramount importance for adequateheat transfer on the one hand, and the minimization of hot spots on the other.The goal is an even flow distribution without local jets or hot gas streaksthat may under unfavourable circumstances cause mechanical damage as wellas excessive local heat fluxes and hot spots. Due to the high velocities andmass velocities used (Table III) and the severe space restrictions usually en-countered in primary or secondary cycles of nuclear power plants, the problemis difficult and in any case, warrants close attention. Baffles or vanes may berequired in some cases; their proper size and shape will be found by carefultesting (41].

A second fluid flow problem - gas channeling - stems from the fact thatthere are no intermediate headers in a nuclear once-through SG. In the pluggedcondition, the primary and secondary side in the neighbourhood of the pluggedtube or tubes may, therefore, be seriously out of balance. Excessive over-temperatures in individual tubes or cylinders of helices may occur, depending .

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on the degree of mixing of the primary fluid [23} which again will depend on flowrates, longitudinal and transversai tube pitches, etc. A method of adjustingorifices on the basis of individual exit temperature measurements has beendeveloped (46].

Flow instability on the steam/water side is another problem. It may occur ina PWR steam generator ¿s chugging and steam blanketing of the tube plate if

the recirculation ratio of the natural circulation system is too low and may leadto thermal cycling of tubes and lube plate and to excessive steam wetness.In the once-through steam generator of an HTGR, the effects of flow instablitycould be even more serious due to the higher temperatures involved and the lar-gdr temperature fluctations which are possible in this type of SG. It has beenshown that static instability (maldistribution) will not exist in this type of SG.However, under unfavourable ccmditions, large flow pulsations and oscillationsof the single-channel or rnulti-channel mode may occur, possibly leadingto transient film boiling, to thermal cycling, to excessive transient tube wall

temperatures in the post-dryout region as well as in the superheater and in thesuperheater exit header or tube plate, and to the encroaching of water intothe austenitic part (if any) of the superheater* which is susceptible to stresscorrosion cracking. Fortunately, by using high mass velocities and someiiLÎet throttling, the high pressure once-through boiler may be designed so as toÎ:is stable under full-load conditions [20. 27, 28, 47]. However, there willahvays be a minimum part load below which instability will.occur (Pig. 10).

In recent HTGR designs, there is a tendency towards downward flow ofhc-Iiuaa in the core (which keeps the charging equipment cool and avoids lévitationproblems in the pebble-bed cores) and thus xipward flow of helium in the SG.Since counter-current How is required, the steam water flow will in this casegenerally be downward in the SG. It has been shown that the effects of suc& down-Sill boiling on static and dynamic stability should not be significant at full load;there-may, hov/ever, be problems during stari-up and shutdown [47]. A methodof combining upflov/ of helium in the SG wiht uphill boiling would be to ensureby means of internal connecting tubes that the whole boiling region is in upfLowwhile retaining ths overall counter-current flow arrangement. Such a solutionvrould have to bs designed very carefully and would be more costly.

The accuracy to which pressure drop data (friction factors) in the single-aad two-phase regime are known is not very high but generally sufficient. Ahigher degree oi accuracy is required if tubes of different curvature are to be de-¡jijiîed so as to have equal flow rates and, therefore, equal exit temperatures.This is exactly what is required in the helix SG. The effects of curvature onsingle-and particularly on two-phase flow friction coefficients should be knownmore accurately than they are at present [48, 49], Work of this kind, sponsoredby the Waagner-Biro AG of Vienna, Austria, is presently undertaken at theauthor's institute.

Turning to the heat transfer coefficient, its magnitude is known in single-phase flow to some accuracy even for the helix arrangement (50, 51]. HighReynolds Number data for stv^ight tube bundles have recently been published[52]. More work i&, however, required on the DNB and dry-out limits and onthe heat transfer coefficient in the post-dryout region (53, 54]. Transient¡aeat transfer calculations of SG units have been performed [46] but appearto be still in their infancy.

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5. STRUCTURAL DESIGN BASISWhile an évaluation of the structural design basis for heat exchangers

in nuclear power plants is beyond the scope of this paper, a short description"of the working procedure may be given.

5.1 Thermal input data

Steam generators and other main heat exchangers will normally fallunder the scope of Section III of the ASME Code [55]. To perform the assess-ment as outlined in this code, the following input data are required:- the design and all thermal design data, that is a steady state thermal

analysis for full and part load conditions;- a transient thermal analysis for normal operational cases such as start-

•up,shutdown and load changes, and for.abnormal and emergency cases;- a vibration analysis of the tubes.

5. 2 Transient thermal analysis

Tentative wall thickness calculations according to simpWdesign for-mulae may be based on the steady state thermal analysis. The transientthermal analysis plus the number of cycles for each transient (whichis to be specified or has to be assumed) together with thevibration analysis serves as input for the fatigue analysis of the unit. Thus,the full lifetime history in terms of temperature and pressure and theirtransient of each critical part of the unit is used for the assessment.

The difficulties of a transient thermal analysis of the SG have alreadybeen briefly mentioned. They are greatly aggraviated by the fact that,generally, input data from the primary and the secondary cycls are requiredwhich in turn depend on the SG behaviour. A transient thermal analysis ofthe whole system is thus necessary.

5- 3 Vibration analysis

Vibration behaviour of heat exchangers tubes is known only to some extent[29, 56]. As a result of high velocities and mass velocities on the one hand,and the strong tendency to small tubes(in order to achieve a compact design)on the other, dangerous flow induced tube vibrations are more likely in thesteam generator of a nuclear plant than in a conventional one. There are threecharacteristic frequencies:- the acoustic frequency of the channel depending on the sonic velocity and on

the channel (or annulus) width W:f = c/2W

- the Karman vortex shedding frequency depending on gas velocity w, on acharacteristic length, usually the tube diameter d, and on the dimensionless

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Strouhal Number which in turn depends on the bundle geometry:ffe = Slw/d

- the natural frequency of the tube which mainly depends on tube dimensionsand the distance and type of tube supports.

The three frequencies may be calculated with a fair degree of accuracyand it may be checked if - or at what load - coupling of two or all three ofthe frequencies occurs. Much less is known about damping and about what maybe called "dynamic pressure vibration" and may be thought as self- excitingof the tubes at their natural frequency due to high velocity heads without fre-quency coupling to either the acoustic frequency or the vortex-shedding fre-quency. Vortex shedding may, however, take place outside of its naturalfrequency range . More work about this subject is required since, apart fromstress corrosion, tube vibration has been the reason for quite a number of heatexchanger failures leading to forced outages of nuclear power plants (Magnoxstations; EFNPP).

It may be claimed that, with regard to flow induced vibration, helium issuperior to carbon dioxyde as heat transfer medium due to its much lowerdensity (at approximately the same specific heat capacity per unit volume).Furthermore, the helix SG should be less susceptible to strong vibrations thanthe annular boiler, with straight or slightly curved tubes in that it features atube pattern constantly changing around the perimeter {51]; the coupling ofvortex shedding frequency to any of the other two characteristic frequencieswill thus always remain a strictly localized phenomenon. Besides, the strongcurvature of the helix may in itself be beneficial.

5. 4 Stress analysis

For the stress analysis according to the Code, all stresses includingdiscontinuity stresses, steady state and transient thermal stresses etc. haveto be evaluated by analytical or finite-element methods, added up in their cate-gories, and compared to design stress intensity values which depend onmaterial and temperature.

5. 5 Fatigue analysis

Unless certain criteria are met, a fatigue analysis is required. It isbased on the principal stresses, their differences and the alternating stressintensities for each type of cycle. (For nozzles in shells or headers, thestress index method may be used). From the design fatigue curve [55], themaximum, number N of repetitions if this cycle was the only one acting istaken and compared to the actual number n. This yields the usage factor U = n/N.The cumulative usage factor is then found from a summation of all usagefactors for .the individual cycles; it is to be smaller than 1. 0.

It should be noted that the validity of the design fatigue curves given in theCode (55];are limited to metal temperatures not exceeding 700°F (370°C) forcarbon and low alloy steels and to 800°F (425°C) for austeniticstainless steelsand nickel-alloys. These temperature limits are much below what is required

27

for steam generators of gas or of liquid metal cooled reactors. There is,however, an ASME Case Interpretation [57] where data for higher temperaturesare given.

Sometimes in the course of thermal design and assessment, stress andfatigue analysis leads to the necessity or advisability of changes in plant opera-tional modes such as start-up or shut-down procedures. In many cases anestimate of the necessity and the effects of such changes can be obtained atan early date by means of the Beckmann plot (Fig. 11), using model cycles oftemperature excursions with varying ramp height and gradient; the resultingmaximum permissible number of each oí the cycles is determined and plottedagainst the temperature gradient [46].

II sufficiently high cyclic thermal strains are applied to the structuresubject to a sustained mechanical loading, cyclic growth will occur. The per-missible limits of the maximum thermal stress in order to prevent cyclicgrowth, are found by a thermal strain ratched analysis [55].

In special cases elastic-plastic analysis or plastic limit analysis maybe applied [55, 58].

G. DESIGN OPTIMIZATION

The classical design optimization is concerned with problems like:saving in heat exchange surface vs. increase in pumping power;or improvingsteam data, cycle p.nd plant efficiency and thereby reducing fuel cost vs. thecorresponding increase in first cost. Problems of this kind have been dealt withextensively in the lay-out and design of nuclear power plant (10, 11, 12, 30,35, 42, 43, 59, 60]; they are, of course, to be identified and solved whenevera new or modified design is to be finalized or to be applied to different groundi ules.

Design optimization of heat exchange equipment is somtimes carried outv/ith fixed input data (temperatures,pressures, flow rates, pumping power,available space). The more general view of optimizing the heat exchangeequipment as part of the steam cycle and the whole plant under steady statefull power and part load as v/c?.l as under normal and emergency transientconditions should, however, not be neglected [42, 46],

Steam data of power-type reactors today seem to be rather wellestablished (cf. Table hi). An increase of steam pressure for water-cooledraactor would only lead to increase wetness at crossover, unless the boilingsuperheat or the Loeffler cycle of the SCFBR was to come. For the gas-cooledthermal reactor, the subcritical 160 to 180 bar (2.400 psi), 540/540°C (1000/1000°F)reheat cycle is probably to stay, with the supercritical pressure (250 bar)cycle and the 565/5G5°C (1050/1050°F) superheater/reheater temperature aspossible variants. A no-reheat cycle may be preferable for the GCFR, at leastfor the type with metallic cans; and a lower superheat and reheat temperaturefor the LMFBR, unless primary sodium temperatures are pushed up from600°C to 650°C or higher (cf. Table III).

Primary cycle temperatures of gas-cooled reactors with steam cyclewill probably not change very much in future. There is, however, a steady

28

but continuous trend to higher pressures with the associated gains in pumpingpower, heat transfer surface area and power density 142J. For the nucleargas turbine, the optimum cycle data seem to be less clear since the technologi-cal limits of this type of plant have not yet been established. Upper pressuresof between 50 and 100 bar and upper temperatures from 660°C to 1300°C arebeing discussed. For combined cycles or for exotic cycles like the MHD cycle{11, 61], the picture is even more cloudy at present.

7. MAIN AREAS FOR FURTHER WORK

Apart from a series of detailed design problems and from the developmentof new cycle concepts, further work would seem to be required most in thefollowing main areas:

(a) Further improvement of heat exchanger reliabilityUnder this rather general heading, protection from corrosion and wear

and corresponding materials research may be listed as well as further workon heat transfer and fluid flow including flow induced vibrations and transient

.behaviqur, further refinements of design criteria and assessment methods toensure structural integrity over the lifetime quality assurance, and the de.velopment of pressure barriers meeting the stringent requirements of ReactorSafety Committees.(b) Waste heat disposal

: The nuclear power plant is favoured as not «chemical polluting theatmosphere, but there is one kind of environmental effect where atleast water-cpoled reactors are inferior to conventional power stations:thermal discharge to ambient ("thermal pollution"). With net electricalpower Ne, thermal power Nth, power to steam Nst, cooling power to ambientN , plant efficiency rj, and boiler efficiency n^, the ratio of cooling power tone\ electrical power becomes:

Nst • We Vth - "Nth "b - "

or for nuclear stations with n. = 1.0D

The ratio N /N has been assessed in Table IH for several reactor types.Fig. 12 shows N fÑ vs. rj for various types of power plants.

Even if in Inaify countries the thermal discharge problem is not or not yetserious, the "air-cooled" instead of the "water-cooled" nuclear plant might be

29

an interesting aim - despite of the unavoidably higher installed cost - as thesite selection problem would be greatly simplified. Apart from the classicalcooling tower with evaporative cooling ,the indirect air cooling system (62} andthe air-cooled condenser system have been developed.

It should be noted that the nuclear gas turbine power plant is particu-larly suited to air-cooling not only because of its potentially high plant efficiencybut also because its-waste heat is supplied at a much higher temperature thanis the case with the steam cycle. Larger temperature differences in the air-cooled precooler and intercooler will thus lead to smaller additional cost ofair-cooling vs. water-cooling than for the steam cycle. By the same token,utilization of waste heat for heating purposes, for the generation of industrialprocess steam, for agricultural purposes, desalination, or even waste watertreatment should, in the future, become more interesting and would very wellsuit the Brayton cycle.

(c) Heat storageAs more and more nuclear plant capacity is introduced into the grids,

the time approaches when nuclear power will have to take part in the dailyload changes. At that time, at the latest, it should be economic to introducepower storage means into the system, permitting the high capital, low fuelcost nuclear plants to produce base load. • Under favourable geographical con-ditions, pumped storage hydro plants are one solution of the problem.Also underground compressed air storage for air turbines and fuel cellstorage has been considered.

Heat storage in steam accumulators which may thought of as heat exchan-gers of the mixing type, is another possibility. The steam accumulators wouldbe charged during low-load hours and discharged at peak hours. They would becapable of improving the reactor load factor and may thus be an economic solu-tion for the peaking problem in nuclear power stations [63].

8. CONCLUSIONS

Experience has shown that the reliability of heat exchangers, and inparticular steam generators, determines largely the reliability and availiabilityof nuclear power plants. In view of growing emphasis on increased performance,compactness, accessibility for repair and, at the same time, reduction in costs,these major components should receive special attention. Several main areashave been defined where much further work - analysis, research and develop*ment - is necessary, ranging from heat and mass transfer and fluid flow in theprimary cycle to thermal discharge by means of the heat disposal circuit.

In addition, promotion of information and further exchange and dissemina-tion of experience in this important field is required. It is suggested that theIAEA should act as a focus for activities of this kind.

30

REFERENCES

[1] Performance of Nuclear Power Reactor Components (Proc. Symp.Prague, 10-14 November 1969), IAEA, Vienna, 1970.

f

[2] Sodium-Cooled Fast Reactor Engineering (Proc. Symp. Monaco,23-27 March 1970). IAEA, Vienna, 1970.

[3J Advanced and High-Temperature Gas-Cooled Reactors (Proc. Symp.Julich, 21-25 October 1968), IAEA, Vienna, 1969.

[4] ENEA Symposium on the Technology of Integrated Primary Circuitsfor Power Reactors (Paris, 20-22 May 1968).

{5] Power Reactor Systems and Components, Topical Meeting, PowerDivision, American Nuclear Society, Williamsburg, Va.? 1-3 Sept. 1970.

[6] LEWIS, G. T., et al : "Heat exchangers in nuclear power plants",Advances in Nuclear Science and Technology, VoL 2, Academic Press,New York, 1964.

[7] FRAAS, A. P., OZKIK, M. N., Heat Exchanger Design, Wiley & Sons,New York, 1965.

(8] KÂGI, J., The principal design of steam generators for indirect-cyclenuclear power plants, Sulzer Technical Review, Special Number"Nuclex 1969", 4-11.

F9] KHAN, M. A., RISTIC, Mv Operating experience, Nuclear EngineeringInt., June 1970, 521-526.

[101 FÔRSTER, S., et al. , Kernkraftwerke mit Hochtemperaturreaktorund Gasturbine, Energie 20, 1968, 278-284.

f i l l FORSTER, S , GILLI, P. V. , Engineering problems of turbomachineryand heat transfer equipment for nuclear MHD power plants, Atom-kernenergie 21 (1968) 205-222.

Ü2] LYS, L. A., Gas turbine fast reactor design, J.Brit. NucL EnergySoc., July 1969, 213-222.

[53] Proc. Int. Conf. on Nuclear Fusion Reactors 'Culham, 17-15September 1969), BNES, London, 1970.

JAHNS, w«, Design and properties of the Advanced Pressurized \\kterReactor FDR for the German nuclear research ship, Kerntechnik 6(1964) 324-332.

31

[15} HALL, V. C., The nuclear steam supply unit (Palisades PWR),NucL EngJrtg. IntyJanuary 1970, 34-37.

{16] Van HULST, G. , PIETERSE, G. L. , Evaluation of the Heat TransferArea and the Steam Temperature as a Function of Power, for a Ver-tical Steam Generator, by Means of a Digital Computer, Euratom-Report EUR 2183. e (1965).

Î17] BYERLEY, W. M., Steam Generators for Nuclear Power Plants, ASMEPaper 68-WA/PWR-2 (1968).

[18] DIETRICH, J. R. , Heavy-Water Reactors, Power Reactor Technology2 (Winter 1963/1964), 85-98.

[19] KRIZEK, V., "Sectional Steam Generators for the CzechoslovakNuclear Power Plant A-1" [1], 321-326.

[20] GILLI, P. V. , et al., Assessment Study of Steam Generators for a1,250 MW (th) High Temperature Gas.-Cooled Reactor, Dragon ProjectReport 458 (1966).

[21] OECD High Temperature Reactor Project Dragon, Seventh to TenthAnnual Report, OECD, Paris, 1966 to 1969.

[221 DEAN, J. R., et al,, "Integrated Primary Circuits with IndividuallyRemovable Boiler Units for High Temperature Gas Cooled Reactors)'[4], E N - I f 3 9 .

[23Î FRITZ, K., "Some Design Aspects of Integrated Steam Generators forGas-Cooled Reactors", {4}, EN-1/1.

[24J CAMBRÓN, P. J. , O' TALLAMHAIN, C., "Boilers in the High-Temper-ature Gas-Cooled Reactor'1, [3}, 571-583.

[251 HRYNISZAK, W., STEAD, R., "The Development of Nuclear SteamRaising Equipment", [ll, 327-346.

[261 GEORGE, B. V., TAYLOR, P. A. 3 Pod boilers (Hartlepool AGR Survey)Nucí Engng. Int., November 1969, 983-985.

[27J KÂGI, J., DOROSZLAI, P., "Special problems concerning the mono-tube steam generator in the nuclear power station", Proc. Third Int.Conf. Peaceful Uses Atomic Energy (Geneva 1964) 8. UN, New York(1964) 609-615).

[28] KÂGI, J., Some considerations on the use of the once-through principlefor steam generating in nuclear power plants, Sulzer Technical ReviewNo. 1/1964Í

[29] WARREN, L., "Steam Raising Unit Design", Proc. Symp. on HighPressure Gas as a Heat Transport Medium (London, 9-10 March 1967)I. Mech. E. ,

[30] HENNINGS, U., "Possible Solutions for Integrated Steam GeneratorsoftheTHTR", [4L EN-1/16. ,

i

[31] KÂLJN, W., The steam generators of Fort St. Vrain nuclear powerplant, Sulzer Technical Review, Special Number "Nuclex 1969" 12-19,

132] SCHUETZENDUEBEL, W. G., HUNT, P. S., Review of Design Criteriafor Steam Generator of HTGR Plant of Public Service Company ofColorado, ASME Paper 69-WA/PWR-5 (1969).

[33] BABCOCK & WILCOX Co., Boiler Division, Sodium-Heated SteamGenerator program, TID-20588 (1863)

[34] SMITH, F. A., Interpreting the French liquid-metal-heated steam-generator program, Power Reactor Technology £ (Spring 1966), 69-73.

[35] SCHNEIDER, G. A., STOKER, D. J., Steam cycle influence on fastbreeder reactor design, NucL Engng. and Design 4 (1965) 351-359.

[36] BUDNEY, G. S., Sodium Heated Steam Generator Design ConsiderationsASME Paper G8-WA/NE-19 (1968).

[3,7] Session on LMFBR Components. Trans. Am. NucL Soc. 13 1 (1970).

[38] MONSON, H. O., et aL, "Components for sodium reactors", Proc.Third Int. Coaf. Peaceful Uses Atomic Energy (Geneva, 1964) 8, UNNew Yorl. (1964) 588-599.

[39] CAMPBELLJR. H., PFR Design and Construction-A Progress Statement,Nuclex 1969.

[40] DUFFY, J. G., WAGNER, H. A., "Operating experience with majorcomponents of the Enrice Verrai Atomic Power Plant". [1], 635-646.

[41] HOLZER, J., et ai. , "Operating Experience with the Dragon SteamGenerators", [1] 301-319.

[42] GILLI, P. V., The power density of integral steam generators for HighTemperature Gas-Cooled Reactors, Neue Technik BÍ, j9 (1967) 10-17.

[43] TWARDZIQK, W., HEWING, G., Wármeübertragende Apparate furHochtemperaturreaktorenanlagen mit Heliumturbinen, Energie undTechnik 22(1970) 156-160.

[44] GROTLOH, K., Water separators and reheaters in nuclear powerstations, Sulzer Technical Review, Special Number "Nude 1969",35-40.

33

[45] DONNELLY, R. G. , Slaughter, G. M., Fabrication of the Molten-SaltReactor Experiment heat exchanger core. Welding Journal, 1964,117-124.

[46] FRITZ, K., LIPPITSCH, J., "Advances in Steam Generator Design",UL 347-360.

147] FRITZ, K., GJLLI, P. V., Stability Behaviour of Steam Generators withUpward Flow of Helium, Dragon Project Report 625 (1969).

{48] GILLI, P. V., Der Reibungsbeiwert von Einphasenstrômungen in ebenund râumlich gekrummten Rohren, Osterr. Ing. -Zeitschrift 7 (1964)362-370.

149} SCHMIDT, E. F., Warmeubergang und Druckverlust in Rohrschlangen,Chemie -Ingenieur-Technik 39 (1967) 781-789.

[50] KAYS, W. M. , LONDON, A. L., Compact Heat Exchangers. NationalPress, Palo Alto, Calif., 1967.

{51] GILLI, P. V., Heat-Transfer and Pressure Drop for Crojss-Flow throughBanks of Multistart Helical Tubes with Uniform Inclinations and UniformLongitudinal Pitches, Nucí. Set Engng. £2(1965) 298-314.

[52] HAMMEKE, K. , et aL , Wârmeuber gangs -und Druckverlustmessungenin querangestromten Glattrohrbündeln, insbesondere bei hohenReynoldszahlen, Int. J. of Heat and Mass Transfer Jj)( 1967)427-446.

[53] Boiling Heat Transfer in Steam-Generating Units and Heat Exchangers.Proc. LMech.E. 180 (1965-66) Part 3C.

[54] CARVER, J. R. , KAKERALA, C. R. s SLOTNIK, J. S., Heat Transferin Coiled Tubes with Two-Phase Flow. TID-20983.

[55] ASME Boiler and Pressure Vessel Code, Section III: Rules for Construc-tion of Nuclear Vessels, 1968 Edition, ASME, New York, 1968.

[56] Session on "Vibration in Heat Exchangers", ASME 1970 Winter AnnualMeeting, November 29-December3,1970, New York.

[57] ASME Boiler and Pressure Vessel Code. Case Interpretations. Case1331-4. 1967.

[58] Use of the Computer in Pressure Vessel Analysis. ASME, New York1969.

[59] PROTSENKO, V. P., Analytical determination of optimum characteristicsof saturated steam generators, Teploenergetika 11 2 (1964) 36-39.

34

[60Ï BAMMERT, K., BÜNDNER, A., A method for the optimum layout ofindustrial nuclear power plants with helium turbines. Atomkernener-gie 15^(1970) 240-248.

[61] Electricity from MHD 1968 (Proc. Symp. Warsaw, 24-30 July 1968),6 Vols. IAEA» Vienna, 1968.

[62] HELLER, L., FORGO, L., "The Heller System Air CondensationProcess for Atomic Power Stations'.1, Proc. Second UN Conf. Peace-fulUses Atomic Energy (Geneva, 1958) 2 840-841.

[63] GILLI, P. V., FRITZ, K,, "Nuclear Power Plants with Integrated SteamAccumulators for Medium Term Load Peaking". IÂEA/ECE Symp. onEconomic Integration of Nuclear Power Stations in Electric PowerSystems (Vienna, 5-9 October 1970).

TABLE L MAJOR POWER REACTOR TYPES PRESENTLY BEING BUILTOR DEVELOPED

Wat

er

30

*j3 «!lj*Ira

Heat .TransferMedium

H2°

D2°

C02

He

H2Na

NaK

Li

LiF-BeF2

ThF.-UF.4 4

Thermal (and Epithermal)Reactors

Fast Reactor

Number of Cycles

1

BWR;SGHWR;C/H20

-

«

HTGR+GT

NERVA

-

-

-

.

2

PWR

CANDU;PHWR

AGRjDf»°/C02

HTGR

-

«•

SNAP-8

-

-

3

mt

•M

-

-

••

••

«•

«* *

MSBR

1

SCFBR

*»

-

GCFR+ GT

••

.

-

-

. -

2

?•

••*

GCFR

-

-

-

••

•»

3

«»

-

-

«w

-

LMFBR

-

••

••

FusionReactor

3

-

-

-

«•

-

-

-

Li/NaK

*»

35

TABLE IL WATER CIRCULATION AND TUBE CONFIGURATIONIN STEAM GENERATORS

TypeofFlow

tí0

5C-»yoT-tO4>

-

•s,¡(4JC<u8o

•a2oí55

•o0)0ho

SH

rt

I0)

CO

m4)

CM grt

M

04

r-t

Type ofHeat

TransferSurfaces

Evaporatoronly

Economizer

Evaporatoronly

Superheater

Economizer4 Superheater

Economizer+ Superheater4 Reheater

LoefflerBoiler

Superheatand Heheat

Superheat

Superheatand Reheat

1

Heat Transfer Medium

None

-

BWR;SGHWR

C/H2O

-

SCFBR

-

-

-

Water

PWR;PHWR(U -tubes)

CANDU(II -tubes)

-

-

-

-

-

IntegratedPWR;

Otto Hahn ;D20/C02;KKN;EL-4(helix)

-

Gas

-

-

D20/C02:A-l

(U-tubes)

EarlyMagnox(meander)

-

-

GCFR(helix)

Magnox;AGR;HTGR;GCFR(helix)

LiquidMetal

I

;

4

i

-

-

J

PFR(U- tubes) *

-

EBR-II;Desi.2nStudies(straight) •'

EFXPP ;(involute);BR-350;DesignStudies; ISNAP-8 (Hg) 1(helix» !

Desi en 'Studies .(helix)

36

TABLE 1IL TYPICAL STEAM GENERATOR DATA FOR LARGEPOWER PLANTS

Heat Transfer Medium(Coolant)

——————————— i ————————————

Plant Type

Net Power MW(e)

Geometric Data2Cross- section, primary side m

Cross- section, restricted, ave m2Tubes outer diameter mmNo* of tubes, totalMean tube length m

. Heat transfer area (od) mNumber of SG unitsHeat transfer area per unit m2

Net SG volume, total m3

Net SG volume,per unit m3

Heat transfer area density m2/m3

Cycle Data, GeneralNet plant efficiencyBoiler efficiencyThermal power to SG MWThermal power from SG MWThermal power to ambient MWThermal power to ambient MW/MWe

Primary Side DataCoolant pressure barCoolant temperature, SG in CCoolant temperature, SG out CCoolant temperature drop degCDensity, SG in kg/m3

Density, SG out kg/m3

Specific heat capacity kJ/kgdegCSpecific heat capacity kJ/m3degCSpecific heat capacity kJ/m3degCCoolant mass flow rate te/ sFlow rate, SG in m3/sFlow rate, SG out m3/s

H O ;Dl°

PWR

1000

5.45.422180001619500365002709072

.331.03030303020302.03

155316284326957575.43.74.117.525.223.1

C°2

AGR

625

3016341)600172

He

HTGR

1000

402022/30220077

GCFR

1000

402022/252200102

11000 13200 16800813803444332

.411.0150015008751.4

406502803702339.8419.63284.8209123

622002644450

.421.02380238013801.38

507503504002.54.15.2413.121.41.14450278

628003065155

.391.02560256015601.56

856353402954.56.75.2423.835.31.66369248

Na

LMFBR

1000

3615

FlueGas

Conven-tional

1000

550400

22/30 38/44200034

1000940

13200 118000344002408055

.411.02440244014401.44

56004501509509501.261200120012.913.613.6

1118000236002)236005

.38

.892640235013501.35

1(2000)(160)(1840).28.821.09.3.91.2845701560

37

TABLE IIL (continued)

Plant Type

Mass velocity kg/ m2 sVelocity, SG in m/ sVelocity, SG out m/ s

3)Secondary Side DataLive steam pressura barLive steam temperature °CReheater outlet temperature CFeed water temperature CEnthalpy rise, live steam kj/kgEnthalpy rise, total kJ/kgLive steam rate te/hSpecific live steam rate te/h MW

Heat Transfer Data.Mean heat transfer coefficient

W/m2 degCMean temperature difference degCMean heat flux kW/m2»Mean power density MW /m

PWR

32404.664.28

51265(220)207

1910191057005.7

45003515511.2

AGR

30013.17.7

170540540160

2717313717202,75

f'~

HTGR

5722.513.9

1705405402052522294229802.98

V

16001} 1200851364.3

1501809.6

GCFR

8318.412.4

170540

-1902588258835603.56

14001101548.5

LMFBR

860.9.9

1705005002402247258734003.4

23008018410.1

Conven-tional

3.211.43.9

1705405402602271269136103.61

8025?)20*'.1

1) integral fins, 4mm high, increasing gas-side area about 3 times;accounted for in heat transfer coefficient

2) including furnace chamber, excluding air preheater

3) LMFBR: tertiary side

4) much higher values in furnace chamber

TABLE IV. SOME MATERIALS USED OR SPECIFIED

Type ofRector.

BWR

r\7R

AGR

IÍTGR; ''GCFR

LMFBR

SNAP- 8

Type ofUnit

FeedHeaters

SG

SG

. £G

SG

raxSG (Hg)

Type of Part

Tubes

Tubes end Claddingcî Tube Plate

Clodding of PrimaryHeaders

lleheater Tubes

Economizer Tubes

Evaporator Tubes

Superheater Tubes

Hch«:atsr Tubes

Economizer Tubes

Evaporator Tubes

Superheater Tubes

P.ehcatcr Tuboe

Tubfes

Tubes

Tubes

Material used

Monel

Ihcoloy 800; Inconel 600; .Monel 400

304

Cu-Ni 90-10; 304 L

C-Steel

9 Cr - 1 Mo

316

316

C-Steel; 15 Mo 3

15 Mo 3; 2 1/4 Cr-lMo

316, Ihcoloy 800; Inconel 600;Inconel 625

316; Ihcoloy 800; Inconel 600

Ihcoloy 800;2 1/4 Cr-lMo;2 !/4Cr-lMo-lNb-Ni

304; 304L; 316

Ta

39

TABLE V. COMPOSITION OF SOME MATERIALS

Designation

C-Steel

15 Mo 3

21/4 Cr- 1 Mo(10 Cr Mo 910)

9 Cr* 1 Mo

AISI Type 304

1.4301 (X5 Cr Ni 189)

AISI Type 304L

AISI Type 316

1. 4550 (X 10 Cr Ni Nb 189)

Involoy SOO**)

Ihconel 600++)

Inconel 625~H")

Monel 400"f+)

Approximate ChemicalComposition

Cr

-

-

2.25

9

19

18

19

17

18

20 .

16

22

-

Mo

-

.3

1

1

-

-

<»

2.5

-

-

-

-

-

Ni

-

-

-

-

10

10

10

12

10

32

76

61

66

Cmax.

.2

.15

. 15

.1

,08

.07

.03

.08

.1

.04

.04

.04

.12

Cu

-

-

-

-

-

-

-

-

-

.3

. 1

.1

31

MaterialType+>

F

F

F

F

A

A

A

A

A

N

N

N

N

Approx.Cost

$/ kg tube;

.5

.7

1.0

2.0

3.5

3.5

3.8

4. 0

4.0

5.5

7.0

9.0

6.0

F * ferritic; A = austenitiçj N = Nickel alloy

or equivalent (brand name)

40

McgreUd pvnt

I»•e

LMFBff

Fig. 1 Typical heat transfer ¡dots forseveral reactor types

DRYER

BOTTOM VIEWPRIMARVWATER II

Fig. 2 U-tube, shell type steam generatorunit of a PWR [15]

Fig. 3U-tube, U-shell type steamgenerator of a D O/COreactor [191 2

1 CO. inlet¿2 CO outlet3 H2O inlet4 HO outlet

Fig. 4Pod boiler unit of an HTGR [20]

42

w

Fig. 5 Gas-cooled fast reactorwith pod boiler (GGA)

8STT

Fig. 6 Helix steam generator design fora LMFBR [36]

Fig. 7 Evaporator/superheat modulewith a hockey-stick configurationfor a LMFBR [37]

Fig. 8 Regenerative heat exchanger designs for anIITGR or GCFR with gas turbine [43]

A Straight tube designB Straight tube design

with two concentrictube bundles

a LP inletb LP ouletc HP inletd HP outlet C Helix design

Fig. 9Combined steam dryer/reheater of a PWR

Fig. 10Typical dynamic flowstability plot of anuclear once-throughsteam generator [20]

45

Fig. 11Permissible number of cyclesas a function of temperaturegradient (Beekmann plot)

02 OS I 2 í W 100 «•TEMPERATURE GRADIENT ¿T/4t

Fig. 12Relative cooling power forseveral types of thermalpower plant

s \

•LARGECONVENTONALPLANTS

iií

\ AGR.HT6R. LMFBR.GCFR

HTGR» GT

0.1 02 03 (H 0.5 a&»• NET PLANT EFFICIENCY t\

0.7 08 0.9

THS STATUS OF HEAT AND NASS ZRABSF4R RESEARCHRELATE» TO THE CAKDIT POWER RHACTOF PROGRAM

by"G.X>« McTherson

A. Presentation to fka Pa:iel Oiscuraion on Heat etna Mase Transfer inKuotear Power Plants¿ Sponsored by fhe International Atomic tinergyAgency » Vienna, 14-17 September» 1970.

ABSTRACT

This is a survey of the heat and mass transfer research insupport of Canada's pressurized and boiling water cooled, heavywater moderated power reactors. In the case of pressurized coolantthe fuel elements cay be power United by the critical heat fluxcausing dryout at low coolant qualities and the booster rod chan-nels may be limited by the critical beat flux causing departurefrom subcooled nucleate boiling. In the case of boiling coolantthe average coolant quality is much higher end while dryout may belimiting» consideration is being given to infrequent operation inthis condition*

AC Chalk River the major host transfer activity is aimedat improving the prediction of conditions leading to dryowt ordeparture from subcooled nucleate boiling and post dryout heattransfer in multi-element fuel bundles. Besides ad hoc testing ofspecific bundle geometries the program involves the preparation ofa computer code for the prediction of subchannel coolant conditionsand experimental support of this program. Safety considerationshave led to a growing experimental progrea in support of transientand accident analysis. Areas of research which are important toreactor safety are recommended for coordination by the Agency.

Atomic Energy of Canada LimitedChalk River Huclear LaboratoriesChalk River, Ontario, Canada

47

1.0 IntroductionTo date, all commissioned and committed power reactors in

Canada are heavy water moderated and water cooled. Of these, thefirst generation is cooled by pressurized heavy water and thesecond by boiling light water. In both cases the fu^l consistsof UOa pellets sheathed in zircaloy to form elements, which aregrouped in cylindrical bundles» 0.5 m long* Ten or twelve of.these bundles are located end-to-end in a pressure tube whichforms one of several hundred fuel channels of the reactor. Thispaper reviews the heat and mass transfer studies in support ofthis program and identifies two areas in which the Agency mightplay an important role.

2.0 The yressuriaea-IIenvy-Watar-Cooled Reactor, CANDU-PHWEarly heat and mass transfer studies aimed at avoiding the

onset of nucleate boiling in the fuel channels as predicted by theJens & Lottes correlation [1]. This required an estimate of thelocal coolant flow and temperature and hence the mixing of thesingle phase coolant among the subchannels of the fuel bundles*

Mixing measurements were done at low pressure using hotwater or salt injection in certain subchannels and at high pressurein an K8.0 reactor loop where mixing was inferred from subchannelcoolant temperatures. Experiments were done with both smooth andwire-wrapped 19-element bundles and the ¿results used to select awire-wrapped bundle free from nucleate boiling. Our present statusin .the development of a single phase mixing correlation is summarizedi» 12}.

Good estimates oí subchannel flous ars obtained by assumingequal pressure drops based on subchannel hydraulic diameters. Theheat transfer coefficient is calculated with a fora of DittusBoelter correlation reported in [3}. This information togetherwith the mixing correlation permits a check that nucleate boilingwill not occur.

The requirement to avoid nucleate boiling has been relaxedfor the CAKDU-PHW's committed recently and in the Bruce GeneratingStation boiling is allowed up to a few percent outlet quality.

48

These reactors will operate at heat fluxes safely below departurefrom nucleate boiling. Thus» a power rise or flow reduction wouldlead to higher coolant qualities where the critical condition isdryout. Dryout correlations based on tests of this fuel give a CPR(critical power ratio) close to 2. It is interesting that with theBruce design where soné channels are subcooled and others boiling»the CPR for flow instability is lower* at a value of 1.6. However,neither dryout nor flow instability are uniting factors in thedesign.

In the natter of accident analysis the heat and masstransfer behaviour is similar to that in boiling water reactorswhich are discussed in the following section.

3.0 The Boiltng-Light-Water-Cooled Reactor. CASDÜ-BLW3«1 Pryout

Since the inception of the CANDU-BLW program the major heattransfer research effort has been devoted to the fundamental studyand prediction of the critical heat flux phenomenon called dryout.

Dryout tests were first done out-of-pile on single» eleertrically heated elements [4] and have progressed in complexity toin-pile tests of multi-element nuclear fueled bundles ([5] andothers» unreported). Currently we correlate the data from the rests

í

of a given geometry in terms of the average coolant conditions atthe dryout point and the tneiuodyndiaic boílias-length-averaged heatflux up to the dryout point [6]. In this way teses with an axialJyuniform heat flux distribution can be applied to the non-uniformcase of a reactor.

Simultaneously* we are doing research in support of acomputer program, SASS, which predicts subchannel flow conditionsand subchannel dryout. Eventually this program will requirecorrelations for steam and water turbulent mixing» cross flowbetween subchannels» droplet deposition» entrainment and thedetailed local flow conditions leading co dryout.

One series of supporting experiments is the measurement ofsubchannel cross flow and turbulent mixing with single and two-phasemixtures. The first phase, dealing with outflow from an axial slit

49

in the valí of a tube, is completed and reported In (7). Dischargecoefficients were obtained for the air and the water of an air-waternixture. Work is now in progress on turbulent mixing through a gapbetween two représentative subchannels of a rod bundle array* Theinlet air and water flows to the subchannels are individuallyadjusted to give identical pressure gradients and then tracers areinjected into one subchannel and samples taken at the outlet of both.Gas chromatography and lithium flame spectroscopy are used to obtaintracer concentrations and hence average nixing rates. Initialresults show that the turbulent mixing rate depends strongly onmixture quality, exhibiting a peak at about 50% void fraction. Thisvork will be extended to boiling Freon.

Another series of experiments was designed to measure dropletdeposition in an annular-dispersed two-phase flow at high pressure.The inner wall of an annulus consisted of a heater and film extrac-tion sinter separated by various unheated lengths. The outer wallalso contained a sinter at the level of the inner wall sinter todetermine the liquid distribution. The heater was maintained at dry-out while tube and rod film flow rates were measured. Fron rod filmgrowth rates, droplet deposition fluxes were obtained and a relation.Cor the entrainment flux deduced. The study also shoved that forL/D ratios of several hundred and low pressure drop a fully devel-oped flow can exist with.the liquid film and droplet spray inequilibrium. À droplet interchange model was proposed in which theflow is divided into a variable density film and a gas-droplet core.Whoro data are available good agreement is found with predictionsox'mean filia thickness, maximum-to-mean film thickness ratio, filmcrest velocity and liquid holdup [8].

Studies of the mechanics of dryout have been done in a lowpressure steam-water system {9]. Analysis of the forces on thefilm at a dry patch boundary shows that surface tension is the dom-inant upstream force and vapour shear the dominant downstream force,although when roll 'waves exist their inertial effect provides anadditional major downstream force 110]. In a continuation of thiswork droplet movement, heated surface temperature distribution andwall shear will be measured in the vicinity of the dry patchboundary where Freon is the test fluid. •>

50

Until our understanding of «se. phenomena is considerably;"' Í

improved we shall rely heavily on ad hoc testing for design purposes;once the subchannel analysis approach is perfected it will probablybe used in the selection of the fuel design for a given reactor anddryout tests will be limited to confirming the behaviour of thedesign selected. •-:

Meanwhile a method has been developed at Chalk River topermit fuel bundle design on a heat transfer basis with little ref-erence to expensive dryout teats. It involves the comparison ofmany possible arrangenents of a given number of elements in termsof the subchannel enthalpy imbalance and heated perimeter. From acomparison of experimental critical heat flux with the associatedimbalance in subchannel enthalpy the latter can be related to amaximum achievable critical heat flux and thus an enthalpy imbalancepenalty factor determined. The product of this penalty factor andheated perimeter is a figure of merit and the arrangement with thehighest figure of merit is selected as the best design on a heattransfer (i.e. power to dryout) basis.

Confirmation of this selection technique can now be doneby fluid-modeling the dryout behaviour of the full scale geometryselected. In [11] the dryout results for an 18-element 9-ft. bundlein water are compared with predictions based on tests of the samegeometry in Freon-12. The predictions fit the water data with anRMS error of 6.18% which is excellent when compared'with an RHSerror of 5.87% io fitting the Fréon data alôiié.5 A Fréon loop isunder construction at CUalk River and will havér ¿tté capability ofboth confirming this selection technique and'of fully Vesting allfull-sized^ fuel channels currently envisaged for CANDU reactors.

i." : ' " '•'

3.2 Post-dry out s'r;

A-promising improvement on current CÀNDU-BLW designs requiresoperation at higher outlet coolant quality and possibly a lower CPRfor dryout than the current value of 1.5. Since this is likely tolead to short, infrequent periods of dryout operation the post-dryout behaviour of fuel bundles must be studied.

51

Post-dryout testing has progressed from out-of-pile testsof single, electrically heated elements to in-pile tests of nuclearfueled bundles. Tests of simple geometries {12] have shown that amodified Miropol'-skiy heat transfer correlation best fits the fullydeveloped post-dryout data. However the same correlation under-predicts all heat transfer coefficients measured on a large assort-ment of bundles by at least 20%.

While this discrepancy is being studied a droplet depositionmodel is being developed as a more fundamental approach to theproblem. This study may lead to a more accurate correlation forcomplex geometries and will be a necessary addition to the subchannelanalysis code when dealing with the post-dryout regime.

Post-dryout operation also raises questions of the metal-lurgical effects on the fuel cladding of rapid temperature fluc-tuations which occur at the boundary of the wetted area and of theeffect on element bowing by large temperature gradients which mayoccur across the element. These effects are being studied inin-pile tests at Chalk River.

3.3 Coolant Void DistributionBecause of the strong neutron absorption by light water the

coolant void distribución may have an important effect on the localneutron distribution, reactor kinetics and safety analysis. Thevoid distribution is a complicated function of mass flux, heat flux,inlet subcooling and channel geometry. In an analysis of thisproblem 113] the temperature distribution of the subcooled liquidwas first expressed as a function of dimensionless heat transferand condensation parameters. The corresponding void fraction, validin both subcooled and bulk boiling regions, was then computed by anempirical slip ratio correlation. The calculated void distributionsagreed better than other available correlations with data fromseveral sources. In the future we plan steady state and transientvoid measurements to perfect the model and extend it to transientconditions. A fast response void meter is required for the tran-sient measurements and work is continuing on the development of animpedance-type instrument.

52

3'* g*jraIÍ6l Channel Flow StabilityIn a CASDH-BLtt reactor the possibility of flow Instability

«mong the parallel coolant channels way» ,le&4 to premature dry outand control problems. K*per^w*nts. ha^e been performed ,«t Chalk Hiveron both eteam-water and Preen aulttrchannel test loops and ananalytical model, POISE, developed to explain the results.

The nodel is based on the solution of time and space depend-ent conservation equations together with correlations of ¡void,pre9sure drop and heat transfer and the appropriate boundary con- <ditions. The resulting non-linear equations are SO!VÍMÍ '«sing, r 'finite differences and a momentum integral nethod, following theprocedures used in H YD HA {14}. The POIi'X program* «>ssesses; thetransient effect of a step power increase on the flow of w«terthrough a boiling channel. In response to such an increase flowoscillations occur. If the channel is operating in a y tabluregion these oscillations ate damped, otherwise they persist ordiverge.

POISE has been shown to predict both the instabilitythreshold power and oscillation period for simple geometries [15].However when applied to a channel containing a 19-element heatedbundle POISE gives a conservative estimate of the instabilitythreshold power (16).

} !

ïiv-pile and out-of-pile experiments have been done recentlyusing nalti-element bundles and analysis is continuing with theobject of improving the accuracy of FOISE predictions.

v ' « ' • '

4.0 Trana ion t and Acct den t Cond; i t ipnjsIn this section we Include heat transfer and flow changes

during power transients, blowdown due ta a coolant system rupture,pump failure and post-accident emergency cooling. In gênerait theobject of these studies la to determine the fuel temperature.. his.tor>» .' • " ' • ' • ' 'and its consequences and the reactivity e f fec t caused by large . .changes in coolant density. The results are usually applicabilité..^both CANDU-PHW and CAKDU-BLW reactors.

53

4.1 AnalyticalTwo nain computer programs are used In the safety analysis

of CANDU power reactors: RODFLOW, to predict the effect of severedisturbances such as pipe failures and large perturbations inreactivity or coolant void, and HYDNA-2, a more economical versionot ROD FLOW used for transients involving oni> ¿,-iall changes IKcoolant pressure.

In RODFLOW the heat transport system is divided into nodesin vhich steady-state inventories of mass and energy are placed.After the start of the transient the momentum equation is used totransfer mass and energy between nodes. The pressure is calculatedfor each node as a function of the mass and energy content and thepressure differences between nodes determine the flows. Flowreversal is accommodated by this technique.

A detailed pump model is used which accounts for the inertiaof the pump-motor-flywheel system as well as the flow characteristicsof the pump under abnormal conditions.

The discharge from the break is calculated on the basis ofthe coolant enthalpy and pressure in the node with the break.

The fuel dynamics are calculated with a multi-region modelin which the regions are spaced at equal radial increments. Theheat balance equation between generated, conducted and stored heatsis solved by a finite-difference method. The program has built-incorrelations to predict heat transfer from the fuel for single-phase»two-phase, post-dryout and superheat forced convection. Oryout ispredicted using the local conditions assumption and an empiricalcorrelation.

