ir

. V085,

Natural circulation

ystes t

ary cntiocallytea

experimental investigations carried out in a rectangular natural circulation loop are presented. Finally, a

al ford fromcondisince

als (19

friction factor correlation predict the loop behavior well if theform losses for the bends are accounted. Similar observation wasmade by Vijayan (2002). Based on the above discussions, it isdifcult to arrive at any conclusion.

s opinion on thelaws in publishedion for further in-experimental in-ctangular naturald for friction factor

s for naturalcirculation loops

Different correlations have been reported by different re-searchers based on their experimental investigations in naturalcirculation loops. Some of these correlations compiled from liter-ature are given in Table 1.

Vijayan and Austregesilo (1994) showed that steady state massow rate in a uniform diameter single phase natural circulationloop can be expressed as

* Corresponding author.

Contents lists availab

Progress in Nu

ls

Progress in Nuclear Energy 75 (2014) 105e116E-mail addresses: knaveen@barc.gov.in, navbarc@yahoo.co.in (K. Naveen).proles in natural circulation loops. Vijayan and Austregesilo(1994), Cammarata et al. (2003) and Fichera and Pagano(2003) observed that friction factor was different than thatpredicted by the conventional forced convection laws. Further,these studies concluded that the friction factor for natural cir-culation loops was higher than that given by constant propertyforced ow friction factor correlations. Huang and Zelaya (1988)studied natural circulation in a rectangular natural circulationloop and observed that the conventional forced convection

important because of lack of any unanimouapplicability of conventional wall constitutiveliterature. This provides the necessary motivatvestigations in the eld. In the present study,vestigations have been carried out in a recirculation loop and a new correlation is proposein horizontal pipes.

2. Previous research on wall constitutive lawthe presence of three-dimensional effects such as ow reversals,non zero cross stream velocities and non axisymmetric velocity

Therefore, it is important to gain more insight into the role of theseconstitutive laws in loop dynamics. The issue becomes more1. Introduction

The applicability of conventionlaws for wall friction factor derivements carried out under adiabaticlation loops have been questioned(1975) and Damerell and Schoenhhttp://dx.doi.org/10.1016/j.pnucene.2014.04.0110149-1970/ 2014 Elsevier Ltd. All rights reserved.ced ow constitutivesteady state experi-

tions to natural circu-long. Creveling et al.79) attributed this to

The importance of friction factor in predicting single-phasenatural circulation loop dynamics can hardly be overemphasized.Ambrosini and Ferreri (2000) showed that accurate and reliableprediction of loop stability and transient behavior is stronglydependent on the choice of friction factor. Naveen et al. (2011)observed that the conventional forced convection correlations failto predict the dynamic and stability behavior of these loops well.Wall constitutive lawsFriction factorSingle-phase new correlation for wall friction factor is proposed for ow in horizontal pipes under diabatic conditions. 2014 Elsevier Ltd. All rights reserved.Investigations on single-phase natural cPart 2: Role of wall constitutive laws

Kumar Naveen a,*, Kannan N. Iyer b, J.B. Doshi b, P.KaReactor Engineering Division, Bhabha Atomic Research Centre, Trombay, Mumbai 400bDepartment of Mechanical Engineering, IIT Bombay, Powai, Mumbai 400076, India

a r t i c l e i n f o

Article history:Received 29 October 2013Received in revised form31 January 2014Accepted 16 April 2014

Keywords:

a b s t r a c t

Unlike forced circulation sow. Literature study showcantly modied by secondthe applicability of conveinvestigated both theoretitutive laws derived from s

journal homepage: www.eculation loop dynamics.

ijayan a

India

ms, natural circulation systems need to be started from the state of zerohat under low ow conditions, the velocity eld near the wall is signi-onvection currents particularly during diabatic conditions. In view of this,nal forced convection wall constitutive laws to these systems has beenand experimentally. First the applicability of conventional wall consti-

dy state forced convection experiments is examined. Next, the results of

le at ScienceDirect

clear Energy

evier .com/locate/pnucene

ucleNomenclature

A area of cross section, m2

Cp specic heat at constant pressure, kJ/kg KD pipe diameter, mfF fanning friction factor, dimensionlessfD Darcys friction factor, dimensionlessg gravitational acceleration, m/s2

