Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

--------------------------------------------------------------------------------------------------------------------------------

Modelling of Nuclear Reactor Channel Tem-perature Distribution at Steady-State Using

LabVIEW Simulation Program

F. M. BSEBSU*, and A. A. ESTUTI**

*Tajoura Nuclear Research Centre P. O. Box 30878, Tajoura, Tripoli / Libya

bsebsu@ yahoo.com **Technical University of Budapest, H-1521 Budapest, Hun-

garyFax: +36 1 463-3272, *Phone + 36 1 463-2183

A bstract This paper shows the possibility to use graphical pro-gramming language (LabVIEW) to determine the axial temperature distribution of nuclear reactor channel, at steady state, and com-pare our results to Pascal program THERMAL and with safety report analysis of KFKI reactor fuel channel as a sample problem of the im-plementation. The use of LabVIEW environment as tool for above calculations was in good agreement with THERMAL code and KFKI safety report. . Finally, the results of this calculation are at equilib-

rium and starting core with maximum and average core loading.NomenclatureTf1 = Reactor coolant inlet temperat-ure, C

Cp. = coolant specific heat, J/Kg.K

= maximum heat flux rate , W/cm2i = coolant mass flow rate, Kg/sec

Ki = wet and heated contours, cm = heat transfer coefficient, W/cm2 KR = channel thermal resistance ,K/W Tm (z)= axial centre line fuel temperat-

ure, CZ = axial distance, cm Tf(z)= axial coolant temperature, CDe = equivalent heated diameter, cm AAl+U= cross sectional area of Al and

Uranium ring, cm2

Tcl (z)= axial cladding surface temper-ature, C

AH2O= cross sectional area of water ring, cm2

He = extrapolated length, cm = Thermal conductivity coefficient, W/cm.K

1. IntroductionThe main purposes of heat transfer analysis are accomplished

by choosing the operating temperatures within the detailed and precise limits. The basic of the worldwide LWR safety research pro-grammes is to develop computer codes to analyse the abnormal events. These codes are to be based on physical understanding, yet these codes have become so large and complex that few people un-derstanding all of the models employed or the numerical tech-

1

Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

--------------------------------------------------------------------------------------------------------------------------------niques. There are a lot of computer codes, but I’ll mentioned about:[1]

RELAP5 code is an advanced, one-dimensional, code based on a non-homogeneouse, non-equilibrium mode (Ransom et al, 1978).

TRAC-P1A (Pryor and Sicilian, 1978) embodies the current state of the art and features a nonhomogeneouse, multidi-mensional fluid dynamic treatment.

For design engineers its less expensive and easier to use nu-merical simulation for studying the system and optimising its per-formance. By using simulation one can determine the axial temper-ature distribution in reactor coolant channel and parameters gov-erning the heat transport rate at the channel wall. On anther hand, these parameters can then be used to choose materials and flow conditions that maximise heat transport in the channel.

In the Western reactor design a channel with single passage is usually used (Fig.1). In the Eastern reactor design, however, a channel design with a multiple passage is common, usually, the later type is modelled as a single equivalent channel if the famous thermohydraulic computer programmes such as RELAP to be used. The error introduced by this can be avoided by taking the geometry into considerations. Therefore, it is desirable to have a programme suitable for the calculations of the thermohydraulic of a channel with multisections (Fig.2). In addition the use of big programmes is time consuming. In design and operation simple methods are desir-able.

Fig. 1 Single Passage Fuel Channel Fig. 2 Multiple Passage

Fuel ChannelSIMULATION [1] Definitions In general the words ‘to simulate a system ‘mean to obtain the hypothetical operation of a system under given condi-tions. The main term ‘system’ refereed to here may be defined as a combination of several elements which all perform together for a particular purpose. For example, the reactor coolant channel is a

2

Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

--------------------------------------------------------------------------------------------------------------------------------component of the reactor coolant system and at the same time is a system itself. This system can contain subsystems and these sub-systems individually can be a system, which contain again subsys-tems and so on.

A coolant channel of the nuclear reactor can be a thermal sys-tem because it responds thermally to environment excitations. Cal-culation of clad surface temperature is an example of system simu-lation, which is very important from safety point view to avoid sur-face boiling at any part of the cladding surface of the coolant chan-nelTools for simulation

Once a mathematical model representing the system under study has been formulated, it has to be solved. For practical sys-tems such mathematical models are usually complex and need to be solved by a computer. The researchers have several ways to ac-complish this task: - Use one of high level programming languages such as FOR-

TRAN, PASCAL, or C to solve the model. This method is tedious and time consuming. It should be avoided unless necessary.