4.2 Required Experimental SupportThe accuracy of such programs depends heavily on experimental

data. In particular it depends on 1) the heat transfer rate duringthe transient, 2). the associated transient void distribution, and3) the void-reactivity transfer function. The experimental workrequired to obtain this information is discussed below.

54

4.2.1The heat transfer rate must be known throughout the fuel-gap- .

cladding combination both before and after dry oui ouc.¿c¿. Tu it»implies an understanding '6~f the behaviour of the fuel, gap andcladding during the transient, thé coolant heat transfer coeffí- :

clents before and after dryout and the conditions at which tran-sient dryout occurs. Due to the interdependence of these'factors 'this information cannot be obtained in a single experimentalfacility - both in-pile and out-Of-pile facilities are required. • .• ......

For example» consider the transient heat transfer from a !

highly irradiated uranium dioxide fuel channel clad jn ¿iicaloy".r)'"•':--!''-Depending on whether the transient is due to a power excursión • : • • ' • " > - ' • >or a loss of flow either the fuel temperature o'r the cladding "'•"'• "• •"'temperature will rise first. The differential expansion, which isdifferent in each case,r may significantly affect thé heat flow inquite diffèrent ways. Thus the cladding temperature, which isusually measured in this sort of experiment» will be determined byboth the fuel element behaviour and the coolant heat transfer' coef-ficient. Furthermore the cladding may teach a temperature at whichthe internal fission gas pressure is sufficient to cause swelling«nd thus a reduction in the available coolant flow. To study thissort of behaviour the heat transfer coefficient mist first b • known«nd for this reason out-of-pile heat transfer tests are essentialto the accurate analysis of in-pile tests. To cover the wide rangeof conceivable transient and accident conditions the scope of the

Nrequired test program is much greater than the equivalent steady-state heat transfer program.

*•.*"-*'''

A knowledge of the local coolant void is needed for tworeasons: to permit correlation of the transient heat transfer datadiscussed above, and, in combination with local reactivity measure-ments to determine the void-reactivity transfer function. Thus,both in-plle and out-of-pile void measurements are also requiredover a wide range of conditions.

55

4. 3 Current Support Work

4.3.1 Blowdown - Depressur l z i t j L o a i f t j k e p r i a a r y c o o - a t i tcí rcuit

Early work consisted of full-scale blowdown experiments onpiping arrangements specific to reactor designs. These tests vieredone with pressurized water and unheated fuel. Because the fuelwas unheated the results were misleading.

A more fundamental study of blowdown at typical CANDU-BLWconditions is in progress at Chalk River. A two-phase annular flowat high pressures was blown to atmospheric pressure and detailedmeasurements made of flow tube pressure gradient, rarefaction wavevelocity and flow discharge during the first 100 ros after ruptureof a diaphragm at the downstream end of a pipe. The rare.f actionwave velocities were within 6% of theoretical values. During thefirst 100 ros the flow discharge agreed with values predicted bythe homogeneous model. This is contrary to steady state criticaldischarge rates which agree with an annular two-phase critical flovmodel. The flow tube pressure gradient changed from its pre-b low-down value to the critical discharge value in about 100 ms [17].The next phase of this program will be done with a heated testsection.

An experimental program is planned to study the effect onfuel cladding of a loss of coolant resulting from blowdown. In thecase of highly irradiated fuel a loss in system pressure will causean excess pressure within the cladding due to gaseous fission prod-ucts. Simultaneously* the loss ox coolant will lead to high clad-ding temperatures which may exceed the lower limit for plasticstrain. Hence, at some time before the emergency coolant begins toflow the cladding may swell and so obstruct the coolant. The pro-gram is planned to examine the likelihood of this happening and theconsequent radio-iodine release. An out-of-pile series of testswill be done first, using un fueled zircaloy tubing, to study theeffects of internal pressure, rate of temperature rise and maximumcladding temperature. An in-pile test will then be done to studythe behaviour of nuclear fuel ele'ments at conditions which, in thefirst series, were shown to cause swelling and rupture of the clad-ding. The results of this work should provide important limitingconditions needed in the evaluation of emergency cooling systems.

56

4.3.2Emergency coolant nay be .injected frota that end of the

reactor which is at the higher pressure, subsequent to the rupture,or it «ay be sprayed from sparge'tubes which form a structuralcomponent of the fuel string. 'Furthermore it may be highly sub-

ï ' s *" *"• . *cooled, saturated or boiling, the cooling efficiency depends onthe method of injection and the coolant conditions selected. Aprogram to study these questions has been started at- Chalk River.In the first phase an electrically heated 19-clement buihdle will belowered through a guide tube into a pool of water. Thermocoupleson the bundle.will indicate rewetting times and differences insubchannel rewetting behaviour. Variable parameters will includeheater temperature, coolant temperature and insertion velocity.

4.3.3 £t»mp__F¿i 1 ureAnother cause of loss-of-flow may be pump failure. In this

case the concern is, with the rapid corrosion and the melting of thehigh temperature-cladding.

Pump rundown tests have been done both in-pile and out-of-pile. In an in-pile test using 3-element bundles the flow was reducedfrom 220 g/cm*s to about 2.5 g/cm*s in 1.2 seconds. The reactor wastripped 1.6 seconds after the initiation of the pump trip. Duringthe next ten seconds the eight thermocouples attached to the clad-ding indicated temperatures which rose smoothly towards maximumvalues of 850*C. The initial température rise rates and asymptoteswere significantly lower than predicted by our -transient code. Sub-sequently the fuel model in this code was modified to include theeffect of cladding expansion and it then agreed much better with thedata. It «as Interesting to observe that at che end of every te?.f .within one second of switching on the pump, temperatures begandropping and the cladding rapidly rewetted. .Similar tests on astring of six 36-element bundles, generally «verified these results.

A major uncertainty in both of these in-pile tests is the.value of the flow which persists after the rundown. OuV solutionis to begin the test with the main flow to the test section inparallel with a small flow representing the post rundown value.

57

The pump rundown can then be simulated by closing e valve in themain flow line thus reducing the test section flow to the prese-lected post rundown value.

Pump rundowns have recently been done out-of-pile on thesame 36-element geometry* The results should provide the transieraheat transfer coefficient required to interpret the fuel behaviour-effects in the in-pile tests.

The in-pile 36 -element string is equipped with sel£-po-.?£i:-:. :flux monitors which continuously indicate the local neutron flux.From readings taken during various steady state conditions andduring the pump rundowns we have been able to determine the voidreactivity coefficient and local reactivity changes during trau&«voiding. From this information we can estimate the void-reactiv*transfer function due to voiding any portion of the reactor core.

4.3.4 owerVe recently ran the out-of-pile 36-eleuent bundle through

power excursions from various values below the critical dryout p <:•-.-to various values beyond. The main objective in these tests is t?.measure the delay between the time dryout power is exceeded anddryout actually occurs. The results have not yet been analysed.

4 . 4 The Long-term Consequences of Transient and Accident StudiesThe study of transient and accident conditions should hn .

two very important long-term consequences: reduction in designCPU's aad more rational safety standards. The reasoning is

\explained below.Uncertainties in predicting the onset of critical phenomena

normally form an integral part of the design safety factors. Forexample» to provide a true dryout CPR of 1.35 where the uncertaintyin predicting the dryout power is ±20%, the design CPR must be 1.69.A reduction in the uncertainty of the dryout prediction would reducethe design CPR without reducing the true CPR. Thus the designpower could be raised with no sacrifice of safety standards.

58

In the absence of experimental information designers rightlytake a'conservative approach. For examplebefore we had in-pile• •> •„ •/ î :. •post-dryout experience the CPR was chosen"high enough to avoid any.'i-. •'chance' of dryout at normal operating conditions and abnormal con-ditions leading to dryout were assumed to result in fuel, failure.We now know that dryout does' not necessarily cause fuel failure and,at some:reactor conditions;» cao be endured safely throughout thelife of the fuel. More accurate laformation of this nature can beapplied either .to reducing .the appropriate Safety factor or toreducing the containment requirements. •:The-sosie public safetystandards..would still apply but the design would be more rationallybased*

5.6 Other Work Associated with CAHDU Reactors . . ... :5.1 I»ow.grea*ure Heat Transfer and Fluid Pytttfnics •' • ••'•" ' :

To provide for Xenon override CARDU reactors are sometimesfurnished with booster rods. These are multi-element bundles of

•.-.,?!•• • ' • • • • • • ' . •-••••' '-••• x" '"highly enriched fuel which may be inserted into the core for shortintervals of time and whiW^re force-convection cooled by moderatorat near atmospheric pressure". Since the override effect is propor-

• •' ,«.*.. .•**.'%tionel* to'ttteir operating'power it is essential" to know the power• » *•' • - • " C -' •limitations imposed by onset of significant' void» departure from

nucleate bailing and. flow instability. An-^analytical study of flowinstability is in progress and is based on<the results discussed insection 3.4.

He have recently begun an experimental study of the onset- . . " • • • $ * . * • i * *"of significant void and departure from nucleate bofHug in a

19-element bundle. Resulta .will be used to evaluate correlationscurrently in use .and to evaluate 'the subchannel analye&s <«odesdiscussed, .in section 3.1» The .«iitcoaie of this work sh^urd reducethe uncertainty in predicting these phénomène and hence lower théminimum design CPU's, . . . . . <

5.2 Corrosion Product Heat Transfer and Transport StudiesThé movement of corrosion products about the primary'circuit

of water-cooled power reactors is of interest for two reasons:

59

1) the concern to avoid fouling of heat transfer surfaces and» 2)the problem of the radioactive contamination of circuit componentsby corrosion products which have beea carried into the core by thecoolant, been activated there, and carried back to the out-coresurfaces. Studies of both aspects have been -done at Chalk River.

The effect on dryout and oost-dryout heat transfer has beenstudied in-pile. Tests were done before and after the addition offerrous hydroxide solution to the coolant. The resulting reddish-brown deposit which formed on the fuel cladding caused a slightincrease in critical heat flux and a significant decrease in post-dryout heat transfer coefficient 118].

The experimental technique used in transport studies involvesexposing a large-surface-area source of the pertinent corrosionproducts, which has been previously nade radioactive by irradiation,to recirculating high-temperature water. A sidestream is takeu to.atest section which is monitored with a germanium-detector gammaspectrometer. Deposition and release rates at the test section sur-face can be measured continuously under a variety of transient orsteady-state hydraulic «ad chemistry conditions. A series of testsis being done to determine the importance of various parameters andwill be followed by a more thorough series.

The ultimate aim of the work is to understand the mechanismof radioactive corrosion product transport and to find methods forcontrolling its movement.

5.3 Heat Transfer to Superheated S tea»Besides the interest in superheat generated during transient

and accident conditions, some interest remains in steam as a reactorcoolant. Analytical work is directed towards the prediction oflocal cladding temperatures in a fuel bundle. It involves theanalysis of data for bundle heat transfer to air and carbon dioxide.Ultimately the subchannel analysis codes will be used to handle thisproblem.

Some superheat heat transfer information will be gainedduring an in-pile study which is Just starting at Chalk River.

60

5.4 Surface RoughnessMicroscopic surface roughnesj» is being considered for three• 3:0.".¿f ." '• • •' ';'-'''separate effects:

- to improve the heat transfer rate in water, post-dryout or steamcooling by reducing the thermal boundary layer thickness.- to iaprove the dryout characteristics of fuel cladding byincreasing the surface force leading to rewetting.- in two-phase flow» to reduce the liquid film flow rate on unheatedsurfaces and so increase the available liquid to wet the heatedsurfaces.

An experimental program with these objectives is now in prog-ress. First results show that one type of .roughness on the heatedsurface caused a significant improvement in post-dryput heat transferbut no obvious improvement in the dryout heat flux.

5«5 Work in.Support of the Organic Cooled CARDUf ,-)ff5o far my '.3£enarks have been limited .to commissioned or

committed power reactors. As yet the organic cooled CANDU has notbeen committed but the supporting heat and nass transfer activitiesfall logically within the topic of these discussions.

- t ¡i • • • '

Performance of the organic cooled WR-1 research reactor at¿~• 0

the tthjtteshell Nuclear Research Establishment has been excellentover its five years of operation, and the technolo>gy for an organiccooled CANDU is well advanced. The concept offers advantages ofhigher thermal efficiency, negligible radiation fields and very lowfuelling costs. The heat transfer program associated with theorganic coolant covers:1) forced convection heat transfer in bundle geometries at heat

fluxes to 300 W/ctn2 and linear, velocities to 17 m/s.., " . . •• '2) effects of low boiling components of the coolant on forced

convection and the increase in heat transfer coefficient bysurface simmering.

3)' the limitations on heat transfer rates due to the boiling crisisor to rapid surface decomposition ait high surface temperatures.

61

In addition a fundamental program is under way on turbulentflow structure of £ingle phase fluids in simple and complex geom-etries. This program is of general validity to any single phasecooJLant system. Both hot-wire and laser-doppler anemoaetry arebeing weed.

6.0 Chalk River _.gxT>erien.ce__.in_ international CooperationIn the areas under discussion AECL has cooperated mostly

with the USAEC, the UKAEA and CISE. We have found these exchangesvery useful for keeping abreast of new developments and for acquiringthe results of certain studies which were not supported in Canada.The following examples illustrate the importance of such cooperationto the Canadian program.

Through a USAEC-ABCL cooperative agreement large powerout-of-pile heat transfer tests have been supported at ColumbiaUniversity. The results, have formed the foundation of dryout cor-relations and flow stability analyses used in the design of ourpower reactors. This agreement has also supported the analyticaland experimental work at Hanford which led to the COBRA subchannelanalysis code.

Early success at Vinfrith with Freon/water modeling of dry-out tests prompted AECL to enter this area. Fluid modeling hassince become one of our most important experimental tools. Onesignificant step along this route was a CHF test series done by theAtomic Power Constructions Ltd. (Uli) using a test section fabricatedby the UKAEA to permit simulation in both Freon and water of a testdone earlier at Columbia University under the above-mentionedcooperative agreement. Comparison of the results gave convincingevidence for proceeding with the fluid modeling concept (11].

A fuel string consisting of six 36-element bundles wastested for dryout behaviour in the 01 loop of the NRU reactor atChalk River. This experiment is being duplicated in the largeout-of-pile heat transfer loop at Piacenza, Italy and the heattransfer results will be exchanged.

These are only a few examples of many exchanges andcooperative studies that have benefited all the participants.

62

7.0 Recommendation for a Role by the IAEA in these ActivitiesThere are two important areas discussed in this paper which

deserve international attention. The first is subchannel flow con-ditions and the associated film flow and dryout models, covered insection 3.1, the second is transient and emergency conditions coveredin section 4.

I believe these areas deserve international attention becauseeach has a strong influence on the safe operation of water cooledpower reactors and o.i the consequence? of accidents over large sur-rounding areas. Since the area of influence of any reactor nayextend beyond international borders it is In every country's interestthat all information pertinent to the safe dcsiga and operation ofpower reactors be made available to reactor design teams andlicensing boards.

The IAEA could play an important«role in several ways: itmight sponsor symposia to bring experts together and coordinateresearch programs, seminars for the newer nuclear countries to learnfrom the experienced, or special sessions at large conferences oftechnical societies. In addition the Agency might form an inter-national team to recommend correlations and safety standards ofdesigii. Contributions of this nature would admirably suit theobjectives of the Agency and play an important role in power reactordesign.

8.0 •References1. Jens, W.H. and Lottes, P.A., "Analysis of Heat Tranafer,

Burnout, Pressure Drop and Density Data for High PressureWater," ANL-4627, 1951.

2. Rogers, J.T. and Rosehart, R.G., "Turbulent Interchange Mixingla Fuel Bundles," Proc. Can. Congress of Applied Mechanics,University of Waterloo, May 1969.

3. Nixon, M.L., "Heat Transfer to Water Flowing Turbulently inTubes and Annuli," CRKL-165, February 1968.

4. Moecfc, E.O., Matzner, B. , Casterllne, J.E., and Yulll, G.K. ,"Critical Heat Fluxes in Internally Heated Annuli of Large

63

Diameter Cooled by Boiling Water at 1000 psia," 3rd Int. HeatTransfer Conf., Chicago» 1966.

5. Winter, E.B., and Page, H.D.,'"Fuel Bundles T&ken to Dryout inNRU Reactor," AECL-2362, 1965.

6. McPherson, G.D., "Dryout in Boiling Water Reactors," AECL-2376,May 1967.

7. Madden, J.M., and St. Pierre, C.C., "Two-phase Air-water Flowin a Slot-type Distributor," Symp. Fl. Mech. and Meas, inTwo-phase Flow Systems, Brit. Instn. of Mech. Engrs.,University of Leeds, September 1969.

8. Moeck, E.G., "Annular-Dispersed Two-Phase Flow and CriticalHeat Flux," AECL-3656, July 1970.

9. McPherson, G.D., "Axial Stability of the Dry Patch Formed inDryout of a Two-phase Annular Flow," accepted for publicationby the Int. J. of Heat fc Mass Transfer.

10. Thompson, T.S., and Murgatroyd, W., "Stability and Breakdownof Liquid Films in Steam Flow with Heat Transfer," 4th Int.Heat Transfer Conf., Paris, 1970.

11. McPherson, G.D., and Ahraad, S.Y., "Fluid Modeling of CriticalHeat Flux in an 18-element Bundle," submitted to Nuc. Eng»and Design.

12. Groeneveld, D.C., revised by Moeck, E.O., "An Investigationof Heat Transfer in the Liquid deficient Régine," AKCL-3281,December 1969.

13. Ahtnad, S.Y. , '.'Axial Distribution of Bulk Temperature and VoidFraction 'in a Heated Channel with Inlet Subcooling," acceptedfor publication by the ASME.

14. Currin, H.B., Hunin, C.B., Rivlin, L,, and Tong, L.S. "HYDNA -Digital Computer Program for Hydrodynaroic Transients in aPressure Tube Reactor or Closed Channel Core," CVNA-77, 1961.

15. Carver, M.B., "The Influence of Certain Design Variables onthe Hydrodynamic Stability of a Heated Channel - A DigitalComputer Study Supported by Experimental Data," 67-HT-66,ASME-AIChE Heat Transfer Conf., Seattle, June 1967.

64

16. Carver» M.B. , D'Arcy, D.F. » 'WikhawiBer, G.A., Casterline, J.E.,and Matzner, B., "Instabilities in Flow Through MultirodBundles and Their Effect on ííryout," ABCL-2716, Septeaber 1968.

17* Fhito, R.F,, "Results of Two-phase Slowdown Experiments,Part I; Straight Tube Test Section," AECL-3664, July 1970.

18. Groeneveld, B.C., Thibodeau, M., McPherson» G.D., "Heat TransferMeasurements on Trefoil Fuel Bundles in the Post-*dryout Regime -vlth Data Tabulation," AECL-3414, July 1970.

65

.Problems, of Cooling Disturbances and Sodiu:n Boiling, . .in Pact Reactors

D.SniidtInstitut für RopUtorontwicklung

' ' * 'I ."•' ;

Kernforschungszentrum Karlcruho

1. Introduction• - •" • tUnder normal 'conditions liquid rae tal cooled reactors do not present

important unsolved problems of heat triuicfer. Except for some openquestions on local hoat transfer in rod bundles ths thermal designof a sodium cooled co¿c. iïs a straightforward mat tor, and most unccr-

- V . ' •!.,taint Íes are of a true stochastic nature, 'fney depend more on toleran-ces of different variables than on the limited basic knowledge ofheat transfer.

A different eitur.tior. occurs with rcspeofc to cooling disturbances.They r.:ay eithsr bo of '&• local nature affecting a number of subcJiannclewithin the rod bundle or they may reduce the coolant flov; for the cn-

•; '."ft :"!' ' • > . . . > • • ' • ' :

tire subassembly. In tho former case of local flow reductions orblockages wa at first have the problem of the temperature distributionwithin the wake of the disturbance, i.t second the possibility of sodiuaiboiling. In the latter case of complete subaueerably flow failures the! ' " . 'i . • , • ,single phase flow does not present fundamental problorar>, but h?re eJ.sosodiu-n bo il ins nicht occur.

Sodiu-n boiling, is tif^itïy connected to safety. Since we are considering. ,~ «¿ -. .. .

single aubauseiíblics or ports of subafísomblies, tlïe reactivity gainof voiding is of email imjvortancc . However, . soaie, , cases of sodiujn, boil-ing in narrow channeln will result in a .ccciplcte dryoul; of the rod .surface, thus o.yichly leading to fucîl melting A subs-cqucnt reentc-yof liquid, sodiu-n may start a th<mr.&l interaction between sodium -and fuelof an explosive nature. By this a fact ffcllure propf;satio3» pay be . envi-saged as a hypothetical possibility. Tno reaction rate, and, therefore, theexplosive force of codiu.T.-fuel-intoraction(S.?I) is governed by the heat

67

transfer between the hot fuel and the liquid sodium.Among other para-meters the fuel particle size (area of heat transfer) and the heattransfer coefficient (influenced e.g. by the Leidenfrost phenomenon)are of outmost importance.

The safety risk of these phenomena at present can be made negligibleby early detection with special ins rumentation. However, a better phy-sical understanding is required and may even allow for a reduction ofthe expensive instrumentation ¿~l6_7«

Within the field of this conference on heat transfer cooling disturban-ces in liquid metal cooled reactors present the following, as yet onlypartially solved fundamental problems:

a) Flow and temperature distribution behind local obstructions in amultirod-bundle in <the liquid phase.

b) Sodium boiling in narrow channels at flow reduction.

c) Local boiling behind flow obstructions.

d) Occurrence of dryout ("burn-out") in canes b) and c).

e) The thermal interaction between hot or molten fuel and sodium alsois mainly a heat transfer problem. However, this will not be dis-cussed in this paper.

The following paragraphs give a sho: t review of the present status oftopics a) - d) with spsciax emphasis on our own work.

2. Wakes Behind Flow Obstructions..inMultirod Ooometry (Liquid Phase)

Pig.l shows as an example of a flow obstruction in a bundle the blockageof a spacer grid by some foreign objects at subchannels 2 and J. Theoriginal flow velocity v is reduced to some value v. anywhere betweenv and 0. Naturally a flow component Vp eventually will restore thecoolant flow.and the region of disturbed flow and temperature may havethe shape indicated by tho broken lino. Other disturbances like rod de-formations can be imagined.

68

The theoretical treatment of this problem presently is incomplete.Several codes ¿~l,2,3,4,14,\^J have been developed on basically thesame principles. The three-dimensional array corresponding to fig.l issubdivided into a number of finite elements corresponding to axial sec-tions of the subchannels. For each node a balance for mass , momentum(pressure) and energy (heat) is formed for the exchange with the imme-diate neighbours. Reasonable assumptions have to be made for frictioncoefficients and eddy diffusivities.

The most elaborated and flexible program of this type is -the Britishcode SAMBA ¿~1,1%J?. Nevertheless for a larger number of nodes it mayrun into numerical difficulties with respect to convergence and stability.Our code THESYS /~2 7 is intended to avoid some problems of this nature.

The main drawback of these programs is an incomplete physical model.While uncertainties in friction coefficients and eddy diffusivities maybe corrected by adjusting some free parameters to experiments, the mainmissing effect is that of macroscopic eddies, where macroscopic meanslarge compared to the size of the nodes. These may result in a kind ofsecondary flow superimposed on the main channel flow in varying direc-tions and affecting the mass and heat balance between nodes and thepressure distribution as wel]. Besides of the numerical problems thesephysical reasons may define a lower limit for the node size. It is,however, true that the narrow connections between the subchannels tendto decrease the superimposed flow. Aleo an increase of the remainingvelocity v. above zero diminishes this effect.

The direct experimental approach with inultirod arrays, true heat fluxand sodium is difficult, expensive and very time-consuming. The tempe-rature distribution, which is the main* safety concern, can be measuredreasonably well. The flow distribution, however, being the main linkto the analytical models, can hardly be determined in this case. There-fore, besides of sodium experiments as engineering tests more basicwork is necessary, using transparent liquids like water. The measurementof flow distributions and comparing them to calculations is its mainpurpose. The temperature distributions in liquid metal naturally cannotbe simulated because of the different Prancitl number, here one has to

69

rely on additional theoretical considerations.Experiments have been started at Karlsruhe. Pig.2 shows a typical resultfor the wake in a two-row bundle. This picture has been obtained witha Laser-interferometer in this "two-dimensional" simplified geometry.The shape of this model is shown below the interferogram. To get theinterferences the air flow used here has been made visible with ether.

Sodium Doiljng in Narrow ChsnnnJr. at P3pw.K:wopeneQus_ Reduction

Before we turn to the effect of these local temperature distributionson the onset of boiling, we consider the sin.pler case of a homogeneousflow reduction in all subchannels of the bundle with subsequent boiling.Work on this has been done at Karlsruhe since several years /~5»6,7J*.

Sodium boiling in channels in moat caces of interest is of an oscillato-ry type, i;e. the channel exit velocity varios in a nearly periodicmanner. This should not be confused with the iiometirr.es observed insta-bilities, where boiling and non-boiling periods fellow in time. Thelatter behaviour will not occur at, heat fluxes and channel dimensionstypical for fast reactors. Phenor^nologieMilly the boiling process fora complete loss of flow can be described by the follov;ing sequentialevents:

a) Heating of the liquid up to a certain temperature above saturation.

b) Flashing of the superheated liquid at a certain location. The firstbubble will have the vapour pressure corresponding to the superheat.By this it will suppress all other bubble nuclei co that only thefirst bubble is able to grow. Schleehtendahl /~11,12_7 has derivedthe conditions of superheat, geometry and temperature profile whichlead to this single bubble boiling.

c) The cylindrical bxibble grows and expells the liquid from the channel(fig.2)« A liquid film of some tenths of a mm thickness stays onthe wall and feeds the bubble by evaporation.

d) When the bubble reaches the cold «odiun above the channel, its pres-sure will be reduced, the evaporation of the liquid film increases,and thereby cools the surfaces, and the temperature drops

70

e) After the pressure decrease a return flow of the liquid is possibleand the channel may be partially refilled.

f ) a) - e) are repeated until the sodium film in the not refilled partsof the channel dries off (after several tenths of seconds).

If there is a superimposed coolant flow, the oscillating type of boilingalso prevails. Depending on the pump head, the degreee of orificing atthe channel inlet etc., the pressure of the growing bubble has a feed-back on the flow or on the inlet and outlet velocity, respectively, whichagain influence the temperature, so that the whole process becomes morecomplicated. Basically the phenomena are the same. Except for the oscil-latory behaviour the flow is very similar to the wellknowri annular regime.However, during each vaporization flash the quasi-annular single bubbleflow type primarily is caused by the described influence.of superheat.If this flow type becomes stationary at diminishing superheat, it easilytransforms into the very similar annular flow. In Karlsruhe Peppier¿~8,9_7 and Schleisiek /~10_7 did about 250 boiling experiments withinduction heated tubular test sections of 50 crn length with temperaturesup to 1000°C and heat fluxes up to 700 W/em (generated in the wall byskin effect). In a number of runs the flow area in the heated tubes wasreduced to a narrow annulus by an inner displacement tube. The hydraulicdiameter of this annulus equals that of the reactor rod bundle. Pig. 4shows an example of a test-section with the instrumentation and the in-duction coil, fig. 5 is a photograph of the actual test loop, which forsafety reasons is within a nitrogen-filled containment.

It is not possible here to describe in detail the many results. For theinstationary, oscillating boiling Schlechtendnhl ¿"ll,lS_7 has developeda quantitative model on which the code BLOW-2 is based. It describesquite well all phases of the process including repsated oscillations.However, the model docs not take into account the pressure drop of thevapour flow. Tnis has some Influence on the period and amplitude of theflow oscillations and on the final dry-out of the liquid film as well.A modified version of the code including these effects is under develop-ment.

71

Since BLOW-2 has been developed for channel boiling, the influence ofradial flow or temperature variations is not considered, as they mayoccur in a bundle. Experiments with a natural size glass bundle haveshown, that under normal conditions the subchannels in the bundle behavelike independent parallel channels with respsct to expulsion and returnflow. Radial flow and temperature variations rather belong to local in-fluences as they will be treated in the next section.

t. Local Boiling Behind Floy Obstructions.

In par. 2 the temperature effects of local flow obstructions ave out-lined. If tho flow is blocked over a larger number of subchannels, localboiling might occur. Contrary to the aforementioned case of channelboiling the vapour bubble grows into the flowing cool liquid. Comparedto a small area at the" upper and lower end of the channel in tho caseof channel boiling now the condensation surface is relatively large andenhances a rapid bubble collapse aftor a first growing phase. This willbe even wore pronounced by the effect of the neighbour rods. While thebubble grows, they increase the mixing of the displaced liquid with aresulting low temperature at the liquid-vapour-intcrfr.ce. When the bubblecollapses the returning liquid again has to flow through the grid of rods.The surface may be even broken up. In a first theoretical model Oast ¿~1? 7therefore treats the return flow of the liquid towards the bubble centeras a number of separate Jets. Under these conditions a complete bubblecollapse has to be expected, which helps to prevent dryout as discussedin section 5»

The experimental work on local boiling in a bundle is not yet very faradvanced. For bundle experiments the same considerations on difficultyare true as mentioned in the preceding section. However, in a simplemanner soné features of a Multichannel geometry can be simulated in atubular, induction heated test section of the loop shown in fig. 5«This is.,explained by fig. 6. The induction hsated circular tube containsa star-shaped filling body so that the annular flow area is dividedinto six connected subchannels. This array, called "negative bundle",allows to simulate the boiling behaviour if some of the subchannelsare blocked.

72

Especially boiling in à subcooled environment thus may be studied in asimple manner. Also the experiment might be helpful by comparing it toboiling work under identical geometry with transparent simulationliquids. By this the influence of the different Prandtl-numbers mightbe found. This finally might help in the evaluation of bundle experi-ments with simulation liquids. Then bundle experiments with sodium mightbe necessary for the final proof only.

Naturally it has to be kept in mind that for the application to reactorsafety the geometry may be distorted during the events, whereas here anundisturbed geometry is assumed. In reality the cladding may burstduring the boiling process, fission gas may enter the channel etc..

5. The Problem of Pryput

All experimental evidepco, shows .the existence of a.remaining liquidfilm on all solid surfaces along which the typical single bubble grows.

O rtPor a heat flux of 200 W/cro at 900 C the evaporation rate of this filmis about 0.7 mm/sec. This means that the filai stays for some tenths ofa second before it dries. From then on the fuel temper.'iture rapidly in-creases and eventually melting may occur ."'So from the safety point ofview the liquid film has to be restored early enough. In the case ofoscillatory boiling this may be achieved either by a complete bubblecollapse or. by other means of liquid supply.

In the first place again diyout for channel boiling is considered. Kx-periment and theory as described show that under reactor conditions thebubbles oscillate, but do not collapse. Since the high vapour velocitiesat the channel exit prevent any other restoring of the liquid film fromabove, the only way of avoiding di'yout is to push enough liquid sodiumfrom below along the channel by the pressure head of the pump. A simplemodel, therefore, can be based on a pressure balance between the pumphead and the pressure drop of the vapour flow:The liquid sodium enters the heated part of the channel (fig.?) with

/the velocity v. and the temperature T>. The heat flux is q. After thesaturation temperature is reached at x , the first vapour bubble begins

0

73

to grow at x.. driven by a pressure according to a superheat- T „. . In fig. ?a the growing piston type bubble is shown. Sodium,.,.sup

vapour is generated from the liquid film remaining on the wall. This,therefore, results in an efficient heat removal. In fig. ?b the bubbletouches at x. the upper sodium pool, where rapid condensation takesAplace. (For pool temperatures of % D C in /~9_7 condensation fluxes of2 — —500 - 1000 W/cra have been found for the time of one oscillation.)Between x^ and XA the vapour flew is subjoct to a pressure drop Ap «• J3 * M VIf Ap is smaller than the pressure head Ap generated "by the pumps,the liquid column can partially replace the bubble and at x., a newbubble can be generated. Because of the statistical fluctuation of super-heat and the temperature increase in the liquid x~ in reality nay vary.In fig. 7c the second bubble displaces the first one while the liquidplug in between renews the film on the heated wall. The orifice 0 incombination with the pumping head inhibits any appreciable reverse flowduring the growth phase of the bubble.

Therefore, in the framework of this model a sufficient critérium forthe conditions of the dryout of the wall film can be formulated. It is

App < APV

If this is valid, a second bubble cannot be formed, the liquid filmcannot be renewed by the liquid plug and the first bubble stays untilthe liquid wall film begins to dry it some place.

In fig.8 the results of the calculation with the critérium (1) are com-pared with some results of Peppier ¿~9_7« Here the dryout heat flux isrelated to the static pressure ijn the test section (as described in ¿"8 7)•Parameter is the purcp pressure head. In the experiments it has been 1.5 at.The curves correspond to the theory outlined here. On the right handside of the respective curve dryout should occur. The points give data ofoobserved dryouts. It has to be noted that the points on the 1.5 at curvecorrespond to 5 or J ir.oasurercents respectively. Only one dryout fct theupper left occurred at a rather low heat flux. Its validity is not quite

74

clear yet. However, it has to be restated, that (1) is a sufficientcriterion only and additional effects may promote on earlier dryout.More experiments are under way. In any case the theory indicates theright order of magnitude. The choice of the friction factor f for thevapour flow turns out to be not critical.

In view of the simplifications of the theory the agreement with theexperiments is satisfactory, More refined models of dryout in oscilla-tory channel boiling have to take into account

a) the fact, that the liquid plugs coming from below may be dispersedinto little droplets. By this effect a type of mist-flow developsand a dryout may occur even with a liquid fraction of the order of15 °/o at the outlet,

b) the effect of large vapour velocities, as they easily develop in thenarrow channels, on the stability of the liquid film. Some experimentsindicate a destruction of the film by hydrodyncxiic forces.

Uy considering thesue effects the more sufficient criterion may be de-veloped into ono sufficient and necessary.

For local boilinc a complete bubble collapse is likely even if a con-siderable number of channels is blocked. Tnis is closely connected tothe mentioned surface breaking and mixing effect of the neilabouringrods. So & d-'j'out may not occur if t,ie geometry stays intact. Naturallyit has to be kept in mind that this is unlikely at some 900°C at longerperiods of time. Any experimental evidence here is not available yet.

6. Conclusions

Most of the unsolved heat transfer problems in fast reactors are connec-ted to safety aspects. Here the main point is the possibility of failurepropagation by the sodium-fusl-interaction and its initial conditionslike wakes and local boiling and dryout.Prom this resu.1. os the amoxint of

75

fuel melting and the conditions of this melting process. Besides allthese effects are basically connected to the multirod geometry of thefuel subassembly and to the properties of the sodiuni coolant, mainlythe superheat and the thermal conductivity. In this field a lot of inter-esting research remains to be done, as has been pointed out.

References

7 R.W.Bowringî HAKBQ - A Computer Programme for the SubchannelAnalysis of the Hydraulic and Burnout Characteristics of RodClusters. AEEW - R 524, AEEW - R 582, 19 7

7 K.Doetschraann: TJffiSYS. Personal communication, July 1970

7 W.Baumann: MISTRAL - TSiermodynamischer tfischstrbmungsalgorithnjusfür Stabbündel. KPK 988, Juno 1968

7 D.S.Rowe: COBRA II - A Digital Computer Program for Thermal-Hydraulic Subchannel Analysis of Rod Bundle Nuclear Fuel Elemente.BNWL-1229 UC-80, February 1970

¿f*5..7 D.Srcidt, W. Peppier, E.G.Sclilechtcndahl, G.F.Schultheiss:Sodium Boiling and Fast Reactor Safety. }CFK" 612, Sept. 1967

/"6_7 D.Smldt, P.Fette, W. Peppier, E.G.Sch}.cchtcndahl, O.F.Schultheios:Problems of Sodium Boiling in Fast Reactoxvs. KFK 790, EUR jJ960 e,June 1968

_7 E.G.Sch3.cchtenaahl: Die Ejektion von Natrium aus Reaktorkühlkanülcn.Hukleonik, 30/5, 19(>7* PP-270

W. Peppier, E.G.Schlechtendahl: Experimental and Analytical Inve-stigations of Sodium Hoiling Events in Narrow Channels.to be presented at the Symposium on Liquid lîetal Heat Transfer andFluid Dynamics, New York, Nov. 29 - Dec.?, 1970

r

76

¿~9_7 W.Peppier, E.G.Schlcchtendahl, Q.F.Schultheiss:Investigation on Dynamic Boiling in Sodium Cooled Fast Reactors.Nuclear Engineering and Design, Vol.34, No.l, 1970

7 K.Schleisiek: Heat Transfer and Boiling During Forced Convectionof Sodium in an Induction Heated Test Tube.Nuclear Engineering and Design, Vol.14, No.l, 1970

E.G.Schlechtcndahl: Sieden des KUhlrnittels in natriumgekUhltenschnellen Reaktoren. KPK 1020, EOT ¿1302 d, June 1969

/*12_7 E.Q.Schlechtendahl: Theoretical Investigations on Sodium Boilingin Fast Reactors. to be published in Nuclear Science andEngineering, 1970

¿~ 13_7 K.Gast: Lokale Kuhlungsstd'itingcn ira Kern schneller natriujnsekUhlterReaktoren. to be published

_7 C.V.Gregory: Personal communication, June 1970

^ W.Baumann: Personal communication, June 1970

_7 K.Gast, 'D.Smidt: Cooling Disturbances in the Core of Sodiiwu CooledFast Reactors as Causes of Fast Failure Propagation.Nuclear Engineering and Design, Vol.14, No.l» 1970

77

a "2 IV,

:Y//

!i.

-X

y/),

/

Fig. I Example of flow obstructionm subchannels 2 and 3

78

Fig. 2 Flow Distribution Behind a Blockage

79

Il III

>E

LOWER ï

PRESSPEAK

Fig. 3 Channel Voiding (Simplified)80

Thermocouple

Figure 4Testsection with Instrumentationand Induction Co//

Pressure Pick-up

Thermocouple

Induction Coil '"

Bubble Detector — \ —

81Testsection AÍ2.5

'•!'«•* ir ' '¿5-ï** i'

Pig. Karlsruhe Sodium Boiling Loop

82

Section A-A

Section B?B

No

Fig- 6Test Section (Negative Bundle)

83

(a)

q 3

r

(c)

condensation

evaporation!(low pressure)

-HO

t_•—m»r

( b )L

> evaporation(high pressure)

(d)

new bubble —B q-

t_r

i-aFig. 7 Oscillating boiling in a narrow

channel .

00VI

î

1

Experiments Peppier [12]pump head 1,5 at-Calculation according equ.for different pump heads

o."

5x (number ofexperiments)

heqt flux [w/cm2]

O 100 200 300 400

Fi g. 8 Dryout heat flux vs. static pressure in the testsectionparameter : pump head

Panel on ¿teat ana Mass Transfer in Uuclear PowerPlants

(Vienna, 14 - 17 Septesiber 197O)

Bubble Formation and Departure with Sub-cooled Boiling inWater-cooled Channels of High Heat Flux Density +_________

F. Maylnger, D. Hein, W. Ktthler

1.) Introduction

In pressurized water reactors, the cooling fluid enters théfuel element in a sub-cooled condition and is heated during itsflow through the core of the reactor nearly to saturation tern-'perature. Due to the high heat flux density in many parts of .the core the heat is transferred by sub-cooled boiling.

For lay out calculations of the reactor core the exact knowledgeof the density of the cooling fluid is very important becausethe thermo-dynamic properties have a large influence on the nuclearbehaviour of the reactor. There are several papers dealing- inan experimental and a theoretical way with the problem of voidfraction with sub-cooled boiling. Papers treating the problemon a theoretical way are for example given by Bowringfl} Lavinge¿2Jand LevyJVj.

Regarding a water-cooled channel with high.heat flux one candistinguish as shown in fig. 1 four regions. In the first regionthere is due to the high sub-cooling of the water a pure singlephase flow. The heat transfer from the heated wall to the fluid

The work was done at the M.A.N. laboratories andsponsored by the GKSS.87

&M / \2**tt

Siedtzonen in hochMosMen tfonotenbn' unttrkuhlter

fiC?. 1

is done by single phase forced convection. Due to the heat imputthe temperature of the cooling fluid is growing and finelythe temperature of the heated wall reaches a value at which atnormal rough surfaces bubble creationfthat is boiling,starts.The sub-cooling of the fluid yet is so high that the vapourbubbles formed in the immediate neighborhoud of the wall cannotgrow beyond the thin boundary layer and begin, starting fromthe bubble head/ to condénsate soon again. Flowing up in thechannel the temperature of the cooling fluid rises and the growingvelocity of the steam bubbles is enlarged until a bubble dimensionis reached at which the forces acting on the bubble make thebubble leaving the wall and flowing along with the fluid. Ontheir way through the channel than the bubble is again condensedin the sub-cooled core of the liquid. From this point of thebubble departure - the point is marked with B in fig. 1 - thevoid fraction in the channel rises rapidly.

The point at which the energy balance assuming thermo-dynamicequilibrium predicts the first steam formation is marked with C.In reality at this point of the channel there can exist alreadya very high void fraction. Because of the stored energy in the

88

vapour in the forro of latent heat the liquid is reaching thesaturated temperature not at the point C but later downstream,narked as point D in fig. 1. From this point D the whole trans-ferred energy is used to avaporate the water and the lines forthe real quality and the quality calculated according to thetherxno-dynamic equilibrium go inside.

Regarding the different models given for example by Bowring,Lavinge or Levy one realizes that in most of these models thepoint of bubble departure is used as criterion for the first.. «••> •.•••<vapour formation in the channel. This means that the voidfraction which is caused by thin bubble layer adjacent to thewall is neglected.

2.) Measurements of the Beginning of Sub-cooled Boiling

In point of fact the greatest uncertainty of most of the theo-retical models is just in the exact prediction of the inceptionof boiling, i.e. the determination of that point along the channellength where boiling takes place for the first time. Experi-mentally the start of boiling can be convienently determinedby spacing several thermo-couples on the length of a fuel rodand recording the variation of the surface temperature as theheat flux is gradually increased. Since when bubble formationstarts the heat transfer coefficient rises suddenly a.pronouncedjump will be observed in an oszillographic recording of the tem-perature variation which marks the inception of nucleate boilingat this point.

Fig. 2 shows typical oszillograph traces obtained in this manner.The object of the test was the nine-rod-bundle, shown in thelower part of the illustration in which the center rod wasfitted with several thermo-couples spaced over the length andcircumference of the rod.

89

c.

fig. 2

Plotted against time as the abszissa are the electric heatingcurrent I simulating the nuclear heat input as well as the tem-peratures at two points on the rod surface. In addition thetemperature differe?Sf the fluid between the points 3 and 4was measured at the outlet of the coolant from the bundle.Point 3 is located in a flow zone which compared to point 4 hasa higher enthalpy increase, because of the proportionallygreater heated circumference. As the heat flux increases thistemperature difference rises initially the curve showing a pointof reversal on inception of sub-cooled boiling and the agita-ting effect and turbulance produced by bubbles eventually re-sults in vigorous mixing leading to a noticable temperatureequalisation between the 2 sub-channels.

By means of such simple measurements the start of boiling canrelatively easy be determined by the discontinuity in thetemperature-time curve of the rod surface. Comparing the testdata with the results derived from the various mathematicalmodels considerable discrepancies will be found to exist. Infig. 3 results of the measurements are compared with theoreticalprediction. In this figure there are plotted for a pressure of100 bars and a mass flow rate of 150 g/cm2s, the lines for

90

Btostnablfsiri finrn

Crue*: X» atMtngtrotnm: '»<fe

ia nKanallàngr t

Messung

fig. 3

bubble formation calculated according to Bowring f1J and forbubble departing calculated according to Levy £V] and comparedwith corresponding measurement results. There are 2 differentlines for the calculated results predicted by the theory ofLevy [aj one evaluated with mixing in the sub-channel and theother one without mixing. One can see that the measured pointslay below the curves for bubble formation and that the agreementbetween theory and measurement becomes worth with growing sub-cooling. This effect can be seen on the one hand from the factthat the measured and calculated curves diverge versus the inletof the test section and on the other hand also in the much worthagreement of measured and calculated values at the high sub-cooling of 6O°C. Prom this one can suppose that especially athigh sub-cooling there are certain influences which are not re-garded in the existing and discussed models.

Plotting the heat flux at which boiling starts against the lengthof the channel one has the disadvantage that conclusions onlycan be drawn for a certain geometry. But using the heat fluxas ordinate and the local sub-cooling as abszissa with the massflow rate as parameter more general statements can be made.As expected and shown in figure 4 boiling starts at lower heat

91

fluxes with decreasing sub-cooling. For a sub-cooling decreezero the lines for constant mass flow rate must run into a value ofthe heat flux which is very small but different from zero.

On**: W0o(

fio. 4

oesWàrmestromdicHe tei SitdtbtçiM olíFunktíon der íirllichtn Unttrkijhtung 29Í.22 Í

Regarding the influence of the mixing which is very important forcalculating the sub-cooling all measured points for a given massflow rate lay on a single curve, that means there was no influenceof the position in the channel on the inception of boiling* Thiscan be used as a criterion that the boiling inception is onlydepending from the local sub-cooling and not from the positionin the channel.

It can be expected that the heat transfer coefficients are differentacross the circumference of the rods because, the distances to theopposite heated walls and thus the local boundary conditions vary.From this one. can conclude that also the starting point for thebeginning of boiling varies across the circumference of a rod.To test this, two thermo-couples were fitted to a rod in thisway that they were arranged in an angle of 45° at the circumferenceof the rod but at the same distance from the heated end.

92

Fig. 5 shows the results of these measurements and a scetchof the arrangement of the thermo-couples. Thermo-couple 1 waslocated exactly opposite to the other rod and thus recorded thewall temperature and the inception of boiling for the smallest

fig. 5

distance between the two heating surfaces. Thermo-couple 2was just across the biggest distance between the heated surfacesin the rod bundle. In the diagram of fig* 5 the heat flux atwhich boiling starts is plotted across the mass flow rate. Re-garding the results one can see that the curves for small massflow rates lay very narrow together and for rising mass flowrates they tend to diverge more and more. This means that theboiling border across the circumference of the rod which is shownschematically on the left hand of fig. 5 by a dotted line tendsto show more and more higher amplitudes at the circumference ofthe rod.

The nearly horizontal behaviour of the temperature curve givenby thermo-couple 1 means that between 2OO and 2SO g/cm s theflow velocity has no influence on boiling inception. One explana-tion can be found in the fact that here the boundary layer has

93

reached such an extend that it limits the local mass flow rateat this point in the narrovœt gap. Due to this fact the areain the diagonal direction of the rod arrangement has to carrya higher mass flow rate which carses the boiling to start athigher heat fluxes*

3.) Bubble Growth and Collapse

Measuring the temperature of the heated wall and thus determiningthe. beginning of boiling gives only a limited information aboutthe formation and behaviour of sub-cooled voids. One of the bestway to look at this problem probably is the visual observationof the bubble behaviour. Pressurized water reactors are runningat high pressures that is at 10O to 16O bars and it is verycomplicated bo build test sections with windows withstanding thishigh pressure and to work with them. Therefore investigations intothe behaviour of steam bubbles in a sub-cooled liquid flow werecarried out at a pressure of 3 bar in a single-row rod bundle withthe intention to get first qualitativ information about the bubblebehaviour in the sub-cooled liquid. The boiling processes werephotographed by means of a high-speed camera. This permittedinformation to be obtained in the rate of bubble growth, bubbleseparation and condensation of steam bubbles as a function ofsub-cooling and flow velocity.