Grf lm Grashof number, D3r2bg(TweTf)/m2

Grm modied Grashof number, D3r2bgQH/(Am3Cp)H loop height, mK molecular thermal conductivity (W/m K)L length, mNG geometric parameter, dimensionlessP perimeter (m)Pr Prandtl number, CP m/KQ total heat input rate, WRaf Rayleigh number (D3bgDTlm/na)Re Reynolds number, DW/Am

K. Naveen et al. / Progress in N106Ress CGrm=NGr (5)

where Grm D3r2bgQH/(Am3Cp), NG Lt/D, C (2/p)r andr 1/(3 b) with p and b obtained from a Fanning friction factorcorrelation of the form, fF p/(Ress)b. On a logelog scale, Eq. (5)represents a straight line. Eq. (5) is universally applicable tonon-uniform diameter loops also. Therefore, the results have beenexpressed in terms of these dimensionless numbers. Vijayan et al.(2001) carried out experimental investigations in a rectangularsingle-phase natural circulation loop with different combinationsof heater and cooler orientations. They investigated the loopsteady state and stability behavior for Vertical Heater HorizontalCooler (VHHC), Vertical Heater Vertical Cooler (VHVC), HorizontalHeater Vertical Cooler (HHVC) and Horizontal Heater HorizontalCooler (HHVC) congurations. Naveen et al. (2011) obtained thefollowing ts for the experimental data reported in Vijayan et al.(2001):

For VHHC Ress 0:40879Grm=NG0:43751 (6)

For VHVC Ress 1:4092Grm=NG0:3757 (7)

T temperature, Kt time, s

Table 1Friction factor correlations for natural circulation loops compiled from literature.

Reference Type ofloop

Correlation

Crevelinget al. (1975)

ToroidalfF

151

Re1:17 Laminar flow

0:88Re0:45 Turbulent flow

(1)

Widmannet al. (1989)

ToroidalfF

17:98

Re0:91 Laminar flow

0:76Re0:49 Turbulent flow

(2)

Vijayan andAustregesilo(1994)

Closedrectangular

fD 22:26

Re0:6744(3)

Cammarataet al. (2003)and Ficheraand Pagano(2003)

Closedrectangular fF

8 1600 W

(4)For HHVC Ress 7295Grm=NG0:4196 (8)The following correlations have been deduced using the scaling

laws dened by Vijayan and Austregesilo (1994) for Darcys frictionfactor from the experimental ts for different heater and coolerorientations:

For VHHC fD 15:4528

Re0:7143(9)

For VHVC fD 0:8025

Re0:338(10)

U uncertaintyW mass ow rate, kg/s

Subscriptsb bulkD Darcyf lmlm lmh heaterin inletL laminarout outletss steady stateT turbulentw wall

Greek symbolsb coefcient of thermal expansion, K1

m uid viscosity, Pa sn kinematic viscosity, m2/sr density, kg/m3

ar Energy 75 (2014) 105e116For HHVC fD 4:2415

Re0:617(11)

A comparison of friction factors summarized above is shownin Fig. 1. In addition, two forms of conventional forced convec-tion friction factors are also plotted. These are: a law withsmooth transition between laminar and turbulent ow

fD 64=Re2 0:316=Re0:252

q and a law taking friction

factor as maximum of that given by Poiseuille and Blasius lawsfor laminar and turbulent ows. These approaches are used insimulation of natural circulation loops to avoid unrealistic os-cillations in numerical simulations. The rst approach was rec-ommended by Ambrosini and Ferreri (2000) who investigatedthe effect of Blasius law for turbulent forced ow, Churchill(1977) correlation and a law with smooth transition between

laminar and turbulent ow fD 64=Re2 0:316=Re0:252

q

on single-phase natural circulation loop stability. The secondapproach was used by Vijayan et al. (1995) during their inves-tigation on single-phase natural circulation loop dynamicbehavior. It is seen from Fig 1 that there is a considerable scatterin the friction factors. The following conclusions can be drawnbased on the discussions till now:

(a) The friction factors derived from experimental data arehighly loop specic.

for laminar region, friction factors were on an average 35% higher

c 6.32 and m 2.58 0.42Pr2.46Gr0.41and the range of applicability is 5900 < Re< 9600; 11,900 < Gr < 353,000; 1.05 < mb/mw< 1.47 and 8 < Pr < 15. All uid propertiesare evaluated at bulk uid temperature.

Meyeret al. (2008)

Laminar andturbulent

fF fLh1 fTt=fL6:4

i1=6:4(18)

where

fTt fTh1 ft=fT2

i12 (19)

fL 16Re

"1 2:81 104

RePr

Grf

0:42#(20)

fT 0:0791Re0:25m=mw0:2 (21)

ft 0:01249Re=20006 (22)

ucle(b) Even for the same experimental facility, the friction factordepends upon the heater and cooler orientation. Hence, ameaningful comparison can be made only by comparing theexperimental data for facilities having similar heater andcooler orientations.

(c) While for some loops, the experimentally observed value offriction factor is higher than that obtained from conventionalconstant property forced convection friction factor laws forothers it is lower. Hence, their utility as a general purposecorrelation appears to be limited.

The inability of conventional friction factor correlations appli-cable for forced circulation under adiabatic conditions to predictpressure drop under diabatic conditions was recognized long backby Deissler (1951). Deissler (1951) proposed a correction factor forfriction factor under diabatic conditions long back. The proposedcorrection factor was based on the ratio of uid viscosity at the walltemperature and that at bulk mean temperature. Since then, anumber of correlations have been proposed. A summary of thesecorrelations is given in Table 2.

During their experimental investigations on pressure drop un-der combined forced and free convection in horizontal heated

0000100010010.01

0.1

1

10

Dar

cy's

Fric

tion

Fact

or

Reynolds Number

Creveling et al. (1975) - Eq. (1) Widmann et al. (1989) - Eq. (2) Vijayan and Austregesilo (1994) - Eq. (3) VHHC - Eq. (9) VHVC - Eq. (10) HHVC - Eq. (11) Max. of 64/Re and 0.316/Re ((64/Re) +(0.316/Re ) )

Fig. 1. Comparison of friction factor given by different correlations.

K. Naveen et al. / Progress in Ntubes, Morcos and Bergles (1975) showed that the heat transfercoefcient and the friction factor under mixed convection condi-tions are well above the values obtained using constant propertypure forced ow correlations. Bishop et al. (1980) studied the effectof buoyancy on friction factor in laminar upward ow in cylindricaltubes and noted that friction factor is dependent upon thewall heatux. They observed that for aiding ow the frictional drop is higherthan that predicted by conventional laws applicable for forced ow.Experimental investigations by Tam and Ghajar (1997) showed thatthe value of fully developed friction factor increased with increasein the heating rate for a xed Reynolds number. Owing to thepresence of secondary ow, the effect of heating on friction factorwas signicant in the laminar and transition regions. In the tur-bulent region, the secondary ow effect is suppressed by the tur-bulent motion and hence no increase in friction factor wasobserved in this region. Further, it was observed that heating sta-bilizes the ow and delays the ow transition from laminar totransition region. The correlation proposed by them is similar tothat proposed by Deissler (1951) and Test (1968) except that theexponent in viscosity correction factor is dependent on Gr number.

Based on their experimental investigations with ow undervariable heat transfer conditions, Meyer et al. (2008) showed thatTable 2Friction factor correlations for pipe ow under diabatic conditions.