Use general-purpose simulation programs such as LabVIEW, and many others. These languages provide for general mathe-matical functions and integration procedures in addition to in-structions available in high-level languages. There is also facili-tating the introduction of new model functions in the form of blocks with inputs and outputs. A system may be composing of such functions by connecting their inputs and outputs.

Procedure for simulation Use of a computer is mandatory for system simulation in most

cases. In general the procedure of system simulation may be bro-ken down into the following steps:

Setting up system model based on:§ Measured data or,§ Physical knowledge about the examined system.

Preparing input data, Programming, Execution of simulation, Analysis of the result to modify the simulation model struc-

ture or parameters based on the simulation results.In the following we shall introduce the one of most useful tool for simulation LabVIEW LabVIEW [3]

LabVIEW “Laboratory virtual instrument Engineering Work-bench “ is a powerful and flexible instrumentation and analysis soft-

3

Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

--------------------------------------------------------------------------------------------------------------------------------ware system where LabVIEW programs called virtual instrument (Vis). A VIs consists of a front panel and a block diagram. The front panel specifies the inputs and outputs and features the user inter-face for interactive operation.

Behind the front panel is the block diagram, which is the ac-tual executable program. The components of the block diagram, icons, represent lower-level instruments and program control struc-tures. You ‘ wire ‘ the icons together to indicate data flow in the block diagram.

2. Mathematical model of Reactor Channel [1,4]

The fuel channel can be divided into four hydraulic regions. The most inner channel is a tube, marked by “ A ”, followed by a channel with annulus cross section, marked by “ B ”. The outer wall of the next channel is hexagonal, while its inner wall is a circle. “C” marks this channel. The last region, marked by “ D ” is that part of the channel, which belongs both to the given assembly and its neighbouring assemblies.

The starting point of the modelling is to simulate the system as presented before the axial temperature distribution along the channels “ A ” and “ D “ is given by:

The axial temperature distribution of the cladding surface along both channels “A ” and “ D ” is given by:

The axial temperature distribution of the centre of fuel meat is given by:

The above algorithm is valid only for the two regions from our model as mentioned before “A” and “ D ” as shown in Fig.3. But, for another two regions: “ B ” and “ C ”. The temperature distribution along these channels is not the same as in channels “A” and “ D ” because each channel gets the heat from both sides. For example, The channel “ B ” gets the heat from the fuel element (1) and (2). The temperature distribution function is given by:

4

Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

--------------------------------------------------------------------------------------------------------------------------------For engineering analysis, the difference between the wall temperat-ure and the bulk flow temperature is obtained by defining the heat transfer coefficient ( ) through the dimensionless Nusselt number [5]:

Nu = f (Re,Pr,Gr, ) =

The Nusselt number in both experiment and theory show that for al-most all non-metallic fluids is given by the Seider and Tate equation [6] :

Nu = 0.023 Re0.8 Pr0.4 ( )

For more accurate calculations and for cases when w = b the Dit-tus-Boelter equation is the most universally used correlation in the reactor calculations [7]:Nu = 0.023 Re0.8 Pr0.4

For 0.7<Pr<120, Re>10000, and L/D>60. All fluid properties are evaluated at the arithmetic mean bulk temperature. By transform-ing the above mathematical relations to 1.0 PASCAL computer pro-gramme (THERMAL), and

2.0 LabVIEW simulation programme. The main flow diagram as shown in figure 3[8]

VA 1 VB 2 VC 3 VD

AL U AL

1 q q

2 A q B C q D

3 q q

r* 0 18.38rAL 3.0 5.5 8.5 11.0 14.18 16.80

rU 0.7 0.7 0.74 rH2O 3.0 3.0 3.18

1.58de 6.0 6.0 6.176

5

Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

--------------------------------------------------------------------------------------------------------------------------------6.274

K 18.85 34.56 53.41 69.12 93.53 110.85 18.85 87.97 162.65 110.85

AAL+U 66.76 153.15 255.50 AH2O 28.27 131.90 251.20 174.1

* All dimensions are in mm and mm2

Fig. 3 The axial cross section of a channel

3. Sample Problem description [8]

Using the Budapest research reactor (KFKI reactor) as a test-ing sample problem does the implementation of the computer pro-gramme. The Budapest Research Reactor is a tank type reactor, moderated and cooled by light water. The reactor is in a cylindrical reactor tank, made of a special aluminium alloy with a diameter of 2300 mm, and a height of 5685 mm. The heavy concrete reactor-shielding block is situated in a rectangular semihermetically sealed reactor hall. The area of the reactor hall is approximately 600 m2. It is ventilated individually. The fuel of the research reactor is of the VVR-SM type (Russian product). It is an alloy of aluminium and uranium-aluminium eutectic with aluminium cladding. The uranium enrichment is 36 %, the average U235 content is 39 g/fuel element. The fuel element contains three fuel tubes, the outer tubes are of hexagonal shape, while the two inner ones are cylindrical. The act-ive length of fuel elements is 600 mm. The equilibrium core consists of 223 fuel assemblies, with a lattice pitch of 35 mm. A solid beryl-lium reflector surrounds the core radially. The reactor is equipped with boron carbide safety and shim rods. There is a one stainless steel rod for the purpose of automatic power control [7].