An interesting discovery made with these measurements was thattwo differently behaving types of bubbles were observed, depen-ding from the local sub-cooling and the heat' flux.

Fig. 6 gives schematically the behaviour of these two bubble types.

94

fig. 6

Bubble type I occurs mainly at low heat flux levels and low de-grees of sub-cooling, i.e. the liquid has reached almost saturationtemperature. This bubble type is characterized by slow growth.Until the .steam .bubble attains its maximum volume, it will movealong with the flow keeping in contact with the superheated boun-dary layer all the time. At a pressure of 3 bar, the type I bubblesgrow to a mean .diameter of 2 nun and. have a life of about 25O msreckoned from the beginning of bubble growth until complete con-densation.

In contrast to this, growth of the type. IIbubbles is spontaneous.The steam bubble attains an average size of p.6 mm and, on separation,penetrates almost perpendicularly into the sub-cooled liquid bulkto condense within a very short time. Bubbles of this type tendto form at higher heat flux levels and higher degrees of sub-cooling.Their life of 3 ms is only about 1/100 of the life of the type Ibubbles. To illustrate the violent .separation and condensationprocesses, a steam bubble is shown in fig. 6 which was producedby injecting steam into almost saturated water and which showeda similar behaviour. One can clearly see the deformation occurring

95

as the bubble separates.

A series of photographs of the type I bubble is ¿iown in fig. 7,

!ï ,*% . I I Í Í Vi AY! f *t I! 1! i t-il K I : |» K '! »^ Í i}^ i

f i» .* ! - i l t 'tt- ; ^1•' : ¡ ' .'• !Lf..¿Jük.J

P Í 1 M

il : ' : 1LJf'LJi 1L>^J

——«iï-_u^ 1r~"i« "*~i i?"1i « i t. *>»' ,V€' I i:1 i-ü"t 1! !Lf f._,

fig. 7

In order to permit both the process of growth and condensationin the test section filmed to be studied, arrows have been enteredshowing simultaneous examples of a bubble forming (marked bydashed arrow) and a condensing bubble (solid arrow). The frameinterval in this film was 3 ms. The flow velocity was 1 m/s andsub-cooling of the liquid about 20 degrees centigrade. The growingsteam bubble in the last frame shown has not yet reached itsmaximum size. Special attention is drawn to the fact that the con-densing bubble in the last frame has only 1 % of its maximum volumeon separation.

The frame series showing in fig. 8 the growth and condensation of abubble of the type II was taken with a frame interval of O.6 mswhich is only 1/5 of that in the frame series for the type I bubble.

96

j f " • " • •»* .1 {*'"""" rl{ ir""™""»: ,"*•••• —¡i \t*, ; • ! > i f - • ' ! • ' • » ** ! ' * í i _ i. • ' • ! *»Ji ir

;. tt ,f

' ?. > It Ü i -. i- iI \ -f Í ' " ' ' li ». i

if>\ • r i

' : 1 - i : ; ' i. • .î i! » , i » !! i11/.!.L... T".r •»• * . - » t . ¡ ..j -jjí,,..,: *s . ... . :•:... . ..., ..>.it-

(¡jij{t ií:i; «t.i' .'..'<

fig. 8

Whereas the water velocity was maintained constant at 1 ms, sub-cooling in this case v/as approximately 70 degrees centigrade.

If it is true that two types of bubbles differing in their be-haviour will form dependent on the heat flux and local sub-cooling, it should be possible, by appropriate parameter selection,to observe both types at the same time.

A series of frames where this can be seen is reproduced in fig. 9.The dashed arrow indicates a condensing bubble of the type Iwhereas the solid arrow shows the growth and condensation of a steambubble of the type IÏ. Both types of bubbles exist on one and thesame heating surface ana very close to each other. Sub-coolinghere is approximately SO deg.C.

Ifî i'lüíT Hi irl!:"y!;ih>]i!|¡

fig. 9

97

The question new arises why two types of staam bubbles didifferent behaviour can form under identical conditions and whatexplanations can be offered for this phenomenon.

It! appeared reasonable to assume that the differing behaviourwas due to a proportion of non-condensable gases in the type Ibubbles. However, tests made tc study this showed that, on separefrom the boundary layer, bubbles of the type I tend to condense,as observed, usually completely, but at least to 1/5 of their na:'.!mum diameter. This in turn means that there could have been onlyabout 1 volume % of gas in the steam. In the opinion of severalauthors, a fraction as small as this cannot exert such a decisivoinfluence on bubble behaviour during the condensation process.The graph in fig. 1O plotted by Chao [ 4^J will serve as an exampleto demonstrate this.

0.1 O.Í 0.3dmtnsionsbst Zttl

0.4

Ktmtn gtltta tur. Jo f 10Pi '3000

lOer Einfluf) nichtkondensierbarer Cose i ,„„ ¿«70 \ouf den Kondensaticnsvorcanq r>a& Choo\ 2SSS-' •'

fiç. 1C

It follows from this graph that a bubble that condenses down to20% of its initial size tends to differ in its behaviour froma pure steam bubble only just before it attains it final size.Consequently, air has to be ruled out as a cause for the differi:behaviour.

98

*•) Discussion of the Essie Mechanism

Por a better understanding of the different behaviour of thetwo types of bubbles it is proposed to discuss the basic mechanismsinvolved in detail. Fundamental work on this has been publishedby Bosnjakovic [5] , Frita [el , Jakob f?! anâ Linke jYJ .Theoretical and experimental studies in this field have meanwhile beengreatly intensified, mainly due to the development of nuclearreactors.

Observing a steam bubble from the time it starts to develop untilcomplete condensation takes place, the following phases can bedefined:

1. nucleate bubble formation2. bubble growth3. bubble separation4. condensation

The first phase, i.e. nucleate bubble formation, is not proposedto be discussed here.

4.1 Bubble growth

Once a bubble nucleus has attained a certain size, it will con-. • /tinue to grow because the pressure forces in a bubble will nolonger be in equilibrium with the surface forces. Bosnjakovic £5]developed an analytical model for the growth of steam bubblesin a superheated liquid which starts from the assumption that theevaporation process is determined by the heat transport from thesuperheated liquid to the bubble surface. Th'is model has beenadopted by several authors as a starting point for computing thegrowth of spherical bubbles.

99

fig. 11

Plesset and fcwick 9J derived an equation - market (1) in fig. 11 -which predicts the growth of the bubble in direct proportion withthe liquid superheatAfasVf • Compared to the derivation of theequation for a plane problem, allowance is made for the sphericalshape of the bubble by including the factor

Zuber ¿lOj extended Bosnjakovic's theory by taking into considerationthe influence of the temperature field around the growing bubble,This means that only part of the enrgy of the superheated layeraround the bubble is extended for evaporation whereas the greaterpart is transferred direct to the liquid. On this basis, Zuberobtained the curve marked (2) .

As a third equation, a formula derived by Cole and Shulmanhas been selected. An important quantity in this formula is theJakob number which states the proportion of energy stored in aliquid volume compared to that stored in the' same volume ofsteam. The exponent stated for time is again 0.5.

By comparison, a bubble of the type II has been entered in thegraph. It should be borne in mind however that the superheat ofthe boundary layer while being very difficult to determine at

100

the same time has a considerable influence on bubble growth.

The equations given in fig. 11 are valid for ths growth of a bubbleunder conditions of sub-cooled boiling only until the steam bubblehas attained a diameter which is equal to the boundary layer thick-ness.

-ÍL/J' »*'-

ÜJ- 1 ... .........j» -+"«**« fc.*.4s* \\.-,'j&

fig. 12

When the top of the bubble reaches the sub-cooled liquid therewill be a condensation process occurring simultaneously with theevaporation process at the root of the bubble. This will give riseto a mass -transport as demonstrated in fig. 12 in the steam bubbledirected from the root of a bubble to its top. This mass transportwhich Scriven 0-21 - in contrast to prevailing opinion - assumesto provide the main contribution to heat transfer will howeverconsiderably influence the behaviour of the bubble.

4.2 Bubble Separation

The. condensation process at the top of the bubble appears to in-fluence the pressure conditions in connection with the mass trans-port from the root to the top of the bubble in a manner that thegrowing bubble flattens initially. Shortly afterwards, during theseparation phase, it will contract and shoot into the liquid flow.

101

SSffl

fig. 13

The theories predicting the separation of bubbles under conditionsof forced convection are based on a balance of the forces actingon the steam bubble adhering to the heating surface as shown infig. 13. Neglecting minor forces, Levy f\VJ obtained an equationwhich contains only forces parallel to the heating surface/ i.e.in the direction of the flow. This may be valid for the type Ibubbles. An exact definition of "separation*1 is however importantin this case: one can speak of separation when the steam bubblestarts to move in the flow direction or when the bubble separatesfrom energy supply from the boundary layer. Whereas the formerdefinition appears essential for the force balance, the seconddefinition is of importance for 'die behaviour of two-phase flow.

For the bubble type II, a force balance in the z-direction appearsinadequate. The almost vertical penetration of the bubble intothe bulk fbw during condensation suggests that the forces perpendicularto the heating surface should by no means be neglected. The inertiaforce and the force due to the mass transport in the bubble areshown in fig. 13. It should be noted that these are dynamic forces;it appears unlikely that treatment as a chain of quasi-stationarystates would be successful here.

102

4.3. Condensation of Steam Bubbles

After separation, i.e. after cutting off the energy supply fromthe boundary layer, the bubbles './ill condense in the sub-cooledliquid. The equations describing this process are similar to thoseused to describe bubble growth. Of course/ the inertia forcesshould not be neglected.

<«ffj

-•ti) Lamb:

Wochîtn and Kcnaensitren

fig. 14

Zuber suggested a dimensionless plot of the growing and condensingsteam bubbles, the radius R of the bubble being made dimensionlesswith the maximum radius R, while making the time t dimensionlesswith the time t^ that a bubble requires until it has attained itsmmaximum radius. Consequently, the length of time required by abubble for condensing would be three times that it requires forgrowing. Experiments have shown however that the condensation timediffers only negligibly from the time the bubble grows. Lamb fisltherefore suggested that the time for the decrease in bubble growthbe referred to the condensation time. Lamb's equation has beenentered by means of dashed lines in fig. 14., It can be seen thatthere is much better agreement with the experimental data. While thecircles are referred to t / the solid dots were calculated withthe condensation time. It whould be pointed out in this connexionthat the theoretically developed equations consider spherical steambubbles which condense uniformly. No allowance is made for theviolent deformation on separation and drift flow in the wake ofthe bubble.

103

5.) Effects of Sub-vo o loe! Boiling ~r- PressureDrop

The pressure losses of two-phase flow are closely associated withthe flow regime, i.e. the steam quality and its distribution acrossthe flow area. As an example for the influence of the sub-cooledvoids on the pressure dcop in fig. 15 an oszillogram is shown.

fig. 15

There is plotted versus the time the temperature of the heated wall,the heat imput and in addition the pressure drop across a grid-plate at the end of the fuel rod test section. The measurements 2were done at a pressure of 1OO bars and a mass flow rate of 150 g/cm swith a sub-cooling at the inlet of the test section of 2O°C. Thegrid plate was placed approximately 4O cm downstream of the endof the heated length of the test section. This is the reason whythe pressure drop is not rising immediately with the beginningof the sub-cooled boiling because the steam-bubbles had enoughtime to condense again in the sub-cooled core of the liquid. Prom2the temperature traces one can see that at approximately 25 W/cmboiling starts at the end of the test section and that at 35 W/cmover the whole heated surface of the rods sub-cooled boiling canbe observed. The heat flux at which according to the energy balance

104

the saturation temperature in r.na fluid at the cvitlet of the channelis reached amounts uo 8O w/cm**. At this heat flux we can observe «in the diagram an increase in the pressure drop of 25% and at 13O W/cmOf 170%.

In this connexion perhaps the question rises which of the above-mentioned two bubble types has the bigger influence on the pressurelosses. In the case of bubble type I which primarlily occurs withlow decrease of sub-cooling, the bubbles move with the flowand therefor they may have a friction-like influence. The bubblesof the type >I, on the other hand, because they penetrate into theflow almost perpendicularly would disturb the flow to an appreciableextent and would contribute -co a high momentum exchange betweenthe boundary* layer at the wall and the sub-cooled core of the flow.As an example measurements of two-phase pressure losses in aninternal flow tube at atmospheric pressure are given in fig. 16.

Zwfiphasendruckverlust

fig. 16

This graph plots the pressure losses as a function of mass flowfor constant heac flux levels. Sub-cooling at the inlet of thetest section was 6O°C. It is of interest to note the shape ofthe curve at the point where under conditions of decreasing mass

105

flow and constant heat supply boiling starts first, i.e. wherebubbles of the type II exist. While at high rcass flows straightsingle phase flow prevails the pressure losses start to rise relativto the parabola of pure water flow. This rise is attributed to theinception of boiling with bubbles of type II. Afterwards the curvehas an inflexion point and the pressure losses tend to increaseto a lesser extent as the mass flow decreases. In this regionbubbles of the type I prevail. Finely the flow attains saturatedtemperature at the exit and due to the marked increase of the .steamquality and the resulting acceleration of the flow the pressurelosses tend to increase again.

6.) Sununing up

The results of the studies undertaken to date and the conclusionsdrawn from these do not yet provide clear cut information whichwould fully explain the difference in behaviour of the two bubbletypes. It is therefore proposed in further defined tests, to in-crease the parameter "pressure" up to 3O bar. Again in these tests,the processes taking place on the heating surface and in the flowwill be recorded by a high-speed camera* These tests assume im-portance for evaluating the processes in reactors seeing thatthe ratio of the specific volume of steam to that of water willhave decreased from 55O at 3 bar to as little as 1/1O of thisvalue at 3O bar.

106

T-iteraturverzei chnis

1.) R.W. BowringPhysical Model, Eased on BubbJs Detachment./ and Calculationof Steam Vo.idage in the Subcooled Region of a ChannelHPR-1O Dez. 1962 OECD Balden

2.) P. LavinceModele Devolution du Titre du Taux de Vide en EbullitionLocale et Zone de TransitionCEA - 2365 1963

3.) S. LevyForced Convecticn Subcooled~Boiling~Preâiction of VaporVolumetric FractionGSAP - 5157

4.) B.T. Chao. P.P. WittkoCollapse of Vapor Bubbles with Translatory MotionJournal of Keat Transfer/ Febr. 19675.) F. Bosnjakovic

Verdairpfung und FlussigkeitstiberhitzungTech. Mech. und Therrood. BD. 1, 1930

6.) W. Fritz, K. EndeVerdan;pfuncsvorgang nach Kinematographischen Aufnahroen anDampfblasenPhys. Zeitschrift 37, 1936

7-> M. Jakob, W. FritzVersuche ûber den VerdampfungsvorgangPorschung 2. BD. Heft 12, 1931

8.) M. Jakob, V?. LinkeDer WSrmeubergang beim Verdaiqpfen von FlUssigkeiten ansenkrechten und waagerechten FlechenPhys. Zeitschrift, 36, 1935

s<) M.S. Plesset, S.A. ZwickOn the Dynamics of Small Vapor Bubbles i-n liquidsJournal of Mathematics and Physical Vol. 33,. 19551O.) N. ZuberThe Dynamics of Vapor Bubbles in Monuniform Temperature Fields

Int. Journal Heat Mass Transfer Vol. 2, 196111•) fi* Cole, E.L. ShulmanInt. Journal"He"at Mass Transfer

107

12») L»EV Scri.venOn the Dynamics t>f Phase GrowthReport P 659 Shell Development Co. 1958

13.) H. LarbHy drody nard. csp. 37O, 6th éd., Cambridge university Press, London (1932)

108

Review of Heat and Mass Transfer Studies Relatedto Nuclear Power Plant in Progress in theFederal Republic of Germany_____ by F. Mayinger____ ______

1. PrefaceNuclear equipment design and manufacturing activities in theGerman industry cover a wide range of various types of nuclearreactors. Starting from water-cooled reactors of the boilingwater and pressurised water type, this range extends to thegas-cooled thermal converter and the sodium-cooled fast breeder.Consistent with this wide range of equipment, extensive effortsare in hand to investigate and study heat and mass transfer inthe various components of these reactors. Considering theirobjectives, these efforts can be broadly divided into basicresearch, component development and safety studies*

Tasks have essentially been distributed between the big nationalnuclear research centres, specifically Karlsruhe and Julien,and the R&D laboratories of the various companies engaged inthe design, development and construction of reactors. Thevery limited scope allowed for this review permits only abrief selection and summarised discussion of major work inhand. While there exist various possibilities of grouping andclassifying the víork in this report, it appeared useful to thereviewer to discuss current wo'rk according to its objectivesunder the headings of fast reactors, water reactors and gas-cooled reactors.

2. Past ReactorsThe sodium-cooled fast breeder continues to be in the forefrontof the development in the Federal Republic of Germany. Detailedwork in hand includes studies on both superheated steam andhelium cooling. For the sake of convenience and conciseness,brief reference is made to this work under the heading gas-cooled reactors.

109

Basic studies of liquid metal heat transfer, specificallyaspects relating to the boiling of liquid metals haverecently been suggested by the special nature of the safetyproblems in this type of reactor. Extensive work III in thisfield for an improved understanding of the phenomena involvedin the boiling of liquid metals is in progress in the Institutefor Reactor Development of the Karlsruhe Nuclear ResearchCentre. Investigations have centered mainly on questions ofindividual bubble ejection, boiling lag/liquid superheatingand vapour recondensation and, consequently, refilling of thecoolant channel subsequent to individual bubble ejection. Forclear and straightforward information, reference is made tothe papers by Smidt III and Pepplor 121 which contain a .summaryand the principal results of this work.

Individual bubble ejection should be looked upon as one aspectof the overall problem of dynamics in liquid metal boiling and,therefore, the Institute for Reactor Development of theKarlsruhe Nuclear Research Centre initiated a series or studies15* 1 relating to associated boiling phenomena such as localflow disturbances and dryout. These studies have shown thatwhile the onset of boiling in a liquid-metal-cooled core isliable to cause damage to the fuel elements it must notnecessarily result in serious safety engineering problems.Seeing that subsequent pulsations tond to exert a substantiallygreater influence boiling tests should not be limited to thephase of defined bubble growth. In most cases, complete stagnation.of flow was found to occur directly after onset of boiling withresultant local burnout. Initial superheating appears to havelittle influence on the progress of boiling. It is howeverof fundamental Interest for initial bubble formation. Anumber of investigations into this aspect have been made bySchultheiS 1^1 whose work covers, inter alia, the influenceon the onset of boiling of the properties of the heatingsurface and the oxide concentration in the liquid. Mentionshould also be made of the investigations carried out by theInstitute for Thermodynamics of the Munich Technical universityinto the boiling of mercury. X-ray flash photography has shown

110

that , in contrast to sodium, the boiling mechanics of mercuryare similar to those of water.

An important pre-requisite for the thermal design of fuelelements is an understanding of the local thermodynamic andhydrodynamic conditions. Mixing orocesses within the flowplay an important role. Velocity and temperature distributionin various fuel element geometries have therefore been thesubject of theoretical and experimental studies undertaken by .the Karlsruhe Nuclear Research Centre. The Reactor DevelopmentInstitute in particular has investigated the influence ofeccentric and asymmetrical configurations I7,8l. Large-scaletests have been made by the Reactor Components Institute ofthe Karlsruhe Nuclear Research Centre using a 6l-rod clusterin order to ascertain the influence of various types of spacerson lateral coolant mixing 19,101. The tests have included boththe grid-type spacers and helical wires applied to the rods.The results have shown that spacer design strongly influencesmixing rates in the bundle. Balanced temperature profileshave been obtained t;ith fuel element bundles having three orsix helical rib spacers per rod. Wire spacers have proved togive the least favourable velocity profile.Measurements of the heat transfer under conditions of forcedconvection in sodium have also been carried out byReactor Components Institute, using a concentric annuligeometry IIIX. The results of the experiment have lainwithin the middle band of published data and can be representedas a simple function of the Peclet number» Closely associatedwith heat transfer and mixing is the pressure drop in th« flowthrough the coolant channel. Investigations.in this respecthave been made by Hoffmann 1101 using fuel elements with gridand helix-type spacers.

Larga-scale development and testing of components for sodium-cooled fast breeders is being carried out by Interatom ofBensberg. This company operates a large sodium test loop withseveral megawatts capacity for this purpose. Intended less forheat transfer measurements as part of basic research than for

ill

full-scale testing, activities there are not directly relevantto the areas under review.

3. Heat Transfer Problems in Water-Cooled ReactorsIn water-cooled reactors, both pressurised and boiling waterreactors, thermal studies have -concentrated mainly on problemsof boiling and two-phase flow as well as specific flow aspects.In view of the commercial acceptance of water reactors, relatedresearch and development has been mostly carried out in company-owned laboratories and research centres. AEG1s research centrein Grosswelzheim has work in hand on a number of two-phaseproblems for the boiling water reactor whereas work undertakenby Siemens AG in their experimental facilities in Erlangen hasbeen mainly of an experimental and theoretical nature and relatedto the pressurised water reactor. Extensive research anddevelopment work in the field of two-phase flow has been handledby M.A.N. in Nuremberg in its nuclear power experimental facility.There are also two government agencies working in this field,namely, the Institute for Measurement and Control Engineeringof Munich Technical university, which has evolved a number ofcomputer programmes for the design and safety evaluation ofwater-cooled reactors, and the GKSS (Society for Nuclear PowerUtilisation in Shipbuilding and Shipping) in Geesthacht whichhas tackled detailed aspects of the operation and developmentof the reactor in the nuclear srip W0tto Hahn11.

It has been estimated that there are over 10,000 publishedreferences in the field of two-phase flow. In spite of thisvast amount of research, there are a number of aspects oftwo-phase flow in need of clarification. This includesprimarily the flow mechanics in sub-cooled boiling. Extensivetests have been carried out by M.A.N. in Nuremberg to obtaininformation on the inception of boiling, bubble formation andbubble separation 1121. During these tests, two differenttypes of bubble having a different life span were observedin the sub-cooled liquid. The behaviour of these bubbles isessentially influenced by the dynamics of the boiling process.

112

Probably due to boundary layer influences, the onset of boiling. • T ..• i *• i * e- ' r í ~ * ' >:occurred much earlier than predicted by the models known frompublished work. Prom this derive decisive influences on steamquality and, consequently, the reactivity coefficient in highheat flux channels of pressurised water reactors. Anotherimportant problem forming the subject of basic investigationsis the flow stability in boiling water reactors. Results ofextensive tests will be found in work published by AEG I1J5I.Carried out under reactor conditions, these tests also includedstudies of the influences of various core internals such asswirl inducers Il4l on the dynamic behaviour of boiling waterchannels.

In connection with basic research into two-phase flow,mention should be made of the work done by the Institute forReactor Components of thé Karlsruhe Nuclear Research Centrewhich, while not relating'to the development of pressurisedor boiling water reactors, was associated with the researchwork for the steam-cooled fast breeder. These investigationsinto heat and mass transfer under conditions of phase changeusing a water/superheated steam system to study the passagethrough a liquid of gases' admitted through perforated platesand nozzles. Thé experiment covered such aspects as the size,shape and frequency of bubbles occurring as a function ofthroughput and thermodynamic conditions of the steam.

In pressurised water reactors where no boiling prevails in thechannels under rated conditions heat transfer is apt to beassisted by swirling flow. This is the subject of a paper 1151originating from Siemens AG which contains data obtained withpropeller-type swirl inducers in round tubes and an economyanalysis of swirling flow versus straight turbulent flow. B'lowtests in the single-phase range for the development of fuelelements for pressurised water reactors cover a wide field inthe experimental work done by Siemens AG. These have included,inter alia, tests to study coolant flow distribution in thereactor core, coolant velocities in the individual fuel elementsand the development and testing of flow detectors for velocity

113

measurements. Optimisation of the annular space between thereactor vessel and the moderator vessel has been anotherobject of experimental investigations as have been flow teststo study the geometry of various reactor plenum spaces. Workof special interest in connection with flow investigations inreactor components has been done by M.A.N. on the hydraulicdesign of the Grenoble high flux reactor 1231. Because of thewide velocity differences, there were special problems to besolved in guiding and distributing coolant flow and in theorigin and prevention of hydrodynamic difficulties. Intensivedevelopment work is in hand at AEG on cyclonic steam separatorsin boiling water reactors 116,171. The facility availableenables large units to be tested IlSl.

As already mentioned, the Institute for Measuring and ControlEngineering of Munich University has in hand a number ofstudies of heat and mass transfer problems in water-cooledreactors. The range of application of the computer programmesdeveloped by them typically extends from the stability problemin boiling water cycles 1191 through the analysis of processeson pressure reduction during coolant loss 1201 to the predictionof pressure build-up in various spaces of the containment duringthe maximum credible accident 121I and thus covers both thefield of reactor development and safety analysis.

By their very nature, safety studies, especially burnout tests,play an important role in the research for pressurised waterand boiling water reactors. Particular reference is made tothe extensive burnout studies that have been carried out byM.A.N. for many years. Starting from measurements on simplegeometries, such as internal flow tubes, these have recentlybeen extended to include primarily fuel element clusters ofvarious configurations for pressurised water and boiling waterreactors under steady state and transient operating xjonditions122,231. Studies in the range of unstable operating conditionscentered mainly on determining the influence of power and massflow transients I2jJI on the critical heat flux in boiling. Ithas been found that the mass flow transient can be treated as

114

quasi-steady-state while high rates of power increase arelikely to resu.lt in slight improvements of burnout performance.Burnout tests are costly and call for complex facilities withextremely high energy requirements if carried out on fuel rodclusters with water. Multiple savings in complexity and costare obtainable by using fréon as a model fluid instead ofwater.

There already exists some published information on conversionformulae and similitude relationships. M.A.N. has launchedburnout tests in a large frecn loop on clusters of up to64 rods under steady state and transient operating conditionswhich are intended primarily to clarify the influence of fuelelement geometry.

Little research has been done on the emergency cooling performanceof fuel elements in pressurised water and boiling water reactorsduring and after the maximum credible accident. In view of this,AEG and Siemens AG have recently joined forces to embark on anextensive research programme which is expected to extend overseveral years. AEG are investigating the heat transfer andburnout behaviour under conditions of pressure reduction andcoolant loss during the maximum credible accident while Siemensare exploring the possibilities of spray cooling and coreflooding in the subsequent phase. Initial results on heattransfer during flooding are available for plain internal-flowtubes and facilities for emergency cooling tests on representativecore sections and for studies of burnout during coolant loss areunder construction.

4. Studies in the Field of Gas CoolingIn the field of gas-cooled reactors,.development work in recentyears has centered on the pebble-bed-core thorium high temperaturereactor and on the experimental reactor of the Schleswig-HolsteJnNuclear Power Station using rod-type fuel elements. A survey of

115

work in progress at the various research facilities in connectionwith gas cooling reveals that this is not specifically alignedwith these reactor concepts. On the contrary, the work inhandcovers a wide spectrum of basic research. Among the laboratoriesdealing with such problems are especially the Institute forNeutron Physics and Reactor Engineering of the Karlsruhe NuclearResearch Cen'cre, the Institute lor Reactor Components of theJulien Nuclear Research Centre and the experimental facility ofthe BBK company. Naturally, most of the project-oriented workis being done in BBK1s laboratory including analogy and modeltests relating to problems of heat transfer on the sphericalfuel elements and the flow distribution in the THTR core.Using the similarity relationships, heat transfer in the reactorcore has variously been analysed by deduction from masstransport between naphthalene balls and air.

Considering that superheated steam can be treated as a real gas,the thermal studies that have been carried out by the KarlsruheInstitute for Reactor Components are also relevant to thedevelopment of the steam-cooled fast breeder» These are relatedmainly to the lateral mixing of the coolant in multi-rod clusterswith plain and finned rods 124,251.

Investigations into the pressure drop and heat transfer oncluster geometries of the most different configurations covera wide field, A number of fundarsntal studies of friction inturbulent flow both ia clooc-u ~~.nïiOiu of any cross section I26land in parallel-flow rod bundles of different gecmetry withspiral wire and grid-shaped spacers 127,281 are being carriedout by the Institute for Neutron Physics and Reactor Engineeringof the Karlsruhe Nuclear Research Centre. Also in Karlsruhe, theInstitute for Reactor Components is making pressure loss testson bundles up to 61 rods. These tests 1291 aligned to thedevelopment of the steam-cooled fast breeder have been madewith smooth and artificially roughened rod surfaces withspiral wires and fins serving as spacers.

116

Also originating from the two above institutes nave been anumber of heat transfer studies. The influence of surfaceroughness on heat transfer 1301 has been systematically .treated by the Institute for Neutron Physics and ReactorEngineering. Additional developmental studies of heat transferin gas or superheated steam flows 151,321 are being carried outby the Institute for Reactor Components. In both instances,measurements have covered both the average and local heattransfer coefficients for smooth and rough surfaces withbundles of different configuretions.

A wide range is covered by the studies in progress at theReactor Components Institute of the Julich Nuclear ResearchCentre. These range from heat transfer tests on Magnox fuelelements having different fin shapes, such as taper fins andlateral fins, work to measure heat transfer, pressure dropand oscillating behaviour of parallel flow and cross flow rodbundles at high and very h;i,gh Reynolds numbers to basicresearch into the local values of pressure .distribution andheat transfer on the circumference of individual rod and therods in a bundle* Results serve both for bas i c: ¿research andthe development of primary and secondary reactor components,such as steam raising units for gas-cooled reactors.

5. ConclusionThe present review does not claim ta be a complete,survey ofresearch efforts in the field of heat and mass transfer innuclear equipment in progress in the German Federal Republic.Future objectives are naturally closely associated withcurrent reactor development. It is expected that a strongimpetus for this work will derive from a number of safetyengineering problems and considerations which are bound to - -arise in the field of the sodium-cooled fast breeder andthe pressurised water and boiler water reactors.

117

L i . t e r a t u x . v e r . z e i c h n l s

1.) P. Smidt u.a.Problems of Sodium Boiling in Fast ReactorsKFK 79O EUR 396O e

2.) W. Peppier, G.F.SchultheirLiquid Metal Boiling ResearchKFK 874 EUR 4157 e

3.) W. PeppierExperimental and Analytical Investigations of Sodium BoilingEvents in Narrow ChannelsSymposium on Liquid - Metal Heat Transfer and Fluid DynamicsNew York CityInstitut fur Reaktorentwicklung Kemforschungszentrum Karlsruhe4.) E.G. SchlechtendahlSieden des Kühlmittels in natriumgekühlten schnellen Reaklxrcn

KFK 102O EUR 4302 d5.) G.F. SchultheissExperimental Investigation of Incipient Boiling Superheat i:i rfcJ.1

CavitiesSymposium on Liquid - Metal Heat Transfer an Fluid Dynaroic-Hew York City Nov. 29. - Dec. 3. 197OInstitut fur Reaktorentwicklung Kemforschungszentrum K&rlsruhe6.) G.F. SchultheissThe Effect of Oxide Concentration on Incipient Boiling Superheatof SodiumEuropean Liquid Metal Boiling Group Meeting at Casaccia

April - 9 - 10 1970Institut für Reaktorentwicklung Kernforschungszentrum Karle¿uhe7.) F» HofmannFlow and Temperature Distribution Including Coolant Mixing inSodium Cooled Fuel Elements with Eccentric Geometry

KFK 1155 IAEA - SM - 13O / 4O8.) M. FischerTemperature Distribution and Thermal Stability ih Asymrr.etribal

Triangular Rod - ClustersKFK 724 EUR 4178 e

9.) W. BaumannFuel Rod Bundles with various Spacer Designs for Sodium CooledFast ReactorsKFK 1154 IAEA - SM - 13O / 38

1O.) H. HoffmannDer Druckverlust in Brennelementen natriumgekühlter Brutr a'c-toren mit gitter- und wendelfôrmigen AbstandshaltertypenKernforschungszentrum Karlsruhe Inst. f. ReaktorbauelementsPSB - Bericht Nr. 341, Dezember 1969118

11.) H. Hoffmann, G» Hennrich , : r jExpérimente lié Untexsuchung des Wârmeuberganges bei turbuleaterStrômung von Natrium ira konzentrischen RingraumPSB-314, Dezember 1968 , , .•>.*•-•

i -* -f '

12.) F. Mayinger, D. Hein, w. kôhlerBubble Formation and Departure with Sub-cooled Boiling inWater-cooled Channels of High Heat Flux DensityIAEA - Panel on. Heat and Mass Transfer

13.) R. SchSneberg . ¡StabilitStsuntersuchungen fur SiedewasserreaktorenEUR 4012 d, 1970 (AbschluBbericht)

14.) R. Sch_5njBbe.rg_y _._H. ErnstDynamic behaviour of a water-cooled boiling channel with twistedtapesNucí. Eng. and Design, Vol. 12, .No. 2, p. 249 (197O)

15.) D. Thomas . - -.,Warmeubergang , Druckverlust und wlrtschaftliche Wermeubertragungbei Drallstrômungeh ',Chem.-Ing.-Techn. 42 (197O), S, 680 - 686

16.) G. TischerUntersuchungen an Zyklonen zur Dampfabscheidung in Siede-wasserreaktoren(AbschluBbericht, Teil I) Vertrag Euratom - AEG O83-66-1 TEED -.AEG/E - 323 - 118O, Dezember 1968

17.) K.H. GrabenerUnters uchungen an Zyklonen zur Dampfabscheidung in Siedewasser-reaktoren { - ...{Ahsçhl.uabericht, Teil. II) Vertrag Euratom:- AEG Q8 3- 66 1 TEED

Februar '18.) g."rKisbnf'''.K. Lochmanhy :0. Schad -. . ,Grofitechnische Versuche für Entwicklung und Prüfung von

Kernkra f twerkskomponentenATW 6, Juni 1970

19.) H. Wagener , .Simulation der HydrodynamiJc von SiedewasserreaktorenLaboratorium für Reaktoriregelung und AnlagensicherungBericht MRR 73 Juli 19 7O

20.) H. KarwatBruch-SThe code to investigate blow-down of boiling water reactorsystemsMRR 53, November 196721.) D. Bros cheDynamischer Druckaufbau in Druckabbausystemen

MRR 44, Mai 1968

119

22.) F. Mavinger, O.Schad, E. WeissInvestigations into the critical heat flux in boiling waterEUR 3347 e 1967

23.) W. Kastner, F. MayingerBumoutmessungen im Rahmen sicherheitstechnischer untersuchungenM.A.N. Bericht Nr. 45.O3.O1

24.) W. Baumann u.a.Experimentelle"~"Untersuchung Jer Kuhlmittel-Quervermischungan Vielstabbündeln, bastehencl aus unberippten, ein-, drei-,und sechsfach berippten BrennstâbenKFK 8O7

25.) W. Baumann u.a.Cross Mixing by Natural Turbulence in Fuel-Element BundlesSonderdruck "Atomkemenergie"ATKE 14 - 20 (107 - 111) 1969

26.) K. MaubachReibungsgesetze turbulenter Stromungen in geschlossenen, glattenund rauhen Kanâlen von beliebigem QuerschnittKernforschungszentrum Karlsruhe INK -4/69-2227.) K. RehmeDruckverlust an Stabbündeln mit Spiraldraht-Abstandshaltern

Forsch. Ing. Wes. 35 (1969) Nr. 428.) K. RehmeWiderstandsbeiwerte von Gitterabstandshaltern fur Reaktor-

brennelementeATKE Bd. 15 (197O) Lfg. 2

29.) H. Hoffmann» G. Hofmann, S. LeistikowExperimentelle Untersuchungen des Druckverlustes und des Lang-zeitverhaltens der Abstutzstellen an einem Modell-Brennelementaus Incoloy 8OO-Rohren mit sechs integralen Wendelrippen alsAbstandshalter in einer isothermen HeiBdampfstroraungKFK-1O28, September 1969

30.) M. Dalle Donne (E. Meerwald)Heat Transfer from Surface Roughened by Thread - Type Ribs atHigh TemperaturesProceedings of the 197O Heat Transfer and Fluid Mechanics In-stitute Stanford University Press31.) V. Casal, R. WaggottDer EinfluB geoir.etrisch definierter Rauhigkeiten auf Wârme-Obergang und Druckabfall in lángsdurchstrdmten 7-Stabbundeln

KFK-8O6/ November 196832.) W. Baumann, V. Casai/ H. Hoffmann, R. Holler, K. Rust

Brennelemente mit wendelfôrmigen Abstandshaltern für SchnelleBrutreaktorenKFK-768, April 1968

33.) D. Hein, H. Klgpper, F. MayingerThermohydraulische Auslegung des Reflektorraums des Hoch-flufireaktors GrenobleTo be published ZATW October 1970120

Heat and Mass Transfer in Nuclear Power. Research activities in Sweden

B Kjel1strom 0 NylundAB Atoatenergi ASEA-ATOM ABStudsvik VastarásSweden Sweden

1. Research centers in SwedenThe dominating part of the]; Swedish research in heat and mass transferwith applications to nuclear power is made at the following fourinstitutions.

AB Atomenergi., Studsvik Nykoping (AE)Heat transfer laboratory (Mr. J. Flinta)Engineering section ' Js- (Mr.'1C. Luthman)

ASEA-ATOM AB¿ Vastarás (AA)

CbAlmersJLastLlMte^of^ Jje£hnologjfJU Gothenburg (CTH)Department of Power Engineering (Prof. L Nordstrum)

Rpval Institute of Technology» Stockholm (KTH)•M» «•» ••• «H» «MB 4M» <MV •» MM null ^M ; ' '. • ' .^ "„ * ~, *" *

Nuclear Engineering Laboratory •-,- (Prof. K Betíker>..-.rr- • i '"• v.,'• t'i .'-.•

As will be evident from the following» the efforts are concentratedon problems with application to boiling water reactors. Problems relé-,vant for other coolantsrare, however, also studied.

j. ' * '2. Earlier research work

Earlier research work comprises theoretical and experimental studieswith close connection to the different Swedish reactor projects» aswell as such of more general character. Problems relevant to boilingwater reactors» pressurized water reactors, reactors with nuclearsuperheat and gas cooled reactors have been considered.

The results have been reported in internal reports (most of whichcan be made available on request) in. the AE-report series and in technical and scientific journals.

i

121

Earlier research as well as present program has been concentrated onproblems with immediate application to the reactor contracts earnedby the company. At present BWR:s, having a. total power of 2350 MW,are in different stages of construction. The first reactor, Oskars-hanm plant No 1, is now being commissioned.

The major part of the research work is naturally of commercialcharacter. However, some results from the heat transfer and hydro-dynamic tests with rod bundles in the 9 MW PRIGG-loop have beenpublished.

Earlier work» comprise mainly studies of experimental techniquefor sodium heat transfer experiments. Results are reported ininternal reports (which can be obtained on request) or in STU-reports.

2: •*.Earlier works as «ell as present program is concentrated on funda-mental experiments with two-phase flow, particularly in the highpressure region (100 - 220 bar). The results are presented in inter-nal reports (KTH- NEL- reports , which can be obtained on request) .

3. Present activities and activities planned in the near futureIn the following, present and planned research projects are describedin brief terms. The institute running each project is indicated by aletter code, which can be interpreted by means of section 1.

3. !_. J8¿sic__research and development work_1. Comparison of sampling methods for determination of moisture

content in two-phase flow. (AE)Experimental

2. Development of a theory for estimation of turbulent transportcoefficients in different types of flow. (AE)Theoretical

122

3. Influence of deposits on heat transfer and pressure drop forf )£«, in a fcubja. _ (AE).;,The=pr«tical; and experimental

4. Influence of the tube material on the heat transfer at filmboiling for elevated pressures. (AK)Experimental

5. Development of steam-water separators for de - salination plants.(AE)Experimental

1. Development of an advanced computer program for heat transferanalysis of rod -bundle fuel elements (co-operation between AE,AEK, RisS Denmark and IFA, Kjeller Norway).

The following parts of the project are carried out in Sweden:

1.1. Studies of flow distribution» void distribution» pressuredrop and fcurrï out in a 9-rod bundle with non-uniform heat-ing. (AE) Experimental

1.2. Heat transfer at post burn out in a 9-rod bundle. (AE)Experimental

1.3. Basic study of two-phase flow in annular channels includ-ing film thickness measuremen.s on inner and outer walls.(KTH)

2. Development of an advanced computer program for calculation oftemperature and pressure transients following a loss-of-coolantaccident. (AE)

Theoretical studies supported by experiments on specific problems.A large scale experiment comprising measurements of pressure tran-sients and void transients (at different locations) after a suddenpressure release is planned.

3. Discharge of saturated water through long tubes. (CTH)Experimental

123

4. Development of a prediction method for two-phase pressure drop fordiabatic and adiabatic flow. (AE)Different flow cases are studied experimentally. Present programcomprises experiments with sudden expansions» tube bends and elbows.

5. Burn out in horisontal and vertical tubes with circumferentiallyvarying heat flux. (KTH)Experimental

6. Heat transfer at post burn-out in long vertical tubes. (KTH)Experimental

7. Study of the possibility for a pressure recovery after a vortextype steam generator. (Zestoklon) (AE)Experimental

8. Development work on thermal insulation for concrete pressure vessels,(AE)Experimental

1. Turbulent heat and momentum transport for flow of a gas in arod bundle. (AE)Theoretical and experimental studies

2. Heat transfer by radiation from C0_. (CTH)Theoretical

1. Heat transfer for flow of sodium at the inlet to a flat channel(CTH)Theoretical and experimental

1. Temperature transients in fuel and canning for non-constant material properties. (CTH)Development of a computer code.

2. Influence of Pu - content on the thermal conductivity of UO, atelevated temperatures. (AE)Experimental

124

"The Problem of Predictl ng Hf>atTransfer. in Pas Cooled-.. Cu rrent S ta jus and Fu turg Êrosr ec ts

byB.K. Launder and D.B. Spalding

Errata'S.-eet

p.8 Table 2.1: 'h stagnation enthalpy1 should read 'K-stagnationenthalpy*.

p.8 21. below Table 2.1: 'stress function^ ' should read 'stre.ara function,"^'p.10 1.4* 'sam^-line1 should read 'sane line'op.17 eq(2.1-5)* the left side of the equation should read:

p.18 eq(2.1-7)'

p.18 eq(2.1-8):

p.24 1.2:

P-32 1.3»p.32 1.51

p.45 sketch:

p.50 Reference 13:

Fig.3.2»

the left side of the equation should read:-V >'- r ¿.-tí, •• \ • ' ' v¡' 'o /íveÜA „ -JGL

the left side of the equation should read:

oxj

the termn,. ,CW on the right side of eq (2.2-7)•i f 1C ftshould apper r only once.'0 127 " should read '-pipUJ. ».•is most practically ocuring1 should read•in most practically occurring'.the vertical grid lines should be continuedover the rib profile shown to the right ofthe sketch.•Staffiibertragung1 should re»id 'Stoffubertragung1

Left hand ordinate should read '^i/u ' whereu. is the centre-line velocity of jet. (u. ist aC

in fact zero.)The riirht hand ordinate is missingj it should be:

o. The scale is the same as that of the

left hand ordinate

125

Objectivesof Paper

1. To characterise the problem of predicting heat transferrates in present and future gas-cooled nuclear reactor(physical aspects, computational aspects, what isalready known and what it needs to be).

2. To emphasise that available prediction procedurescould now be used more extensively, so as tosupplement experiment and to reduce the cost ofdevelopment.

3* To indicate what research would be most immediatelyfruitful in enlarging predictive capabilities.

126

•*• Injhroduction(a) Initportance. There is little need, at the presentconference, to empnasise the value for designers of nuclearreactors of reliable means .of foretelling the distributionsof temperature and heat flux that will prevail in their pro-jected reactors. Because this foreknowledge is so valuable,much time and money are devoted to advance experimentalwork on model fxiel elements, f inned-tube heat-transfer .matrices, and other components of complete reactors* Suchexperiments provide the constants and functions in theformulae that the designers must use when selecting theoptimum configuration.

However the cost of obtaining this knowledge is notsmall. Tn order to limit it, the range of conditionsinvestigated must be restricted; and this restriction detersdesigners from envisaging configurations that are veryremote front those of which they have prior experience. Itcan therefore be plausibly argued that the cost of develop-ing prediction procedures for heat transfer significantlyfroids back the progress of nuclear power developments.1**) The role of the digital computer. However, thatheat-transfer research has been expensive in the .past does

: . '

not mean that it must always be so. Ijndeed - and this isthe main message of the present paper - means are to handfor radically reducing it. The adoption of these means cantherefore substantially accelerate the development ofnuclear power.

127

The new factor in the situation is tbe widespread;availability of the digital computer, coupled with the

recent development of numerical techniques which enable itto handle heat-tr&nsfer problems. Everyone knows thatcomputers have transformed the engineer's capacity to makecalculations; and this power has been extensively used foroptimising nuclear-reactor designs, the heat-transfercorrelations of the experimentalist being among the inputsto the computer. Not everyone is however aware yet of theability of the computer, once the appropriate numericaltechniques have been developed, to supplant the experimentalinvestigation by acting as a mathematical simulacrum of thephysical process. It is this latter possibility that canso substantially cheapen the prediction process. It is thison which we- shall concentrate in our paper.

To serve as a mathematical model of a fluid-flow andheat-transfer process, the computer merely needs a suitableprogram. But suitable progrès are not easy to develop,and certainly cannot be provided by those whose onlyexpertise is computer programming itself; for the successof a computer program as a mathematical model depends on itsemployment of correct numerical techniques and of appropriatephysical hypotheses. Neither of these could be learnedfrom textbooks; both had to be developed, in concert, bypainstaking research.

The hydrodynamic and thermal behaviour of gas-cooledreactors can be described by a set of simultaneous, non-linear, partial, differential equations. There still exist

128

no satlsfacfïQjc.yitrrchniques for solving these in> entirelygeneral circumstances; hoxvever, some practically importantclassed of problem are already soluble ,, and others Focnwill be if Ctirrent research is expanded. Most completesuccess has been attained in the modelling of steady flowb,

, as distinct from unsteady onesj fortunately it is thesethat are most prevalent in nuclear reactors, and it is

j

these to which we shall confine attention in this papar. ." i% iTti#"'steady flows in question can be classified, frorp

thé mathematical point of view, into two-dimensional andthree-ciiiaerisicmal, and into parabolic; .and elliptic. The ;

present state of computational ability jis summarised by* í

table 1.1. :

Table 1.1. Summary of current ability to solve'i '

differential equations of sbeady convectiveheat flow.

--- jHmettsional i t yType oi ->- ^.Equation ^ ** ,

v." • • • • : : • .. ',>ParabolicrLC'V— -'

Elliptic

2

Methods existe.g. Re£v..[l]

Methods existe.g. Réf. [2]

3

Methods underdevelopment i

No methods asyet'. Ü '

129

Table 1.2. Some examples of flow situationIn the classification of Table 1.1

DimensionalityTypeEquation

Parabolic

Developing axi-symroetrical flow inpipes and annuli,unstalled diffusers,nozzles, with roughor smooth walls,with or withoutswirl around thesymmetry axis.

Developing flowsof non-circularcross-sectionwith unsymmet-rical wall condi-tions. Develop-ing flow along rodclusters.