Reference Type of ow Correlation

Deissler(1951)

Laminar fF 16=Remb=mw0:58 (12)

Test (1968) Laminar fF 16=Re1=0:89mb=mw0:2 (13)

Allen andEckert(1964)

Turbulent fF 0:0791Re0:25mb=mw0:25 (14)

Morcos andBergles(1975)

Not specied(Re < 400) fF 16=Re

1

0:195Ra0:15f

151=15(15)

Tam andGhajar(1997)

Laminartransition

fF 16=Remb=mwm (16)

m 1.650.013Pr0.84Gr0.17The range of applicability of the correlationis 1100 < Re < 7400; 17,100 < Gr < 95,600;1.25 < mb/mw < 2.40 and 6 < Pr < 36.

fF h1 Re=ab

icmb=mwm (17)The coefcients a, b, c and m are inletdependant. For a bell mouth entrance,the values are given by a 5340, b 0.099,

ar Energy 75 (2014) 105e116 107than that predicted by Poiseuille equation. Further, it was foundthat with a viscosity correction, of the type given by Eqs. (12)e(14),the predictions improve only by 5%. The increase in friction factorwas attributed by them to the secondary ow effects which couldnot be taken into account by the viscosity corrections given by Eqs.(12)e(14). They noted that secondary ows distort the velocityprole near the wall in such a way that the gradient near the wall ismuch steeper. This gives rise to higher friction factors. Further, thestudies by Tam and Ghajar (1997) andMeyer et al. (2008) show thatthe effect of heating on friction factor was signicant only in thelaminar and transition regions. Since the secondary ows distortthe near wall velocity prole in different ways in a horizontal andvertical section, the frictions factors under diabatic conditions areexpected to be different for vertical and horizontal sections. Thisinference is also supported by the friction factor correlationsplotted in Fig. 1. Friction factor correlations plotted in Fig. 1 fordifferent natural circulation loops are derived from steady stateexperimental data. Under steady state conditions, thewall and uidtemperatures are expected to be same throughout the loop exceptin heater and cooler provided the insulation heat losses are negli-gible. For adiabatic pipe sections, the conventional wall constitutivelaws derived from steady state constant property forced convection

of 15 thermocouples were installed at different locations to mea-sure the uid temperature. Out of these 15 thermocouples, 9thermocouples measure the uid temperature in the main loop.Four thermocouples measure the uid temperature at inlet andoutlet of each cooler. One thermocouple, having 2 mm diameter isinstalled in the middle of expansion tank and another thermo-couple is installed in the pipe connecting the expansion tank andmain loop. Thermocouples are calibrated in the range of 0e150 C.A differential pressure transmitter (DPT) with ameasuring accuracyof 0.25% of the span is used to measure the differential pressureacross a 1060 mm long section (including heater) in bottom hori-zontal tube. The DPT is calibrated in the range of 15 to15 mm ofwater column. The negative range is provided to measure the owin the reverse direction. All the temperature and pressure drop databeing measured using thermocouples and DPT respectively, arerecorded using a data logger. These are recorded at a frequency of1 Hz using Graphtec make digital recorder. The heater power ismeasured using a wattmeter and is recorded manually.

3.2. Experimental procedure

The purpose of these tests was to study loop behavior understeady state conditions. It is well known that natural circulationsystems take a long time to reach steady state. In fact Crevelinget al. (1975) and Vijayan et al. (2007) observed waiting periodsclose to 2 h before ow stabilized. In the present study also, it wasobserved that loop takes long time to reach the steady state. Themain loop uid exchanges energy with the expansion tank and itmay take very long time to reach a steady state. This may introducesignicant errors at low powers. To overcome this problem, in thepresent study, a new approach has been adopted for experimental

Fig. 2. Experimental facility.

ucleexperiments are applicable. Hence, the increase and decrease infriction factors as indicated by correlations derived from steadystate natural circulation loop experimental data are mainly becauseof changed near wall velocity prole in heater and cooler. Since thesecondary ows distort the near wall velocity prole in differentways for a horizontal heater and vertical heater, the friction factorsfor different heater orientations are also expected to be different.The same is expected for cooler orientations also. Hence, it isrequired to have friction factor correlations based on heater andcooler orientations. In the present study, the issue of friction factorfor horizontal heater and horizontal cooler has been addressed.