AXIAL TEMPER-ATURE CALCULA-TION

INPUT DATA Calculation the main Channel B(Channel data) Hydraulic parameters

6

Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

-------------------------------------------------------------------------------------------------------------------------------- Channel C Channel D

OUTPUT RES-

ULTS

Fig. 4 The flow diagram of simulation processes [1]

The axial cross-section of fuel channel of the KFKI reactor is shown in Fig. 3. The most important parameters of the ring shaped U-AL fuel, of the Aluminium cladding, and of the cooling channels (r,

). Moreover, the wet and heated contours (K), the equivalent dia-meter (de), cross-section area (A), and the heated surfaces are presented and the main geometrical data of the VVR-SM type as-sembly also are presented in Fig 3.

4. Calculation and ResultsThe axial temperature and heat flux distribution along each

channel of the fuel element for both of calculations (THERMAL [1] code, KFKI[8]

group, and LabVIEW[3]) are shown in figures 5 - 10 respectively.

7

Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

--------------------------------------------------------------------------------------------------------------------------------

Fig. 5 Axial temperature distribution for KFKI fuel channel calcu-lated by THERMAL code at equilibrium core with (Max. and average) loading [1].

8

Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

--------------------------------------------------------------------------------------------------------------------------------Fig. 6 Axial temperature distribution for KFKI fuel channel calcu-lated by calculated by THERMAL code at starting core with (Max. and average) loading [1].

Fig. 7 Axial temperature distribution for KFKI fuel channel calcu-lated by KFKI group at equilibrium core with (Max. and average) loading [8]

9

Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

--------------------------------------------------------------------------------------------------------------------------------

Fig. 8. Axial temperature distribution for KFKI fuel channel calcu-lated by KFKI group at equilibrium core with (Max. and average) loading [8].

Fig.9 Axial temperature distribution for KFKI fuel channel calculated by LabVIEW at equilibrium core with (Max. and average) loading.

10

Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

--------------------------------------------------------------------------------------------------------------------------------

Fig.10 Axial temperature distribution for KFKI fuel channel calcu-lated by LabVIEW at Starting core with (Max. and average) loading.

5. ConclusionIn this paper, we have used a LabVIEW program environment

to simulate reactor coolant channel axial temperature distribution, and compared the results of the this simulation by results of a simple computer programme THERMAL and KFKI reactor safety re-port analysis for channel as shown in Fig.3. The results of the above methods are given in the following table:

Reactor Maximum Clad Surface Temperature Results [C]

State Loading KFKI[8] THERMAL[1] LabVIEWEquilibrium Maximum 97.72 100.50 98.56

core Average 70.84 71.13 67.50Starting Maximum 97.03 101.9 105.88

core Average 79.90 81.21 79.60

From above table it is to be noted that there is a good agreement between the results of three calculation methods with error per-centage less than (2%) if we take the KFKI safety report analysis results as a base of our comparing.

11

Proceeding of A (The Third Conference on Mechanical Engineering), Gépészet 2002 conference 30-31, 2002, Budapest, Hungary (V. I, Page17-21), May 2002.

--------------------------------------------------------------------------------------------------------------------------------

6. References[1] BSEBSU, F. M. and G. Bede, (1997), A Simple computer pro-grammes for the calculations of reactor channel - Temperature dis-tribution, Polytech TUB Hungary, under publishing.[2] A.A. ESTUEI [3] LabVIEW[4] BSEBSU, F. M. (1995), “ Physics and Thermal hydraulics reactor modelling “, M.Sc. Thesis, Technical University of Budapest, Hun-gary.[5] Neil Todreas and Mujid S. Kasimi, (1990), “ Thermal Hydraulic fundamental and elements of thermal hydraulic design “, Hemi-sphere publishing corporation, New York, USA.[6] Maurizio Cumo and Antonio Naviglio, (1988),”Thermal Hydraul-ics Vol. I”, CRC Press, Inc. USA.[7] J. M. Delhaye, M. Giot, and M. L. Riethmuller,(1980), “thermo-hydraulic of Two-Phase systems for industrial design and nuclear engineering”, McGraw-Hill Book Company, New York, USA. [8]KFKI - Atomic Energy Research Institute,(1994), “ The Budapest research reactor safety report analysis “, Budapest, Hungary..

12