Elliptic

Flows transverse tounf inned-tube bundlesin plane and axi-symmetrical ductswith sudden enlarge-ments, in stalleddiffusers. Fullydeveloped flow inducts of non-circu-lar cross-section,e.g. eccentricannuli with orwithout swirl, rodclusters.

Flows in ducts ofarbitrary shape,with recircula-tion in all threeco-ordinatedirections.

Table 1.2 illustrates what situations of practicalinterest fall into the various classes» By comparison ofthe entries in the two tables, one can deduce for examplethat:i) The prediction of flow and heat transfer in rod

clusters lies already within the field of establishedexpertise, provided that the conditions vary soslowly along the duct that the flow can be regardedas fully developed. It does not matter whether the

130

rod surfaces are smooth or rough, or- whether theij:temperatures are uniform or varying.

ii) If the gYg QP gnt. of the flow along the section isprecisely the subject o± interest, existing methodsare not adequate. For phenomena of this kind, theauthors and their colleagues are at present engagedin constructing prediction procedures; they willbecome generally available within the next few years.

Some details concerning .these predictionprocedures will be discussed below.

(c) Models of turbulence. Almost all the. convectiva-heat-transfer processes of the nuclear-power industry areconcerned with turbulent flow. Here tpo%there have beenimprovements in quantitative understanding that, have --revolutionised our ability to predict turbulent-heat-transfer phenomena. ;

Some details will be given in section 3 below. Hereit will suffice to mention th.it, whe.*r«as a fev; years agowe had only Prandtl's mixing-length hypothesis to guide us,there now exists an assembly of well-tested differentialand auxiliary equations, the solution of which leads to therequired distributions of the transport properties of theturbulent flow; and these equations we are able to solve.

There were two serious disadvantages to Prandtl'smixing-length model. The first was that the magnitude ofthe mixing length itself, knowledge of which was necessaryfor the prediction of heat transfer, had to be supplied tothe computer program; and this knowledge could be obtained

131

as a rule only from experiment. The second was that, inany case, the hypothesis implied that the effective thermalconductivity of a turbulent flow was finito only wherethere was a finite gradient of velocity; and this iscontrary to the experimental findings in practicallyimportant circumstances.

The new models of turbulence are free from thesedrawbacks. The empirical input which they need has a moreuniversal character; being the same for all geometries ofduct, it can be determined from experiments that do notneed to be repeated when a new configuration comes inquestion. Moreover, these new models can indeed predict,what experiments reveal, that sometimes the effectiveconductivity is highest in just that region in which thevelocity gradient vanishes. The reattachment area of aseparated boundary layer- is one of these regions,(d) Outline of the remainder of the paper. This intro-duction has made the main points of the paper. The remainderwill be concerned with detailed discussion of the computa-tional and physical aspects of the problem, and withenumeration of some of the research steps which it seemsimmediately fruitful to take.

132

2. Some Details of the Computational Procédures

2.1 JSxis ; t i ti g PjToç.g dur es- , - • : - >, ••- ' •• - •""- ' " -'" " " '

2.1.1 Two- D j.jmen s ion al P ar abo lie F l o w s

(a) Th e d 1 f f er en t i a 1 e cu a t. i o n s

Reference [13 has provided a general and economic

procedure for the solution, of the transport equations governing

two-dimensional parabolic flows. The procedure chooses as

independent variables the distance co-ordinate in the mainstream

direction, x^, and the cross-stream normalised stream function* - *T<P, defined as ——— T- . é is related to the cross-stream*E~ *I

distance, x by the identity:

(2.1-1)

lines c}

and jj. and $E .are prescribed or

determinable functions of x-*.

What may appear, at first sight,

to be an unnecessarily cumber-

some choice for the cross-

stream co-Qr$inate in fact enables

the cro.$s-stre.am velocity u^ to be

eliminated without the appearance " '

of integrals in the resultant

transport equations'. T?hus,rthe general form of the transport

equation becomes:

A A (2.1-2)

• : 1-1 • i'•In practice fa and $„ are chosen to be the values of ^ prevail-ing along the internal and external edges,of the boundary layer,thus consideration need be given only to regions where $ liesbetween 0 and 1. 133

where the dependent variable, <pt may stand for any transferableproperty. To convey an impression of the range of physicalprocesses to which equation (2.1-2) may be applied, Table 2,1lists some of the dependent vaxiables whose variation has beenpredicted with the procedure of reference C13.

TABLE 2«It Some Examples of Variables for which « mav stand

Symbol Meaningu,

kcn

streamwise velocityswirl velocity

stagnation enthalpy

mass fraction of species j in a reacting

or non-reacting multi-component mixture

turbulence kinetic energyrms turbulent fluctuation of temperaturenumber of droplets within a particularsize range (e.g. fuel sprays)

The coefficients a and b in (2.1-2) are calculable functions of•x.^ involving the edge values of the stream function §. Thecoefficient c of the diffusion term takes the form:

wherein effective values of the viscosityueff effand the Prandtl/Schmidt number; these effective values includethe influences of both molecular and turbulent contributions tothe transport processes.

134

The terni 'd* accounts for source and sink terms which

tend to raise or lower the value of <p. The particular form

of d will depend on the physical meaning ascribed to <p but

by way of example, when u^ is the variable in question, d

would contain terms expressing the tendency of streamwise

pressure gradients or buoyancy forces to increase or decrease

the strearawise velocity.

(b) The difference equations" • • 1 *T. : '

A central task in any finite-difference procedure is

the simulation of the partial differential equations by a

set of algebraic equations which interrelate the values of

<p prevailing at a finite number of discrete points in the

solution domain. Just, which neighbouring values of cp exert

an influence on the value at a

node P is largely dictated by

character of the flow. Por

parabolic flows, downstream\events exert no influence on

upstream values; it is this

feature which enables their

solution to be accomplished by

•marching* progressively down~

stream given an initial starting

— 1 ..(

—— -4

'

1 •'

JU —— .,

*. —— <

.

X

v : ! -•

—— (• —— <

y-f<

\ ah Y * "— 9-r<

> — () .!.-<

> ——————— <

> J~--t

^ »

3 ——— « ——> ——————

r-*'I * —— Wo influence

values.

profile. The problem thus reduces to that of determining the

unknown values of <p along a constant-x^ line 'D' from known

values at the edge of, the .grid and along the upstream line 'U',. * v ".

In Reference C^3 the q>'s are found from the solution of a setof *imuitanéóüs equations of the form:

135

A (2.1-4)

Thus the value of q> at each of the interior nodes along D is

expressed in terms of the values at the two adjacent nodes on

the same-line; the influence of the (known) <p's along U is

contained in the term C. Since the cp's are known at the edges

of the grid line the equation set (2.1-4) contains just enough

constraints to enable the interior values of q> to be determined

uniquely.

The algebraic equations should, of course, mirror

consistently the implications of the partial differential

equations which they replace. The sketch below shows how this

is ensured. To each nodal point is apportioned a small area(or rather, volume) of the

flow and the algebraic rela-

tion between cp. and its

neighbours is established by

integrating equation (2.1-2)

over the control volume

surrounding the node*. To

evaluate the integrals pre-

sumptions must be made

concerning the variation of

CD between nodes. Since in

•A desirable consequence of deriving the difference equationsfrom a control volume analysis is that the integral conservationequations for <p are satisfied exactly over the whole flow (avirtue which is not always possessed by the more commonly usedTaylor-series-expansion techniques). For this reason it is apractice we have preserved in all our finite-difference researches<

136

a parabolic xlow diffusion in the x^-direcatón is negligible

it is appropriate to presume conditions within each control

volume to be uniform in the st^earowise direction. Por the

cross~stream direction an exact analysis of tine combined

effects of lateral convection and diffusion shows that q>

varies exponentially with o>» However, in most cases, the

departure from a linear variation is small and because the

computation of exponential functions is expensive of computer

time, a linear q>~m profile is assumed between nodes. In

those few circumstances where high lateral convectivo fluxes

render this assumption inaccurate, a correcting adjustment is

made to the coefficients of t&e («'s in (2.1-4).. * i ~ . '

It remains to prescribe a procedure for solving equation

(2.1-4). It is first remarked that if. the A's, B's and C«s

are known the equation set is linear and the <p's may easily be

determined from the solution of a tri-diagonal matrix. In fact,but one

the C's for all qrequations/are known because they contain only

upstream terms; the exception is the u-~equation where C also1 ulcontains the streamwise pressure gradient over the controlvolume. Por external flows however - ~- is prescribed};.for

... ': - - •? vJ Ox-jthese circumstances therefore all the C's are known. The same

ff

is not strictly true of the A's and B's for they contain terms

involving the downstrsam <p's - which are themselves unknown*

In practice, however, they vary but slowly in the streamwise

direction and hence they nay safely be evaluated at the upstream•*i

end of a forward step. By thus linearising the difference

equations a very rapid non-iterative solution of the equations

is tii us facilitated.

1.37

Precisely the same practice as the above is adopted forinternal flows as well though here some ingenuity is requiredfor ~J7— is not known a priori (and, hence, neither is C. ). Inox^ ———————————— u^fact the magnitude of the local jressure gradient is a consequenceof the way in which the flow develops, its value being justthat which will cause the boundaries of the stream to coincidewith the walls of the duct. The practice adopted is thus asfollows:(i) a reasoned estimate is made of the pressure gradient

over the forward step and then, with this value insertedin C , the difference equations are solved to determineulthe downstream q>'s.

(ii) Unless the assumed pressure gradient is exactly correct,the downstream flow area will not be the same as theduct area. However, in estimating the pressure gradientto be applied over the next forward step, account is takenof this discrepancy, and a value chosen such that, whenthat step is completed the difference between flow andduct area \-/ill be dî.r .nichc'i.Although in the course of a calculation the duct and flow

areas may never exactly coincide it is easy to keep the differencebetween them negligibly small.Cc) Some Applications of the Procedure

The finite difference procedure outlined in the aboveparagraphs has been incorporated into a Fortran IV computerprogram - GENMIX 4 - organised in such a way as to facilitateits application to any parabolic flow*.

*A listing and description of the program is contained inReference C13 and card decks may be obtained from the HeatTransfer Section at Imperial College.

138

fThe versatility has been achieved by allocating to

subroutines all those component tasks of the computation .which

are not special to any specific problem. Por the majority of

problems, therefore, a user will need to make few if any

changes to these subroutines. He is thus enabled to focus

attention on adapting the main program to accord with the

specification of his problem.

The above sketch shows the actual flow whose solution is,

provided for in the main program of GENMIX 4. Of course, this

specification will seldom match exactly a user* s requirements;

however, by changing a few Fortran statements, the. program can

be used to predict parabolic flows with quite different boundary

conditions. Por example, by making 9 zero, eliminating stream

<2> and. faking xeftd and xoufc equal to *last the geometry becomes

that of a symmetric annulus. Alternatively, if the flow to

be predicted is a free jet, streams (1) and (2) are eliminated,and x end

Figure 2.jl projvides three examples of internal flows 'to

which, predictions have been obtained by making such small139

modifications to GSNMIX. The first shows laminar flow develop-ing through a circular-sectioned tube at uniform wall temperature.The Stanton number and skin friction coefficient fall steeplyat first as the flow develops and then eventually level offat their fully-developed values.

In the above case, the starting profiles of velocity andtemperature were uniform. Any initial profiles may be specifiedhowever and, by way of example, figure 2.1b shows the flowdevelopment near the entrance of an annulus. At the entranceitself two discrete fluid streams enter at different velocitiesand, moreover, the molecular weights of the two fluids differ:step distributions of velocity and mass fraction are thereforespecified as the initial profiles* As the predictions show,at x^ = 0.5 the profiles of velocity and mass fraction havebeen considerably smoothed out by the action of turbulent mixing.Note that in this example the higher velocity stream had thesmaller molecular weight and,in accordance with the momentumprinciple, the velocity of this stream is the more affected bythe mixing process.

The third example concerns the flow in a plane wedgediffuser. In this case, th.e conversion of the program froman axisymmetric to a plane geometry is achieved by the changeof a single Fortran statement. Predictions show that, becauseof the rising pressure along the diffuser axis the skin frictioncoefficient falls rapidly at first. The growth of the wallboundary layers, however, eventually tends to diminish thepressure gradient and, as predictions show, the frictioncoefficient then levels off. In all three of the above

140

examples the recommended practice for estimating the stream- .wise pressure gradient leads to predicted flow widths whichdiffer from the actual widths of the ducts by less than 0.1% -a figure which is probably within the tolerances of manufacture.

Figure 2.2 provides examples of predictions of two externalflows where, in each case, there is a need to protect the wallfrota the effects of a hot external stream. In the firstexample protection is achieved by blowing a jet of cool fluidalong the wail. The predictions show what experiment confirms:namely that the denser the injected gas the greater the distanceover which effective cooling is provided. The second exampleshows the effect of cooling a porous surface by injecting coolerfluid through wall itself. The predictions display that in thisway one can effect a substantial decrease in the surface heat-transfer coefficient.

As a final example, figure 2.3 considers the problem ofcondensation in a tube where the presence of incondensablegases offers the major resistance to the condensation process?

. ..' *' '• 'the condénsate is thus supposed to be immediately absorbed into

f

the wall. The predictions show that because of the non-condensable

gases the condensation rate diminishes rapidly with distance

along the axis. In this particular example the streamwise

pressure gradient is strongly dependent' upon the local condensa-

tion rate which is itself unknown at the upstream end of a

forward step. However, as figure 2.3 shows, the standard practice

for estimating the change in pressure over each forward step

still leads to a predicted flow radius which differs negligibly

from that of the pipe.

141

In the foregoing examples we have placed emphasis on the

variety of convective flow phenomena which may easily be

predicted with the aid of the GENMIX program. The accuracy

of these predictions, of course, depends on the provision of

a sufficiently realistic model of turbulence; this topic is

one to which we shall be devoting attention a little later*

2.1.2 2-Dimensional Elliptic Flows

(a) The differential equations

Elliptic flows, unlike the parabolic flows considered in

the previous section, will not in general possess a single

predominant direction of motion over the flow region considered.

There is therefore no advantage to be gained from choosing

different types of variable (such as x^ and <u) for the two-

co-ordinate directions. There is however great incentive to

preserve generality and this desideratum is aided by choosing

a co-ordinate system of which at least one family of surfaces

can be curved so as to fit the shape of the region for which

calculations are to be made. Por this reason, the procedure

of Reference C23 formulates the transport equations for an

axisymmetric system with respect to general orthogonal co-

ordinates Ç- and C2* The third co-ordinate direction, §, is

that generated by rotating any point on the §- - §2 plane

about the symmetry axis.

The |^ - and c~ momentum equations (for the velocities

u- and Up) each contain a term involving the spatial gradient

of static pressure, the treatment of which would pose certain

difficulties. By replacing u^, and Up by the stream function

142

f, and the vorticity, o» hoy/ever, ones not only eliminates

entirely the appearance of pressure but also avoids the

necessity of making explicit recourse to the mass-conservation

equation. The form of the elliptic transport equation for a

general property cp roay thus be written:

convection direction-1 direction~2 sourcesdiffusion diffusion

(2.1-5)Equation (2,1-4), it is noted, contains the same ingredients

as the general parabolic equation (2. 1-2); the only essential

difference is that, for elliptic flow, diffusional transfers

in two orthogonal directions are accounted for.

The hydrodynamic field in the C-^-Cp Plane ^s determined

from the solution of equations in which &» stands for $ and Q/r

(r is the radial distance of a point from the symmetry axis).

Threse equations are solved for all elliptic flows; in addition,

transport equations are solved for such other variables as exert

appreciable influence on a particular problem.

The coefficients a, b^, bp and c and the source term, d,

differ according to the meaning of <o and the co-ordinate

system chosen. Here it is perhaps appropriate to quote just

the simple form of the str earn- f une tion , vorticity and stagnation-

enthalpy equations in cartesian co-ordinates for flows where

the density is uniform and where conditions are such that the

stagnation enthalpy is a conserved property:

143

(2.1-6)

(2.1-8)It is noticed that the stream-function equation takes

a particularly simple form-it is merely the kinematic relation-ship linking the definitions of f and p.(b) The difference equations

Por elliptic flows, the valueof any dependent variable at apoint in the flow will be affectedby the edge conditions prevailingalong all sides of the solutiondomain. Consequently, in construc-ting a finite-difference analogueof equation (2.1-4), the differenceequations for a.point P must containthe influence of neighbouring values on all four sides (comparedwith the 3-sides influence of parabolic flows).

Following the practice of section (2.1-1) the differenceequations are derived by integration of the general ellipticequation over a control volume surrounding each node. Certainassumptions must, of course, be made concerning the way thatthe convective and diffusive fluxes across the cell boundariesand the source term are affected by neighbouring nodes.

144

Because the great majority of engineering flow's1 are 'those for

which the Reynolds number is high, the trfatment of the

convective terms is especially importar* h . In Reference t'23

these terms are treated by an "upwind-difference" procedure;

its principle may be explained by reference to the above

sketch. When the flow of fluid across the cell wall nw-sw is

from left to right the value of cp crossing the cell wall is

taken to be that at W; likewise when the flow is from right

to left, the fluid crossing the cell wall has the value of &

at P. Thus the value of co along nw-Sw is always that which

prevails on the upwind side of the cell wall.

After completing the integrations and regrouping the

terms, the outcome of the control-volume analysis may be

expressed:

where the C's , containing the influence of convective and

diffusive effects, control how heavily a neighbouring value

of 0>- should weigh in the determinations of «v,; the effects

of sources of <p are contained in D. There is one such équation

for each y at every interior node of the grid. With conditions

prescribed for the boundary nodeô, there will then be just as

many equations as there are unknowns. '• • '

The set of equations given by -(2.1-9) is not linear because

the C's and D's in general depend on the o's; an iterative

procedure must therefore' be employed for their solution.

145

Reference £23 adopts the fallowing Gauss-Seidel iterationscheme. To start with, guessed values for all the &'s areassigned to each interior node and from these, initial valuesof the C's and D's are determined. A visit is then made toeach node of the grid in turn during the course of vh ich thesubstitution formula (2.1-9) is employed to calculate a newvalue for the vorticity, Op» at every node. When a completesweep has been made, the procedure is repeated, firstlyupdating the values of the f's and thereafter the remaining<p*s. With new values thus assigned for all <j>'s at everyinterior node, a second cycle of iteration is begun, startingwith recalculation of the C's and D*s. This procedure isthen repeated until the changes in the values of the variable.?between successive cycles become negligibly small.

However, will the sequence of operations outlined abovein fact lead to a converged solution? Most earlier attemptsto solve elliptic flows adopted a central-difference approxirr.».-tion for the convective terms; except at modest Reynoldsnumbers, these attempts invariably failed to obtain convergedsolutions to he difference equations. This failure may betraced to the fact that the central-difference formula leads ~va set of equations which are abidingly unstable when theeffects of convection much outweigh those of diffusion. Here:..resides the essential and decisive superiority of the upwind-difference formulation: for, no matter how high the prevailingReynolds number, this representation enables converged soluble:..to be obtained from the use of successive substitution algoriv.:

146

(c) gome^gppliçc. Lions of the procedure

In devising the finite difference procedure of Reference

[23 great eroph«sis was placed on generality; only by so doing

could the procedure be of more than incidental value in predict-

ing the elliptic flows which arise in engineering practice.

The computer program which embodies the procedure therefore

takes care to preserve the general features of the method.

In one respect, however, a concession is made in the interests

of ease of organisation and, for the user, ease of application:

this is that the program, in its printed form,considers geometries

in which, in cartesian or cylindrical-polar co-ordinates, the

boundary surfaces of the flow may be chosen to coincide with

grid lines. Even witiv this limitation, the range of practical

problems is still large; and the worker who gains experience

by applying the program to one of these geometries first will

not later find it difficult to tackle flows with more complex

solution domains.

An impression of the capability of the program may perhaps

best be conveyed by reference to jome predictions. Figure 2.4

presents some results of Runchal £33 for the flow in a pipe

downstream from a sudden enlargement. As the predicted

streamline pattern -reveals there is "a recirculating zone just

downstream of the enlargement and, as ^experiments have confirmed

the maximum heat-transfer rate occurs at the reattachraent point

of the flow. A further example is provided in Figure 2.5 where

Mitchell's C43 predictions of flow in a plane finned channel

are shown. The predicted Stanton-number distribution implies

that the heat-transfer rate is highest on the top surface

147

and along the leading vertical edge of the fin, in accordancewith experimental data.

Por the nuclear power industry, fully-developed flows in

non-circular ducts form a very important sub-class of elliptic

flows. As an example of such a flow, Figure 2.6 shows Yang's*

predictions of flow in an eccentric annulus both for the case

of a stationary and for a rotating core tube. For this

problem the basic program was modified to make use of the

so-called 'bi-polar. co-ordinate system. The circumferential

grid lines thus form a family of eccentric circles, the extreme

«embers of which are the internal and external surfaces of the

annulus. As Figure 2.6 indicates, quite modest rates of

rotation causes circumferential convection which substantiallysmooths out the variation in Nusselt number around the surface

of the core tube which is present without rotation. The

rotational motion, generated in the above problem by rotating

the core tube about its axis, could equally well have been

induced by a stationary core tube, prepared with spirally-

wound ribs around its surface - such as are used in certainAdvanced Gas-Cooled Reactors.

2»2 Procedures Currently under Develepment

(a) Unsteady tv/Qrdimensioiial flows \-tith recirculation

In the top right-hand box of Table 1 are mentioned

developing flows in ducts of non-circular cross-section; these

will be the main subject of the present section of the paper.

However, it will be useful to introduce the discussion by way

*W.M. Ying, Imperial College: private communication

148

of a mathematically related class of phenomena, namely that

of the development with time of the elliptic flows described

in section 2.1.2.

Figure 2.7 shows some results of computations made by

an adaptation to the unsteady development of a viscous fluid

jet, impirsg.irq on a wall at right-angles to the axis, of the

elliptic-flow program of Reference C 2 D . The adaptation and

computation:; have been made by K. H. Ong at Imperial College*

It wil l be seen that the computed flow exhibits the advance

of a toroidal vortex, and its eventual disappearance from the

field of observation, just as vs observed in practice.

The method of. adaptation can be indicated briefly as

follows. Fox the hydrodynamic part of the computation, the;

main dependent variables are the stream function •> and the

vorticity Q, just as they are for steady flows. Moreover

the link, between ^ and n which expresses the mass-conservation

principie is precisely the same for unsteady as for steady

flows, provided that the density is uniform as in the present

case: knowledge of the instantaneous vorticity distribution,

together with the boundary condition, enables the instantaneous

stream-line pattern" to be determined directly. The equation

governing the vorticity distribution is however modified by

the addition of the term 30/9^» which,' in finite-difference

form, is expressed as (op ^-Op fc.iV^t where op ^ and Qp . ^

are the o's at a point P in the field at the k'th and (k-l} fth

instants of time separated by the interval 6t.

The consequence is that the finite~difference equation

for Op u. can be written:

•Private communication.149

* <>W,kCW * °E,kCE

* (fiP,k-l " °P,k)/6t ; (2.2-1)

here the C's are coefficients representing the effects of

convection and diffusion, and are the same as for the steady-

state equation; the final term represents the effect of the

time-dependence.

Now equation (2.2-1) can be re-arranged so that o« j.

appears only on the left-hand side. The result isî

nN.kCN * °S,kCS * °W,kCW * °E,kCE * °P.k-l/6fc

* C * 1/6 1

(2.2-1)

This equation scarcely differs in form for that for the steady

state (for which 1/ot •* 0); and the set of such equations can

be solved therefore by the steady-state computer program.

A convenient, if somewhat approximate, interpretation

would be that the un s t eady-f lo w problem is solved as a sequence

of steady-flow ones, for a succession of finite time intervals;

and the p distribution at the beginning of a time interval

influences the Q distribution at the end of that time interval

by appearing as the "source" terra. (Qp u_3/&tV(Cj, + Cg *

CE + 1/6 t).

150

(b) Deve3 opine? flow r i)i a duct of irregular cross-section

At /irst sight, it may appear that the similarity

between the unsteady-flow problem and that of flow developmenti

along a duct is so complete as to allow the same method of

computation to be employed; one would simply exchange the

time dimension for that of length along the pipe. However,

there are two important differences which significantly

complicate- bho situation. They are:

(i) Because there are changes in longitudinal velocity from

section to section along the duct, stream tubes may

increase or decrease in cross-sectional area. The

principle of conservation of angular momentum requires

that this change in area should be accompanied by a

change in the rate of "spin", i.e. the vorticity, about

an axa s aligned with the length of the duct. The well-

known bath-tub vortex is an example of the workings of

this principle. In other words, additional source

terms appear in the vorticity-transport equation,

associated with the finite longitudinal acceleration of

the fluid.

(ii) Whereas, in the unsteady-state problem, all particles

advance through time at the same rate (we all, alas,

get older at the same inexorable speed), passage down

a duct is subject to no such restriction. The particles

near the x^all proceed more slowly than those near the

centre of the duct; and elsewhere in the flow, these

same particles may have drifted into the centre of the

duct where they can move, downstream at a faster rate

151

than their earlier sluggish one* A consequence, thoughnot an obvious one, is that the velocity components inthe cross-stream direction are no longer bound togetherby the existence of a scalar stream function» We mustdispense with the f~Q relation as a means of expressingthe implications of the continuity equation»The first of these differences is easily accounted for:

we are well able to handle source terms in the differentialequations; and even those whose variability tends to causeinstability in the numerical procedure can always be domesti-cated after more or less trouble. The second differencerequires however a more radical response: a new differentialequation must be employed so as to allow the u^and Ug fieldsto be deduced from that of o«

This is not the place to derive the differential equation.However, it may be usefully stated (in its simplest possibleform) as:

<2.2-3>

What is noteworthy, when comparison is made with equation2.1.6 above, is that the velocity Ujhas taken the place ofthe stream function f, while the gradient of vorticity appears(with other terms) where the vorticity itself appears.

This equation can be solved, in conjunction with thatfor the transport of vorticity, by an adaptation of thetechnique of Reference C23. This development has not yetbeen completed; but it is in progress; and there is no reasonto believe that it will not be successful. We can expect

152

before long to have a procedure for predicting developing

flows in ducts of 'arbitrary cross-section that is as satis-

factory in respect of generality and ease of use as is that

for fully-doveloped flows.

(c) ,A second approach to the developing-flow-in-ducts problem

There are those who doubt whether the vorticity is truly

a convenient variable for use in three-dimensional flows; and

it is not as obviously suitable for use as in two-dimensions.!

ones. The alternative is to use the three velocity components

and the pressure as the main dependent variables. The only

questions are how should they be expressed In finite-difference

form and by what process of successive- substitut ion should

they be solved?

The Imperial College team is at present devoting its

attention to the following scheme :-

(i) Suppose that the distribution of all variables is given

at an upstream section across the duct and ~ that the task

is to find their distribution at a downstream section.

(ii) Guess the distribution of pressure at the downstream

section and then iterate on the u.-jU^and u equations

until the downstream values of these variables satisfy

the relevant momentum-conservation principles.* " ' ' '

(iii)Examine the resulting set of velocities from the point. " • ' • ' . '. •

of view of the mass-conservation principle. l In general,

this will not be satisfied. Express the infractions of" •• , , , î' -. ,

the principle in terms of "effective mass sources" at

each location.

153

(îv) Adjust fhe pressures at the individual points on thedownstream grid in directions and by amounts which willalways suceed, when continued for long enough, to reducethe mass sources to negligibly small values.The main difficulty lies in the devising of a strategy

of pressure adjustments, in response to mass-source distribu-tions, which will infallibly cause a reduction in the masssources and indeed will cause the required reduction in theminimum number of operations. At the time of writing, thisdifficulty has not been entirely circumvented; but this isjust a matter of time, and of the systematic collection ofinformation about the way in which the mass sources and thepressure adjustments interact.

2.3 Some Proposals for Research on Computational Procedures(a) Two-dimensional parabolic f1ows

It is rare that one can report that further research isunnecessary; but it certainly seems to be the case that thereis no great urgency about improving the present means ofsolving the parabolic equations of the two-dimensionalboundary layer. The method of Reference C13 is fast andgeneral enough for almost all purposea.

Lest this assessment should appear too negative, onepossible development which is relevant to nuclear power maybe mentioned. Becker (e.g. References [53,£63) has proposeda method for isotope separation which involves the use ofsupersonic flows in strongly curved channels. The computer

154

program of Reference [13 would require appreciable modifica-, : •-> -i • r .",.••". < ' '.<•,,-

' , ' '• • JÍ • •tion before it could be applied to this case, because itcannot at present handle such intense Iciteral pressuregradients. This is a development which would be worthmaking, and which might well have an impact on the developmentof .nucljear power; for it would provide a theoretical meanss .. . ..of predicting the role of the transport processes in Decker'sapparatus that, until now, has been lacking. This is justone example of the way in which the use of predictionprocedures can replace costly experimentation and can placeT" ' •

on a more secure footing the decision about' whether a design

has a prospect of economic and technical success» .

(b) Two raimen s ion al e11i p ti C f1ows

The method of Reference C23 has already been subjected

to numerous detailed improvements, but more of these are

awaiting practical trial or implementation. Nevertheless,

the main need here seems to be the employment of the method

for the prediction of heat-transfer processes of the relevant•>

kind, with a view to supplanting some of the experimental work.that currently has to be carried out, or of making its outcome

• • - • • • ' •more fruitful.

We have been encouraged to learn recently that two nuclear

research establishments have in fact already begun to use

the elliptic flows procedure for such research. The Aktiebolaget

Atomenergi at Studsvik, Sweden, have initiated a programme

to apply the procedure to predict the fully-developed heat

transfer rates in an ÂGR rod cluster and the CEGB Nuclear>,' r*1 • '

Research Laboratory at Berkeley, England is predicting the

155

influence on heat transfer of the recirculating flow between

the end of one fuel pin and the start of the next (illustrated

in the sketch). The lat-

ter project has had to

adopt an axisymmetric

model of what in an

actual reactor, is a

fully three-dimensional

flow. Even where such

idealisations, are necessary, however, there seems little

doubt that the elliptic flows program in i te present form can

be exploited to great advantage on problems concerning gas-

cooled reactors.

(d) Three-dimensional flows

We have already mentioned the work which the Imperial

College team is doing on developing flows in ducts. It goes

without saying that we think this work to be important; but

probably the magnitude of the I.C. effort is large enough for

it to be unnecessary for others to.join.

For fully three-dimensional flows however (the bottom

right-hand corner of Table 1,1), the situation is quite

otherwise. Here there is great need for the development of

computational methods. Modern computers are only just large

enough to handle problems of this kind; and great skill will

be needed to effect economy of storage and computer time.

This is perhaps a field in which international co-operation,

assisted by the Atomic Energy Agency, should be considered.

156

3. Some Details.. Concerning Turbulence Model s3.1 Bacjcground

The development of the finite-difference proceduresdescribed in Sectior¿ 2 has both stimulated the demand forand enabled the supply of turbulence models with a widthof applicability far greater than those hitherto available.The demand arose because the full potential of the generalnumerical procedures could be exploited only by theprovision of turbulence modele of equivalent generality.Their supply became technically feasible because thefinite-difference procedures could solve transport equationsfor any turbulence property which might exert an importantinfluence on the mean-flow characteristics.

In Sections 3.2 and 3.3 we shall be conveying the mainfeatux'es of these recently developed turbulence models andshall be showing some predictions which results from theiruse. In the present section the nature of the turbulenceproblem and the evolutionary route to these new models willbriefly be oxitlined.

The essential task of a turbulence model is to providea specification for the determination of the turbulentfluxes of heat and momentum which appear in the mean-flowtransport equations. In Section 2 these fluxes wereexpressed through the introduction of 'effective turbulenttransport properties; thus in cartesian co-ordinates andtensor notation, the turbulent fluxes may be written:

157

OU- OU.+ l) (3.1-1)

X

and

<p,

The turbulent Prandtl number , a , may be assumed to beCD» Auniform is T.ost practically occuring flows (a value of 0.9for wall ílcwá is of ton assumed) -¿ud therefore the mainproblem becomes tnat of prescriba ng the turbulentviscosity, g,r .

When turbulent fluxes far outweigh viscous transports(as they d'j> in most regions of a turbulent flow), the localvalue of iju, may be expected to depend only on the fluiddensity and on the local state of the turbulence. Thelatter may be characterised in terms of velocity and lengthscales, Iv'j and L which are representative of the energy-containing parts of the turbulent motion. Thus, fordimensional consistency, M™ must take the form:

(3.1-3)

where C is a constant. Until x-ecently, the most generallyapplicable formula for U(T| available to the engineer wasPrandtl' s mixing length model. In numerous earlier reportsand publications the Imperial College team have provided

* The effective total viscosity, M f,:1 of equation (2.1.3)is the sum of u and um .

158

evidence of the models capabilities; in this paper, however,only its shortcomings are emphasised, the reason being thatnewer models now supersede it in respect of accuracy andgenerality.

In Section 1 the two main deficiencies of Prandtl'smodel were identified; they were that:i) iV'J was supposed to be proportional to the product

of the mean velocity gradient and the length scale;thus, whenever the local velocity gradient becamezero so did MI§ and, \vhat was more serious, so didPqp,T

ii) The length scale had to be prescribed and in mostcircumstances its value could be determined only byexperiment »

îîore recently prooosed models by Enmions [7] and Glushko [8]overcame the f-irsi: objection by interpreting jV'j as thesquare root of- the turbulence kinetic energy. The lattervariable was determined fiom che solution of a transportequation for the'turbulence ¿cinetic. ueryy, .'.. The seco.:3(and more serious) objection remained, however, because Lwas still prescribed by ad hoc algebraic formulae. As aconséquence, these energy models offered only smalladvantage's- over the mixing-length proposal. What was neededwas the provision of a second transport equation from whichthe length-scale distribution throughout the flow could bedetermined.

159

3.2 Existing models based on the solution of twoturbulence •cransport equationsThe models whose nature and capability are described

in this section provide transp -rt equations for two turbulen.ceproperties from whose solution the value of UT may be found»One of these equations is that for the turbulence kineticenergy. Por the second transport equation, the length scaleitself is the dependent variable which first springs tomind. However, since the turbulence energy is also to bedetermined, any variable z of the form k™Ln would be suitableand one choice for the constants m and n may offer someadvantage over another,

There have been several transport equations proposedfor z over the years. Including notable early contributionsfrom Kolmogorov [9], Chou [10] and Rotta [11] whose workhas provided guidelines for our own endeavours. Only withthe development of the solution procedures described inSection 2, however, has it been possible to test and refinethe equations to the point where they will enable accuracyof prediction in a range of circumstances»

The equations for z have been derived by a variety ofpaths, each cf which has included a mixture of intuitionand exact analysis. In practice, all possess a common formwhich in cartesian tensor notation may be expressed:

•»diffusion of z] -f z[--i- ( +

160

In order that the empirical constant's C^ and €2 should leadto accurate predictions both near to and far from walls, thediffusion term which has been left unspecified in (3.4),must take on different forms according to the particularmeaning ascribed to z. If the exponent, n in the definitionof z has the value -1, then the. simple gradientrepresentation:

Nett diffusion of z = -5—- [S rj§-] (3.2- 2)

is adequate. Por other choices of n, an additional term'!j •"' r.' .

must be added to (3.2-2).The equation for the turbulence kinetic energy mayv

be written in a form which closely parallels that of thea-equation:

x o ^ c ~ Z1/n(3.2-3)

Cquafciohs (3.2~1) and (3.2-3) both express the fact thatchanges ¿n 'fc and Jc occur through three agencies:> . . . •i) diffusive transfers which arise from spatial gradients

'..'•• • "in the turbulence properties , . . . . . . .

ii) inter actions between the turbulehce and gradients ^nthé- mean velocity field,

iii) direct action by the turbulence aloné.The solution of equations (3.2-1) and Q.2.-2) enables

to be found from equation (3.1-3) or rather, its

161

equivalent in tenus of the new variables k and z:

«îJSl:•* n 1/n (3.2-4)z

The turbulence model expressed through equations (3.2-1)to (3.2-4) contains five* empirical constants, C , C^, C2»a and a. . Their precise values will depend on the part-icular variable chosen for z, but in all cases the Prandtlnumbers a and afc may both be expected to be close to unity»Moreover, the values of the C's may be determined withinnarrow limits by drawing on the following well-establishedexperimental results:i) Turbulence behind a grid decays inversely with time

«7(which implies that C2 = - («¿n + m)).ii) Near a wall, in a two-dimensional boundary layer,

du.,(HJ, "gjr- / pk) is approximately equal to 0.3. It maybe deduced from the kinetic energy equation that Cshould thus be approxinately 0.09 (i.e* (0.3)a).

iii) For the same conditions as (ii), the mean velocityincreases logarithmically with distance from thewall. This enables C^ to be expressed in terms ofthe other constants.

Final tuning of the constants is made 'by computer optimi-sation of predictions for a range of experimental conditions.Table 3.1 lists, by way of example, the values which theconstants should take if z is chosen as k3 /3/L (Hanjalicand Launder [12]). This variable may be interpreted as the

* One more if n ¿ -1 162

the kinematic dissipation rate of turbulence Jcinetic

energy, e t, .since, with m = 3/2 and n « -1 the Icinetic-

energy equation (3.2-3) Recomes:

5x7

Table 3.1: Values of constants for the energy-energy dissipation model (k - e)

:.n^4i: :6;0t "

cl

Í.45

<?2

2:rO

•.flr ;;..:-•

. : . ' • ' • > :

I.I

:-,0^ ,

'•)'.!.:••) ..'':•

1.0

,The space of time that, has elapsed since these two-equation models became the-,sub^ect ,pf intensive scrutinyand development, is ^,9 short that the task of exploiting ,T«itheir full potential ,4s f,ar from complete. To date they ¡ ;have been us.ed extensively only for the prediction ofsteady, two-dimensional, boundary-layer flows. This -class. • j 1 1 • •of flows, however. > .embraces a sufficiently ¡wide range ?ofturbulence phenomena .for there to be no doubt that, when- r . ."• •'- . ~> •' ' • 'applied to the mqf.e general classes of elliptic and thfcôe-dimensional boundary-layer flows, these models ; will permit'' '.;" ' • ' -<•-••• t

a certainty of prediction sufficient for many design.purposes. . ."• '"' • i? •" ' •' • • •

Some impression of this widespread applicability may• o *" '.

by gained from Figs. 3.1 and 3.2. .These compare predictionsand measurement^ of me on velocity and turbulence-energy

163

profiles in two distinctly different kinds of turbulentflow: namely, a well boundary layer developing in a uniform-velocity free stream and a plane two-dimensional jet. Thepredictions} obtained with Hanjalie and Launder*s model(with the empirical constants given in Table 3.1) are insatisfactory agreement with the data.

It is perhaps instructive to examine what is theimplied distribution of Prandtl*s mixing length,

3ul 4-Lm s T/P iTx""' • As Fi9« 3.3 shows, the distributionsare quite different for the two flows. If the mixing lengthmodel were used to predict these flows, the specifieddistributions of mixing length (of which two common choicesare shown in Fig. 3.3) would have to differ accordingly.

Even among turbulent flows of the same type, with themixing length model one had to make bothersome changes toI»m-distributions to bring accord with experiment. For theplane mixing layer, the plane jet and the radial jet, forexample, the mixing lengths had to be taken as 7%, 9% and13% of the width of the respective flows. It is encouragingto contrast this disparity with the predictions of Rodi andSpalding [13] obtained by solving transport equations fork and kL. With the same set of constants this modelpredicted mean velocity profiles and rates of spread forthese flows within the accuracy of thé experimental data.Likewise, Ng and Spalding [14} have shown that a single setof constants leads to accurate predictions of both flow nearthe entrance of a pipe and that which occurs far downstreamwhere the velocity profile becomes fully developed. Withthe mixing length model, however, one had to choose the

164

maximum value of L to be 60% larger for the latterracondition than for the former.

The conclusion to smerge from the above comparisonsis that turbulence models wlrch determine MT from twotransport equations possess a degree of generality that isnot to be found in any simpler models.

3*3; Tur bu 1 ence_ mod els cur renit 1 y under de ve logmen_t»' "(a) ' Flpv/st a t low turbnl ence Reynolds numbers

" >, _•'.'-•The form of the two-parameter turbulence models givenin Section 3.2 is"not directly applicable to flow in theimmediate vicinity of a smooth wall where turbulenceReynolds numbers are low (jjtp/M < 30). Within this (usuallyvery thin) region, laminar viscosity exerts appreciableinfluence on the turbulence structure. Consequently, termswhich express this viscous influence must be included inthe transport equations for k and z and the "constants"which appear in these equations become functions of(UT/M) •

In the majority of circumstances one does not need tosolve the transport equations within this viscosity-dependent zone because, for a substantial region near thewall, (J.IT/M) is a nearly universal function of the normal-distance-Reynolds number, (p^v/V^* One raa thereforeimpose experimentally well-proven boundary conditions on

í ~"the transport equations at some position near the wall, butfar enough from it for the high Reynolds number form of theequations to be valid.

165

If, however, it is precisely the non-universalbehaviour of the sublayer which provides the crux of theproblem, then, for accuracy of prediction, the transportequations must be solved throughout the flow. Suchcircumstances arise in strongiy accelerated flow throughnozzles and in flow through pipes, particularly at lowbulk Reynolds numbers, where, through steep radial temper-ature gradients, there is a large variation of \i and pacross the viscous sublayer. The latter situation appearsto be that which prevails in projected designs for HighTemperature Reactors,

Already, substantial progress has been made indetermining the low-Reynolds-number form of the equations.Jones and Launder CIS] have recently completed a series ofpredictions of surface heat-transfer rates in stronglyaccelerated flows using an extended form of the k-eturbulence model. In Pig. 3,4 a typical example of theirpredictions is compared with experimental data and withpredictions previously obtained with the mixing-lengthmodel. The main point of interest concerns the variationof Stanton number in the region of strong acceleration.The acceleration leads to a decrease in the turbulenceReynolds number near the wall which in turn causes a rapidfall in the measured Stanton numbers. Further downstream,the boundary layer recovers from the acceleration and fora while the Stanton number rises. Predictions with themixing-length model display a quite contrary behaviour:over the initial part of the acceleration, a rise inStanton number is predicted and, when the acceleration ends,

166

the heat transfer rate falls smoothly. Predictionsobtained with the new turbulence model, however, faithfullyreproduce the measured behaviour*to) TurbulenjÇfî jnodels emplp- ring transport

equations for the turbulent fluxesIt seems likely that models which determine jju from

the solution of two transport equations will, for themajority of the engineer's needs, offer the best balancebetween accuracy and economy. There are certain flows,however, where it is desirable to take a more detailedaccount of the turbulent motion. Two examples of relevanceto flow in Advanced Gas-Cooled Reactors will be given:i) It is well known that, in fully-developed flow in

straight non-axisynunetric ducts, secondary motionsare present in the plane of the duct cross-section.Although these secondary velocities are usually only1 or 2% of the streamwise velocity, they may exertconsiderable influence on the heat-transfer ratesand friction losses 5.n *.î-~ dnct« The motions arisebecause the partitioning of the turbulence energyamong its three components varies asymmetricallyover the duct cross-section. Now, it is an impliedassumption of two-equation models that the individualturbulence intensities exert an influence which maybe accounted for by presuming them to be directlyproportional to the turbulence energy; for thisreason, the prediction of turbulence-driven secondaryflows cannot be properly encompassed within theframework of a two-equation model.

167

ii) Measurements in a variety of duct flows (e.g. References[16], £17-) have revealed that the turbulent shear stressmay become zero where the mean velocity gradient is zeroor vice versa - an effect which cannot easily beaccounted for with an effective viscosity type of model.Although in most circumstances this effect is of concernto purists only, in ducts composed of both smooth andrough surfaces, the disparity between surfaces of zeroshear stress and zero mean velocity gradient may besufficiently great for there to be consequent influenceson the wall shear stresses and heat-transfer rates.

To bring the above phenomena securely within the capabilityof prediction requires the provision of turbulence models whichdetermine some or all of the turbulence stresses, ujuî, by wayof transport equations similar in form to that for the turbu-lence kinetic energy. For the case of two-dimensionalparabolic flows, Hanjalic and Launder [14] have developed andtested an equation for the shear-stress component - u£u¿which is solved simultaneously with transport equations for eand k. Pig. 3.4 compares predictions obtained with thisaugmented turbulence model with experimental data of fully-developed flow between parallel planes with one smooth andone roughened wall. The predictions are in excellent accordwith experiments and display faithfully the disparity betweenthe positions of maximum mean velocity, zero shear stress andminimum kinetic energy. It is. of interest to note that theirshear stress equation (with - tTjjuJ replaced by S, forbrevity):

168

V*reduces to:

«r

when the effects of convection and diffusion of S surenegligible* Thus, in its simplest form, the shear-stressequation reduces to the constitutive relationship between

outS, UT and -T— adopted by the two-equation models ofSection 3.2.

Donaldson CIS], Her low and Hirt [19] and the ImperialCollege team are giving some attention to the developmentof turbulence models which solve transport equations notonly for the shear stresses but for the normal stresses,uT** and the heat fluxes ul<p as well. These models, it isremarked, do not need to make use of a formula for Uj inthe mean transport equations. The task of devising suchmodels is not a trivial one, for the greater the number oftransport equations, the greater the number of empiricalconstants to be determined and, for recirculating flows,the more challenging the numerical task of obtainingsolutions* It will thus be a year or so before thesemodels can be recommended for general use. To give anindication of their capability, however Fig. 3.5 showssome récent predictions by Ying and Launder* of fully-developed flow in a square sectioned duct. It is seen that

• The constants C~ and <?« take the values 2.8 and 0.9respectively.+ Private communication

che inclusion of terms expressing the influence of thenormal stresser, leads to satisfactory predictions of thesecondary flow and of its effect of secondary flows on theoverall friction in the duct.

3.4 Some proposals for research on turbulence models(a) Application of existing 2-eauafcion models

to elliptic flowsThe two-parameter turbulence models outlined in Section

3.2 have been devised in a form which is applicable equallyto elliptic and boundary layer flows. Their use, however,has been confined almost exclusively to boundary-layer flows- a seemingly paradoxical situation since it is especiallyfor elliptic flows where one needs a transport equation todetermine the distribution of turbulence length scalethrough the flow. A most urgent task is therefore theemployment of these models for the prediction of heat-transfer processes in flows governed by elliptic differentialequations.

It may be helpful to give one example of the kind ofresearch that is here in question. Heat transfer from thefuel pins of Advanced Gas-Cooled Reactors is enhanced bymachining discrete ribs around the outer surface of thefuel-containing tubes over which the coolant gas passes.The search for the optimum rib profile, balancing the con-flicting demands of high heat-transfer rate and lowfriction losses, has hitherto been based entirely on

170

experimental research. However, with the aid of a 2-equation turbulence model, the elliptic flow program ofReference [2], and a modest expenditure of computing timeit would be possible to predict the heat-transfer perform-ance of a particular rib profile.