It will be shown later that for the HHHC geometry, very fewexperimental data, except that of Mousavian et al. (2004) is avail-able in literature that spans a large variation in Ress. The experi-mental data reported in Vijayan et al. (2007) shows a large scatterfor Ress values around 1000. Further most experimental dataappear to have a large friction factor (resulting in low Ress) thanthat estimated by Vijayan and Austregesilo (1994) using standardforced convection correlations. It will also be shown later thatforced convection correlations predict unidirectional pulsatingbehavior for Vijayans loop (Vijayan et al., 2007) at 220 W whileexperimental investigations show bidirectional pulsating behavior.Numerical experiments on sensitivity of nature of oscillations withfriction factor indicated that a higher friction factor was able tocapture the bidirectional pulsating behavior. Hence, it was decidedto systematically investigate the behavior of these loops. Since, itis the horizontal heater horizontal cooler orientation which pre-sents a variety of interesting phenomenon; the investigations havebeen carried out for horizontal heater and horizontal coolerconguration.

3. Overview of the experiments

3.1. Description of the experimental loop

The experimental loop consists of a uniform diameter rectan-gular natural circulation loopmade of borosilicate glass (Fig. 2). Theprimary loop glass tube has an inside diameter of 26.9 mm and awall thickness of 1.65mm. The loop consists of two heaters and twocoolers. However, only horizontal heater and horizontal coolerconguration has been investigated experimentally. The length ofthe horizontal heater is 665 mm. The heater is made up of 1 mmdiameter nichrome wire evenly wound on the outside of the glasstube. The heater power is varied with the help of a dimmerstat andis measured using a wattmeter, which had an accuracy of 2.5 W.The loop consists of two coolers. One of the coolers is at the highestelevation and the other is in the right vertical section. The length ofthe horizontal cooler is 1000 mm and the length of the verticalcooler is 800 mm. The cooler is a tube-in-tube type heat exchangerwith outer tube having inside diameter of 43 mm and wall thick-ness of 1.5 mm. The coolant ow to the secondary side of the cooleris provided from an overhead tank. To measure the cooler sec-ondary mass ow rate, a rotameter is installed in the cooler sec-ondary line. The rotameter has a measuring range of 0e10 lpm. Thecooler secondary ow is adjusted using a globe valve mounted inthis line. An expansion tank, made of borosilicate glass, is providedin the loop at the highest elevation to take care of swell andshrinkages in loop inventory during the transient. The expansiontank consists of a 97.3 mm internal diameter and 100.3 mm outerdiameter cylindrical tank having a shell length of 280mm. The tankis connected to the main loop through a 20 mm outer diameter and18 mm inner diameter tube of 252 mm length.

Temperature of the uid in the main loop is measured atdifferent locations, as shown in Fig. 3, using mineral insulated

K. Naveen et al. / Progress in N1080.5 mm diameter chromel-alumel (K-type) thermocouples. A totalar Energy 75 (2014) 105e116investigations at power less than 200 W. The loop is rst operated

ucleK. Naveen et al. / Progress in Nat a power higher than that at which steady state data is to becollected. This increases the temperature of uid in expansion tankalso. The power is then lowered to the desired value. Since the uidtemperature in the expansion tank is now higher than that of theuid in the main loop, the steady state is reached much faster thanin the previous case. In all the experiments the cooler secondarymass ow rate was kept 5 lpm and the average cooler secondaryinlet temperature was 30.4 C.

3.3. Data reduction and uncertainty analysis

The steady state mass ow rate is estimated from the measureddata using the following equation

W QCpDTh

(23)

where Q is the heater power, Cp is the specic heat of the uid andDTh is the temperature rise across the heater. The heater inlet andoutlet temperatures are measured using mineral insulated 0.5 mmdiameter chromel-alumel (K-Type) thermocouples. The signalswere compensated for the DC drift.