The solution domain which would be chosen for thecalculations is shown in the sketch. In the streamwise

HI

x/,B

^T7- / t>' / / / / / / / /C

direction, it extends over one complete rib profile andreaches far enough from the wall for flow conditions to beconsidered uniform along the boundary AB (in practice thismeans about four rib heights from the wall). As is indicated,the distribution of grid lines should ideally be chosen sothat there are many grid nodes near the rib surface wheretemperature and velocity gradients are steep»

The rib performance will be markedly affected bytemperature and velocity profiles in the immediate vicinityof the surface where turbulence Reynolds numbers are low.The two-equation turbulence model employed should thereforecontain the terms expressing this low-Reynolds-numberinfluence on the turbulence structure.

For the case where the heat flux along the tubesurface is specified, solution of equations for the vorticity

171

stream function*, stagnation enthalpy and for two turbulenceparameters would yield predictions of th=? tube wall-temperature distribution and the nett frictional force onthe surface of .the tube. Confidence in using the predictionprocedure could be established by considering first the caseof square ribs for which detailed experimental data areavailable. Thereafter the most fruitful aspect of theresearch would begin: namely the exploration of theperformance of rib shapes which hitherto had not"beensubjected to experimental scrutiny.(b) Extensions to existing __2-equa t ion, model s

When the motion of fluid elements, is substantiallyconstrained by body forces arising, for example, throughcentrifugal, Coriolis, buoyancy or magnetohydrodynamiceffects there will be a corresponding influence oh thestructure of the turbulent motion. A worthwhile researchundertaking would, therefore, be the inclusion of terms inthe turbulence-transport equations which simulate theseinfluences. With such terms included, a two-equationturbulence model should be able to take satisfactoryaccount of the turbulence development in Seeker's isotope-separation apparatus referred to in Section 2.(c) : Remarks on research on higher order model s

While it is possible to solve transport equations forany number of turbulence properties, the computing time -and hence the cost must increase at least linearly with thenumber of equations. It is, therefore, désirable to use

* and., for spirally wound ribs, the swirl-velocity equationas well.172

the simplest turbulence model which will yield predictionsof acceptable accuracy. It' is for this reason that we havegiven prominence to research on two-equation models for, webelieve, this level of closure will be sufficient for manyproblems.

Of course, as we have mentioned in Section 3.3, itis known that the satisfactory prediction of certain flowphenomena requires the provision of more detailed turbulencemodels. In view of the considerations of the previousparagraph, however, it seems that the current level ofresearch activity in the development of multi-equationturbulence models is sufficient at present. When, withinthe next two years, the basic forms of these models areestablished, there will then be a need to apply and refinethem in just those flows where two-equation models havebeen found to fail, in some respects, to bring the desiredaccord with data. At this stage there would appear to bea good case for a more widespread co-operative researchprogramme co-ordinated and assisted by such organisationsas the IAEA.

173

4* ConclusionsThe paper has reviewed the nature and capabilities of

procedures for predicting convective transport processes inflows such as those which occur in gas-cooled reactors.These procedures have two principal ingredients: a schemefor the numérica], solution of the governing transportequations and a physical model for the determination of theturbulent fluxes of heat and momentum. In the course ofthe paper we have examined both these aspects, dealing withprocedures which are currently available and those whichare still under development. Our conclusions may besummarised as follows:1, Currently Avallab_ler Procedures

Well-established numerical procedures now exist forsolving the equations governing the transport of heat,mass and momentum in general axisymmetric flows. Forthe prediction of turbulent flows, the usefulness ofthese procedures has been enhanced by the provisionof turbulence models which calculate the effectiveturbulent diffusion coefficients from the solution oftransport equations for two turbulence properties.These models possess a degree of -universality whichis far superior to any that were hitherto available.As a result of thesje innovations, the heat transferdesign of many pieces of equipment can now profitablydravL_pn the outcome of computer predictions tosupplant much costly experimental testing»

174

2» Procedures under DevelopmentWork is now well advanced on the provision of finite-difference procedures for the solution of tiroe-depend&nt axisymmetric flows and of 3-dimensionalboundary-layer flows in i*ucts. Among the importantproblems which fall within the capabilities of thelatter procedure is the detailed prediction of heat-transfer rates in the developing flow through an AGRrod cluster.In parallel with the above research, substantialprogress has been made in devising turbulence modelswhich take a rather more detailed account of theturbulent motion than do existing procedures» Thesewill find application in predicting the effects ofturbulence-driven secondary-flows on heat transferrates and those (relatively few) other phenomenawhose prediction cannot be satisfactorily achievedwith the existing two-equation models»

Finally, it is remarked that, with mutual co-operationin research and a sufficient supply, of resources, the siibjectof single-phase convective heat transfer may, by the endof the decade, achieve the same secure' analytical status as .is currently enjoyed by the subject of heat conduction*

175

References1. PATANKAR, S.V. and SPALDING, O.S. : "Heat and Mass

Transfer in Boundary Layers" 2nd Edition, Morgan-Grampian, London 1970.

2. GOSMAN, A.D., PUN, W.M. , HUNCHAL, A.K., SPALDING, D.B.and WOLDFSHÏEIN,. M. : "Heat and Mass Transfer inRecirculating Flows" Academic Press, London 1969.

3. RUNCHAL, A.K. : "Predictions and experimental resultsof flow past a sudden enlargement in a circular pipe"Proc. Internal Seminac on Heat and Mass Transfer inRecirculating Plows, Herceg Novi, Yugoslavia 1969.

4. MITCHELL, N. : Unpublished data; results quoted inReference [2].

5. BECKER, E.W. : "The Separation Nozzle Process forUranium Enrichment" Report KPK 1002, Kernforschung-szentrum, Karlsruhe, June 1969.

6. BECKER, E.W., BIER, K., SCHUTTE, R. and SEIDEL, D. :"Separation of Isotopes of Uranium by .the SeparationNozzle Process" Angewandte Chemie, Vol. 6, 1967.

7. EMMONS, H.W. : "Shear Plow Turbulence" Proc. 2ndU.S. Nat. Congress App. Meen., ASME 1954.

8* GLUSHKO, G.S. : "Turbulent Boundary Layer on a PlatPlate in an Incompressible Fluid" Izv Akad. NaukSSR, 1965.

9. KOLMOGOROFP, A.M. : "Equations of Turbulent Motion inan Incompressible Fluid" Izv. Akad. Nauk SSR, 1942.10. CHOU, P.Y. : "On Velocity correlations and the Solutionsof the Equations of Turbulent Fluctuation" Quart.

Appl. Math., Vol. 3, 1945.11» ROTTA, J. : "Statistische Théorie nichthomogener

Turbulenz" Zeit. f. Physik, Vol. 129 and Vol. 131,1951.

12. HANJALÏC, K. and LAUNDER, B.E. : "The Prediction ofStrongly Asymmetric Boundary Layers" Imperial CollegeMech. Eng. Dept. Report, in preparation.

13. RODIt W. and SPALDING, D.B. : "A 2-Parameter Modelof Turbulence and its Application to Free Jets"WSrme- und-Staffübertragung, Vol. 3, 1970.

14. NG, K.H. and SPALDING, D.B. : "Prediction of 2-Dimensional Layers on a Smooth Wall with a ?-equationModel of Turbulence" Imperial College, Dept. of Mech.Eng. Rep. BL/TN/A/25, 1970.

176

15. JONES, W.P. and LAUNDER, 8.E. ; "The Prediction ofLaminarisation with a" 2-equation Model of Turbulence"Imperial College, Mech. Eng. Dept. Rep. in preparation,1970.

16. HANJALIC, K. and LAUNDER, B.E. : "Fully Developed Flowsin Rectangular Ducts of Non-Uniform Surface Texture"Imperial College, Mech, Eng. Dept. Rep. BL/TN/48,1968.

17. LAWN, C.J. and HAMLIN, M.J. : "Velocity Measurementsin Roughened Annuli" CEGB Nuclear Laboratories Rep.RD/B/N1278, 1969.

18. DONALDSON, C. du P. :' "A Computer Study of anAnalytic Model of Boundary Layer Transition" AIAAPaper No. 63-38, 1968.19. HARLOW, F. H. and HIRT, C.W. : "Generalised TransportTheory of Anisotropic Turbulence" Los Alamos Sci. Lab.

Rep. LA 4086, 1969.20. KLEBANOFF, P.S. : "Characteristics of a BoundaryLayer in Zero Pressure Gradient" NACA Rep. 1247, 1955.21. BRADBURY, L.J.S. : "The Structure of a Self-preservingTurbulent Plane Jet" J. Fluid Mech., Vol. 29, 1967.22 MORETTI, P. and KAYS, W.M. : "Heat Transfer throughan Incompressible Turbulent Boundary Layer with.Varying Free Stream Velocity" Int. J. Heat and MassTransfer, Vol. 8, 1965.

177

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179

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180

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187

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IN S^UAftg DUCTS»

HEAT AND MASS TRANSFER IN HWGCRTYPE A-l FUEL ASSEMBLIES

Vaail KrettSKODA Concern, Nuclear Fbw.ec* Plant Division,

Plzeñ, Czechoslovakia

Gas cooled fuel assemblies of rode type designed for usein Czechoslovakia!! heavy water reactors are characterized byrelatively high intensity of heat flux and extensive finningof heat surface* High intensity of heat flux gives rise, besidethe fining, to an intensification of fuel assembly cooling* Theoriginal concept of fuel assembly was based on large number ofsmooth rods (up to 200) with fuel diameter of 4 mm* Relativelyhigh coolant velocity in "smooth" fuel assembly had an unfavorableinfluence on dynamic stability of the fuel assembly. As a con-sequence of experimental investigations, the fuel diameter hadto be increased from 4 mm to d, 3 mou Such a change of fuel dia-meter gives rise to use of fuel rod with finned surface.

In. paper the results of experimental investigation of pres-sure drop coefficient, heat and mass transfer coefficient, velocityand temperature distribution in bundles of smooth and finned rodsare described. Uniformly heated rods represented model of eithercentral part or full cross section of HiïGCR type fuel assembly.further, some results of investigation, on other types of fuelassembliea carried out by collaborating laboratories are presen-ted.

The questions concerning a heat removal from fuel assembliesof gas cooled power reactors are very important due to relatively

191

low level of a heat transfer coefficient. One of the main featu-res of Hïra type A-l represents possibility of achieving highspecific power density and this fact demands the. structure ofplant having high unit power, however the sufficient fuel heatremoval must be guarr anted. The nuclear reactors heat powerincreasing leads, to an improvement of economy factors and isdesirable from the point of view of reactors to be competiti-ve» The increasing of reactor unit pov/er gives rise to newrequirements concerning heat removal from surfaces, from the pointof view of efficiency, heat transfer intensification, productiontechnology and compactness*

.The analysis of the state of art of theoretical and experi-mental works concerning rod bundles cooled in-line specifiednecessity of further improvement of the theoretical solution,of flow and heat transfer matters /31/ and experimental inves-tigation of pressure drop and heat transfer characteristics andthe investigation, of the flow picture in smooth and finned rodbundles /23, 24» 27 + 30/« There is- a large amount, of theore-tical and experimental works A + 20/, studying pressure dropsand heat transfer 'in smooth rod bundles, however-, relativelyof a few works concern the problems of the pressure drops andheat transfer in finned rod bundles /21 + 30A The analyticalsolution in a such complicated channel geometry is nearly im-possible» The necessary experiment for our fuel assemblieswere carried out on different types of the rod bundles, whichwore specified on the basis of future concept aspects:* Further,.some experimental results are described.

Problem of fuel 'assembly pressure drop plays an importantrole particularly in gas cooled nuclear reactora because ofconsiderable influence of pumping power on total efficiencyof this typ of nuclear power plant» From pilot vject of first

192

Chechoclovakian nuclear power plant fuel assembly, whichconsists of bundle of rod fuel elements, follow main featurescf investigations'in this field. Both maximum allowable fueltemperature, and high power density leads to considerable exten-sion, of heat transfer surface» Beside the extension of fuelsurface itself» the use of cladding material with high coeffi-cient of thermal conductivity enables the extension of heattransfer surface by intensive finning» A comprehensive researchconcern ing hydrodynamic parameters of finned rod bundles was.carried out* Main goal of investigation was to determine basicparameters of finned heat transfer surfaces, with regard to itsuse. in fi?GCR*

The motion of viscous compressible fluid for noni-isothermalflow may be described by means of fundamental differential equa-tions » the equation; of motion, the equation of continuity andthe energy equation* further we have to apply the equation ofstate and equations which characterise dependence of thermal pro-perties of coolant on pressure and temperature» These fundament-al equations in non-dimensional, form represent a closed systemof 9 aquations for 9 unknown parameters* Solving thia system ofer.uat.".ons and boundary conditions one should derive relation

<*•

Eu « e. Prt , , — ' «y. ftr» CD

lUperiaental* investigations were carried out w:.tn regard to va-riable- parameters from equation (1) except of ] s carnet er whichraprefonts the influence of temperature coefficient*

In order to assure direct comparison of measurement to thatof other authors, Uuler nucb9r was replaced by coefficient offriotion Ji derived from, relation

(2)\ PC» rtty193

criterion Cl) follows the range of both fin and 'únalep¿r&aetere under invest i gat ions» ¿ith regard to technology ofÍU31 element cladding the main research was concentrated onhelical fins* The fin pitch influences turbulisation of theflew *nd intensification of the heat transfer along the fuelelement as well, eo that the mentioned parameter, which iffcharacterised by the angle of fuel element axis and the pla-ne of helical fin, was, investigated in large range*

ilg» 1 shows as an example measured values of friction coe\~ficie-.it as depends on 3e number and different fin pitch for onetype of fins.

¿ig. 2 a 3 show the influence of helical fins with differentïiu:ûbsr and height of fins on relative increasing of friction fas-tor in comparison with that of straight fins. There is evidentthat the influence of helical fins with given height and numberci f 1:3 takes place for the case of fin pitch being lesa thafc

to the case of friction factor one should deriver.u criterion.

(3)

were 'carried out on tv/o types of finned rods/27| 23, 29» 20/ which were choseu a» most convenient ones fromtha psint of view of further development of fuel assembly*

First type cf finned reds has 3 high fins which play doublerole: extension of heat. transfer surface and spacing of fu&l

second one has 12 an 15 fins low fins respectively;at the sane timg have special grids.

roat transfer expnriuentsvvere carried out on models v;hich1; %:. ï-aprsssnted central part of actual fuel assembly. Number ofdi-?i*tr»nt types of rods iras cut comparing to that of hydrodyno:r«icir.vestijationo. Fi¿» 4. shews cross sections of 2'> mai. o.d. and?•> an e.d» bundle respectively.

of heat transfer coefficient v>re based on the194

equationA/e • de

(4)

Thermal properties, of air were related to average parametersin measured section» Equivalent diameter in «ul bundles was cal-culated from, the whole wetted perimeter including fins and freeflow passages; of the bundle* .-.j

Ifutual comparison of finned surfaces under investigationis based on the use of power coefficient, which represents theratio of the energy output to frictional power output, relatedto the unit of surface per 1°C

*••£... t»where

/ '• rjAf.¿ L G

Roda with three fins

Fig. 5 shows thé friction coefficient & for the case ofdifferent fin pitch in bundle of 7 rods with 3 fins placed in26 mm i.d. channel . There ia evident -that in the fin pitchrange oo> to 600 am. & « const, and the curve for large 39 numbersfollows Srenkel relation for circular tube taking into accountthe influence of roughness

The friction coefficient increases- with square order forthe cas« of fin. pitch s * 600 mm. Such increase can be described

195

a*

and above mentioned relation is valid starting from the values s 600 mm which corresponds to the angle of fin pitch /0 * 2,4°«Fig. 7 shows dependency Nu against Re* Heat transfer coefficientin. the range a = «> 4 600 is constant. The result is similax»to that of pressure drop coefficient* Measured values can beexpressed analytically as

/* (8)

Relation (8) differs from, that for heat transfer coefficientcalculation in smooth circular tube having the coefficient ofmultiplication approximately 15% lower. Lower values followfrom the use of equivalent diameter calculation in which thewhole fin perimeter is considered as a part of wetted perimeter*For s = 600 mm. the increase of heat transfer coefficient takesplace. The increase is linear ( taking into account possibleinaccuracy of measurement ) and can- be approximate by analyticrelation

A/t/c * Aft/eo I 1 +0,052 (A - Zifn (Q\9 »•"•* • V«7/

Optimum fin pitch waa determined using power coefficientof heat transfer surface. Power coefficient is linear functionof the pumping power-* In the range s = oo * 600 mm the powercoefficient is constant, for s - 600 mm the power coefficientincreases.

Î2Siï - FiS* 8 shows frictioncoefficient of six bundles of heated rods with 12 and 15 finsrespectively placed in 70 mm. i.d. channel with s » 550 mm* There

196

la evident the influence of fin number on the friction coef-ficient* Values, of measurement in the case of 15 fins aregenerally lower than those of 12 fins* Such a result takesplace due to the flow in intermediary fin space* In the caseof heat transfer surface with greater number of fins the .inter-mediary fin space decreases, the flow velocity decreases, sothat the viscous sublayer increases*

On the base of a comparison of measured friction coeffi-cient with circular tube formula involving actual roughnessinfluence allows that the measured curves have contradictorybehaviour than calculated ones. The friction coefficientcalculated in accordance with above method is increasing incontrary to actual course* Such a behaviour is typical forall curves* The number of fins has the same influence on theheat transfer coefficient as it had on the pressure drop coef-ficient. Fig. 9 shows Nu number against Re number* Rods with1$ fins have 1% lower value of Nu number than those of 12fins. In the case of the bundle of 21 rods the influence ofnon-uniform fuel cross section to free flow passage ratio isevident* The values of heat transfer coefficient are lowerthan those calculated according the analytic formula, probablybecause of the fact that the nonuniform rod distribution givesrise to a flattening of the velocity distribution in largeflor area and consequently larger part of a coolant is pas-sing through it»

The influence of fin pitch on hydrodynamic and thermal para-meters of rods with low fins was investigated on four bundles of7 and 6 rods in 36 mm: i*d* channel* Fig* Ua and lib respectivelyshow the heat transfer coefficient and the pressure drop coeffi-cient against the angle of fin pitch* The values of both coeffi-cients are constant; in the range of s * «e + 300 mm* In the ca-se of s - 300 mm (angle of fin pitch ft » 3°) both heat tran-sfer coefficient and pressure drop coefficient are increasing*

On the base of said analyse of geometrical variables thegeneral relation for heat transfer coefficient and pressure drop

197

coefficient calculation were found.Pressure drop coefficient can be calculated as follows

-*(10)

Equation (10) can be completed by relation which characterisesinfluence of fin pitch in the case of a * 300 mm

*s » «&« f ' * *«*- *>*(/*-*) C*J (n)

vâiereCf « $OS5 - f^p Cr * 1.65 rods with 12 fina

rods with 15 fins

The following expression is convenient for heat transfer coef-ficient calculations

4?Re • Pr

This expression is completed by following one which considersthe influence of s * 300 mm

- 3) (13)

whereCu * £ /3 • /o"J Cr ««?OV • X>~* ods with 12 fins

Cif •$& * to"* C¥ .• */5- il9"3 rods with 15 fins

The expressions given above are in good accordance withexperimental measurements. Fig* 12 shows mutual comparison ofpower coefficients corresponding to all bundles under investi-

198

gâtions «.In order to find the influence of finned surface geo-

metry and roughness on basic hydro/dynamic and heat transferparameters the investigation with flat models «ere carriedout /32, 33, 3 4/. The same result was obtained: the closerfins, the worse heat transfer coefficient. Fig. 13 and 14respectively show the results of heat transfer and pressuredrop measurements. The comparison of different finned annuli

, . 3* .from the point of view of power efficiency was carried outby Malak /35/« The detail results concerning friction coef-ficient and heat transfer coefficient were obtained in thet « Tcase of channel with o.d. 81, 70, 3 and 64 mm having insidelongitudinal fin* One of the main author's conclusion is thatthe Re number loses its role of determinating criterion» forthe case of closely finned heat transfer surface.

PATTERNS

Heat removal from nuclear fuel assemblies consisting ofin-line cooled rod bundles is specified by certain peculiari-ties which make the calculation more complicated that» usually,for example in the case of ordinary heat exchanger:

a) In the fuel assembly the heat flux distribution withlimited maximum temperature is given. In the case ofinsufficient cooling of some fuel element the overhea-ting could take place and consequently the failure ofthe whole assembly is more probably;

b) Replacing of failed fuel assembly is much more compli-cated and expensive.

From said above follows the importance of detail knowledgeof flow and temperature patterns in rod fuel assembly foroptimaliaation of hydrodynamic and thermal design and forachieving of reliable and safe operation.

199

Design of fuel assembly included invest5.¿rtion of velocitydistribution in the bundles of smooth rods. *'•***) object of the-se experimentswas to find the influence of b- allé parametersand spacers on the velocity distribution in i'ael assembly crosssection /3l, 36A Fig. 1? shows the form of valocity field inradial direction before and beyond the spacer. Fig. 16 showsthe velocity distribution across the bundle. Prom both figuresthe influence of non-uniform rod distribution in differentparts of bundle on the velocity distribution is evident* From,the distortion, of velocity distribution caused by grids followsthat the cross flow takes place in the fuel assembly. If oneassumes the influence of turbulent diffusion, there is clearthat the partial mixing of fuel assembly flow exists and consi-dering of this mixing in calculation might have a favorableeffect from the point of wiew of local overheating coefficient*That was the reason for carrying out investigation concerningthe flow mixing in smooth rod bundles /31/* As a criterion ofmixing phenomena the eddy diffusivity coefficient was used*The mentioned coefficient was measured using, method of scalar-quantity propagation from the point source in uniform flowwhich could be described in cylindrical coordinates by theequation

wec .- fj..jBL./rf£.L«* ] fl410* M r Or I Or/ 9g* J i1*'Assuming €0 , Q and W constant, the solution of equation(14) is as follows

where S « r2 + ¿r*After simplification and transformation to logarithmic

form we obtain

200

*•If one determines concentration of scalar quantity

for some values of radius and plots' the diagram of function£n(Sc)*f (&-*), the gradient of line is equal to - j£-

and the eddy diffusivity coefficient £¿ can be determinedin a such way*

ïreoâ 12 (CFgClg) as. a scalar quantity source was usedapplying above method to the rod fuel assembly investigation*After Freon injection into main, air flow the concentrationof it on certain distance from the point of injection wasmeasured» ?ig. 17 shows curves of constant concentration ina part of the bundle for one case of Freon injection* Aftersubs tract ¿on of concentration marked by dot-and-dash linesthe obtained values were processed 'by the use of equation(16) end the average values of eddy diffusivity coefficientwere found* In this particulary ease the eddy diffusivitycoefficient reached.the value of 1,16.1CT5 cm /sec. Knowledge,of £0 and gas temperature difference in adjacent flow secti-ons of bundle enables to find (if t6 « ¿y ) the heat fluxesbetween sections and so the influence of flow mixing on fuelassembly temperature field*

Experimental investigation of temperature field of thecoolant in smooth rod bundles was carried out by means ofelectrically heated fuel assembly model with 37 rods /3lAThe model was placed in open air loop and tested up to Re »« 2*10?* Fig. 18 shows the measurement results. There isevident that the generated heat from c en train row of rods,is concentrated in the very, neighbourhood of heated rods andonly a small part of heat is transferred in adjacent sections*After superimposition of. temperature fields originated due toa local rod heating we obtain the temperature field which isvery naar in fact to the actual temperature field when overallheating of the bundle*

201

There was carried out detail theoretical calculationof ¿low and heat transfer in square and triangular arrayof smooth and finned rod bundles respectively. The resultaare presented in /31A

The local parameters of fins and flow sections of rodbundles were investigated by means of enlarged models /32ARelatively considerable differences of local values of shearstress in circumferential direction of the fin and the maincross section were found* Results are shown on fig* 19» 20*

Prca the point of view of safe and reliable operationof nucloar reactors fuel assemblies the detail informationconcerning the temperature field in fuel rods is necessary.for two reasons:

- there is given the maximum allowable temperature,- mechanical stress of the rod due to temperaturegradient could effect the long-term strenght offuel rods.

In the case of gas cooled reactor a, considerable distor-tion of temperature field in the spacers area is taking pla-ce. Chore was worked out the method of t&iapei tare fieldsimulating by means of electrically heated ro<;s with followingmathematical treatment which enable to find the temperaturefield in actual fuel element rod /14, 29, 31/« In the spacersarea the substantial intensification of heat transfer wasfound end there is possibility to utilize this effect. Fig.21 shows results of temperature field measurements expressedby means of diaensionless îiu number as function of dimension-less distance for some types of spacers. Detail informationsabout the method of simulation of both steady and unsteadyfuel rod temperature fields by the means of eletrical analo-jgy are given in /37, 31A

202

CONCLUSION

The hydrodyñamic parameters measurements carried outon iiffortra. t¿/?f-3 of fuel s sonblies enabled to obtain théclear picture of ¿low in ¿uel rod b.unl s snd estimate theinfluence of heat transfer surface parameters under investi-gation from the point of view of hydrodynazaic and heat transfer<

The calculating formulas valid for given heat transfersurface geometry were found, analysing these relations onecan conclude the conventional equation for smooth rod bundlesusing dit as the characteristic dimension cannot be used. Ap-plication of Freon method enable the investigation of flownixing in complicated fuel assemblies* There is necessary toknow detail flow picture in fuel rod bundles from the pointof view of the optimisation of the fuel assembly as a whole*Future development in this field is desirable for the calcu-lating methods to be improved.

Besides that, the method of simulation of temperaturefield in spacers, area has been worked out and experimentallyproved* Such a method seems to be very useful from the pointof view of fuel rod temperature field in various fuel assembly*arrays to be found.

The author wishes to express appreciation to his col-leagues, in particular to Ing. J. Kajer, Ing. K. Stëpének,Ing. J. Ylëek and Ing. P. Weber for their assistance andvaluable remarks.

203

SYJ30LS

Ag/m3/e

EFGL

*

oC,

4

A/deg//m2//kg/s//m/

NeN

0PavQ

APAPJar33c(Té

AT/

Ai/m2/

/m//N/m2/Ag/8//N/m2//ffi//kg/k3/AM//m2//deg/

/deg//m/s/

/m//W/A2deg//degrees/

mass concentrationequivalent diameter, 4 F/0energy coefficientfree-flow area of the bundleair mass flowlength of the working sectionnumber of finsnumber of rods at the given radius ofthe bundleelectric power output in the workingsectionfractional power output from the unitof surfacewetted perimeteraverage pressureinjected quantity of Freonpressure drop in the working sectionroughness of the surfacedensity of coolant in the working sectionfin pitchheat transfer surfaceaverage -temperature difference betwen thesurface and the coolant, (tw - tay)average surface temperature of the bundleaverage temperature of the coolant in theworking sectionair temperature rise ir. t... v/orking sectionflow velocitydimensionaless temperature, T .-

VTocoordinateaverage heat transfer coefficientangle of the helix of the finstotal rod cross section /to channel crosssection ratio

204

Jt - coefficient of friction of the bundleJlv A'/mdeg/ - thermal conductivity of air%0 - efficiency of the heat transfer surface,£ /a2/s/ - eddy diffusion coefficientBi - Biot number2u - Euler number ,Nu ~ Nusselt2»r - Erandtl numberHe - Reynolds number,

/!/ Grimble H.E., Report AECD - 3975, 1954/2/ Wantland J.L, : Compact Turbular Heat Exchangers.A3C- Report TID, 7529, $25, 1957/3/ Miller P. et., A.I.CH.3. Journal, 2 N&2, 1956/4/ Dingee: Reactor Heat Transfer Conference, New ïork, 1956/5/ tnternational Development in Heat Transfer, Boulder,London III, N 63, 1961 •» 1962/6/ Hoffman H.lV. : Heat transfer with axial flow in rod clustersReactor Heat Transfer Conference of 1956/I/ TourneauB.: Trans. ASMS, 79, N e, 1751, 1957/3/ Sutherland V/«A»: Heat transfer in parallel rod arrays',C.2.A.P. - 4637, 1965 'and Transactions of ASMS, 13, 1965/9/ Injatov A.I* - Teploenergetika 3, 1957AO/ Subbotin V.: Atomnaja energija 4, K- 8, 1961/ll/ Pirsova 2.V.: KnergomaSinostrojenie 3, 1964, IF2 N 5,17, 1963/I2/ Eifler '.7., Kucl. 3n . and Design 5, 1967/13/ PTeaasr K. : WTariteubergang und Druclcverlust an Reaktorbre-nellenent in "Fora langsdurchstromten Rundstabbundel,iTul-430-Rb, Jülich 1967/M/ Ka¿op J., apráva &CCDA ZJ3, Ae 1175/Dok/15/ Dcissler K., Heactor Heat Transf. Conf. of 1956,Report H-31/!»>/ Bulëjev N.I., Sb. TeplopereüaSa, AÍí S33R, 1962A7/ Ibraginov, At. energ. 21, 101, 1965/IB/ î/iôcing S. : Analysis of Fluid Flow and Heat Transfer ina Triangular Array of I-ara?.l3l Heat Generating Rods,Nucí. Eng. and Design 4, 1966

205

/19/ Rapier A.C.: Calculation of Velocity Distributionsin Hod Clusters, Journ. &ech. Eng. Science, V.7,196.5/20/ Disrayer O.S., Nucí* Ss. and Eng., 25 343-*358, 1966/21/ Klitin a j.:-Teploonergetika 5, 1964/22/ Sejnina A.V., Sb. 2idkije metally, Moskva 1$67/23/ Kotrnoch J. Stepanek K., Zpráva Skoda ZJE, Ae 0557A>ok/24/ Stursa J. zpráva SVÜSS 68-05012/25/ Inst. Mech. Engineers and the British Nuclear EnergyConf», London 1961/26/ ¿ubbotin V*: Atomnaja energija 9,4,1960/27/ Krett V Sokol J., správa Skoda ZJB, Ae 1126/Dok/23/ Krett V., Intenzifikace pfestupu tepla v proutkovempalivovém olánku, kandidátská diserta ní práce,brezen 1969/29/ Krett V. Sokol J., zpráva Skoda ZJE, Ae 1776/Dok/30/ Iu?ett V. Sokol J., zpráva Skoda ZJE, Ae 1777/Dok/31/ í/Iouelov¿ní terœodynssxick ch jevû v aktivní zonerychl ch reaktorûr CSSH-SSSR Konference 2.1970,Babylon, ÔS3H. (Sbomik OISJ? Zbraslav)/32/ J. 3inoriek. Základni teraokinetické problémy palivov^chSlanlcu teslcovodnich reaktorû chlaaen ch plynem» Sbor-nik OÏ3J? Zbraslav. Konference o palivov ch filáncíchv Piesianech./33/ K. í báíek, • Zpráva SVîJSS 70-05003/34/ J« Stursa, Zpráva SVÓSS 6.5-C5030/35/ J. i-lalák, Správa dJV 21S7«R.T./3o/ J. Kotrnoch, X. St§pánek, Zpráva SKODA Ae 697/Dok/37/ ¿* Bíca, Správa SVÚSS 68-05026

LTi'T O!? ILLUSTSi.TIOMS

Fig* 1 ?c-de£ure drop coefficient of six rods bundlerig» 2 Influence of fin height on pressure drop coefficientrig- 3 JDifr.uonea of fin number on pressure drop coefficientFir:, 4 Cross section of some bundles

5 ijeper.deney of pressure drop coefficient on Reynoldsnucbsr (7 rods 3 fina bundle o.d. 36 mm)6 ispsr.aency of and Ku on the angle of helix in 3 r*ods

206

7 The dependency of the Nu on the Re for various.•••• fin pitch of 7 rods 3 fins bundle,8 Coefficient of friction of 0 70 am finned rodsbundle model.9 Dependency of the Nu on the Re for the 0 70 mamodel.10a Dependency of pressure drop coefficient on therod cross section -./tec channel cross section ratio

Fig, lOb Dependency of the Nu on the rod cross section/ tochannel cross section^ . . ._. ._ 'P5.g, lia. Dependency of pressure drop coefficient on the fin'

lib Ja pendency of the Nu_on bj § fin. pitch angle{# 36 cía model) ~~T~"Fig. 12 Po:ver coefficient of different finned surfaces(N « 500 V//m2)F;Lg. 13 Heat transfer on finned plates /33/?ig. 14 Jsper encjT ftu and on -fin pitch/-t¿, He ~I«'iS> 13 .Ixod.. bitadle velocity distribution in radialdirectionTig. 16 "Kod bundle velocity distributionPig, 17 Preon concentration due to: injection in the point "A"Pig* 18 Temperature field of coolant (measured values) inthe c,YT¿r.étry plane due to both full heated bundleand partially heated one.Ti¿* 19 i;opjr.ue cy of shear stress on the angle /32/~i£« '¿0 Velocity distribution in .fanned- rod bundlesubchanicl '' . ,lî'ig, 21 Variation of heat 'Transfer.. cje-efíícieKt in spacers

207 i-

PARÁ»£T£RS Of ft/NOUT

01-.J* .1 -r?A-It

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CMAV£L CIAMSTSR

NUfISSff OF POOSfíODfue eorroft ûf FIN

e s

p.;r,í5!?z3 DIÎOP r,^ o? six

tos

PAfiAMfTMS OF M£ASUR£fUNTREYNOLDS NUMBER tf*/u*CHANNEL OlAf1£T£ff M&M,NUMBlft OF ffOOS(too tuAfierea ATTH£ BOTTOn Of fit*

FM JMCKMfSX"

0,3 0,9 í 1,1

PIG.2 INFLUENCE OF FIN HEIGHT ON PRESSURE DROP COEFFICIENT

6of

REYNOLDS

NVMSSfí OFftODSWû OlAM£T£ff ATTH£ BOrrOM OF FMft A/FM THICKNESS

NUMBER OFFINS

38.S*

02 o,3 qs <tt qr o¿ 0,9 1 tt /> %*«• ¡80 SO S* 40

FIG.3 INFLUENCE OF FIN NUMBER ON PRESSURE DROP COEFFICIENT209

FIN PITCH 3 FINS RODe» » 80 * 1200 am

7 HODS, 12 FINS 12 FINS RODs a 80 + 1300 mm

Ê SODS, 15 FINS 15 FINS ROD8 * 80 * 1300 £22

FIN PITCH e » 550 «m19 RODS, 15 FINS

24 RODS, 12 FINS

FIG.4 CROSS SECTION OF SOME BUNDLES

210

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Txg.5 DSJPSNJBKWCy OF PRESSURE DROP COEFFICIENT ON RSÏNOLDS Kü:¿3E3(7 ROIS 3 PIUS BUKDLS' o.<ï. 36 ara)

o ^ t ^ e â f û / 2 f t f f fDSPSNL'ÏÏECÏ OF Jl AND Ku ON THB ANGLE OP HELIX IN THECASE 0F 7 RODS 3 FIÎÎS ÜODEL.

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Tas r.7?r,\T.?.ï:jY o? IKS KU ON THE Ke ros VAHIOÜS FIN PITCHC? ? ROSS.3 FÎ^S BuîîILS.

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CISKT OP FRICTION OF 2Í 70BUNDLE ilODEL.

212

n PIKKSD RODS

Fig. 9' DEPENDENCY OF THE Nu ON THE Re FOR THE gf 70 mm MODEL

7ig»10a DEPENDENCY OF PRESSURE DROP COEFFICIENT ON THE RODCROSS SECTION / TO CHANNEL CROSS SECTION RATIO

J00

2*0220

ÎffO

"oro T

Fig.lOb DEPENDENCY OF THE Nu ON THE ROD CROSS SECTION/ TOCHANNEL CROSS SECTION

213

o s toFig*11a DEPENDENCE OF PRESSURE DROP COEFFICIENT ON THE FIH

PITCH ANGLE (¿ 36 ÍÍM7 RODS, 15 FINS6 RODS, 15 FINS

7 RODS, 12 FINS6 RODS, 12 FINS

to tff

DSPSNDSWCÏ OF THE !Tu ON THE FIN PITCH A(¡ 36 O MODEL)

214

Tig.12 POWER COEFFICIENT OF DIFFERENT FINNED SURFACES(N » 500 W/a)

ÉÍ 36 no MODEL6 RODS, 15 PINS6 RODS, 12 PISS7 RODS, 15 -FINS7 RODS, 12 PIUS7 RODS, 3 FINS

70 me MODEL19 RODS,21 RODS,24 RODS,19 RODS,21 RODS,24 RODS,

12 FINS12 FINS12 Pi:í315 FINS15 FINS15 FINS

ft <** ' "

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Fig.13 H2AT TRANSFER ON FINNED PLAXSS /33/«215

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216

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217

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218

ruso:: CCKCEÎIIIÏATIOH sus TO INJECTION IN THE POINT

219

Fig.18 TEMPERATURE FIELD OF COOLANT (MEASURED VALUES) IN THE SYMMETRYPLANE DUE TO BOTH FULL HEATED BUNDLE AND PARTIALLY HEATED ONE.Re » 1,29 x 105; x/d0 « 56,0; ç « 24,65 x 103 W/ra2

Symbole:a* superimposed temperatura field; b- temperature field due tofull heating; c« firat row of rods heated; d- second row ofrods heated; o* third row of rods heated; f* fourth row ofrods heated*

220

12

S¿-V+,

v

w

0,92 0 3 f 9 & t 5 & 2 l

Pig. 19 DEPENDENCY OP SHEAR STRESS OH THE ANGLE /32Ar

221

VELOCITY DISIRIS'JTION IN ROD BUSELS SUBCHANNEL

222

Mi»Afo*

totoCO

Fig.21 VARIATION OF HEAT TRANSFER COEFFICIENT IN SPACERS AREA.

Report on ctivity of theInstitute of Nuclear Research in the field of Heat and lía SB

Transferáwierk* PolandJ.Madejskl

This short review of activity of the Institute of NuclearResearch in áwierk near Warsaw, Poland, in the field ofHeat and lia ss Transfer contains information on theoreticaland experimental works carried out in the.period of lasttwo. years* A number of papers on this theme has been or willbe published in scientific journals; these papers arementioned in references* Most resulta of investigations»however, are to be found in Institute Internal Reports*The general feature of She activity reviewed is the basicresearch in heat transfer, and specifically in conductionsforced convection and boiling and two»»phas8 flow* Frperimental.works on liquid sodium technology have been carried out*A few problems of therraoelasticity, related to heat conductionhave been also solved, and recently onlyVproblera concerning:radiâtion,namely the theory of compact radiation heatexchangers?*L1« Conduct ion.1.»,1.« Mathematical methodaû Several so--, tions of non-stationaryheat conduction problems with linear : : non-linoar boundaryconditions have been, obtained by use <«i variations! methods.

225

Blot's variatioiial principle has been utilized by RAPAL3KIand ZYSZKOW8KI /9,10/ and by J&YSZKO'.VSKT /1T/. T?iey obtainedinteralia solutions for siraplo geometries with radiation ont*

the surface.RAPALSKI and SSCZUREK /8/ have studied acre complex geometriesby the same method, namely the cylindrical reactor fuel elements*3YSZKOY/SKI has formulated a new variational principle for heatconduction,KRAJSV/SKI /5/ analyzed the use of the variâtional methods ofRitas, and Trefftz; he has compared the results of these methodswith exact solutions for slabs.S2CZUREK has studied the application of the method of momentsin the case of a sphere heated by convection with constanthe&i transfer coeffieient.KADSJSKI has obtained exact solutionsfor related problem of time-variable heat transfer coefficient;this problem is connected with the heating of solid particlesintroduced into hot tjas stream»1»2« Phase transformation. MADBJSKI has obtained exact seriessolutions for the Stefan problem of simple geometries withboundary conditions of the first» second and third kind*numerical calculations for these cases have been performed by/SZCZURBK and the results presented in graphs» The case ofphase transformation in.an infinite mould has also been studiedfor the case of slabs and spheres.1.3. Analogue techniques. Liebnann's resistance - resistanceanalogy has been used by STRUPC2EV/SKIto build a universalanalogue computer, the version improved in comparison withthe original Liebmann solution» With help of this computer

226

several solutions for stationary and nonstationary termperatursfields in s.g« nuclear fuel shipping casks, beryllium moderatorblocks, reactor shields etc» have been obtained*1 » 4» numerical .techniquee. The code for transient conditionsin water cooled fuel channels with multitube fuel elements hssbeen developed by KfcîIOTEK» CIECKAEOtflCZ /2/ has studied tempera-ture transients in fuel elements having in view the digitalcontrol of boiling water reactors»

'2¿ Póreed convection»g;i« Channel flow, KRAJEffSKI /6/ has found the turbulent velocityfield in channels of complicated /non-circular/ cross-sectionby use of an integral transformation. The results for triangu-lar cross-sections as compared with experimental data are verygood, The same method has been used by KRAJEV7SKI for the caseof fuel rod bundles, for which temperature distribution in theliquid has also been calculated by uso of the methods ofTrefftz, and by perturbation method.Slug flow in channels with mixed boundary conditions for thetemperature field and with non uniform heat flux has beenstudied by GOL03 /3»'/» who obtained theoretical solutionsby use of Laplace transformation for circular pipes and annuli,Experiments: on turbulent heat and mass transfer in rod bundles

*are planned by ZMYSLOV/SICI; in this experimental rig the influenceof spacers on the mixing effect will be also studied*2.2* Fixed and moving beds. Model studies of flow resistancein a bed of spheres have been performed by V/ISRUSZ; theseexperiments were connected with the erection of an experimental

227

3 VSS pebble bsd heat exchanger by B3ZOZOV/SKI, DHL et al.»Recently WÏERUSZ hue carried out a aerx.-_• of experimenta J.w/ingin view the evaluation of the volumetric heat transfer coefficientin a fixed bed of spheres:*The experimental technique consisted in pulse perturbation of thecoolant temperature* Linear dependence of the volumetric heattransfer coefficient upon flow velocity has been observed*

*¿» Boiling and .two phase flow,^«K .Pool boiling and crisis» Report on thia topic will bepresented on the IAEA Panel separately.ft«2». Plow boiling» Preliminary experiments on flow boiling crisisof low-pressure water have been performed by MOLDYSZ.A high-pressure water-boiling experimental loop for 150bar and300 KW designed by ZLIYSLOV/SKI, is actually under erection* Inthis rig rod bundles /up to 20 rods of CDS millimetres/ willbe tested for burnout with inlet water velocities up to 2 metresper second* The material used for the boiling tube is boilei*steel K18*p. 3. Two-phase flow. STOHMA has performed experiments onisothermic two-phase air-water flow in vertical tubes» He alsodeveloped a formula for calculation of average and local voidfraction based on his own experiments.¿SOMMA's formula has been compared with experimental data ofMarchaterre and Roglund, and other investigators» withsatisfactory results* The study of two-phase pressure drop hasbeen also undertaken»CXECHAITOWICZ /1/ has presented the analysis of transient processesin vapour condensers using the methods of two-phase flow theory*•• 228

4» Liquid sodium technology»Having in view the future application 01 sodium in fast reactorcooling, a email sodium loop has been installed, and a greaterone /300 KST/ is actually under project*A number of equipment components such aa sodium level indicator,differential manometer, diffusion trap, electromagnetic linearinduction pump with moving magnetic field, magnetic ¡lowmeter,oxyg3n concentration indicator etc* has been built and operatedsatisfactory. This instrumentation has been designed by WIERUiJL,KAMIKSKI et al..5» Theraoelaeticity.Thermoelastic problems, connected with heat conduction, have beenstudied by RAPALSKI, who developed a variâtional principle forsuch cases /7/.

References;

/1/ Ciechanowicz W, The dynamite of a vapor condenser, Núcleo:?Engineering and Design, Ko 7, PP. 1-8, 1968.

/2/ Ciechanowicz 17., and Solberg, K.O., On transient digitalcontrol of a linear model of the Halden boiling water reactor,accepted for publication in the Nuclear Science and Engineering.

/3/ GoStos, S«, Theoretical investigation of the thermal entranceregion in steady, axially symetrical slug flow with mixedboundary conditions, accepted for publication in the Int.Journal of Heat and Mass: Transfer*

/4/.Go£os, S., The dependence of the Nusself number upon thedistribution of the heat flux along the boundary of an

229

axially symmetrical duct with metallic coolant, accepted for¿publication in the Nuclear Engineering and Design,

/£>/ Krajewski, B«, Application of variational methods to problemsof unsteady heat flow, Archiwun Mechaniki Stosowanej, No 5»vol.20, pp,535-547, 1968.

/6/ Krajeweki, B., Determination of turbulent velocity field ina rectilinear duct of non-circular cross section, acceptedfor publication in the Int.Journal of Heat and Mass Transfer*

111 Rafalskit P., A varia tional principle for the coupled thermo-elaatic problem, Int»Journal of Engineering Science, Vol.6,PPÍ46S-471, 1368.

/8/ Rafalski, P,, and Szczurek, J«, Transient heat conduction inmultiregion systems with non-linear boundary conditions withan application to nuclear reactors» Nuclear Engineering andDesign, No>l, vol.9» pp. 123-130, 1969.

/9/ Rafalski, P., and ¿yszkowaki, V;,, On the varia tionalprinciples for the heat conduction problem, AIAA Journal*Ho 1, vol.?, pp. 606-609, 1969.

/10/ Rafalski, P,, and ¿yszkowski, W., Langrangian approach tothe nonlinear boundary heat-transfer problem, AIAA Journal,Ho.8, vol.6, pp. 160$-1608, 1968.

/11/ ¿yszkowski, W«, The transient temperature distribution inone-dimensional heat-conduction problems .with nonlinearboundary conditions, Trans. ASME, Journal of Heat Transfer,Paper Ho; 68-HT-6, 1968.

230

Soné basic thermophysioal problems ofnucleate pool boiling

J»lkde;)Bki

In spite of abundance of experimental data on heat transferin pool boiling the state of knowledge on this topio seemsto betf unsatisfactory* The various recommended formulas showsometimes enormous discrepancies, which indicate that theseformulas» based on definite experiments» very Often can not beextrapolated and utilized for other working conditions»Since pool boiling data represent a basis for flow boilingcalcóla tic,-3, and the latter are of great importance in manyindustrial branches including nuclear reactor engineering,the problem of pool boiling should be considered as one of themost important in heat transfer*In order to learn the mechanism of the phenomenon furtherexperimental and analytical studies are needed» the scope o£w¿hich should be more thermophysioal than technical» Hereaftera few problems of pool boiling will be discussed» and somehypotheses presented* She following lines base on personalopinions of the present author, and some ideas need experimentalverification*Incipient nucleate boiling»Boiling is preceded by convection without nucleation wherefcyliquid at the heated wall is superheated» and the amountof superheat is A£«Babbles begin to grow and depart at some value of superheatwhiohdlaracterizes. the begin of nucleate boiling» The value

231

dependa very strongly upon liquid subcooling ATC» and

greater the latter the greater the former. The next factorinfluencing the value ÁT¿ is the surface geometry» namelyin such a sense that e*g* boiling on thin wires begins athigher AE± than in the case of flat plates*Decisive on incipient boiling is the influence of actual micro-geometry of the heated surface* This miorogeometry is due tomachining conditions and to the properties of foreign solidparticles suspended in liquid and desorbed onto the surface*The research of surface microgeometry is a difficult andtedióos problem which» however, must be solved at least*She essential feature of. the miorogeometry is the statisticaldistribution of cavities defined by characteristic radii R¿«This distribution determines a certain maximum radius R1,wj&hioh governs the incipient nucleate boiling. The smaller Rthe smoother the surface and .the greater the value ASi of thebegin of bubble formation.The problem of incipient nucleate boiling has been studied bythe present author [1»2] • Por axisymaetric vapour nuclei ofsemiellipio/idal shape the following approximate formula wasderived

. «ft,~ ' •>• 'A1where

and Ot denotes the heat transfer coefficient in the conditionspreceding the nucleate boiling*

232

fhe heat flux at the begin of boiling is equal to

«here

is the subcooling.In natural conveotion on a horizontal flat plate the proportion

is ttfte, wherefore the ¿eater the subcooling the greaterand the greater should be the superheat ¿1T¿.Simultaneously the higher value of the heat flux q¿ is obtained*Similar situation occurs in the case of very thin wires, and aostlikely one nay assume RI » D/2, where D denotes the wire diameter.According to Mikheev for very snail Rayleigh numbers it is

* 1/2, whence

and the heat flux eguals

this yields

which is shown in Pig.1 for the case of water at athmospheriopressure* Circles denote experimental data of Kaznoysky andSviridenko £3].

233

fluía it can be seen that liquid subcooling is very importantin the study of incipient nucleate boiling» The value of 4?omost "be controlled very carefully in experiments. This can bedone e.g. by multilayer the naos tat in g of the pool in which theinvestigated heating element is immetfed.Because of the influence of the temperature gradient at thesurface on the begin of boiling the pattern of natural convectioncurrents may be of importance» Considering for instance the caseof a flat horizontal plate one may observe convection cellsin which the temperature gradient is smaller in the centre ofrising liquid; therefore at these places the nuclei becomeactivated sooner» This hypothesis should be verified experimen-tally» of course, in order to be sctee whether the incipientnucleation site is wholly accidental or wholly determined byhydromechanics of the natural convection currents.»The possibility of independence of the incipient boiling condi-tions upon later conditions of stabilized nucleate pool boiling,connected with the known phenomenon of hysteresis, be also noted»Boiling on thin wires.The study of boiling on very thin wires has no technical impor-tance, and the physics of the problem differs essentially fromthe case of flat plate or circular J5 tube» In particular» thepossibility of wire burnout preceding incipient nucleate boilingwhich has been stated experimentally {3}» is a characteristicfeature of that geometry. A similar phenomenon does not occurfor geometries of greater characteristic dimensions ,• wherevirtual nuclei are of the shape of sphere and the like.In the case of a very thin wire of diameter of several microns thevapour nucleus may be of the shape of an annulus, surroundingthe wire» A primitive model of such a nucleus of thickness h

234

and width s la shown in Pig. 2. For this nucleus the thermody~namical potential /Helmholtz function,/ may be calculated takinginto account the temperature distribution, and an extremist inrespect of the parameters h and s may be found*This yields two equations» determining the dimensions of thevapour nucleus, and it follows that in certain conditions,understood as critical, the width a grows infinitely* In theseconditions, illustrated by the curve in Pig. 3, incipient boilingcoincides with the wire burnotft* The corresponding heat fluxis the greater the smaller is the wire diameter, and the greateris the subcooling* The described phenomenon has been observedf3j at wire .diameters smaller than 10 microns* Experimentaldifficulties connected with realisation of studies with suchextremely thin wires should be noted*Characteristics of the surface state*The state of a surface machined and covered with deposits/contaminated/ may be described mathematically by the statisticsof micvocavities n¿/ft¿/, where n¿ is the population, or thenumber of cavities of radius R¿ - per unit surface projection*The total population of cavities or virtual nuclei equals

where Rk is the radius tt of smallest cavities, and R^ that ofthe greatest* The dimension R determines the begin of nucleateboiling, and the partial cum

ït'M235

is equal to the number of vapour columna /bubble chains/ in theregime cf isolated bubbles'after the activation of nuclei of theclass RJ,The characteristics of the microgeometry iij/S / might be foundby means of a tedioas analysis of the profilograms, or on thebasis of interference pictures* On the other hand, by use of aprofilometer the mean square roul|ghness may be found, the latterbeing perhaps identic with the mean square cavity dimension R__defined by the formula

/11/The surface occupied by a cavity of dimension R¿ is proportional

oto RÍ • wherefore the sum

f. /12/£»fThence it may be concluded that

f

Thus profilometer measurement of the surface microgeometryyields mostly the value of the total number of cavities*Por more accurate study of the surface state the profilograph,and not profilometer, is needed*The purpose of such investigations follows from the fact thatduring the boiling experiments the measurement of contaminatedsurfaces is difficult, if not impossible. However, although thedeposits may change the conditions of cohesion, and adhesion,

236

knowing the global data for clean mid dirty surfaces one mayjudge about the microgeometry of contamine; bed surfaces»

First crisia of boiling,This problem has been always and is now very vividly disputedwhat regards its mechanism and cause. There exist two mainopinions» the first of which suggests the transverse coalescenceof bubles on the heating surface to cause the first crisis» endthe second beldfcfeSs ftt to be a phenomenon of hydrodynaœicalinstability, These statements should be finally clarified andanalyzed both theoretically and experimentally,The problem is urgent because - on the contrary - it seems thata unique opinion about the reason of the crisis of film boilingdoes exist. In the case of a flat horizontal plate this is atypical instability problem of the Taylor type» in which themass forces and the surface tension forces govern the phenomenon.Turning to the first crisis /or the crisis of nucleate boiling/ÍÍ seems that the theory of Helmholtz instability, as appliedby Zuber and Berenson» is a misunderstanding,That analysis consists in assumption that before the crisis thereflow upwards vapour jets in selected places of a horizontal plate»and besides the liquid flows downwards. The instability of such jets,results in breaking into chains of bubbles» and therefore thetheory based on such a model may be useful for determination ofthe regime in which vapour jets exist /e.g. boiling on glass/,These jets are formed in effect of theEongitudinal coalescence of

Jr

bubble chains.From theory and empirical correlations based on the mentionedanalysis of Helmholtz instability model it follows that the first

237

critical heat flux does not depend upon the surface state* Thisconclusion is very often objected, because in many experiment^it has been stated beyond douni that; the surface roughness has &very great influence on the first critical heat flux.Assuming that tie boiling curve Q(AV depends upon surfaceroughness and suggesting the existence of a certain criticalY. «superheat 'tyj » which is inpf&ident of the surface state, onenay obtain the value °f j dependent upon surface roughness.Such criterion of the first crisis of pool boiling has beenproposed and developed by the present author on the basis ofinstabilityanalysis of two two-phase layers without taking intoaccount the surface tension forces. Average densities of theselayers are different, because in the boundary layer the bubblesgrow up to the departure moment after which the waiting periodfollows, whereas in the upper layer the vapour bubbles flow withapproximately constant rise velocity.Such an analysis applied to the regime of isolated bubbles yieldslow critical superheats, which indicate merely the transitionfrom that regime to the regime of vapour mushrooms /a more complexform of big bubbles/. Nevertheless the similar analysis as appliedto the regime of vapour mushrooms gives sufficiently high valuesof critical superheat, which show that such an approach is reaso-nable and further studies of this idea are promising*

Problems of bubble dynamics*She problem of bubble growth is still an object of interest a&well experimental as theoretical. Also the conditions of bubbledeparture are not thoroughly researched as yet. Incertain condi-tions /low pressures, reduced gravitational acceleration/ thebubble departure results from the action of friction forces, inertia

238

In the so called classical conditions the departure diameterfollows from the balance of surface tension and buoyancy forcea»Then the contact angle playa a significant- rôle, a quantitywhich is defined in references by three surface tensions acting onthree interphase surfaces /liquid-vapour; vapour-3±gzdb! wall;liquid-wall/.Recently Bieniaes JVj has measured the values of the contactangle in the cace of liquid boiling on a surface of a heavierlew-volatile liquid, non-miscible with the former» In this caseall three surface tensions «T, Grander we re measurable, wherebythe measurements were carried out by several methods and comparedwith literature data* From the formula

COS

often met in references, the values of cos{& far greater thanunity have been calculated, which indicates that this formula isfalse* The measured contact angle was observed in the limits 35-50degrees* These results show that in the balance of surface tensionssupplementary forces of adhesion must be introduced. This fact hasbeen already mentioned in the literature of the problem»

of nucleate poo:;, boiling»Up till now much /perhaps toomuch/ attention has been paid tothe analysis of the regime of isolated bubbles, which coversabout 10 percent of the boiling curve* There is evidence, however,about other forms of vapour phase, namely jets /resulted from thelongitudinal coalescence/ and mushroom-bubbles /resulted form thetransverse coalescence/«X& seems that the latter £mc form isespecially important and should be carefully analyzed-at firsttheoretically* I¿ is supposed that after the moment of transversecoalescence on the heating surface a great flat vapour bubble

239

covers a group of liquid drops formed from bubbles by inversion,These problems» as well as, tine question of drop evaporation atidthe conditions of transition of the drop into spheroidal state thave been studied very fragmentarily.It should be pointed out, that such an analysis may result innew criteria for the first orisis of boiling.In %he regime of isolated bubbles the number of bubble chains/columns/ is equal to the number of activated nuclei, whereasin • ¡le regime of mushroom-bubblos the number of chains isi- íviív\derably smaller, because one big bubble "co-operates"v>itii sometimes some scores of nuclei» In connection with that the¡¿umber of vapour "columns" in the regime of mushrooms may be

less important than in the case of isolated bubbles.

Stabilized nucleate boiling»Having in view the phenomenon of hysteresis one should utilizefor stabilized nucleate boiling theory only these boiling curves<£(AT) , which have been obtained with decreasing heat fluxes*Recently the present author has revised [J>] his nucleate boilingtheory fsj , and some simplified formulas follow therefrom. Oneof them may deserve attention; it is valid for the regime ofmushroom - bubbles» in which the number of bubble columns doesnot influence essentially the phenomenon» The derivation of thatformula is exceptionally simple. It is assumed that a qua si statio-nary temperature distribution Tift/J, representing certain averageconditions, exists in the liquid. At the wall y « 0 the tempera-ture gradient determines the heat flux, namely

240

Vapour babbies grow according to the law

V Iderived by Bosnjakovic; in the above formula o(fr denotes thoheat transfer coefficient at the bubble surface /interphasesurface/*If V/ denotes the i velocity of centre of mass of the bubble»then the coordinate y is connected with time t by therelationship dy/dt » w .Therefore

or utilizing /16/

/w

At the wall it is y « 0, and T « TW> T-T8 » Aï» D » DO ,«here DO denotes /by assumption very small/ initial bubblediameter* In such conditions it may be therefore assumed that

Substitution of /18-19/ into /15/ yields

/20/

Subsequently the Colburn analogy

fPrj mi241

nay be taken into account, and this procedure yields

She quantity DC, as it has been said, is the initial valueof bubble diameter* During stabilized boiling this quantitydoes not depend upon the dimensions of a cavity, in whichthe primary nucleus has been situated, because the departingbubble leaves On the place a small bubble of diameter incompa-rably greater than the dimensions of the primary nucleus* This"abandoned" little bubble grows somewhat at first, and afterwardscondenses a little during the waiting period due to the approachof cooler liquid to the wall* Simultaneously the liquid growswarmer, and this results in subsequent growth of the bubble upto the moment of departure. In this way the dimension DC mustdepend not upon microgeometry, but upon the conditions of expe-riment* It can be also assumed that this dimension fulfils theequation /1/ for Rj » DC/£ at TW-TS » 3P and o< • q/A Ï» Thus

gfi,_"whence

If the second term in the denominator is small in comparisonwith the first, then

242

which substituted into /22/ yields

//VÍ /26/

This simplified correlation may be expressed in non-dimensionalnumbers in the form .

53* 5where

and

The constant C0 in equation /2?/ is equal to about 0,12 forwater /data of Cichelli and Bonilla/» 0,15-0,16 for sodiumat 800 - 900°Cf and 0,15 - 0,18 for cesium at -500 - 800°C.

243

References

1* Had e j ski, J., Activation of nuclcation cavities ona heating surface with temperature gradient in superheatedliquid, Int. Journal of Heat ana Mass Transfer, vol.9,p.299, 1966.

2* Made j ski, J., Przyczyny przerwy w dziaïaniu /czasu jaiowego/zarodka pçcherzyka przy wrzeniu, 17 Sympozjum TermodynaraikiTechnioznej, Wrociaw-Karpacz, p. 219, 1966.

3. Subbotin, V.I., Sorokin D.N., Ovetchkin, D.ii. , andKudryavtze*, A. P., Teploobmen pri kipenyi met allow v usloviyaktestestvennoy konvektzyi, Nauka, Moscow, 1969»

4* Bieniasz, B., ïTrzenie cieczy na powierzchni cieczy wysoko-praca doktorska, Rzesz<5w, 1970*

5. Made j ski, J., Improved "th ree-coaponent" theory of nucleatepool boiling, submitted for publication in the Int. Journalof Heat and Mass Transfer.

6* Ma de 3 ski, J., Theory of nucleate pool boiling, Int. Journalof Heat and Mass Transfer, vol.8, p. 155, 1965*

244

245

-£

p'dhATR6T5

10

h

Rg. 2

D-2R

0 1 2 3 4 5

Rg.3

246

INTERNATIONAL CEfiïRE FOR KEAi' AÜB MASSIRANSF3R A8L CO-OPDRAi'IVE RESEARCH

Z. Zarió

International Centre forHeat and Mass Transfer, Beograd.

Introduction

A general feeling among researchers engaged in heat andmass transfer is that an adequate international co-operation inthe field is lacking, which in many respects, prevents fasterprogress in this branch of science*

The intention of this paper is to stress the importanceof an organized international co-operation in the field of heatand mass transfer, and in particular to bring the attention tothe activities in this direction undertaken by the InternationalCentre for Heat and Mass Transfer, located in Beograd, Yugoslavia*

International co— oration^ln

The beginning of rapid development of the science of heatand mass transfer parallels the fast expansion of the nuclear powerresearch ana development efforts throughout tue world in thelate ninteen-fifties. This of course, being due to the importanceof the effective covering of nuclear reactor uses for the bothinvestment costs and the safety of nuclear power plants* Notonly have new large heat transfer laboratories been built innumerous nuclear research establishments, but in addition, theexisting laboratories at universities and research institioashave largely profited from the research contracts with variousAtondo Energy Commissions of many countries, Nevertheless, heattransfer research has never been considered real "nuclear" research,due to the reasoning that we do know much more about the heattransfer in reactor cores than about the nuclear physios of thesecorea. Consequently, only a small part of the overall cost ofthe nuclear power development went to the heat transfer research*

247

In the meantime heat and mass transfer problems becamemore and more important for many other fields of application.i*ot only the development of such new techniques as the spacetechnology required advanced knowledge in heat transfer but alsothe conventional power engineering, faced with the nuclearcompetition, was forced to pay mere attention to the increase inthe heat ratings. Lately many other branches of applied sciences,such as environmental engineering, bioengineering and evenagriculture and medicine, became involved in solving heat andmass transfer problems* Thus, in the last few years, the scienceof heat and mass transfer has become really an interdisciplinaryapplied science.

Today it seems that world-wide concentrated research effortsin nuclear reactor physics has produced expected results, ïhepresent-day-knowledge in reactor physics seems to be quite sufficientfor the reactor design. Due to the importance of heat transferresearch for many other fields of application it would follow t ¿atthe present-day-knowledge in reactor heat transfer is also sufficientfor the design of nuclear reactors.

It is well known that this is not the case. Some problems ofheat and mass transfer still present difficulties in nuclearreactor design requiring further research efforts.

The field of heat and mass transfer is a very vast one,strongly interconnected with various other branches of science,such as solid state physics, fluid mechanics, radiation physios, etc.The complexity of the field poses many difficulties for theinvestigators thus requiring more material resources and man-power.

Moreover, each specific application poses particular researchproblems of heat and mase transfer, the solution of which requiresalso the knowledge of the field of application. For instance,solutions of nuclear reactor heat transfer problems requires theknowledge of reactor physics and reactor materials as well. Taismeans that the material resources are often just enough to solveonly the most urgent practical problems of a given application,and most often only on a semi-empirical basis. The researchersinvolved become uighly specialized for a particular applicationand consequently the exchange of information between the researchersworking on basically the same heat transfer problem in differentapplications is very inadequate.

248

However, basically the solutions of the particular heattransfer problems of various applications often could be readiedwith less expense and more generally, by solving a fundamentalproblem of heat and mass transfer. Researchers in applied heattransfer research are urged fco solve practical problems so taat theydo not find either time nor strength to handle the fundamentalproblems which are general for a whole class of particular problems,fundamental research is left to small university laboratoriesthroughout the world composed of limited material resources andsmall research teams, often graduate students. Thus, majorfundamental problems of heat and mass transfer, often of a verycomplex nature, such as turbulent convection, boiling phenomena, etc.,of vital importance for the solution of many particular problems areleft to small scale research unable to produce general solutions*

In such a situation there is much to be gained by ensuringthat this research, both fundamental, and applied, should becarried out co-operatively, rather than in isolation; and theco-operative lines should run from application to applicationas well as from country to country. International co-operationwiuh the corresponding advantages of shared resources and freely-distributed information, would generally improve the prospects ofsuccess. Moreover, the interdisciplinary barriers, which aredifficult to surmount on small occasions, will yield more easilyto the efforts of a co-ordinated team of workers of varied backgroundsand experience.

Well organized international co-operation in the field shouldinclude*.

- exchange of experience by the direct contact of the researcherson specialized meetings and in mutual visits of laboratories

- concentration and coordination of the research efforts insolving fundamental problems of heat arid mass transfer having ageneral bearing on a number of practical applications

International co-operative research projects exist already inparticular in nuclear power applications, however, there have neverbeen on a world-wide basis and they have always been on veryparticular problems of application.

249

The first wholly international organization acting in thefield of heat and mass transfer, The Assembly for International Heat•Transfer Conference, cas founded only four years ago. As indicatedby its name the Assembly is dealing with the preparations andthe organization of larg* International Heat Transfer Conferences,held every four years, the fir&t 01 which was held this Septemberin Paris. These conferences cover the whole field of heat transferand although very useful for interdisciplinary exchange of ideas,they are too large, and thus they do nob eliminate the need forsaaller meetings on more specialized topics.

i-he International Oentre for Heat and Mass Transfer

Being unsatisfied with the present nodes of the internationalco-operation in the field of heat and mass transfer, a group ofknown researchers from most of the countries active in the field,was concerned with the establishment of an international organizationhaving the objective to promote and foster international co-operationin the field on a world-wide basis.

It was during ;an international meeting prepared by this group,in September, 1968, that the constitutive meeting of such anorganization, called the International Centre for Heat and Mass Transferwas held. At this meeting the members of the principle organs ofthe Centre, the Scientific Council and the Organization Committee,have been nominated from the well known authorities in the fieldfrom eleven countries. Particular objectives of the Centre havebeen laid down as being:

- organization of international seminars and advancedcourses on specialized topics;

- promotion of international co-operative research}- promotion of the exchange of technical information;- promotion of the exchange of personnel;- publication of technical literature;- undertaking of other relevant activities leading to the

general objective of promoting international co-operation in thefield.

The scientific activity of the Centre in the first two yearsof its existance has been devoted to the organization of inter-national seminars on particular, specific topics in the field and

iternational Summer School, "Heat and Mass ïransfer in Turbulentundary Layers», September, 1968, Herceg Novi, Yugoslavia

250

to the preparation of the other activities mentioned above.Three international seminars have been organized so far by

the Centre on the following topics:- Heat and Mass transfer in turbulent Boundary I»ayers ( in-

cluding two-phase boundary layers), September, 1968*- Heat and Mass Transfer in Separated Flows, including

Measurement Techniques, September, 1969.- Heat and Mass Transfer in ideologically Complex Fluida,

September, 1970.Those seminars with a limited number of participants ( 100

to 150 ) from about a dozen different countries all working onsimilar problems have proven very successful and very useful as acomplement ..to,large conferences covering the whole field» Eachseminar has a wholly international organizing committee selectedfrom the best known researchers in the particular area from differentcountries* The committee invites lecturers and selects shortcommunications to be presented at the seminar* The proposalis to hold the next seminar in 1971 on the topic of Heat andMass Transfer in Liquid Metals»

Intentions are that from 1970 on, activities of the Centreshould be broadened so a.-, to embrace other modes of internationalco-operation in the field.

It is felt that alongside with the seminars, advanced courseson the same subject should be held.as a kind of introduction to theseminar. These courses are intended for young researchers,beginners in a given particular area of the research in the fieldas well as to those who wish to enlarge and deepen their knowledgeon the subject* In particular these could be vary useful for thecountries in which the heat transfer research is beginning to bedeveloped. In the courses lectures will be delivered by out- . ^standing scientists in the given topic and they will be printed andmade available as a reference book for the subjet in question*

The exchange of technical information in a field of so manyapplications such as heat and mass transfer is a difficult but avery important task. Important heat and mass transfer papers arefrequently published in journals devoted to other fields of scienceor in local, regional and institutional publications with a limitedcirculation and in different languages. Yearly a number of scientificmeetings of the local or regional character, are held in whichvaluable papers are presented and of which the heat transferscientific community is not aware. In general it is intended to

251

organise in the Centre a systematic service for the collection anddissemination of technical information relating to the field,probably as a part of a larger international system ( UHISISI forexample ). This is a long range project but if it is intended tostart this activity by publishing a quarterly journal in Englishcontaining abstracts and citations of the important papers in thefield, whatever their original language* A parallel step wouldinclude a twice-yearly bulletin of the Centre containing informationon various forthcoming or recently-terminated scientific meetingsconcerning the field.

Co-ordinated international co-operative research is, ofcourse, one of the most important objectives of the Centre. Itis at the same time a most difficult one to handle. The followingscheme is currently under investigation in the Centre both fromthe organization point of view as well as from the standpointof possible financial support.

The Centre intends to draw attention to particular researchprojects which, because of their high importance for science andtechnology, and of their demand for expertise, which is spreadthroughout the world, are especially suitable to be undertaken by aconsortium of laboratories and researchers from various countries*Of course, the Centre will, in this respect, acknowledge all of thesuggestions from various international or national bodies orgroups of specialists.

Once a well defined problem is chosen as the subject of aproject, it is intended to gather together for a given timea working group of the leading scientists in the particular field,whatever their nationality, with the objective of proposingprediction procedures based en the best available data. The groupshould be provided with an excess to all available technical in-formation on the subject as well as to a computer of substantialsize, or a terminal to such a computer.

In the course of the work the group -would identify exper-imental evidence or data which is lacking or which would makepredictions more reliable or more general. The group would thenidentify where this work could be best done. The co-operativeexperimental research can thec be carried on in laboratories thatcurrently exist in the scientifically-active countries.of theworld with a special committee coordinating this work.

252

íhe identification of the most important research problems bysuch groups would then greatly assist planning or choosing theresearch programs in all other laboratories or research establishmentsthroughout the world, regardless of their size and the country inquestion. Considering the mobility of scientists to be one of thenecessary conditions for the improvement of the internationalco-operation, the Centre intends to promote mobility schemes for theselected research problems with a special reference to the researchersfrom the countries in development.

Obviously the undertaking and th; scope of any of the mentionedactivities will depend greatly on the amount of necessary financialsupport required. Because the character of all these activities iswholly international it is natural to suppose that the majorpart of the necessary support is expected to come from the internationalorganizations or specialized agencies of those organizations having inter-est in the field.

253

BASIC RESEARCH AND DEVELOPMENT WORK IN HEATAND MASS TRANSFER IN NUCLEAR POWER PLANTS

S. K. Mehta and S. R. SastryReactor Engineering Division

Bhabha Atomic Research Centre, Trombay, Bombay-85, India

ABSTRACT

Basic research and development areas in the field of Heat

and Mass Transfer with special reference to Nuclear Power Reactors

are highlighted. Efforts involved in the build up of design capability

and the experimental programs are elaborated. In the context of the

proposed power reactor program in India, the facilities available and

the experimental work planned are given.

Recently the Department oí Atomic Energy has proposed a

ten year (1970-80) nuclear power program for Taclia. In addition to

the two units at Tarapore (380 MWo) and Raja-'ithan (400 M'Ve) and

one unit at Madras (220 MWe), one more unit at Madras (220 MWe)

has been suggested. It is also proposed to have additional capacity

of 1, 500 MWo, so that by I960 a total of 2700 MWe of nuclear power

could be installed. The program also calls; for a major effort for

the design and development of a. 500 MWe thermal reactor. The choices

being considered for this are CANDU-PHW type, or CANDU-3LW type

and a modified SGHW type reactor with plutonium enriched fuel.

The above proposed program calls for both design and develop-

ment effort in various fields, such as nuclear and thermal design of

255

reactors, design of reactor components, development of fuel, instru-

mentation etc. The heat and Mass Transfer plays a major role in the

design of fuel and some of the out of reactor equipment like the pre-

ssurizers and heat exchangers. This paper highlights the efforts

involved in the build up of the design capability. This is followed by

an identification of the research and development areas. Lastly the

experimental facilities available at the Bhabha Atomic Research Centre

and the experimental program planned are described.

For the design of a reactor the major development program is

associated with the reactor core particularly towards the realization of

a fuel which is dependable and has high performance characteristics.

The development work is planned to provide the designer with a thorough

understanding of the fuel, cladding and structural materials under various

conditions of operation and their integrated behaviour in course of their

in-reactor residence time with various anticipated environmental condi-

tions like the neutron irradiation and various coolant conditions. Such

a program provides a confidence in the fuel assembly performance and

help to evolve a total design capability. Thus the effort involved may be

considered to consist of:

A) Building up of the design capability

B) Fabrication Technology

C) Out of pile development work; and

D) Inpile development work.

The Heat and Mass Transfer in the Nuclear Power Reactors figures

prominently in the design of the fuel assemblies and the thermal hydra-

256

ulic analysis of the reactor circuits. Consequently the out of pile

development work needed calls for a major effort in the field of Heat

and Mass Transfer. The following pages highlight the efforts called

for attaining the design capability and accomplishing the development

tasks from the point of view of Thermal Hydr avilies.

_Bui?.ding_up of the Design Capability

The in el design involves, (j.) a thoroyc«7.h analysis of tho therms!

hydraulic, and (ii) nuclear characteristics oí ths core with due consi-

deration of the behaviour of the fxu-1 and elaik!;'.r£ daring-thisir in.-.ore resi-

dence time and, (iii) the- stress

The the r ma? hydraulic, ¿«¿lysis, in pelicular, covers tL>>

analysis of the core and thf* trtai icueiear steam supply svi:lr--m to tt.niz.re

that :

a) During the steady operation of the plant (he rr«'.>.i>n«m rated

fuel assembly in the core operates with sufficient dry out margin (cir

Minimum Critical Heat FAUX Ratio, i. e. MCHFR) depending xipon thi

safety regulations and b) During the anticipated plant transients (ae those

due to reactivity insertions, coo?.ant rscirevlation failliras, generator

load rejections etc. ) the core Minirrjurn Critical Heat Fiux Ratio does not

plunge beiow the safety allowable limit. The thermal hydrauîic ar^sJtysis

should be coupled to the nuclear analysis of the core to take care of tho

mutual feed back effects.

This calls for an integrated system of computer codes to be

developed on the pattern of PATRIARCH system of codes developed by

257

UKAEA. An envisaged system of programs to build up the core

design capability for water cooled reactors is shown in figure-1.

Some of these codes are already made or adapted ana the work on the

rest is being planned.

Availability of such codes not only builds up the design

capability but will enable a developing country to understand the de-

sign aspects of the reactor they have or propose to have. This will also

enable the country to operate their reactor efficiently, particularly at the

tizne of trouble shooting and to evaluate any design changes desired.

In the design and operation of the pressurized and boiling water

reactors the power that can be removed from the reactor core is limited

by thermal and metallurgical considerations. The metallurgical consi-

derations stipulate the maximum clad and fuel temperatures while the

thermal hydraulic conditions stipulate the power that can to extracted

while maintaining a minimum critical heat flux ratio. Both these

aspects call for a detailed understanding of the fluid flow and heat

transfer mechanisms in the reactor core. In a pressurized water

reactor the maximum clad and fuel temperatures turn out to be the

limitations. At the same time, normally, no bulk or local boiling

is permitted in the core. The maximum clad temperatures are governed

by the hot spot hot channel factors. In many cases these are based on a

deterministic approach (1) which may result in over conservatism.

These methods assume all the cooling channels in a core to be independ-

ent and treat all the uncertainties in the same manner. However, one

should distinguish between the local uncertainties which may vary from

258

point to point within a reactor and the global, uncertainties which do not

vary within a reactor or atfeast within parts of reactor. A statis-

tical approach covering all these aspects is more justified. Apart

from the analysis, in actual practice the effects of spacers and spacer

grids for individual geometries arc-to be evaluated by sim\2n.ti«5ntest. Sortes

of the other relevant points needing attention in their basic approach

in the steady state analysis are brought out in the discussion on the

development work.

The dynamic analysis which forms an important part of th-5

design evaluates the flow and power instabilities, system response

to perturbations of various kinds and transfer functions needed for tbs

synthesis of various control systems. Most of the dynamic models

assume that the steam and liquid water are in thermodynamic equili-

brium. In some of the cases the subcooled voidage, which may have

significant effects on th^ dynamics, is neglected. Due confederation

should be given to models incorporating the non-equilibrium effects'^).

These models have more relevance in explaining rapid transients as

the void changes are governed by the thermal inertia. Other relevant

aspects associated with the two phase flow and heat transfer which

need more understanding are included in the discussion on the develop-

ment in the following pages.

Development Work in the field of Heat and Mass Transfer

Most of the development efforts in this field are directed

towards the understanding of 'two phase flow and heat transfer. The

problems of study include amongst other aspects:

259

(a) Pressure dr^ps in adiabatíc and diabatic flows

(b) Void fraction and flow regime studies

(c) Mixing phenomena in roc1 bundles

(d) Mechanism, of two phase heat transfer andCritical Heat Flux or dry out phenomena

(e) Hydrodynamic Flow Stability and

(f) Critical flow studies.

So far, most of the pressure drop and flow regime studies have

been carried out in simple geometries and empirical correlations are

arrived at based on experimental data. In simple idealised geometries

these pressure drop correlations may be reasonably dependable. In

the rod cluster geometries the pressure drops due to local components

like spacer grids are evaluated by actual full scale pressure drop tests

by many designers. A need for full fledged analytical models which

enable the designer to predict pressure drops even when changes

are brought about in the geometry is obvious. To carry out the total.

hydraulic analysis of the Nuclear Steam Supply System, the pressure

drops due to adiabatic two phase flow in various components should

be understood well.

Void Fraction and Flow Regime Studies

An accurate prediction of the void fraction in the coolant

channel of a boüing water cooled reactor is essential^). The void

fraction influences the steady state and dynamic response of the reactor.

Also the stability of the system depends upon the core power density

and the void behaviour in the subcooled boiling region. Some of the

260

existing void fraction correlations have nc«lected the relative velocity

between the two phases as well a a the effects of flow and concentration

profiles in the radial direction. Somó other correlations were obtained

by dividing the sub cooled boiling in to a few regions. Such a division

leads to spurious results in dynamic response as a result of the dis-

continuity of void gradient at the regional boundaries.

Appropriate analytical models incorporating the effects oí flow,

concentration and temperature profiles together with the effects of 'ocal

relative velocity are to be worked out. These should also account for

conditions of thermodynamic non-equilibrium. The making o£ these

analytical models calls for an experimental program both in saturated

and subcooled boiling regions. The experimental measurements

should include void profiles, volumetric flux profiles across the coolant

channels, and bulk liquid températures. The studies should include the

behaviour of flow regimes also.

The void fraction data in the rod bundle geometries is

scarce'*). Even the techniques of void profile measurements in

various subchannels are to be established. Most of the design work

is based on very simple tests on simple geometries. Thus a detailed

analytical and experimental work on void fraction distribution in rod

bundles is of immediate interest.

The flow regime identification is essential for a compre-

hensive prediction of pressure drop, heat transfer coefficients, or

critical heat flux. The flow regime specification in rod bundle

geometries is not easy. Even the experimental work carried out in

261

the rod bundle geometries is very limited. A thorough understanding

of the possibility of different regimes of flow existing in different sub.

channels at the same time and their equilibrium both in diabatftc and

adiabatic flow conditions is needed.

Freon modelling of the phenomena especially for studies o,n

void fraction and flow regimes and critical heat flux is within the

reach of most of the laboratories. Also the experiments with freon

can cover a wider range of experimentation. Extrapolation of freon

date to water should be done carefully after a thour^gh understanding

of the basic phenomena.

Mixing and Critical Heat Flux

As mentioned earlier one of the major performance limitations

imposed on the fuel assemblies is the bondition of dry out. This condition

is normally followed by a nearly step increase in the cladding temperature.

Even though a physical failure of the cladding may not occur during very

short transients of this type, there are other problems associated with

this. The increase in sheath temperature gives rise to a high and

accelerated dissolution of hydrogen in the cladding. This in turn will

result in hydride formation at subsequent lowering of the temperature,

as the solubility of the hydrogen decreases with decreasing tempera-

ture. In addition, an operation in the vicinity of dry out leads to an

osculation of sheath temperature. Thus, a thorough understanding

of the dry out phenomenon would be of utmost importance. The rela-

tive importance of the different variables involved is not well defined to

262

date and hence any extrapolation or interpolation re stilts in unknown

risks. Even in one component two phase flow an elaborate experimental

program is necessary to provide for a parametric variation of ail

physical constants of importance. As mentioned earlier one can con-

sider the possibility of using freon models for improving the basic

understanding.

A few points are worth mentioning with reference to the

experimental work on the critical heat flux. The measured critical

heat flux values are dependent upon the detecting systems or measuring

devices'5). An uncertainty in the critical heat flux value may result due

to trip setting point itself depending upon the parameter the detector uses

for tripping the power supply. Normally one of the following three are

used for initiating the tripping of the power to avoid a destruction of the

test section at the time of the dry out: a) the excursive oscillation of

the surface temperature, b) the rate of temperature rise, and c) the

change in the ratio of voltage drop over the exit section (for constant

heat flux experiments) to the voltage drop over the entire test section.

One should distinguish between the effect of an independent parameter

and the effect of parametric distortion. The parametric distortion is

the side effect introduced by an accompanying dependent parameter

while the effect of an independent parameter is being studied. This

occurs mainly because of the interrelation of the parameters through

the energy balance equation and the boiling crisis equation.

For rod bundle geometries, until recently, the prediction of

the critical heat flux was based on the extrapolation of the dry out

263

data obtained for simple geometries. Some laboratories have conducted

and are conducting tests on simulated full scale bund/.e geome-

tries' ' ' with appropriate power distribution, and flow conditions.

This is a high!.y expensive task. In case full scale tests are not

conducted the only tool the designer has available to predict the

critical heat flux in à eompSet'.y untested geometry is a subchannel

analysis. However, in a diábatic flow, with the high complexity

inherent in it, a local or point description of the phenomena may not

be sufficient without the knowledge of the previ ou» history oí the f'.ov/.

Also the mixing process in a complicated ductor geometry ms.y not.

be as simple as the mixing in two simple subchannels. Mixing should

also be studied as a function of flow regimes. More data should be

gathered on the following(4):

(a) Mixing length and the effect of rod-to-rod spacing

(b) Effect of subchannel geometry

(c) Diversion flow enthalpies

(d) Mass transfer in the process of turbulant mixing

(e) Effect of flow regimes on the mixing process

(f) Effect of local components like grid spacers and

(g) Subchannel friction factors.

In addition appropriate critical heat flux correlations for the

inner and outer subchannels and their validity for application to

subchannels of varying geometry should be worked out. So far the

mixing process is studied mainly in steady state conditions. Thus

the mixing process under transients has lot more work to be done.

264

Hydrodynamic Flow Stability

Another item of interest to the designer is the occurrence of

the instabilities, especially in the boiling water cooled reactors. There

are two types of instabilities (i) the reactivity feed back between the

reactor and the steam voids may give rise to excursive oscillations, and

(ii) Hydrodynamic instabilities may occur at constant power. As men-

tioned earlier an appropriate dynamic modelling of the system, is essen-

tiaj. The hydrodynamic stability calls for a detailed understanding,

amongst other things, of density wave oscillations, effects of compre-

ssibility and parallel channel operation^-1 °). Again the dynamic

models have to incorporate the effects of flow regimes and void fra-

ctions while evaluating the pressure drop characteristics. The presence

of flow fluctuations at constant power can lead to a premature boiling

burn out. In such cases the dry out may occur much earlier than pre-

dicted by steady state local condition hypothesis, as a result of ex-

cursive hydrodynamic instability.

It should bo noted that essentially all hydrodynamic experi-

ments so far have been carried out in out of reactor cet ups which

lack the nuclear feed back thtvt can result from changes in coolant

density during a perturbation. These effects aro of considerable

importance in a reactor v/ith positive coo'.ant coefficient. The study

on the effect oí interconnecting subchannels of the type found in rod

bundels, on the hydrodynamic stability would b« of importance.

Critica". Flow Studies

An understanding of the two phase critical flow is needed to

265

enable the prediction of the discharge rates of highly pressurized

steam water mixtures through breaks in vessels or pipes under con-

ditions of anticipated accidents. -This calls for an understanding of

the mechanisms of such flows through short pipes and orifices.

Facilities Available at the Bhabha Atom?, c^ Research Centre

The planned development work in the area of two phase flow

and heat transfer is carried out mainly in heat transfer loops. At

present we have a 100 Kw heat transfer loop. A simplified flow dia-

gram of this loop is shown in figure-2. Some of the loop parameters

are shown in Table 1. The subcoooled liquid from the discharge of the

pump is led to the test section. The steam water mixture from the

test section passes through the separator. The steam from the

separator is super heated for the accurate flow metering and

then condensed in the jet condenser. The condénsate is re-

turned to the pump after tempering with the flow from the cooler.

This tempering helps to maintain the subcooling at the circula-

ting pump inlet. The cooler is in a parallel circuit. A heater is

also provided to achieve the required subcooling at the test section

inlet as called for by the individual experiments. Provision for

isolating the test section lines is provided to enable easy replace-

ment of test sections. There are two positions available for the

test sections. However, at a time only one heated test section can

tie used.

The electrical power supply for test sections is provi-

ded by two transformers. One of the transformers is a 3 phase,

266

100 KVA, 400 V/0-400 V variable transformer . The second trans-

former is a 3 phase/ 1 phase transformer. The secondary of this

unit can supply a maximum of 1667 amps at a variable voltage of

0-60 or a maximum of 3333 amps at 0-30V. From the secondary

of the 3 phase/ 1 phase transformer single phase A. C. power is

fed to the test section. Thus a continuously varying power can be

fed to the test 'section.

The loop is provided with suffi ci cut instrumentation. The

essential ones are mentioned here. Each test section is instru-

mented for £iow and the same signal is used for operating the control

valve to maintain do sired flow through the test section. The cooler

flow is maintained by means of a temperature control valve which

enables the test section inlet temperature control. The steam flow,

for heat balances, is measured after super heating the oteam coming

out of the separator. The flow to the jet condenser from the cooler

is adjusted to achieve proper condensation. This is achieved by the

control of the level in the condenser which in turn operates the !cvsl

control vaive which adjusts the appropriate flow. The cooler secondary

flow is controlled to maintain the required cooler primary water out

let temperature. Provision to measure the test section differential

pressure (0 to 4 kg/cm^) is made. Instrumentation for the test

section out let pressure and the surge tank pressure are provided.

The test section differential temperature, and bulk out let temperature

are also measured. The surge tank level is maintained by bleeding and

feed system.

267

In addition to the loop instrumentation described above the

test section is provided with surface thermocouples closely spaced at

the exit (for uniformly heated test sections) of the section. These are

to be connected to a fast temperature recorder. This is to enable the

detection of the dry out in the test section. In addition a sudden

rise in temperature above the set limit in the recorder trips the

power supply to the test section thus preventing the possible

physical destruction of the test section. Also provision is made

to trip the power supply manually.

In addition to the 100 Kw heat transfer loop described above

an in-pile pressurised water loop is available at our laboratories.

The details of this loop are given in table -Z. A simplified flow dia-

gram is shown in figure-3. The heat removal capacity of this loop is

400 Kw. This can be used for in pile single phase heat transfer experi-

ments in addition to the fuel and material irradiation*

A 1 Mw boiling heat transfer loop is planned to be erected.

Subsequently this can be up rated to 3 Mw. The power source being

installed can cater to the final need. This loop will have a system

pressure of around 100 kg/cm2. The pump being procured can

develop a head of about 18 kg/cnv? while delivering a total flow of

1400 litres/min.

The facilities available and that are being installed are

sufficient for quite a good range of heat transfer experiments and

studies on two phase flow. To enable the experimental work to go

ahead while getting sufficient data the experimenter should have at

268

his disposal eróme special instruments to measure void fractions

and to detect flow regimes, At present we are developing a void

meter based on the use of Thullium gamma source. An air water

rig is erected to enable the calibration of this detector.

Experimental Program Planned at BARC

The basic experimental program is in line with the approach

presented in the problem areas. The program is graded to provide

experimental data starting from simple geometries. As a first step,

using the 100 Kw loop, a few burn out tests and pressure drop tests in

simple heated tubes will be conducted. This set of experiments is

a fore runner to the rest to enable us standardize our experimental

techniques and the instrumentation, especially the void meter and

the burn out detector being developed by us.

The rest of the experiments will be performed in an eccentric

annulus as this simple geometry has many of the properties of a rod

bundle(H). Its size will be made compatible with the power supply and

the flow capabilities of the loop. The test section will consist of an

unheated outer tube and heated inner tube. Conditions at the corner

rod can be approximated by such a geometry. Because the ability of

the fluid to flow around the eccentric rod is much less in the corner

rod than in a circular pipe, test* with this geometry tend to over-

estimate the effects of «ccentrlties. However, various eccentricity

settings can be utilized to reproduce the spacings of corner rod to

channel and the possible variations due to manufacturing tolerances.

269

The objective of the born out program is to get about a

dozen well defined conditions; with the flow rates, pressures and en-

thalpies matching with the reactor conditions of interest, for the

purpose of testing subchannel analysis techniques. The application

of the track analysis will be made based on the assumption that the

local condition hypothesis is valid. If this turns out to be not true,

further work is needed. This will cover locating new track bound-

aries and carrying the track sampling accordingly.

The analysis part of the program is aimed at developing

an appropriate calculation model for use in the rod bundle geometries.

Using COBRA code burn out is predicted with perfect mixing and no

mixing. Further analysis will enable us fixing the mixing coefficients

which are identical with those characteristic of single phase flows.

This assumes that a homogeneous model is valid. Efforts will be made

to evaluate how the computed conditions in the hot track are affected

by the sice and shape of the track.

Following the problems of immediate interest we may

use the 100 Kw loop for further void fraction and flow regime

studies. We have to develop instrumentation for void profile mea-

surements and flow regime detection.

A 100 Kw loop has many limitations on the experimental

work that can be undertaken. We plan to conduct similar studies in

the 1 Mw/3 Mw k>op. In addition studies on short bundles are planned.

Studies on hydrodynamic f?.ow stability including paral?.e;. channel

operation will be under taken in the bigger heat transfer loop. The

270

100 Kw loop gives us confidence on the experimental techniques and

instrumentation while tests of more direct application will be under,

taken using the 3 Mw loop.

References

1. A. Arriendóla; A Statistical Method! for Evaluation of Hot ChannelFactors in Reactor Design', KFK - 843 (July 1968)

2. P. Bakstad and K. O. Solberg; A Mode?, for the Dynamics ofNuclear Reactors with Boiling Coolant with a New Approach tothe Vapour Generating Process, KR - 121 (August, 1967)

3. N. Zuber et al. ; Vapour Void Fraction in Subcooled Boiling andin Saturated Boiling Svstems. Third International Heat TransferConference, August 7Í-12, 1966. Vol. V

4. R. T. Lahey and F. A. Schraub; Mixing, Flow Regimes, and VoidFraction For Two- Phase Flow in Rod Bundles.

S. L. S. Tong; Boiling Heat Transfer and Two. Phase Flow, JohnWiley and Sons, Inc.

6. R.T. Lahey Jr. , B. S. Shiralkar, DMW. Radcliffe; Two- Phase Flowand Heat Transfer in Multirod Geometries, GEAP- 13049, March1970.

7. S. Isreal, J. -Castcilino, B. Matzner; Critical Heat Flux Measure-ments in a 16 -Rod SirnrJation of a BWR Assembly, Trans. ASME,Journal of Heat Transfer, August 1969

8. George Yadiroglu, Arthur E. Bergles; An Experimental andTheoretical Study of Density. Wave Oscillations in Two- Phase Flow,M. L T. Report No. DSR 74629-3, December 1969.

9. R. S. Dalease and A. E. Bergles; Effects of Upstream Compressibilityon Subcooled Critical Heat Flux, ASME, Paper 65- H -67

10. L. G. Neal and S. M. Zivi;- Hydr odynamic Stabüity of Natural Cir-culation Boiling Systems - Volume I. « A Comparative Study ofAnalytical Modela and Experimental Data, STL- 372- 14(1), June 1965

11. P. Griffith; Personal Communication - A Suggested Program onthe Use of a Track Analysis in Burn Out Prediction. February 1970

271

TABLE-1

lOO Kw. BOILING WATER LOOP

MAX. OPERATING SURGE TANK PRESSURE : 100 Kj /c*»v

MAXIMUM TEMPERATURE

MAXIMUM SUBCOOUNG

HEAD DEVELOPED BY TUG TUMP

MAX. FLOW DELIVERED BY PUMP

LOOP HEATER CAPACITY

TEST SECTION MATERIAL

AVAILABLE FOR TEST SECTION

MAX. FLOW THROUGH TEST SECTION

POWER SOURCE

: 300 C

; 455 tlr«,./»nin

: 0-25 Kw.

: KANTIIAL-A1

; 35

: 20

: o-ioo KW

272

TABLE r_2

CIRUS-L-5 PRESSURISED WATER LOOP

MAXIMUM UNPERTUBEO THERMALFLUX (AT 40 MW OPERATION OFTHE RE A r TOR)TFST SECTION 1.0.PRIMARY COOP COOLANTNIOXYGEN CONTENTCOOLANT FLOW DIRECTION

COOLANT FLOW RATE: NORMALMAXIMUM

COOLANT TCST SECTION INLETTEMPERATURECOOLANT TEST SECTION OUTLETTEMPERATURELOOP DESIGN PRESSURELOOP OPERATING PRESSURE

AP MAX. ACROSS TEST SECTION

MAX. HEAT REMOVAL CAPACITYOF THE LOOP

5-5 X|0 h /cut /sec.

5-79 cmsDEMINE RALISED WATER9-10LESS THAN 01UPWARDS350 Llt-5/mt400

270 C MAX.

292* C MAX.17-1 Bars

13.7 Bars

30-5

400

273

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Lateral heat transport for turbulent flow of a gas in a rod bundle

Bjorn KjelLstrürnAktiebolaget Atomenergi, Studsvik. NykooingSweden

Summary

The attention is drawn to the fact that unexpected high values for themixing factor in the relation used in the HECTIC-program for calcu-lation of the lateral heat transport in a bundle,arc necessary if agree-ment with experimental data shall be obtained.

In view of some recent experimental' results it is shown that this cannot be explained by a particularly high eddy diffusivity in the gapbetween rods.

To find the explanation further studies of temperature fields in bundleswith non-uniform heating are necessary. Experiments would be pre-ferred but some conclusions might be drawn from a theoretical study.