When designing a test plan, compromises must always be madebecause of the conicting requirements and practical limitations.The present case is no exception. In the present case, single pointthermocouples have been used for measurement of average heaterinlet and outlet temperatures. This has been done to keep the

Fig. 3. Location of main thermocouples.obstruction of ow to minimum. Though thermocouples TE-1(Temperature Element e 1) and TE-2 are closest to the heater,thermocouples TE-3 and TE-13 have been taken as representativeof heater inlet and outlet average temperatures. This is because ofthe reason that some stratication is expected at the exit of theheater and cooler sections and because of the proximity of TE-1 andTE-2 to the heater, these thermocouples may not give the mixedmean temperature. Thermocouples TE-3 and TE-13 are located inthe left and right vertical adiabatic legs. It is assumed that thethermocouples TE-3 and TE-13 give the mixed mean temperature.

The uncertainty of measurements has been evaluated accordingto recommendations made by Bell (2001). The measurement un-certainty has been estimated for each test point separately and hasbeen taken into account when analyzing the results. Each experi-ment is repeated at least thrice. The uncertainty of measurementassociated with temperature measurement is evaluated accordingto Type A method of evaluation (EA-4/02, 1999). The Type Aevaluation of standard uncertainty is the method of evaluating theuncertainty by statistical analysis of a series of observations. In thepresent study, the temperature has been estimated by taking meanof 300 readings recorded at 1 Hz. These measurements have beenrecorded after the ow has stabilized. The standard deviation anduncertainty in measurement has been obtained for 95% condenceinterval. Uncertainty in measurement of DT is given by

UDT U2Tout U2Tin

q(24)

The uncertainty in calculated mass ow rate is given by

UWW

UDTDT

UPP

(25)

The expanded uncertainty of measurement in loop mass owrate is given by the following equation

UW 2UW (26)

Factor of 2 has been taken for a coverage probability of 95%.Uncertainty in power measurement is the biggest contributor tooverall uncertainty in loop mass ow rate measurement. Experi-mental investigations were carried out with different values ofheater power ranging from 40W to 700W. Since the purpose of theexperimental investigations is to investigate the loop behaviorunder low ow conditions, for heater power less than 100 W, ex-periments were carried out in steps of 20 W. For heater powersgreater than 100 W, the heater power was varied in steps of 50 W.The upper limit on heater power was decided by the single-phaseow limit. At heater powers above 700 W, subcooled boiling wasobserved in the heater. A summary of experimental runs is given inTable 3.

A total of 73 experimental runs were carried out. Variation inloop mass ow rate is insignicant for the uncertainty reported incooler secondary mass ow rate. The measured and calculatedvalues along with uncertainty for different experimental runs aregiven in Appendix A. Further details can be obtained from Naveen(2013).

A representative plot of the loop mass ow rate, the loopaverage temperature and the cooler secondary inlet water tem-perature is shown in Fig. 4 for a heater power input of 200 W. Asstated earlier, the uncertainty in power measurement is the biggestcontributor to overall uncertainty in the loop mass ow rate mea-surement. Therefore, at least 5 runs were taken for experimentswith heater power less than 100 W. However, a minimum of 3 runs

ar Energy 75 (2014) 105e116 109were taken for experiments at all heater powers.

4. Development of friction factor correlation

The loop steady state behavior has been predicted using themodel described in Naveen et al. (2011) and Naveen (2013). In allthe numerical simulations, the expansion tank is modeled as a timedependent volume exchanging only swell and shrinkages in themain loop uid. The details of the mathematical model are pre-sented in Naveen et al. (2011) and Naveen (2013). The pressure inthe expansion tank is assumed to be constant. In all the simulations,the wall heat transfer coefcients have been evaluated using thecorrelations proposed byMeyer et al. (2008) and Aicher andMartin(1997) for horizontal and vertical pipe sections respectively. For the

nicant deviation from the data of others. Further, it is seen fromFig. 5 that the conventional forced convection friction factor cor-relations show signicant deviations from observed experimentalbehavior.