The way in which such a theoretical study could be made is discussedbriefly and some of the difficulties which can be anticipated arementioned.

The main difficulty seems to be the estimation of the turbulent Prandtlnumber. Another difficulty is the consideration of secondary flows,the existence of which however in rod bundle flow-cells seems still tobe established.

At the end of the paper some suggestions for further fundamentalstudies in this field are given.

277

T . Introduction

The estimation of the lateral heat transport for turbulent flow in a rodbundle is of large importance for the design calculations of rod bundletype fuel elements for nuclear reactors. The problem has its greatestimportance for gaseous coolants and the discussion in this paper willbe limited to such fluids.

However, most of the existing computer codes for heat transfer cal-culations of rod bundle fuel elements, even with boiling, consider thelateral heat transport in the same way as is usually done for gaseouscoolants - thus parts of the discussion in this paper may be of a moregeneral interest.

2. Subchannel analysis

Most of the computer codes for heat transfer calculations of rod bun-dles axe based on a subdivision of the flow channel into subchannels.

In the HECTIC -program developed by Kattchee and Reynolds [6], thissubdivision can be made in almost any way required by the user - nor-mally however a subdivision by straight lines through the centers ofadjacent rods seems to be adequate, see fig. 1.

The lateral heat transport by turbulent diffusion between two such subchannels "i" and "j" is calculated by the program in the following wayfor an axial segment of length Ax

where AQ.. is the transferred heat energy per unit time, Tfei and T..the bulk temperatures of the two subchannels, 6.. and y geometrical

Hparameters explained in fig. 1, Y an enhancement factor or mixingfactor, the value of which has to be chosen by the user of the programand e.. the eddy diffusivity which is calculated as

eij

278

where D and u are respectively the equivalent diameter and the friertion velocity, the bar and the indices ij indicating that the average valuesfor the two subchannels shall be used.

This is all very simple and straightforward except that the value for the13

mixing factor Y is left open to question.TT

3. Experimental values for the mixing factor Y.> i - <

Numerous investigations have been made with the purpose to determinethe lateral heat transport for flow in rod bundles. An attempt to col-lect all published data from such studies for bundles without swirl pro-moters has been made by Ingesson [5]. The data were brought into

tisuch a form that the corresponding value for the mixing factor Y tobe used in the HECTIC-program could be calculated.

Ingesson [5] also made own experimente in two bundle geometries.

The results of this collection of data are shown in fig. 2 in which theu

mixing factor Y is plotted as a function of the geometrical parameter

Apparently the value for Y can be considerably greater than unity.For instance, for a bundle of triangular array with p/d a U 22 amixing factor of 8. 0 can be calculated from the regression equationfitted to all the experimental data

(3)

It is definitely of a certain interest to find out why the mixing factorattains these high values for close packed rod bundles. The valuesare in fact unexpected high, the authors of the HECTIC-program,Kattchee and Reynolds [6], recommending use of mixing factors ofthe order of unity for smooth walls.

i !•<

The rest of this paper will be devoted to a discussion of this problem.

279

4. Possible explanations for the high mixing factor

It will be sufficient in the following discussion to consider only what ishappening at the boundaries of and within an elementary flow-cell suchas that shown in fig. 3. The flow-cell shown in this figure refers to abundle of triangular array but this does not limit the discussion inthis section to such bundles.

A cylindrical coordinate system x-r-cp also shown in fig. 3 will be em-ployed.

Our interest will be concentrated at the boundary cp « 0°, since it isacross boundaries of this type, cf. fig. 1, the lateral heat transferbetween the subchannels considered by Ingés s on [si takes place.

The actual heat transport out of the flow-cell for an axial segment oflength Ax can be obtained from

or with suitably chosen average values for the eddy diffusivity and thetemperature gradient:

This relation can be compared to eq. (1). It should then be observedthat the factor 2 present in eq. (1) eminates from the fact that twoflow-cells of the type shown in fig. 3, are considered by eq. (1)whereas only one is considered by eq. (5). Comparison between theutwo relations shows that the mixing factor Y takes care of two ef-fects, namely

a) A difference between the true average diffusivity in the gapand that calculated from eq. (2).

b) A difference between the true average temperature gradientin the gap and that approximated by the ratio (Tfe - T

280

These two possible explanations will be discussed in the next' sectionin view of some recent experimental dala.

5. Experimental values for the lateral turbulent diffusion of mom c n-ttim

n 'At the heat transfer laboratory oí AB Atomcnergijii fj!.jLudsvik, Sweden,an experimental study is carried out, the object of which is to supply

> tmore fundamental data on turbulent flow parallel to rod bundles'. These* r ' i 'experiments are not finished and the results given here must there-fore be considered as preliminary. It is not likr.ly however that thefinal results will differ very much from those given here.

The equipment has been described in detail elsewhere [10], Only abrief summary will be given here. .- -• , .

The general arrangement of the experiment and a crosse-section oí thetest-channel is shown in fig. 4.

The walls of the channel are formed by six tub.es, (diameter 15f». 5 mm,length 8035 mm) arranged in a triangular array with the pitch-tp-diameter ratio equal to 1.217, , and by six tubular spacing clernents' ,arranged as shown in the figure. It was assumed when the experimentwas planned that the conditions in the central subchannel would be sim-ilar to those in a very large 'bundle. The results of the measurements,see [ lu], indicate that this assumption was justified.

The main part of the measurements are made 35 mm upstream of theoutlet at x/D = 81 (D defined for the central subchannel) and con-e esist of pitot profce and hot-wire anemometer traverses in the centralsubchannel.

The hot-wire anemometer employed is of the constant temperaturetype, a DISA 55D01 provided with a DISA RMS voltmeter 55D35 and aDISA Auxiliary unit 55D25. Miniature hot-wire probes with the wireat 90° angle to the supports (DISA55 A25) and with the wire at about45° angle to the supports (DISA55 A29) are used. The calibration ofthe DISA constant temperature hot-wire anemometer has beencarefully studied earlier see Kjellstrôm and Hedberg [7a, 7b] andKjellstrôm [8],

281

From the hot-wire measurements the single point correlations between- 2 -2 -2 -T—rthe velocity fluctuations u' ; v' ; w* ; u'v' and u'w' are calculated

as described by Kjellstrôm and Hedberg [?]. By numerical differentia-tion of the velocity field_measured by the pitot probe» the local veloc-ity gradients -~ and —-^ can be obtained,or r OT

This allows evaluation of the local eddy diffusivities of momentum evr xr

and e** as

(6)

Until now only the measurements made for 9=0 ; 12 and 30 havebeen evaluated, c could be calculated for all three angles whereas

\Â 3C* •••^BMB»

< due to the small values for both the correlation u rw* and the gra-xcp « v *dient — ~ at ? = 0° and 30° could be calculated with any accuracyr WP 0only for cp = 12 .

In order to make a comparison to the diffusivity estimated at the sub-channel boundary by the HECTIC-program, eq. (2), it is of particularinterest to make an estimation of the lateral eddy diffusivity c atx<pcp s 0 from the experimental results.

This can be achieved if the second mixing length theory of Prandtl [is]is adopted. In this theory it is assumed that the eddy diffusivity canbe obtained from a relation of the following form:

= k ¿ V q ' 6 (8)P

282

In this relation k is a factor (assumed to be constant by Prandtl [13]but here allowed to be a function of the position in the channel), ¿ is amixing length, the calculation of which will be discussed later and qis the kinetic energy of txirbulence defined by:

q'2 = ~ ( G ' 2 4 - v ' 2 ^ w ' 2 ) (9)

Eq. (8) can easily be generalised to a nonisotropic diffusivity by intro-duction of separate factors k for each diffusivity 00 that k is used

p pxrfor evaluation of e and k- for evaluation oí e

xr PXCP X<?

Here the mixing length will be calculated as suggested by Bulccv [l 3adjusted by a constant factor to obtain agreement with the results ofNikuradse C 123, if the formula is applied to the center of circularchannel.

The resulting relation is the following:

I = 1.136 J1 1 d<P (10)¿ o ?

Calculated distributions of the dimensionles s mixing length t/D areshown in fig. 5.

In order to estimate e for cp = 0° the following procedure has beenused. First the distributions of k were calculated for all three

Pxr>oangles and the distribution of k for <p = 12 . These calculations

*xtpwere made with eq. (8), using the experimental values for the eddydiffusivities and the kinetic energy of turbulence.

The distributions of k are shown in fig. 6 and the distribution of thePxr

=xr

ratio k /k = «îi/«îî is 8hown in fi8- 7

* > p ™

283

It is obvious from fig. é that no significant differences in k can be

established for the different angles. The curve drawn in by best judg-ment, can therefore be used to represent the data at any of the angles.

In fig. 7 a smoothed curve has also been drawn in by best judgment.If it is assumed that the ratio k /k is independent of the angle it

PX9 pxris now easy to estimate e at any angle using the results for q' ,

shown in fig. 8 which also in fact seem to be independent of the an-gle.

The distributions of eM for 9 = 0°, 12° and 30° are shown in fig. 9,xcp "in dimensionless form. At the moment the interest will be concentra-ted at the distribution for 9 = 0 . The other two distributions have beendrawn in mainly to illustrate the influence of the angular position onthe eddy diffusivity.

In fig. 9 is shown, together with the distributions of the eddy diffusiv-ity estimated from the experiments» the eddy diffusivity as estimatedin the HECTIC-program, eq. (2).

This value should be compared to the "experimental" distribution for9 = 0. When this comparison is made, it must be kept in mind that in

TJ

eq. ( I ) , e.. represents the ~.**y diffusivity of heat e whereas the ex-perimental eddy 'liffusivities are valid for transport of axial momen-tum. The ratio of these diffusivities are often referred to as the tur-bulent Prandtl number i. e

(II)

Experimental values for the turbulent Prandtl number for flow ofgases are of the order of unity or slightly below unity (down to about0.7). Although it is realized that the turbulent Prandtl number is nota property of the fluid but dependent of the boundary conditions in eachcase, it can be concluded that the available experience indicates thatthe difference in magnitude between the eddy diffusivities is small.

284

Returning now to fig. 9 and the comparison between the "experimental11

eddy diffusisily and that estimated in the HECTIC-program, it cai> beconcluded that the estimation in the HECTJC-program scents quite rea-sonable»

This means that the first of the suggested reasons for the high valuesfor the mixing factor Y to use in eq. . ( ! ) > seems to be ruled out.

It remains the possibility that the true average temperature gradientin the gap differs appreciably from the estimation in cq. (1).

This can be checked by experiments, but since such experiments wouldbe quite expensive, it seems reasonable to start with some theoreticalconsiderations.

Such a theoretical study has not be en,made yet. However the necessarytool, in form of a computer program, and most of the necessary empir-ical information seems to be available and thus there seems to be nomajor obstacles for such a study.

How a theoretical calculation of the detailed temperature field in asubchannel could be achieved will be discussed briefly in the next sec-tion.

6. Calculation of the detusted temperature field in a subchannel

Mathematically the task of calculation of the temperature field in asubchannel consists of solution of the differential equations for con-servation of mass, momentum and energy. These differential equa-tions are well known and the boundary conditions can easily be for-mulated. This docs not mean that the problem is simple, the maindifficulties being the choice of proper relations for th'e eddy diffus-ivitics and to find a suitable method of solution.

Several theoretical methods for calculation of the temperature fieldin a rod bundle subchannel with adiabatic boundaries in the flow havebeen proposed, of which those of Deisslcr and Taylor [2], Dwyer[3] and Ni j s ing et al. C i l ] can be mentioned. All these methods havecertain weaknesses, a detailed discussion of which would lead too

285

far here. It may be sufficient to mention the slight arbitraryness ofthe method of Nijsing et al. Cl il in which a modified local equivalentdiameter is used without any real physical justification and the dif-ficulties which will be encountered if the graphical iterative methodsof Deissler and Taylor Czland Owyer [3] are to be applied to caseswith a net lateral heat transport through the flow-cell.

The most promising approach seems to be a subdivision of the ele-mentary flow-cell, fig 3, by an orthogonal grid and to use the generalcomputer program for two-dimensional flows developed by Spaldingand his co-workers see Gosman et al. L4l.

In this program the mixing length model of Prandtl C13] for calcula-tion of the eddy diffusivity, see eq. (8) can easily be introduced. It isin fact possible to include the conservation equation for kinetic energyof turbulence as well and let the program calculate also this quantity.If a suitable relation for calculation of the mixing length, such aseq. (10)» is supplied together with a relation between the eddy diffu-sivities of kinetic energy of turbulence, e » and momentum, e , and

a relation for the factor k in eq. (8), a closed system of equationsis obtained, which allows calculation of the velocity field.

Once this has been established the temperature field can be calculatedtjprovided a relation between the eddy diffusivities of heat, ft , andmomentum, ft , can be supplied.

The results of the experiment mentioned in section 5 can of course beutilized to minimize the uncertainty in these calculations. Since theactual velocity distribution and the distribution of the eddy diffusivityof momentum are known from the experiments the only remaining un-certainty is the magnitude of the radial and lateral heat transports.

As long as the heat transports are assumed to diffusive, this uncer-tainty is limited to the value for the turbulent Prandtl number (whichmay be non-isotropic and a function of the position in the channel).

There is however also the possibility that heat is transported by con-vection i.e. by secondary flows within the flow-cell. This possibilityhas been stressed by okinner et al. Cl4],

286

Although the program oí Gosman et al. [4] can easily handle also aconvective heat transport it complicates the problem considerably.

It is therefore interesting in this context that the preliminary resultsof the rod bundle experiment referred to earlier in section 5 do notshow any significant indication of secondary flows, which means thatthe secondary flow velocities are at least smaller than about 0. 5%of the axial velocity. As mentioned earlier no detailed calculationsof temperature fields in rod-bundle flow-cells so far have been madewith the program of Gosman et al. [4]. Such calculations will how-ever be made within the near future and it is hoped that the resultswill help to clarify why the mixing factor attains the high values foundby Ingés son

7» Suggestions for further research work

It is without doubt that further experimental and theoretical studies onfundamental phenomena in turbulent flow and heat transfer in rod bun-dles will be needed if it shall be possible to develop calculation proce-dures which do not need a large amount of new empirical data eachtime a new fuel element configuration is considered*

It is time that the experimental studies proceed beyond measurementsof over-all quantities to measurements of the detailed structure of thevelocity and temperature fields for which purpose the hot-wire anemo-meter seems well suited. As examples of interesting research projectsone could mention

determination, of local eddy diffusivities by the technique describedin section 5 for bundles with rough walls.

detailed studies of the flow in geometries representing the outerparts of a rough bundle where interaction between flow-cells withpartly smooth and totally rough walls occur. The posit 'on of zero-shear sections and the distributions of eddy diffusivities should bestudied.

287

detailed studies of the velocity and temperature fields in bundleswith non-uniform heating including measurements of turbulent tem-perature fluctuations and temperature-velocity correlations. Theobject of such a study would be determine local values for the eddydiffusivity of heat and the turbulent Prandtl number.

determination of secondary flows in rod bundle flow-cell s for dif-ferent pitch-to-diameter ratios and wall roughnesses.

An interesting, but probably difficult, theoretical project would be de-velopment of a computer program which could handle three- dimensionalturbulent flows. (The program of Spalding and his coworkers, mentionedin section 6, is limited to two-dimensional cases which means that ifa detailed analysis of the flow in a rod bundle flow-cell is made, fullydeveloped flow must be assumed). Such a program would except as atool for practical calculations serve an important duty for co-ordina-tion of experimental research efforts, since of such a program existedthe experimentalists would probably plan their experiments in sucn away that the data could be used either to improve the program or forcomparisions with calculations with the program.

7. Conclusions

It is concluded that:

1. The high values for the mixing factor to be used in the HECTIC-program can not be explained by a particulary high eddy diffusi-vity in the gap.

2. The explanations must be looked for in the temperature field. Ex-perimental studies including detailed mapping of temperature dis-tributions in the flow would be welcome. Some clarification canhowever probably be obtained through theoretical calculations.

3. A suitable computer code for such calculations is available and sois most of the empirical information needed. The main remainingpoint of uncertainty is the value for the turbulent Prandtl number.

288

4. The possibility for uon-diffuuive, convective heat transport wi th inelementary flow-cellc of a bundle should not bo neglec»?c!. Experi-ments with a bundle with thu pitch-to-diarm ter ratio 1. Z\'( indi-cate however that if secondary Hows exist v/ithin the flow-cell*,the corresponding velocities are very small, at least smaller than0. 5% of the axial velocity.

5. Further fundamental research on ilow and heat traiiȣcr in rodbundles would be of great value. Eddy difiufivily distributions(momentum and heat), positions of zero shear so<:liont; ;i:id sec-ondary flow velocities should be. studied.

A gcncriil computer code for calculation of threc-di»r,watíiunalturbulent Hows would be welcome.

289

8. NOMENCLATURE

c specific heatd rod diameterD equivalent diameterk factor in eq.(8)t mixing-lengthp center-to-center distance in rod bundleQ heat flowr radial coordinater wall radiuswT temperatureu axial velocity . Lu friction velocity u* s *-ïOv radial velocityw peripheral velocityx axial coordinatey wall distancey distance from wall to section of maximum velocityY mixing factor, general

uY mixing factor for heat transport6 eddy diffus ivity ratio«H eddy diffus ivity of heat* eddy diffus ivity of momentump densitycp angular coordinateT shear stress

Subscripts

av averageb bulki subchannel "i"j subchannel "j"w wallo for «Mo

Special signs

mean value ex. û' fluctuation ex. u*

290

REFERENCES

1. BULEEV N ITheoretical model of the mechanism of turbulent exchange inin fluid flows.AERE-Trane 957 (1963)

2. DEISSLKR R G and T.AYLOR M FAnalysis of axial turbulent flow and heat, t ransfer throughbanks of rodf? or tubco.TID-7529 (pt i) book 2 (1956)

3. DV/YER O EAnalytical r.tudy of heal t ransfer to Hqiiid metals f lovvin» in-line through clocely packed rod bundles.Nucí. Science and Engineering 25 (1966) 3''3-58

4. GOSMAN A D et al.Heal and mass transfer in recir; ulatins f!o'\-y.Imperial College of Science and Technology, Thermo-fluidesection.SF 1 R 13 (Oct. 1968)

5. INGESSON L, HEDBERG SHéaV'transfer between subchannels in a rod bundle.4th International Heat Transfer Conference Paris -Versailles 1970.Paper FC 7. 11

6. KATTCHEE N and REYNOLDS W CHectic II. An IBM 7090 Fortran computer program for heattransfer analysis of gas or liquid cooled raactor passages.IDO-28595 (1962)

7 a. KJELLSTRÔM B and HEDBERG SCalibration experiments with a DISA hot-wire anemometer.AE-338 (1968)

7 b. KJELLSTRÔM B and HEDBERG SCalibration of a DISA hot-wire anemometer and measurementsin a circular channel for confirmation of the calibration.DISA Information nr 9 (1970) 8-21

291

8. KJELLSTRÔM BTurbulence measurements with a constant temperature hot-wire anemometer,Conf. on Applied Physics and Biophysics Stockholm, June4.6 1969

9. KJELLSTRÔM BEvaluation of the flow direction and the Reynolds stresses ina three-dimens ional turbulent flow from measurements witha single hot-wire.AB Atomenergi, Sweden (Internal report RV-144) 1970

10. KJELLSTRÔM B and STENBÀCK APressure drop, velocity distributions and turbulence distri-butions for flow in rod bundles.AB Atomenergi, Sweden (Internal report RV-145) 1970

11. NIJSING R et al.Analysis of fluid flow and heat transfer in a triangular arrayof parallel heat generating rods.Nucí. Eng. and Design 4 (1966) 375-98

12. NIKURADSE JGesetzmftssigkeiten der turbulenten StrOmung in glatten RohrenVDI Forsch. heft 356 (1932)

13. PRANDTL LitUber ein neues Formelsystem fur die ausgebildete TurbulenxNachr. Akad. der Wissenschaft zu GOttingen, Math. -phys.Klasse 1945, 6 - 1 9 reprinted inLudwig Prandtl Gesammelte Abhandlungen Berlin 1961, 874-887

14. SKINNER V R, FREEMAN A R.and LYALL H GGas mixing in rod clusters.Int. J. Heat and Mass Transfer 12 (1969) 265-78

292

Definitions made in subchannel analysisof flow and heat transfer in a rod bundle. Fig.1

Subchannel "i"

— Subchannel "j1

— — — — Subchannel boundary

293

Collection of experimental data for the mixingfactor Y made by Ingesson. Fig. 2

25

20

15

10

10 15 20 253/2

294

Elementary flow cell in ci rod bundle* oftriangular array. Fig. 3

•

Cross - section _ th i ough elgmg n* ary? j low reil .Main flow direction pc»rpendicuk:.r Is the pianoof the paper, outwards.

Definition of cylindrical coordinate system.295

Principal arrangement of the experimentalequipment

Fig. 4

p/dsl.217

De » 0.0992 m

d «0.1565m

Croas-section throughtha test channel

Central subchannel.The measurements a» concentratedto this area.

Tx/IV«

•••••oo_telSSSZ:sssîSf»asi*

Explanations to Fig. 4

1. Air from blower(max. 2 Icg/s)

Flow rectifier

Foster flow metei

Cooler

5. Honey comb

o» Contraction

Test channel

Probe supportwith manipulator

Stagnation presstiof hot-wire protx

296

Calculated distribution of the mixing lengthfor a rod bundle of triangular array withp/d «1.217.

Fig. 5

t/D,

0.07H

0.05-

0.04-

0.03-

0.02-

aoi-

0.00

297

0.8 0.9 1.0y/9

ExperimentaUy determined distributions of thefactor. kp in Prandtls relation for the eddydiffusivity

Fig. 6

Mean values of three experimentsV <p sO°0 <p «12°O tp «30°

Estimated standard deviation O.U

'Pxr

1.0-

0.9

0.8

a?

as-

as-

0.4-

oi3-

0.2-

ai-

oo-

Eq. (8) :.M ,."xr KPxr

Averaoe vohie recommendedbv Prandtl

OJO 0.1 0.2 0.3 4 0.5 0.6 0.7 0.8 05 1298 y/9

2-

1 -

Experimentally determined distribution of theratio £Jy /ejfr forip s 12'

Mean values of three experiments.

Estimated standard deviation 2.4

Fig. 7

12-

lt -

10-

* kr

xr

9 -

8 -

7 -

6 -

5 -

3 -

OX) Q1 0.2 Û3 0.4 0.5 0:6 0.7 0.8 0.9 1.0299 -.'>

Distribution of the kinetic energyof turbulence. Fig. 8

1.9-

1.8-

1.7-

1.6-

1.5-

1.4-

1.3-

12-

1.1-

1.0-

ae-

a?-

Mean values of three experiments

V <p « 0°0 q> « 12*O 9 « 30*

Estimated standard deviation 0.15

00 0.1 02 0.3 0.4 0.5 0.6 07 0.8 0.9 1.0300 y/y

Estimated distributions of the eddy diffusivity Fig. 9for lateral transport of axial momentum atdifferent angles.

Rod bundle of triangular array, p/d =1.217.M•xip

u* D

0.10-

0.09 H

0.08^

0.07-

0.06-

0.05-

0.04-

0.03-

0.1D2H

0.01 -

0.000.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

301 y/y

POST BURNOUT HEAT SR&KSFEB

X. CumoLaboratorio Teonologie ReattoriCentro Studi Nuclear! della CasacMaGood tato Nazionale per 1* Energía totoleareRoma, Italia

Poet burnout heat transfer is» up to now, a rather unexploredfield of research and has many points of uncertainty*Nevertheless it has become, both for the reduction of the safetymargin with respect to the burn-out limit in the boiling systemsand for the development of the once-through systems» an urgentand important problem in the heat transfer research.Indeed such problem has a dual-purpose aspoet» especially innuclear applications:

a safety aspect, in the investigation of the consequencesof a power excursion (or loss-of-flow) accident» when for a periodof time the burn-out power may be exceeded and it is important tosee if the temperatures reach the safety limit;

, a design aspect in the once-through boilers» including,for instance the sodium-heated steem generators in the fast reactorplan n-?, where downward the dry-out point the cooling medium isconstituted by a stream of vapor entraining droplets» and whereit is important to have design criteria to .determine the exchangerlength and the wall temperatures involved.Many problems are associated to the post-burnout heat transfer;for instance s

the determination of the heat transfer coefficient in dependenceon the specific mass flowrate» the vapor quality» the pressure

303

and the flow geometry, far downward the dry-out point,where the wall is definitively drybhe determination of the temperature jump at the dry-outpoint and its dependence from the main flow-parametersthe determination of the wal3 temperature oscillationsaround the dry-out point, which may induce oscillatingstresses, the extension of this unstable zone and the flowsituations under which this oscillating behaviour establishesthe determination of the main parameters under which athermodynamic disequilibrium occurs, i.e. the quality isno longer given by an enthalpy balance but the vaporsuperheats in presence of the liquid, dispersed phasethe determination of the main parameters under which aLeidenfrost-type phenomenon is possible, i.e. the dropletswh -m hit the heating wall no longer remove a significant. uunt of heatthe determination of non-linearities in the heat transferlaw, i.e. heat flux « temperature difference x heat transfercoefficient, and their dependence on the separate contributionsto heat transfer by the vapor phase alone and by the liquidphase alone.

The following remarks will synthesize very briefly some resultswe have reached in answering to the preceding questions, leavingevery physical explanation to the literature each time referred.First of all, the main purpose was to obtain an overall heattransfer correlation which, in the most simple way, mightcorrelate the heat flux with the temperature difference Á&among the heating wall and the saturation point ( A9* TW-ÏR).

2Operating with water at a pressure of 50 kg/cm and withfreon 12 up to the critical pressure, both in upward, once--through flow within vertical, tubular ducts, uniformely

304

8

hsated by Joule effect, w© f\J have gathered many experimentalresulte which, through simple physical considerations /2J7 havebeen partially correlated by ea equation of the type:

0>0089whore (He ) is the vapour phaae Eeynolde mcaber (GXD/j3/u ),gfilia s

(Pr ) is the vapoiAT ph&ss Frcaâtl nuoibsr, X_ A io the vapoure film *0*qua] -y at dry-out, the indâx "fils" meeno that the physicalproperties are evaluated at tho fila température, i.e. the averagebetween the nail and eatur&tioa temperaturas.The influence of the propcuiro on tho overall heat transfer coefficienth has been investigated, for & nuaber of situations, ecrployingfrcon 12. Kao pressure COCGD not to have a great influence on h(fie. 1 ) : the variations cs«o in the order of .'those provided by theusual forced-convoeticn correlations, taking into account the changeswith prcosure of th© physical properties /2.7.The above correlation n&y provide & first-order calculation for watersystems, not to close to the critical point /3.A Very soon we realisedthat only & rough correlation exists among the heat flux andthe overall toirper&ture dump Á&»In other words, for the atoovG-ssemnoneu experimental set up, theheat flux ie a lineer function of ÂÛ9 constant remaining all otherparameters, but tho relation

doss not hold at the limit, when A& approaches zeroThe heat flux *P seems 'to split into two terms:

whose Y seems to pertain to the cooling action of the vaporphase alone and P. to tho liquid phase alone /& , 5.7.

305

COoo»

0.4-oo(M

U 0.3T

0.2-

0.1

04-0.2

G=~300g/cnr sec

IT

Pig. 1 - Heat transfer coefficient versus reduced pressure atdifferent specific mass flowrates.

il • 0.30 •G • MO g/cm1 tMX .0.60

MO

•lJi-

lt < O.OG • 210 j/em1»X . 0.6S

S~ NO MO

* • 0.37G • Sí 8/«m'McX . 1.0

• • O.SSG • 103 a/em'X . «33

I9-

«.«s0 • 103X • O.M

M » as? ¡O »,ÍOOB/ejn'«t ix > aso -v- i

MO no

Eu

«.«.tf6 • 200 g/em'iX . 0.52

n «o noAd-Tw-T» («CJ

MO MO

v * 0.66C • 200 t/tm'ftcX . 0.72

Pií?. 2 - Heat transfer data'Sfbr fréon 12 at differentreduced pressures, specific raass flowrates andqualities . i

307

I

30-1

if 20-;

10-

p « 70 Kg/ en?6 « 220 g / en? sec0 « 0.596 em

W/cm2

W/em2

80 « f <130 W/cm2

20 < y < 50SO* f < 80

O.S 0.6 0.7 09X

• 3 - tp- versus quality X

308

0.9 10

The term <f is a linear function of

of the well known forced-convection type, while V- seemsto depend on the liquid quality of the mixture (see for instancefigs. £ and 3)*-Approaching the dry-out point, wall temperature oscillations majfset~i •» .vith a frequence f which is a function both of theexperimental loop characteristics and of the flow parameters*About these last dependences , the following correlation has beenenvisaged

f = const * —— UA A

where J is the conversion factor between mechanical and thermalunits i Û is the mean vapor linear velocity and the other symbols

Ohave the well known significance.Fi£. 4 provides ah example of the wall temperature fluctuationsfc*- a boiling water (50 atm), once through system electricallyheated f&J.The insertion of twisted tapes in once- through heat exchangers»greatly increasing the quality at the dry-out point, causes asharp reduction in the temperature oscillations,, w.hich are nolonger detected /*?./.At the dry out point it is possible to have, depending mainlyon the specific mass flowrate, or a sharp wall-temperature jump,followed often by a temperature decrease, or a slighter

• • * * * » .temperature increase ¿2J°As an example, these temperature jumps at the dry out point(maximum wall temperature close downward the dry out point minus thesaturation temperature) have been plotted for freon 12 versus thereduced pressure, up to the critical point (fig. 5).

309

a) G>740/«m*tM *»79l6*/em* f «0.525 Hi ff.2.15 Hi

I i

b) 0««2,4 t/em>«.t «-TlOw/M»* f«0.tl« H« %• 2.11 MB

e) G-10.2 (/tm*«tc f« 82,4 »/««»» f«OS6t Ht f(«2.12 Ht

d) 0-6S5 j/em*»»e f. 0.543 Ht ff • 2.00 Ht

Rg. 4- Registrozlonî délie oscillozioni di temperatura olio crisi rilevotesullo sezione di prcva In ni che I -

310

1300-! « 9/cnrr sec

cm2

200

oo

100-i _

O

• G =• G = 96 -r 104• G =195 -f 214o 6=287-312

O

r' V——-..^ „-*•*» >>

<P=9-r10,7

= 13.8 -15.2« G=308-f 322; <P =182^-196

0.2 0.6Fíg. 5 - Wall temperature pump at burnout versus the reduced pressure.

Contrary to an expected trend AT_- does not always decreasewith TC » "but does only at the higaest flowrates.

Only «»t the highest specific mass flonrates these temperaturejumps decreaoe with pressure» with a rather uhespeoted trendIn the first ease the increase in fluid enthalpy» following tovaporization» enhances the mixture velocity with a stronger cooling*Some tine this temperature decrease re&ohes the saturation level»with a wall resetting (£ig. 6). ü¿u dxia-tence of these temperaturejumps of very different emount end of different gradient and thesplit of the total heat flux into <fr and f, » with the problemof investigating the physical structure of <P- » have suggesteda deeper insight into phenomena of the Leidenfrost type.So we have measured the Leidenfrost temperature for animpinging Jet of droplets of water and low-boiling organice(CH Cl» CH Cl) fQj, getting the results reported in table 1.Ho clear correlation e e eso to exist» at the light of the la»of corresponding states of Themodyncadcs, fisaong the Leidenfrosttemperatures of the experimented fluids.Among the other parcasters» the volocity of impinging dropletsU. seeps to be correlated with the Leidenfrost temperature T_through the f ollowing relation /9./:

4/3*«L " TL - *sat * ud

The dependence of the contact tin* s» during which the transferof heat among droplets* and heating «mil becomes» on velocityend dimenoions of impinging &?oplo*;c crA the wall temperature»has been measured employing fast cinom&tography techniques 'fio »1 \J(fig. "• ;.The -»11 texiperature seems to ploy en important role in theformation of the vapor layer beneath the droplet» thus decreasingthe contact time.All the post burnout research has to point out an importantverification: the existence» or not» of the thermodynamic .equilibrium among the phases. When this equilibrium does not

312

exist, it is impossible to set the quality by a thermal balanceand then a fundamental parameter cannot be determined but inexperimentally very complicated «raye.v • ' «•*•••.•, With freon 12 we have detected thermodynamie disequilibria upto computed qualities of 2000, getting, with the high speedvisualisation techniques» a photographic evidence. 27» The

Tab. 1' . 1

Fluido .

Temp, diLeidenfrost

Temp. cri tica

' r.atriacald.: -.u-..?, ciú.bfa-'

zione (TJ.-TJ

Temp, di sa-turazione

.(p«i a-to)

Happorto*y%Sapporiovsc -...:Rapporto

H» '•"

• *s'"c

! p?&3sione1 criticaVPressionsrido-éta i

C2H2012 '

TL»516,5°K.

Tc-544, °K X",

•v

AV1flf3'0!c x:'.r~i

• '>"

I. «333,2 «K

$*• 0-336

TT-^-0.35

•--- -°.' T '""

TÍ"0-*1

iPc«54,4 :Kg/cm2

1T- 0.0184

C Hp CÍ• 2 Z

X"X

TT«3<J?. °KL \ '•^

' Tc»510 °ÍC

ATfl»84 OK

c ;.! • • • •'.

í? «313.°K8

£-0,65C

TT

V « °-778c _ ...

"*.^-0.6^4 Vc

^0»60 Kg/cm?

Tf.0.01665• .xfc

HjO

T_«530 «KL

Tc»647 °K

¿Ï «157 °K9' \

\

T «373 °Ko

ATS«-2-0,242c

TT•ez* °-82^-V.

*sC ;- 0.577C' v

P0«225 Kg.cm2

*Jf «0,00445

313

200112

150-

5

100-2

CVJ£o

ToTsat - 83 °Ç

-2.0

-1.0

-0.5

0.1Jig. 6

0.4Wall temperature (?v), heat transfer coefficient (h) and heat flux (<p)versus the local quality (X). (T± and T0 are the coolant Inlet andoutlet temperatures).

•—!.O

1.5

05

• 55<d<75o 90<d<110* 130<d<160

0 100 200 300 400 500 600

II [cm/sec]

Fig. 7 - Contact time versus impact velocity fordifferent wall temperatures (T ).

315

CO»-•O)

50

40

30

o• y «18 W/cm2

y «23 W/cm2

100 200G [g/cm2 sec]

300

Pig. 8 - Vapor superheating ver*us the specific massflonrate.

50 "+r-———rr-»——^———•<——' - '*•

M

40-

30

20-

G «100 g/cm2 secX0= 0.76

G=50 g/cm2secX0=0.78

í6.0 W/cm2_

G-300g/cm2sec

W/cm2

G=150g/cm2sec\/ — f\Q '

0.1

G=200q/cm sec

W/cm2,.

G=200g/cm2sec- X0=0.34

*11.5W/cm2

I4-

1.0

Fig. 9 - Vapor superheating versus reduced pressure,

-4 .4 .

50

40

« P

Î5

3000

20

10

^

. G-50g/cm"sec• **0.5

Q95

G*50 g/cnfsec1t=0.7 '

075

G-50 g/cm sec* 11-05 '

X0» 0.7

G =100 g/cm sec1t*0.5 'V 0.52

10[W/cm2]

Pi«. 10 - Vapor superheating versus heat flux.

12

G=KX)gA:m2secf^ - f±. ••• ~~f

*J

G»100g/cm"secit=0.7 7

VQ.75

14

20

OO»U)

10

COt->«o

i f +: * T&* ••**•i 7

G =Xo=

0.2356 g/ cm2 sec1.23

100 200 300

Fig, 11 - Droplets* velocity versus droplets1 diameter; apart fromthe large experimental scatter thert is a substantialindependence of the velocity from the diameter, followingto the theoretical prediction. ;

COtoO

- 2JO

atGXo

0.2356 g / cm2 sec1.23 n

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.9m0.5

Fig. 12 - Droplets9 transversal velocity profile (U.) compared with the vaporvelocity profile (U) theoretically deduced; local slip ratiosare wry close to 1.

measure of the vapor superheating in quite difficult for thewetting of innersed thermocouples. With a particular teetsection /"13y it was possible to measure the trend of thevapor superheating ¿TB * TV"T8 versus the leading parameters:specific mass flowrate G, reduced pressure tf and heat flux <P(figs. 8, 9 and 10).Roughly it is possible to writes

<p.<pAi oc ———2.(1 . tf)

G-Gobeing GA and ? convenient reference values.^ o oThe employ of the photographic techniques /"Ï4_7 has given alsoa deeper insight into the constitution of the post burnouttwo-ph*s<s mixtures /"IS,/,Our -oretical studies /"15 , 16 , 17 , and 18.7 on highly dispersedtwo-phase flows have been experimentally confirmed, getting thepicture that the entrained droplets behave as rigid spherulesnever coalescing and uniformely distributed throughout theflow channel, following straight trajectories parallel to the mainflow, with velocities which are almost independent from dropletdimensions and very close to the vapor velocity (figs. 11 and 12).Much has to be done in the future on this particular but importantfield of post burnout heat transfer; we hope that' these firstresults may support an overall picture of the phenomenaim ived, shorting the time necessary for getting definetivelyaccepted correlations.

The referred researches» cited in the literature, havebeen possible only for a valuable group of researchershave given their indispensable contribution.

321

Among then, fundamental are the contributions fromDr. G. Blanchi, Dr. R. Brevi» Dr. G.E. Parello,Dr. 6. Ferrari» Dr. A. Paloieri and Dr. D. Pitimada.

Bibliogra

Brevi R. » Cuno H. » Palnieri A. , Pi timada D.•Heat Transfer Coefficient in Post BurnoutTiro-Phase fixtures"Européen Two-Phase Plow Group Meeting (Karlsruhe» Jims 1969)La Termo técnica (1969)

/"X7 Cumo Iff.» Farollo 6.E. » Ferrari 6."Pest Burnout Heat Transfer and Thermodynamic Disequilibriumup to th3 Critical Pressure"4th International Heat Transfer Meeting (Versailles» 1970)

K. » U3)rk-M5rkenstain P."Singularity of the Heat Transfer in the Two-Phase regionapproaching the Critical Pressure11European Tco-TTin.ee Plow Group Meeting (Karlsruhe» June 1969)Brevi n. ,"Heat Trcnofer in the Liquid Deficient Regime"European Trro-Ph&se ?lov? Group Meeting (Milano» June 1970)Brevi E.» C'JSTD H."Quality In luenco in Post Burnout Heat Transfer"International Journal of Heat and Mass Transfer

Z~6_7 Brevi R. , Cumo U. , Palmieri A. » Pi timada D."Oscillasioni di temperatura alla criei térmica eon mi-seele bifaei"24° Congresso Haz. ATI - Bari» Ottobre 1969La Teraoteonica

322

Brevi R., Cumo H., Palmier! A. > Fitimada D."Forced Convection Heat Transfer and BurnoutMeasurements with Twisted Tapes"A.N.S., 16th Annual Meeting (June 28-July 2, 1970 -Los Angeles» Calif.)Cumo M»» Pitimada D."Sulla determinazione della temperatura di Le.idenfrostcon fluidi organic!"La Rivista di Ingegneria - Hoepli (Kilano)Cumo M., Pitimada D."Sulla determinazione della temperatura di, Leidenfrost"23° Congreeso Naz. ATI - Roma, Ottobre 1968Cumo Mo, Farello G.E., Ferrari G."Notes on Droplet Heat Transfer"10th National Heat Transfer Conf. AIChE-ASMB(Phyladelphia, 11-14 August 1968)

Chem. Eng. Prog. Symp. Series 92, Vol. 65¿^•'_: Cumo M., Farello G.E. » Ferrari 6.

"Heated Wall-Droplet Interaction for Two-Phase FlowHeat Transfer in Liquid Deficient Region"Symp. on Two-Phase Dynamics of the Euratom(Eindhoven, The Nederlands, 1967

¿fÎ2_7 Cumo M», Farello G.E., Ferrari 6."A Photographic Study of Two-Phase» Highly DispersedFlows"European Two-Phase Flow Group Meeting.- Milano 1970

323

Cumo *•» Amello G.E.» Ferrari 6."Sul disequilibrio termodinamico nei deflussi bifase*24° Congresso Naz. ATI - Barí, Ottobre 1969La TermotecnicaParello G.E."Tecniche di visualizzazione dei fenoaeni rapidi"L'Ingegnere (1969)Brevi H., Cuma M."Theoretical Remarks about Post Dry-out Heat Transferwith Two-Phase Plow Mixtures'11969 Int. Seminar of Heat and Mass Transfer (HercegNovi - Jugoslavia, 1969)La TemoteenicaCumo H. » Ferrari 0.•Termodinámica ed evolucione délie misoels bifasi adalto titolo"23° Congreoso Naz. ATI - Roma, Ottobre 1968Cumo If."Consideradcni sulle aiscele refrigeranti ad elevatadispersions di liquido in vapore eurriscaldaljo"22° Congreeso Naz. ATI - 1967La TermotecnicaCumo M."Tentativo di impiego délia teoria dell'informaBionenella termodinámica délie miscele ad elevata disper-sions di liquido in vapore surrieoaldato"24° Congresso Naz. ATI - Bari, Ottobre 1969La Termoteonica

324

Bennet A,W,, Hewitt G.P. f Kearsey H.A., Keeys R.K.P."Heat transfer to steam-water mixtures flowing inuniformly heated tubes in which the critical heatflux has been exceeded1*Thermodynamics and Fluid Mechanics Conventionpaper 27 - Bristol March 1968.AERE-R 5373 (1967)Heineman J.B."An experimental investigation of heat transfer tosuperheated steam in round and rectangular channels"ANL-6213 (1960)Herkenrath H., MBrk-Httrkenstein P."The heat transfer crisis under forced water flow athigh pressures"Atomkemenergie 14 Jg 1969 Heft 6 S 403-407

/"22_7 Bishop AoAo, Sandberg R.O», long L.S."Forced convection heat transfer at high pressure afterthe critical heat flux"ASME - 65 - HT - 31 (1965)WCAP-2056 Pt. VHicque R., Roumy R."Experimental study of the phenomenon of dryout forFreon 12 boiling in a horizontal tube"European Two-phase Flow Group Meeting (Karlsruhe» June 1969)Cumo M.f Farello G.E., Ferrari G."Some observations on heat transfer to freon 12 in thenear critical regime"1969 Cryogenic Bng. .Conf. - UCLA (Los Angeles» Calif. 1969)Cumo fcu, Farello GoE», Ferrari G."Post burnout heat transfer up to the critical pressure"A.N.S. Winter Meeting (San Francisco, 1969)

325

YUGOSLAV ACTIVITIES IN THE FIELD OFHEAT AND MASS TRANSFER RESEARCH INNUCLEAR POWER REACTOR SYSTEMS

byPredrag Anastasiaevie

Head, Thermal Physios and EngineeringDepartment, Boris Kidrië Institute ofNuclear Sciences, Beograd,Yugoslavia

During the last twenty years Yugoslavia has accomplishedimportant economical and industrial progress. It also has founded newlaboratories and.research centers. In nuclear research field more thanfcoott&llion of dollars have been invested for nuclear research insti-tutes and industrial research laboratories with more than 1000research workers.

There have been developed laboratories for heat and masa•transfer research, the most important ones being:

- Thermal Physics and Engineering Department of the BorisKidriS Institute in Beograd

- Research and Development Center for Thermal and NuclearTechnology of the -Energoiovest Company in Sarajevo

- Laboratory./ for Thermal Engineering of the Mine Institute inBeograd

- Nuclear Pow^r Department of the Energoprojekt Company inBeograd

- Thermotechnical Laboratory of the Electricity GeneratingBoard of Croatia in Zagreb

- Heat Transfer Research Group of the JoSef Stefan Institutein Ljubljana

327

The first steps of heat transfer research in our laboratorieswere mainly influenced by the programmes of Nuclear Energy Commissionwhich gave at the beginning particular importance to the problems ofgas cooled reactor systems. In 1964 preference has been given towardswater cooled power reactors.

Eecently, heat and mass transfer research has been substanti-ally extended in relation to work on applied research connected withthe elaboration of conceptual designs of nuclear power plants andassociated thermal calculations and optimizations.

The programme of work encompasses continuation and /or furtherdevelopment of the following activities;

- basic problems of heat transfer intensification from gascooled surfaces

- research on heat transfer in two phase flow- thermo physical characterization of nuclear materials, fuel

elements and assemblies.- thermal reliability of the reactor cores and fuel elements- hydrodynamic behaviour of power reactor channels and their

thermal optimization- thermal problems in connection with containment, concrete

vessel and components: turbines, boilers, heat exchangers and pumpsAecording to this the research resuits obtained in c»ur labo-

ratories and research centres are as follows :

328

Heat and mass_transfer from gas-cooled surfacesOur first theoretical and experimental investigations

have been carried out in two main directions : on the basic prob-lems of heat transfer intensification from gas-cooled surfaces,and on the measurement of thermal and aerodynamic characteristicsof gas-cooled reactor fuel elements.

An approach wa» made to the study of heat transfer condi-tions under both positive and negative pressure gradients. Theresults obtained indicate very favourable conditions for heat tran-sfer under a pressure gradient which causes additional turbulence atthe boundary layer. This would result in a substantially increasedheat transfer coefficient.

Work has also been done on the problems and effects ofheat transfer fr,om corrugated, finned and extended surfaces. Theexperiments contributed to a better understanding of the physicalphenomena associated with heat transfer under such conditions.Various types of cladding surfaces have been examined.

The results obtained showed that basic phenomena mechanismsare mostly talcing place in the vicinity of the heated wall andshould be studied in more details. It is clear that this research

is not only specific for nuclear reactors but it could be extensivelyapplied in other fields. Thus the work has recently been devoted tofundamental research o phenomena in the boundary layer. A method ofmeasurement and statistical analysis of the instantaneous velo-cities and tsmperatures with a single probe in form of a micron-thich wire was developed.Velocity and temperature probabilitydensity distributions were measured in wall layers with variousturbulence intensities. It followed that probe signals containedmore information on turbulence characteristics than what wasnormally supposed. This fact enabled to obtain the additional

329

information on turbulence characteristics in the «all vicinity andeliminated measurement errors due to high intensity turbulence.

On the basis of results obtained in two-dimensional divergent-convergent channel ai£ in the entrance region of the channel withannular flow cross-section , we smarted with investigation inannulary divergent-convergent channel with various inclinations andlengths in order to obtain the optimal geometry providing maximumheat fluxes The heat is generated on the internal surface of theannular channel by constant heat flux. The distribution of localftusselt number for different values of Reynold's number is measuredas well as the velocity and temperature profiles in some cross sec-tions, including the separation regions.

Research on heat transfer in two-phase flowModern water-cooled power reactors are being advanced

towards increasing specific heat generation and promising resultsare expected. This is why the 3aosearch on heat transfer in twophase flow represents a large part of our- activities* The mechanismof two phase flow has shown that heat transfer depends to-a largeextent on the quality of the surface at which the mechanism takesplace. Measurements have been tak¿n of heat transfer during boilingat the liquid cercury surface that may be considered as ideallysmooth. The results obtained have produced a better understandingof this phenomena. At the same time kynetics of vapour phase gene-ration and bubble growth dynamics were also investigated. Liquidphase superheating was studied in order to determine the stabilitylimit and degree of ireversibility of the phenomena. In theseexperiments a new method was applied without any contact of super-heated liquid fcoa the vessel wall.

330

Por the study of burn-out an original method of burn outdetection has been developed , enabling very precise measurementunder given experimental condition and preventing the burn-out ofthe test section. The same group of researdhers is enagaged inthe study of burn-out conditions in twn phase flow b£ binary.liquidsand liquid with solid additives.

In order to study the micro structure of boiling phenomenathe techniques of microthermocouple for temperature fluctuationsmeasurement was developed. From the statistical analyses of thethermocouple e.m.f. the most probable temperature difference ofwater and vapour phases were determined. The measurement showedthat in the water- steam mixture exists the appreciable superheatof liquid.For the bubble boiling regime the most probable tempe-rature difference has a minimum which is at the same place whereis the maximum of the local void distribution. In annular flowregime in dispersed core , liquid droplets are also superheated.Considering the existence of liquid superheat whithin the twophase flow, the equilibrium void fraction calculated from equilibri-um between the liquid and vapour phase is Encorréete and in thesame cases may be remarkably different from exact void fraction.The conclusion is that the real quality is lower than the samevalue calculated by equilibrium model of two phase flow,

Thermo-physical charaeterization of materialsThe problems of thermal contact resistance create a large

proprotion of the experiments undertaken for fuel element develop-ment. A special apparatus has been constructed in the laboratoryfor the invastigation of changes in thermal resistance of uraniumdioxide- zirconium alloy contact under conditions of varying diffe-rent parameters.

331

Work on the problems of thermal resistance of gas-gap has providedinformation most useful in the manufacture of oxid fuel elementsand in the construction of reactor channels. Similar experimentswere performed in the heavy water research reactor in the BorisKidriS Institute.

Measurement method of specific heat«thermal conductivity,thermal diffusivity and other thermophysical properties have beendeveloped or improvedy in order to determine these parameterswith greater accuracy in the condition of extension towards thehighest possible temperatures. The spécifie heat of materialsis determined by anthalpy measurements.The calorimeter providingprecisely accurate measurements was constructed . The error ofmeasuring the specific heat by this method is below one percent.

The modified Angstrom method for thermal conductivityand diffusivity measurement was developed and the laser techniqueswas applied for determination of these parameters at higher tempe-ratures.Thermal reliability of reactor cores

As for safety problems in nuclear plants, the probabilitymethod is applied in order to fi id out the thermal reliabilityof reactor core, cooling channel and fuel elements. Besides, itincludes the study of all consequences relating to reactor struc-ture and surroundings in the case of accidental loss of coolant*

Hydrodynamic behaviour of power reactor channelsWithin the scope of thermal and hydrodynamic investigations,

? series of experiments are carried out in order to determinethe following parameters: steam void fraction, boundary layersuparheating,maximum heat flue and pressure drop in two-phaseflow mixture, in the case of forced subcooled circulation, bubble

332

boiling and high steam quality flow. These phenomenon could beanalysed only in the case when local parameters are known»The methods for measuring the temperature fluctuations in thevicinity of the wall were developed, as well as the methods fordetermining void fraction, velocity, shear stress, viscosity andother parameters which should be taken for analysis .

There are several experimental facilities for thisinvestigations, the greatest of which is high pressure loop withmaximum temperature of 2?0°C, maximum pressure of 55 bar,maximum water flow of 10.000 kg/ h and maximum power of 630 kW.These investigations include theoretical and experimental studyof dynamics of two-phase adiabatic and diabatic systems, andthe influence of the vapour phase compressibility to the flowstability.

For the analysis of behaviour of power reactors andboilers in accident conditions as well as desalination plants designresearch on flow characteristics and evaluation of main para-meters wa0 developed.

Regarding to the nonequilibrium flor character, a spe-cial attention was paid to the experimental determination of realliquid superheating along the channel. Analysis was made of theinfluence of time in which the liquid stream is subjected to thelower pressure than the saturation one. Experimental low pressureloop;¡withxverticalconvergent-divergent nozzle ( enturi type } wasmade. The average local liquid superheating was measured and forsome flow conditions analysed. Superheated or flashing water flowswere observed depending on water flow rate, inlet temperature and.,condenser pressure. Visually observed flashing flow regimes arecharacterized by different intensity of evaporation process andby flow structure of two-phase mixture. Plashing

333

proofs intensity and flow-s truc tore effect the absolute valuesof the local pressure and temperature and define the magnitudeand character of pressure and temperature fluctuations.Tape recording of pressure and tempe -ature fluctuations measuredby highly sensitive thermocouples and pressure transducers andstatistical amplitude and frequency analysis are prepared toobtain the pressure-temperature relationships for differentflashing flow regimes, as the base for better understanding ofevaporation phenomenon, particularly in a blow-down analysis.

Thermal problems of power reactor componentsFor the design and analysis of reactor vessels, experi-

mental and theoretical studies on time- temperature history ofthe concrete pressure vessel and its thermal insulation arecarried out. Besides time and space temperature field measure-ments in the walls of the vessel model, the experiments includeinvestigations of theoretical properties of concrete and metal-foil thermal insulation.

An analysis was ade for the loss of coolant accident, toobtain pressure and temperature time history cf air-water-steammixture in containment volume. This study was made for theevaluation of the leakage of mixture and fission products to theenvironment

The 'study was made to build an experimental turbine withspecial attention to get more information for the working condi-tions with wet steam in the low pressure stage.

Thermal, hydrodynamical and design parameters are analy-sed for manufacturing of steam generator of horizontal type fornuclear power stations, as well as for heat exchangers. Themethods for heat exchangers design were related to our experimen-tal investigations of average and local heat transfer coefficientand pressure distribution measurement along the smooth tubes

334

"bundles, for various "bundle pitch and Reynolds numbers, as wellas for wake phenomena.

According to the main lines in power reactors developmentand specially of fast breeder reactors, the behaviour of reactorcores cooled by liquid metal is analysed and experimental inve-stigations of boiling phenomena of liquid metals are in progress.

There have been analysed the possibilities of Yugoslavcompanies to participate in manufacturing of components fornuclear power stations» These analyses show that the Yugoslavindustry can participate with 4 5 - 6 0 percent in building ofthe first nuclear power station.

Knowledge of the long range economical and other inherentadvantages of nuclear power plants over conventional sourceslead to the evidence that, in spite of its conventional powerresources, Yugoslavia will have to make timely arrangements forthe integration of nuclear sources into electric power system.It is expected that their contribution would increase so thatin 1980 , they would represent about 10 % and by 1990 about20 % of the total output capacity.

335

Topic for General Discussion- a possible role of the I A E A -

THE RECOMMENDATION OF CORRECTIONS AN!) COMPUTER PROGRAMMESPOR USE IN THE DESIGN OF NUCLEAR POK'ER REACTORS

byO.D. M6PHERSOR, Atonic Energy of Canada Ltd.

Many correlations are employed in the design of a power reactor*Usually these correlations are selected Jay the designers', support teamon the basis of a literature review and some experimental work* Hence,there are many correlations to predict any given phenomenon.

It would be a great service ift under the auspieces of the IAEA, aninternational committee of experts would recommend correlations andcomputer programmes for use in the design of power reactors* The committeewould ask those countries actively working on the correlation of a givenphenomenon to submit reports comparing the various correlations-or programmesand recommending those considered best over a given range of conditions. Thecommittee might then do a comparative study of the submissions but eventuallywould make its recommendation on the basis of all information available to it*

This scheme would have many benefits. It would prevent much duplicationof similar studies» Tt would furnish a broader study in each case and soresult in a more definitive answer. It would provide a much needed basisfor the comparison And evaluation of power reactor designs» and» finally,it could be used as the basis of nuclear safety standardization. This isnot to suggest that the committee dictate safety regulations, for each designteam would employ its own factor of safety when applying the recommendedcorrelati on.

Areas which the committee should consider include heat transfer correlationsfor high and lov: pressure water, liquid metals and varions gases in multi-element fuel bundles, prereure drop sr.4 void correlations, dryout in multi-element bundles, departure frois n-reíoste boUir/r at both high and lot: prer»par«r,sub-channel analysis cwcputer prc'_T:-r:::¡oR, trtr>«ient analysis computerand') obviously many others.

337

SÜWMA.HY OP CANADIAN HEAT TRANSFER STUDIES 1970-71

fcr. G. D. FcFHEaSOîT, H^mir: "Hnergy td.

!• Boiling Water Power Reactors

l.l Critical Heat Flux (CHF) and Post Dryout HeatTransfer Correlations for Multi-rod Bundles

(i) Behaviour of 18- and 19-element bundles;effect of length and two-phase inlet;comparison of CHF vs X data beyondintersection of 18- and 19-elementcurves; effect of flux depression andhigh subchannel enthalpy rise rates oncritical power; effect of an end-plateon dryout.

(ii>* Behaviour of a 6-ft 28-element(Pickering) bundle with simulated endplates and uniform heat flux.

(iii)* Behaviour of a 9-ft 28-element(Pickering) bundle with simulated endplates and stepped half-cosine heatflux.

(iv)* Behaviour of a 9-ft 36-element(Advanced BLW) bundle with simulatedend pl«tes and stepped full-cosine .heat flux.CRNL responsibility of items (i) to(iv) lies with 6.A. Wikhamaer andG.0. McPherson

Facility

SWIFT3.75 MM loop

ColumbiaUniversity3.5 MW loop

ColumbiaUniversity~9 MW loop

Don* at Canadian Westinghouse Co. Ltd., Hamilton» under contract withABCL

* Done at Columbia University under the USAEC-AECL Cooperative Program

338

(v) In-reaetor tests on two 6-bundlestrings one of 36-elements, oneof 21-elements.G.D. McPherson

(vi) Proposed in-reactor CHF tests ontwo 10-bundle strings, one of18-elements, one of 36-elements.6.D. McPherson

(vii)° Scaling from Freon to high pres-sure water of CHF tests on a 9-ft18-element uniformly heatedbundle.S.Y. Ahaad and 6.0. McPherson

Cviii) Repeat of (vii) on the largeCRNL Freon loop.S.Y. Ahmad and 6.0. McPheraon

1.2 Sealing from Freon to high pressure waterof CHF tests on simple geometries atvarious pressures.S.Y. Abmad

1.3t Scaling from C02 to high pressure waterof CHF tests on simple geometries atvarious pressures.6.0. McPherson

1.4 Multi-element bundle design andevaluation by consideration ofcoolant enthalpy imbalance.6.0. McPherson

1.5 Refinement of SASS computer program topredict subchannel conditions and dryoutin multi-rod bundles» comparison withsubchannel measurements and other sub-channel conditions programs.B.O. Moeck

Facility

NRU U-l Loop(U-lll Expt.)

Gentilly I

AP.C FreonLoop

Large CRNLFreon Loop

CRHL FreonLoop

UBC CO.Loop '

*Oone at Atomic Power Constructions Ltd., Heston (UK) undercontract with AECL and in cooperation with the UKABE«infrithtOone at the University of British Columbia under contractwith AECL

339

2.* Pressurized Water Power Reactors

DNB behaviour of

(a) a 6-ft 28-element (Bickering) bundle withsimulated end plates and uniform heating.

(b) a 9-ft 28-element (Bickering) bundle withsimulated end plates and stepped, half-cosine heat flux.

G.A. Wikhammer and G.D. McPherson

3. Fundamental Aspects of Two-Phase Heat Transferand Fluid Flow

3.1 Measurement and aaalysis of deposition and.'. ientrainment rates in annular flow.

E.G. Moeck

3.2 Downstream; liquid injection to improve CHFbehaviour of annular heater.E.G. Moeck

3.3 Drypatch stability - a study of the forcesaffecting the behaviour of drypatch.D.C. Groeneveld

3.4 Operation in the liquid deficient region:surface temperature and the growth of thedrypatch.(1) Trefoil of nuclear fuel with three

planes of thermocouples.

(ii) String of 36-element bundles withthree planes of thermocouples.

G.D. McPherson and D.C. Groeneveld

3.5 The effect of surface roughness on liquid filmflow, CHF and post dryout heat transfer.E.G. Moeck

Facility

ColumbiaUniversity-9 MW Loop

FLARE

Freon Loop

X-4 Loop(X-433 Expt.)

U-l Loop(U-lll Expt.)

FLARE

340

3.6**Cro8sflow and mixing between parallelchannelsCRHL responsibility lies withB.O. Moeek and 6.D. McBherson

4. In a t rumen fc a t <etn and Technlatiea

4.1 Development of impedance void metersfor low pressure Freon and highpressure water operation.5.Y. Ahmad

4.2 Design of a window for photography athigh pressure of two-phase flowphenomena.6.D. McPherson and E.O. Moeek

4.3 Sensitivity comparison of surfacemounted and imbedded thermocouples.B.O. Moeek

Facility

Windsorair-waterloop

PLARB andFreon loop

FLARE

FLARE

**Done at the University of Windsor and CRNL under contractwith AECL

341

CAPABILITIES OF TWO-PHASE LOOPS ASSOCIATED

WITH ADVANCE ENGINEERING BRANCH

A. Out-ReactorLoops

(1) FLARE Loop (Fog juoop Advance ^Reactor .Engineering)

Power: 450 kW 450 kW

Inlet Mass water 5000 Ib/h 2250 kg/htlov: steam 1000 ib/h 450 kg/h

2Pressure: 600-1200 psia 40-85 kg/cm

(2) SWIFT Loop (Steam Water .Industrial Fog .Test)

Power: 3,75 MW 3.75 MW

Inlet Mass water 150,000 Ib/h 70,000 kg/hFlow: steam 30,000 Ib/h 13,500 kg/h

2Pressure: 950 psia 67 kg/cm

O) WAFER Loop (Water-Mr Fog Experimental Rig)

No Heat Input

Mass Flow: water 40,000 Ib/h 18,000 kg/hair 5,000 Ib/h 2,250 kg/h

2Pressure: up to 100 psia 7 kg/cm

(4) Freon Loop

Power: 50 kW 50 kWMass Flow: 6,000 Ib/h 2,700 kg/h(Subcooled inlet) 2Pressure: 350 psia 25 kg/cm

342

(5) Small CRNL Fréon LOOP for Fundamental Fluids Studies

B.

(6)

(7)

Power: 4 HHMase Flow: 1000 Ib/h(Sttbcooled inlet)Pressure: 150 psiaColuabla University LoopPower: 3.5 m (present)

5.5 to 11.0 MH(1969-70)

Total 140,000 Ib/h

4 kW450 kg/h

11 kg/cm2

3.5 MW (present)5.5 to 11.0 MW

(1969-70)64,000 kg/hMass Flow:

(Subcooled inlet)2Pressure: 1,500 psia 106 kg/cm

Large CRNL Freon LOOP for Multi-element CHF SealingPower:Mass Flow:(Subcooled inlet)Pressure:

(1) NRX - X4 LoopPower:Inlet Moos Flow:

Pressure:(2) NRX - X6 Loop

Power:Mass Flow:(Subcooled inlet)Pressure:

(3) HRU - PI LoopPower:Inlet Mass Flow:

. Pressure:

1.2 MW165,000 Ib/h

450 psia

250 kWwater 6,600 Ib/hsteav 1,800 Ib/h2,000 psia

200 kW9,000 Ib/h

2,675 psia

4 litfwater 63,000 Ib/hsteam 9,000 Ib/h2000 psia

1.2 MW75,000 kg/h

31 kg/c»2

250 kW3,000 kg/h820 kg/h138 kg/en2

200 kV4,100 kg/h

185 kg/c*2

4 MW29,000 kg/h4,100 kg/h138 kg/cm2

343

ACTIVIDADES EN ESPAÑA, SOBRE TRANSMISIÓN DE CALOR Y TRANSFERENCIADE {.«ATERÍA EN EL CAMPO DE REACTORES NUCLEARES Y APLICACIONES DELA EKERSIA NUCLEAR.

Desde la aparición de los fenómenos de tipo nuclear se ha estado trabajan-do en mi país en los distintos problemas de transmisión de calor y transferenciade materia colaborando en nuestra escala al acerbo de conocimientos mundiciassobre estos temas.

! ! , t •

Desde el año 1950 mi Gobierno se percató de la importancia de la energíanuclear y sus aplicaciones y se constituyó la Junta de Energía Nuclear como Or-ganismo oficial a escala nacional para, estudiar, investigar, desarrollar y cccr-dinar les actividades de'la industria privada asi como las relaciones e intercam-bios internacionales en el campa de la enurgía nuclear. Muchos do Vds. nos hanhonrado con su visita a nuestro país y han comprobado los esfuerzos y realirécie-nes logradas y otros conocen las actividades de nuestra Junta de Energía Nuc?.«D.ra trayés de los Organismos competentes o nuestras publicaciones.

Las actividades de mi país en el campo de transmisión de calor y materiaestán determinadas por dos objetivos principales.

1) Aplicaciones de le energía nuclear (reactores nucleares, aplicaciónde isótopos, desalación de agua do ir.ar, etc.)

2) Estudio de las fenómenos térmicos y de transferencia de materia comoconjunto de conocimientos ordenados.

f> ( . •' • -1O 'T'\El primero de los objetivos responde a las realizaciones nucleares exie~tentes y futuras y la Junta de Energía Nuclear interviene directamente! o colabo-ra con le industria privadai y por ello los programas de la Junta de EnergíaNuclear coinciden con los programas nacionales.

El sogundo do los objetivos ce realiza principalmente en las Universidad'-.y centros de investigación y la Junta de Energía Nuclear colabora a través delInstituto de Estudios Nucleares.

Los problemas específicos quudan encuadrados en IDS programas siguientes:

345

1. Necesidades da Uranio.Según al Plan Eléctrico Español la pot ancla nuclear instalada en 1981

aera da 6.500 MW. Eato supondrá una demanda acumulada en dicho año da12.500 t. de U_0_ (según la programación realizada de entrada en servicioo ode céntralas y demanda de concentrados correspondiente) y un consumo anual,en dicho año, de 1.840 t. de uranio.

Las reservas actuales de uranio existentes en España están cifradasen 9.000 t. de U~0_, con lo que se pone de manifiesto- su insuficiencia pa-ra cubrir las necesidades programadas hasta 1981.

Por consiguiente, un objetivo fundamental será el de desarrollar almáximo la labor de prospección e investigación geológica a fin de descubrirnuevas reservas que hagan contemplar el futuro con cierta tranquilidad.

Secuendalmente con lo anterior se plantea otro objetivo: la mejorade los métodos de tratamiento de minerales, a fin de aprovechar lo máa po-sible el mineral que se obtenga, asf como la Instalación de las plantas pi-loto necesarias para la producción de combustibles nucleares (hasta el UF_en el caso de combustible enriquecido ó U y U0_ en los casos de uranio natu-ral).

2. Elementos combustibles»El mercado español de elementos combustibles alcanzará en 1981, según

el Programa Nuclear español, un valor del orden de los 8.000 millones de pe-setas.

A esta cifra habrá que añadir lo que suponga la reelaboración de lo»elementos combustibles irradiados.

Todo ello lleva a plantearse los siguientes objetivos:-Desarrollar la tecnología de la fabricación de elementas combustibles deagua ligera, con objeto de poder producir en nuestro país los elementoscombustibles para el programa nuclear español.

346

¿-Desarrollo da la reeleboración de combustibles irradiados para llegar ala construcción de plantas industriales de tratamiento de combustiblesirradiados.

3. Bestión del combustible nuclear.Dentro del ciclo del combustible merece especial atención, en los

momentos acutales, el problemas de la utilización óptima del combustiblenuclear*

Esta situación justifica que, con independencia de las actividadesque nos permitan un desarrollo máximo de la tecnología nacional, en ,1a fa-bricación y reelaboración da elementos combustibles, sea necesario efec-tuar un análisis amplio y concienzudo del conjunto del ciclo, con objetode que en cada caso se pueda optimizar el ciclo completo del combustible.

El ciclo del combustible comprende las siguientes fases:i) Obtención o adquisición de los concentrados de uranio, conversión

y enriquecimiento.ü) Proyecto y fabricación de los elementos combustibles.iii) Manejo de los elementos combustibles y de control dentro del

reactor.iv) Transporte y reel&boración de los combustibles irradiados

Los servicios relacionados con las fases i) i iv), señaladas anterior-mente, son de naturaleza técnico-industrial y serán realizadas por la Juntade Energía Nuclear como órgano ejecutivo, con las directrices de la ComisiónNacional de Combustibles.

Dentro de la fase ü) le parte que corresponde a la fabricación deelementos combustibles se desarrollará dentro de la División de Metalurgiade la J.E.N. utilizando especificaciones procedentes de una ayuda técnicaexterior, o, posteriormente, las especificaciones propias.

La Junta de Energía Nuclear considera que debe estar preparada para

347

la realización da estos servicios. Para ello cuenta ya, como hemos dicho/con personal especializado de sus Divisiones, pero es necesario completarla preparación del personal del recientemente creado Grupo de Gestión deCombustible, especializado en estas tareas, y para cuyo adiestramiento seestá negociando el correspondiente contrato con la empresa americana ÑUSCorporation.

El período de adiestramiento, que ya se ha iniciado, continuará enla J.E.N. hasta septiembre de 1970 y, posteriormente,, durante un periododo 8 ó 9 meses en las instalaciones de ÑUS, que facilitará también a laJ.E.N. una serie de códigos apropiados para la ejecución de los cálculosnecesarios. El objetivo de la realización de este programa es contar conal Grupo formado y listo para realizar su labor a finales de 1971.

4. Reactores rápidos.El desarrollo de los reactores rápidos está siendo objeto de una aten-

ción especial. El amplio progrma nuclear previsto para los próximos añosrequiere la incorporación de los reactores ráóidos al abastecimiento eléc-trico español tan pronto como se alcance la comercialización de este tipode reactores, e incluso pudiera ser antes, mediante la construcción de unacentral precomercial que nos permita tener una mayor participación en el de-sarrollo de este tipo de centrales.

Las ventajas fundamentales us la incorporación de este tipo de reac-tores pueden considerarse desde tres aspectos distintos:i) Económico.- La base de la economía de los reactores rápidos es su muy

bajo coste de combustible. El desarrollo de la tecnología que permitareducir las inversiones actuales, dará lugar a una economía conjunta deproducción más ventajosa que la actual.

ü) ConsoryacAfin da recurros nacionales.- Los reactores rápidos permitenuna utilización óptima de los recursos de uranio natural, al conseguiraprovechamientos comprendidos entre el SO y el 75)» frente el 1% de losactuales reactores; por otra parte, el plutonio producido en los reac-tores ténr.icos alcanza su pleno rendimiento en los reactores

348

El desarrollo da la energía nuclear requiere la incorporación de losreactores rápidos e escala mundial si no se quiere que las reservas de ura-nio en el mundo, a precios baratos, sean insuficientes para soportar esteprograma y nos haga recurrir a reservas más caras, que encarecería tambiénel precio de la energía eléctrica producida»

En contraposición lie las centrales que usan reactores térmicos en losque existe mucha tecnología de tipo clásico, los reactores rápidos introdu-cen tecnologías completamente nuevas, singularmente por el uso del sodio co-mo refrigerante.

El programa básico de la Junta ha de tender hacia la asimilación detecnologías con el fin de dar una máxima participación a la industria en laconstrucción de las futuras centrales, seleccionando los materiales más ade-cuados y poniendo un énfasis grande en la completa nacionalización del ciclode combustible.

Las tecnologías que se considera necesario estudiar son las siguientes:i) Proyecto de la Centralii) Componentesiii) Instrumentación y controliv) Tecnología del sodiov) Proyecto de núcleosvi) Materiales especialesvii) Combustiblesvüi) Ciclo de combustibleix) Problemas de seguridad

Estas tecnologías será necesario desarrollarlas de acuerdo con lasdisponibilidades y tratando de conseguir unas instalaciones experimentalesque puedan ser otiles a la Industria on su preparación paru este tipo decentrales.

349

5. Objetivos complementarios.

Todavía con base en el Plan Eléctrico Nacional se plantean aspectosque son necesarios para completar el conjunto de objetivos sugeridos porel mismo*

Así, se considera necesario cubrir los siguientes objetivos:i) Ayuda a la industria, incluida la formación de personal necesario pa-

ra sus programas.

ii) Control de procesos, mediante la puesta a punto de las técnicas correspondientes.

iii) Desarrollo de las actividades sobro seguridad nuclear.iv) Polución atmosférica, polución tCnnica de aguas y estudios ecológicos,

especialmente referidos a los problemas ligados a las radiaciones.

6. Objetivos LJJSpecJLf. Icón de Ir. J.E.N.Con independencia del Plan Eléctrico Nacional, existen otros canpos

en los que la J.E.N. viene ya desarrollando una actividad específica a lelargo de años.

Estos campos y los objetivos propuestos son los siguientes:

i) Desalación Nuclear: desarrollo ds los motados de evaporación, elec-trodiálisis y osmosis inversa.

ii) Xrradioción de alimentos: construcción de una planta pilotoiii} Producción, distribución y aplicaciones de los isótopas.

7. InyQsticTftción básica.

Todo programa tecnológico extenso, debe incluir una investigaciónbásica que le sirve de soporte, al mismo tiempo que permita el desarrollode nuevas técnicas y aplicaciones. Pera estos fines, la J.E.N» dedica apro-ximadamente un 10$ de su prccupeusto y las actividades, en muchos casos etravés del Instituto de Estudios Nucleares, se desarrollarán fundamentalmente

350

t los siguientes campos:i) Física de Altas Energíasii) Física del estado sólidoiii) Investigación química y metalúrgicaiv) Investigación en Biología Molecular y Radiobiología

351

Review of Austrian Activitiesin the Field o;£'Kpat. and Vapg Tranpfftr in Rue1ear Power

by P.V. OILLI

1. Reactor Center Seibersdorf of the Ceeterreichische Studiengesellschaft furAtomenergie (SGAE), Institut fur Seaktortechnik (IH7):(a) High pressure (100 bar) helium loop enclosed in prestressed concrete

pressure vessel with hot liner (in cooperation with industry):Steam generator by Vîaasner-Bir6 AQ»Recuperator and vessel coolinç eystem by Simrcering-Oraz-Pauker Aiî (SCP);Hot liner and penetrations by Vereinigte Oesterreichieche Sisen- und

Stahlwerke AG (VOSST);Gas purification plant by Schoeller-Blerkmann Stahlverke AG (SBS).

(b) High temperature (850-900°C) sodium loop (in cooperation withOebruder BShler AG):

Corrosion tests; heat transfer experiments.(c) Boiling Water Loop:

Dynamic and stability investigations with emphasis on short-time(milli-eecond8*range) behaviour and turbulence.

(d) Development and production of pyrolitically coated particles for HTOH fuel.2. Lehrkanzel und Institut für Technieche !<?armelehre, Technische Hochschule in Hien

(Head: Prof. Dr. M. Ledinegg):Work on two-phase flow (stability, burn-out, pressure drop).

3. Lehrkanzel und Institut für Theoretische Physik, Universitat Innsbruck(Read: Prof. Dr. P. Cap)tTheory of KHD flows.

4» T/ehrkanzel und Institut für Dampftechnik und VJSrmewirtschaft, TechnischeHochschule in Orae(Head: Prof. Dr. P.V. Gilli):(a) In cooperation with T?aacner-Bir6 AG:

Supercritical pressure (250 bar) loop for investigating heattransfer, burn-out, dryout, pressure drop and flow stabilityat suboriti-cal and supercritical pressures of ptraipftt an>1helically curved once through steam generator tubes (preheaterand evaporator zone; to be expanded to superheater ?.one);start-up is scheduled for Kovember 1970.

(b) Thernodynacics of KHD power plants.5. Waagner-Biro AG, Vienna/Oraz:

(a) Steam generator development for HTGR and OCFR.Transient heat transfer and therral analysis, including computer programs.Development «and design of heat transfer loopo for gases, liquids andliquid metals.

353

(d) Development of heat transfer components for KHD plants.(e) Development of components for fuel reprocessing plants (pulse columns,

evaporators).3. Gebrüder BShler AO, Vienna/Kapfeníjergt

Development of hot waste evaporators.7. Schoeller-Bleekmann Stahlwerke ACs

Development of gas purifications plants,Solidification of hot waste.

354

THE PRESENT STATUS OF ANALYSIS BY CALCULATIONOP LAMINAR AND TURBULENT BEAT TRANSFER

byE.R.O. Eckert

University of Minnesota, Heat Transfer LaboratoryMinneapolis, Minnesota, U.S.A.

I know that we have q crowded programme for this morning, so T will make rry remarksbrief. However, I think it will be useful to discuss generally the question, towhat degree we are today able to analyse by calculation laminar and turbulent heattransfer. Flow, either around some obstacle or thron.o-h R0"ie duct, at sufficientlylow velocities iP'always laminar. In many application we can consider it assteady, or at least quasi steady. If the velocity ^s .«gradually increased, the flowbecomes unstable, developing- either waves or vortices, and, in that way, become?»unsteady. If the velocity is further increased, vortices' or waves become morsirregular, break up into smaller units and finally create the complicatedstatistical appearance, which we call turbulence.

'-Tith regard to laminar flow situations, T feel that in very many cases we can today

rcore economically, and probably more exactly, obtain an ans-wer to fluid rrechanlcn,as well as to hr>at transfer, by calculation, especially with the help of theelectronic digital computers which we have. Tn such cases, it ic only necessary

to-make spot checks by experiments, to see that the governing equations which wehave used for the analysis describe all of the physical processes. This applies

not only to the laminar but:also to the transition situation. With electroniccomputers one can today calculate unsteady three-dimensional situations.

As an example, I will present a short film etrip showing a study by F.F.Harlow*)and J.E. Fromm.

is striking.*}' Available through F.A.Palmer Films, Tnc. 611 Howard Street, San Francisco,

under the title "Computer Studies of Fluid 'Dynamics, T-15"

355

The film presents the result of a computer calculation which solves the WavierStokes equations for flow around a bar with rectangular cross-section at a Reynoldsnumber 2OO. The initial potential flow gradually transforms by the formation ofseparation vortices and finally develops the well known Karman vortex street. Theagreement of the result of the analysis with visual observation of the actual flow

The calculation can be extended to include the energy equation, and in thatway to obtain information on heat transfer. One can also include variableproperties and other effects such as buoyancy forces, etc. I feel that alreadytoday, and certainly in the future, one will, in such situations make more andmore upe of computers.

The situation for turbulent flow is different because of the complicated natureof the flow process. To illustrate this point, T shall show another film ptrip

*)produced by S.J. Kline and associates but T will at first briefly explain whatflow situation it presents.

The details of the flow in a turbulent boundary layer which exists in flow ofwater over a large flat plate were made visible by tiny hydro/ en bubbles. Thefilm taken during these studies thus reveals that vortices,mainly with their

• theaxis in/flow direction,exist even in the viscous sublayer and that, as a consequence,the instantaneous velocity profiles fluctuate widely in time. One can also observethat turbulent exchange often occurs over large a fraction of the'boundary layerthickness.

Available through the Engineering Societies Film Library, 345 Fast 47th Street,New York, N.Y. 1001?, Rundetadler et al.: "A visual study of the flow structurein .the fully developed turbulent boundary layer on a flat plate, R-7"

356

The film demonstrates that turbulence is a very complicated process. The customaryprocedure in engineering analysis of workhg with time-averaged equations and empiricalturbulence parameters is useful, but we have to keep in mind that it simplifies theactual complex process radically. The film has also shown that the exchange offluid masses in the boundary layer occurs over quite a wide distance, with thevortices sometimes shooting out from the surface deep into the boundary layer.This raises the question, whether we can, when we wish to study the physicalprocess in detail, even describe the process by differential equations at all.

We obtain differential equations by writing an energy balance, or momentumbalance for a small volume element, assuming that what happens to the volumeelement is influenced only by what occurs in the clore neighbourhood. Thatis correct for the description of laminar boundary layers, because the mean-free path, which transfers information from one point to another, is quitesmall in scale relative to the boundary layer thickness. Tn turbulent flow,we have seen that this is not the case. Thus, it might more closely correspondto reality if we were to use integral equations such as are used in rarefiedgas flow. Experience has shown that flow and heat transfer parameters of interestfor engineering applications can in many cases "be obtained from time-averaged

differential equations, however, we should always be careful to check, throughexperiments,whether the answers are still valid in some new situations.

In other cases answers can be obtained today throu/»h experiments alone.This holds, for example, for the analysis of heat transfer on a wall withsurface roughness. Such a study has recently been carried out as Ph.I) thesis

*)by R.L. Webb at our laboratory. The results will be briefly discussed.

A paper based on the thesis will be published in the International Journalof Heat and Mass Transfer.

357

The experiments are designed to investigate the influence of surfaceroughness on turbulent flow through a tube with circular cross-section. Foratomic energy applications the passages are usually of a different shape, butthe tube with circular cross-section serves as a good standard model on whichto study basic processes.

Fig» 1 is a sketch of the test set up with the flow moving from left toright. The test section in which pressure drop and heat transfer were measuredis on the right-hand side. In order to get fully developed turbulent conditionsan additional rough entry section has been added ahead of the test section and,finally, a smooth section, so that one can be sure that fully developedturbulent flow enters the electrically heated test section. The roughnesselements have the form of circular ribs at certain distances from each other.It is important to avoid any contact resistance between the rings and the surfaceof the tube. Therefore, the rings have been cut out integrally from the solidmaterial which forms the tube wall. This was an expensive process and we owethe Trane Company thanks for producing the tube for us.

Por the first measurements, designed to check the accuracy of the instrumentation,the rough test section and the entry section were replaced by smooth ones.The results, as far as friction coefficient and a Stanton number are concerned,checked the best experimental and analytical information available to withinabout + 2 per cent. In this connection it was, by the way, found that thefrequently used Dittus-Boelter equation represents those only withinapproximately 10 per cent.

An example of the results obtained with the rough •fefcbes is shown in Pig. 2.Parameters which were changed in the investigation include the ratio of theheight e of the roughness elements to their distance p the ratio of e to the

358

tube diameter I>. This is indicated "by the notation in the upper right hand»

corner. 01 for instance means that the height of the roughness element ÍP1 per cent of the tube diameter and the figure 10 indi nates that p/e hap thevalue 10. Pip. 2 holds for p/e » 10. Other values of this parameter veréalso investigated.

Experiments were performed with various fluids. Prandtl Fo. 0.71 was obtainedwith air, Prandtl No. 5.1 with water, and Prandtl No. 21.7 «1th but.hyl alcohol.The? solid pointe denote the friction factor f ?.nd thn open symbols the ítantonnumber St. The Reynolds? number Re is defined wit*- the tube diameter T) as

measured away from the roughness elements. *11 data describing friction factors

could be correlated as shown in Fig. 3.

The parameter on the abcissa and the parameter within the square bracketson the ordinate come from an analysis, which was dpveloped for smooth andsand rough tubes. The effect of the specific shape of the roughnesn element^in thip investigation could be incorporated only empirically. It is expressedby the term (p/e) *" .

The situation is similar for the Stantor. number, shown in "Pi£¿.jl

all the experimental results. Again, the parameter on the abclssa and theparameter in square brackets on the ordinate come from the analysis forsmooth and sandrough tubes. The Prandtl number effect had again to be obtainedempirically by cross-plotting of the results. It is expressed by the term-0.57Pr on the ordinate.

Similar information on other roupflmess shapes and a determination of optimumroughness shapes can today only be obtained by experiments. In the unitedStates, practically all companies developing heat exchangers carry on extensive

359

experimentation in order to find optimum shapes of rough surfaces for heattransfer surfaces.

Some remarks may be in order on the question of optimization. This question canstrictly "be answered for a specific installation only taking into account allinitial and operating costs.

Por general parametric investigations one finds sometimes *B ratio of Stantonnumber over friction factor or Stanton number St to Stanton number St of ao

smooth tube to the ratio friction factor f to friction factor f of r> smoothS

tube listed as an indication of effectiveness from which one could optimiseheat transfer surfaces. Pig. 5 lists this factor on the ordinate.

The parameter on the abcissa 6 indicates essentially the variation of theReynolds number. If one uses the Stanton number frictior» factor ratio as anindication of the effectiveness of a surface,one concludes that for air,with a Prandtl number smaller than 1, a smooth smrfafle has a better effectiveness

than a rough surface. Tn reality we are interested in the ratio of the amountof heat which can be transferred per unit surface area to the power which isrequired to feree the flew over the surface area. This ratio is onlyproportional to the Stanton number friction factor ratio if we keep the velocityconstant in the comparison. A. better judgement of the quality of differentsurface types is obtained by a comparison of surfaces which produce the sameheat flux per unit area under prescribed flow rates and temperature conditions.This requires, in general, different velocities for the different surfaces.That surface which experiences the smallest pressure drop is then the best one.Such a comparison can readily be made using the data in Pig. 2.

360

As an example, let us compare the two tubes 01/10 and 02/10 for air with a Prandtlnumber 0.71. The figure shows that - at a fixed Reynolds number - the tubewith the smaller roughness height has a smaller Stanton number and, therefore,a smaller heat transfer coefficient.

!

Thus, if we want to transfer the same amount of heat with the same surface area,we can operate the surface with the higher roughness elemente at a smallervelocity than the surface with the smaller roughness elements. The pressure

2drops on the two surfaces are now proportional to fRe and one finds in thisway that the pressure drop of the surface with larger roughness height issmaller^by 20 to ?0$ than the pressure drop of the surface with the snailpr* .roughness height.

K_f

Perhaps T may now summarise the main points which T have tried to rnske inmy lecture. First, I feel that in analytical turbulent heat transferinvestigations we have to use strongly simplified models to describe theturbulent transfer processes. These models are very useful in manycases but we should always bear in mind that we may encounter situationswhere we cannot apply these models and where we have to rely mainly onexperiments. The study of rough surfaces to improve the effectiveness of heatexchangers is one example of such a situation.

361

RT•

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6 8 10 20 40 60 80 100 200Rex 10"*

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_ SMOOTH TUBE (SM)

SM Pr 01/10 02/10 04/10 02/20 02/40—— 0.71 o A v o o

^^* I ^^ ^f fcrf

—— 21.7 o A y * e—— 37.6 t> * 13

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ne.

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100 1000

RG.

OEHBRAL PROBLEMS IN HEAT AND MASS TRANSFER IN NUCIJBAR POWER REACTORSConcluding Comments lay Dr, E.R.6. Eckert

Prom the standpoint of basic science, the heat transfer problems innuclear reactors are primarily convectiva in nature, that is, heat transferoccurs by means of forced convection, natural convection or as a combinationof both mechanisms. In examining such -a complex process, a dimensionalanalysis is usually applied. Thus, one can find that the Prandtl numbersinvolved are in the range of 0.02 to about 20, and that, though fairly dis-appointing, the Reynolds numbers are rather high so that the flow is turbulentand the use of. basic equations in their original form becomes impossible. Theavailability of high speed computers and the development of appropriatecomputation codes makes it possible, in almost all cases, to predict laminarflow and the related heat transfer processes including instabilities, for allkinds of fluids. Many situations of turbulent boundary layer and channelflows can also be handled and there is hope that, by further development ofturbulence models, the analysis can be extended to many situations for whichan approach other than experimental was deemed impossible a few years ago.

A look at the boundary conditions occur!ng in nuclear reactors revealsthe following peculiaritiest The fluid flow occurs through channels ofcomplicated shapes with interconnections between parallel channels resultingin cross-flow and other, not easy to handle, effects. Also the heat generationrate varies with the direction of flow as well as around the surface area,which also varies in shape either in a continuous way or through discontinuitiescalled turbulence promoters. It is to be hoped that in the foreseeable futurecalculation methods will be able to handle all such situations. It should bestressed, however, that at the present time these situations still represent apredominantly experimental field of investigation.

367

Under certain conditions, the temperature differences in the fluid arelarge enough to raise the question of the dependence of the heat transferrate upon the fluid property variations. This can "be accounted for withoutgreat computational difficulties.

In generalf there is hope of obtaining useful answers by analysis aslong as one deals with single-phase flow. The situation is more disappointingwith boiling heat transfer because not only the number of parameters involvedis very large but, in addition, some of the quantities which enter into theseparameters are extremely difficult to obtain. For instance, in nucleate boilingthe size of nucleation centres is a highly relevant parameter, but difficult toestablish in common manufacturing practice. It is, however, encouraging torealize that in film boiling heat transfer this difficulty does not exist becausethe area in which the basic heat transfer processes occur has lifted off thesurface so that the microscopic surface configuration itself is no longerimportant.

The papers presented, and in particular, the discussions held at thispanel meeting clearly indicated that gains in the efficiency of nuclear powerplants can be obtained without sacrifice in safety through an improvedknowledge of heat and mass transfer processes and that our ability to predictthese processes requires the use of advanced computers and of refinedexperimental techniques. Both approaches must progress to the point wherethey can be applied to the specific situations which prevail in the variousreactor types.

Safety factors are invariably involved in the design calculations. Theycan be reduced by increased understanding and accuracy in the prediction ofheat and mass transfer processes. In the absence of adequate information,designers of necessity must take a conservative approach. For example, beforein-pile post-dryout experience was available, the critical power ratio waschosen high enough to avoid any chance of dryout, which was assumed to resultin fuel failure. Today it is known that dryout can be endured safely undercertain reactor conditions. Thus, more accurate information can be appliedto a reduction of the appropriate safety factor without major manufacturingdifficulties and without any real sacrifice in safety. For example, in a700 MHe boiling water reactor such a reduction may lead to savings of 5$ in

368

the plant capital cost if, by allowing some dryout, the steam exit qualitycan he raised from 20 to 40 per cent* Additional savings in operating andcapital costs may be achieved by an estimated 5$ reduction in requiredpumping power, as a result of better understanding of, and hence a reductionof the flow instability in parallel channels. The much larger pumping powerrequirement of gas cooled systems obviously offers even larger potentialsavings. Currently there is still a rather wide gap in boiling heat transferfigures, between those which are found in basic research laboratories andthose which are applied to situations occuring in the actual reactor designpractice. It should be possible to narrow the gap considerably in the nearfuture.

The participants of the panel meeting unanimously expressed their feelingthat the time is appropriate for the IAEA to foster the existing, and toinitiate new, forms of international cooperation in the field of heat andmass transfer, in both design and basic research work, since large benefitscan be obtained through further improvement in the economy and safety ofnuclear power plants.

369

Annex I

P r o g r a m m e

LIQUID COOLED SYSTEMSMonday. 14 September9*30 Opening ceremony10.00 PL-410/ 4 HP. P. Mayinger et al.

Bubble formation and departure withsub-cooled boiling in water-cooledchannels of high heat flux density.(Coffee break)

11.15 PL-410/ 2 Mr. O.P. MbPhersonThe status of heat and mass transferresearch related to CANBU power reactorprogramme.

14.30 PL-410/10 Mr. J. Made.i skiSome basic thermophysical problemsof nucleate pool boiling.

15.15 PL-410/ 3 Mr. D. SmidtProblems of cooling disturbances andsodium boiling in fast reactors.

16.00 Discussion period(Coffee break)

17.15 PL-410/ 1 Mr. P.V. GilliReview of problems governing the designoptimization of heat exchangers in nuclearpower plant.

371

Tuesday. 15 September QAS COOLED STSTEtfS9.00 Mr» B.R.G. Bckert

Basic remarks on convectivo heat transferprocesses without change of phase.

10*00 PL-410/7 Mr..B.E. Launder and P.B» Scalding;The problem of predicting heat andmomentum transfer in gas-cooled nuclearreactors.

11.15 PL-410/13 Pr. B. K.1el let roenLateral beat transport for turbulent flowof a gas in a rod bundle.

11.50 PL-410/8 Kr. V. KrettHeat' and mass transfer in HHGCR Type A-lfuel assemblies.

INTERNATIONAL COOPERATIONAND

PANE!. RECOMMENDATION14.30 PL-4ÍO/11 Mr. Z. Zario'

International Centre for Heat and MassTransfer and Cooperative research.

14.50 PL-410/16 Vr. G.D. TtePherson1îie reconroendation of correlations andcomputer programmes for use in the designof .nuclear power reactors.

15*15 - Panel discussion(nomination of working groups for preparingthe Panel recommendation).

372

Wednesday. 16 September PAÎIEL RECOMMENDATION (CONT.)

9.00 - World ng Croup activity period(Cont.)

(Coffee break)

Panel discussion aboutWorking Group drafts.

14*30 - Adoption of Panel recommendation

Thursday, 17 September RATIONAL ACTIVITIES

9.30 Mr. g.I).(film presentation)

10*00 Review papera about national activities(presented by Panel Members).

373

Annex IILIST OP PARTICIPANTS

AUSTRIAProf.Dipl."5ng.Dr.-techn. P.V. GILLI Institute of Heat and Power Engineering,

University of Technology,24 KopernikusgasseA-8010 Graz

. R. STHÜSZOEHICZ

CAUDADr. Q.D. MoPHERSON

Br. V. KRRFT

Viennese Branch of VOEST Technical Bureau,19 PostgasseVienna I

Atonic Energy of Canada Limited,Chalk River Nuclear Laboratories,Advanced Engineering Branch,Chalk River, Ontario

Skoda Works,Unclear Power Plant Division,Plzen

Dr. P. OELIN

Prof.Dr.-Ing. P. XAYIHGBR

Prof .Dr. D. SMIDT

(cont'd)Prof.Dr.-Ing. U. ORIOULL

Heat Transfer Section,C.E.V. Saolay,Boite Postale Ko. 2,91, Oif-sur-Yvette

Teohnisehe UniversitKt Hannover,Institut fur Verfahrensteohnik,14 Wunstorfer Strasse3 HannoverKernforschungscentru» Karlsruhe,Institut fur Reaktorentwiokluag,5 Melserstrasse75 Karlsruhe

Institut fur TherBodynanik,Technisohe Hoohschule Minchen,21 Arcisstrasse8 MBhchen 2

375

J.IUUADr. S.R. SASTRI

ITALYProf. M. CUNO

POLANDProf. J. MADEJSKI

Dr. P. LUIS T LUIS

Bhabha Atomic Research Centre Trombay,Reactor Engineering Division,Bombay

Conitato Nazionale per 1'Energía Nucleare,Laborattorio Teonologie Reattori,Centro Studi Nuclear! délia Casaoeia,Roña

Institute of Nuclear Research»Swierk, Warsaw

Junta de Energía NuclearfDivisión de Ingeniería,Avda. Complutense,Madrid-3

Dr. B» EJELLSTRON

Ing. O. HTLUND

U.K. ___Dr. B.E. LAUNDER

U.S.A.Prof. Dr. E.R.G. ECKERT

YUGOSLAVIAProf. P. AKASTASIJEVIC

Mr. N. TOMSIC

INTERNATIONAL ORGANIZATIONXr. Z. ZARIC

AB Atomenergi,Studsvik, Nykbping/SEA-ATOM,Box 53,S-72104 VSsteras 1

Imperial College of Science and Technology,Department of Mechanical Engineering,London SW 7

University of Minnesota,125 Mechanical Engineering Building,Minneapolis, Minn. 55455

Boris Kidrio Institute of Nuclear Sciences,Thermal Physics and Engineering Department,BeogradInstitute Josef Stefan,Ljubljana

International Centre for Heat andMass Transfer,P.O. Box 522,Beograd

Prof. M. RISTIC

376