The local losses may also play a signicant role in loop behavior.The effect of local losses on ow behavior is shown in Fig. 6. It canbe seen from Fig. 6(a) and (b) that all the data points are far awayfrom the theoretical equation derived using conventional frictionfactor correlation applicable for forced circultion. A comparison ofFig 6(a) with (b) shows that the effect of local losses is not signi-cant for the operating ranges investigated experimentally. Fig. 7shows the straight line t for the present experimental datawhen plotted on Ress versus Grm/NG plane. It is seen from Fig. 7 thatmost of the data points fall on a straight line. This is in conrmationwith the scaling laws proposed by Vijayan and Austregesilo (1994)for single-phase natural circulation loops. The following equationgives the best straight line t for the present experimental data on a

Table 3Summary of experimental runs.

Power range 40 We700 WCooler secondary ow rate 5 lpmCooler secondary water temperature 30.4 (2) C

K. Naveen et al. / Progress in Nucle110present loop, the cooler secondary heat transfer coefcient hasbeen evaluated using SiedereTate correlation for laminar heattransfer which gives a value of 450 W/(m2K) for a coolant ow rateof 5 lpm at 30.4 C.

Vijayan (2002) argued that the following conventional frictionfactor correlations applicable for forced circular pipes predict theloop behavior reasonable well

fF 16=Re Laminar flow0:079

Re0:25 Turbulent flow

(27)

Substitution of the values for p and b from Eq. (27) into Eq. (5)gives

Ress (0:1768Grm=NG0:5 Laminar flow1:96Grm=NG1=2:75 Turbulent flow

(28)

A comparison of present experimental data with steady stateforced convections laws (Eq. (28)) is shown in Fig. 5. Vijayan andAustregesilo (1994), Vijayan et al. (2007), Mousavian et al. (2004)and Misale et al. (2007) have also carried out experimental in-vestigations in natural circulation loops having horizontal heaterand horizontal cooler. Their data is also plotted for comparison.Fig. 5 shows that for the HHHC orientation, the friction factor isconsiderably higher (Ress in the experiment is lower) than thatgiven by Poiseuille and Blasius laws.

0.010

0.015

0.020

20

30

40

50

Tem

pera

ture

(oC

)

ss fl

ow ra

te (k

g/s)

Legends Secondary water inlet temperature26 28 30 32 34 360.000

0.005

0

10

Ma

Run No.

Loop average temperature o Mass flow rate

Fig. 4. Experimentally obtained loop mass ow rates for heater power input of 200 W.From Fig. 5, it is seen that our experimental data is in agreementwith that reported by Mousavian et al. (2004). However, the pre-sent experimental data shows signicant deviations from that ofMousavian et al. (2004) and Misale et al. (2007) for Reynoldsnumber less than 100. This may be because of the use of singlethermocouples used in present experiment for uid temperaturemeasurement. This is also evident from large scatter observed inpresent experimental data at very low powers. Data reported byBau and Torrance (1981) show signicant deviation from the dataof others. This is because of the reason that Bau and Torrance (1981)carried out experiments in an open natural circulation loop andlocal losses and the losses in the line connecting the two coolingsections could not considered. It was not possible to account for thelocal losses because only a few geometrical details were availablefor this loop. Hence data reported by Bau and Torrance show sig-

10 10 10 10 10 10 10 1010

10

10

10

10

Re =1.96(Gr /N )

Re =0.1768(Gr /N )

Re s

s

Grm/NG

Present experiment Vijayan et al. (1994) - 6 mm loop Vijayan et al. (1994) - 11 mm loop Vijayan et al. (1994) - 23.2 mm loop Vijayan et al. (2007) - 26.9 mm loop Mousavian et al. (2004) - 40 mm loop Misale et al. (2007) - 4 mm loop Bau and Torrance (1981) - 25 mm loop

Fig. 5. Comparison of steady state natural circulation ow for loops having horizontalheater and horizontal cooler.

ar Energy 75 (2014) 105e116logelog scale:

Ress 0:2285Grm=NG0:44844 (29)Using the scaling laws dened by Vijayan and Austregesilo

(1994), the following correlation for the Darcys friction factor canbe deduced from Eq. (29)

fD 53:788=Re0:77 (30)

1E7 1E8 1E9 1E1010

100

1000

10000

Re s

s Present experiment Ress=0.2285(Grm/NG)

0.44844

uclear Energy 75 (2014) 105e116 1111000000 1E7 1E8 1E9 1E10

100

1000

10000

Re s

s

Laminar flow correlation Turbulent flow correlation Present experiment

K. Naveen et al. / Progress in NAs discussed earlier, Eq. (30) is also specic to present loop justlike the correlations described in section 2.

A comparison of experimental data with the model predictionsmade using the wall friction factor given by Eq. (18) is shown inFig. 8. It is noted from Fig. 8 that themodel predictions are still awayfrom the experimental observation. The reason for this could be (a)the transition criterion adopted by Meyer et al. (2008) and (b) therange of applicability of the correlation. Eq. (18) assumes the tran-sition from laminar to turbulent ow taking place at Reynoldsnumber equal to 2000, as is clear from Eq. (21). However, in naturalcirculation loops turbulent ow can exist at Reynolds number aslow as 500. Jackson et al. (1989) reviewed the studies of mixedconvection in vertical tubes and noted the existence of turbulentow for Reynolds number less than 1000. In their study on single-phase natural circulation in toroidal loops, Creveling et al. (1975)noted the transition between laminar and turbulent regimes atReynolds number equal to 1500.Widmann et al. (1989)made visualexaminations in their experimental investigations on thermosy-phon in a toroidal loop using Kalleriscopic akes and observed the

Grm/Ng

(a)

1000000 1E7 1E8 1E9 1E10

100

1000

10000

Re s

s

Grm/Ng

Laminar flow correlation Turbulent flow correlation Present experiment

(b) Fig. 6. Comparison of experimental data with theoretical correlation given by Eq. (28)(a) With local losses and (b) Without local losses.

Grm/Ng

Fig. 7. Steady state natural circulation ow in present experimental loop.existence of three different regimes: (a) completely laminar, (b)completely turbulent and (c) partially laminare partially turbulent.During the oscillatory phase transition from laminar to turbulentand vice versa was also observed. Bau and Torrance (1981) madesimilar observations in their experimental investigations in an opennatural circulation loop. Also, the correlation given by Eq. (18) hasbeen developed for fully developed ow while in a natural circu-lation loop; the conditions may not be fully developed all along theloop. Further, Eq. (18) was derived based on experimental data forRe greater than 1000.

Based on the present experimental data, the following correla-tion, which is a modication of the correlation proposed byMorcosand Bergles (1975) and Meyer et al. (2008), has been proposed forthe Fanning friction factor for horizontal pipes under diabaticconditions:

fF fLh1 fTt=fL6:4

i1=6:4 (31)1000000 1E7 1E8 1E9 1E1010

100

1000

10000

Re s

s

Grm/NG

Present experiment Model predictions

Fig. 8. Comparison of experimentally obtained loop mass ow rate with model pre-dictions made using friction factor given by Eq. (27).

where

fTt fTh1 ft=fT2

i12 (32)

fL 16=Re1

1:56Ra0:15f

151=15(33)

fT 0:0791Re0:25m=mw0:2 (34)

ft 0:03862Re=20006 (35)Eq. (31) is similar to that proposed by Meyer et al. (2008) except

that the laminar friction factor is obtained from a modied form ofMorcos and Bergles (1975) correlation and value of coefcient inEq. (22) is obtained from Eq. (30) by substituting Reynolds numberequal to 2000. Figs. 9 and 10 show the comparison of model pre-dictions made using friction factor given by Eq. (31) with experi-mental data in non-dimensional and dimensional formrespectively. Fig. 11 shows a comparison of predicted temperaturedifference across the heater with experimentally observed

tank located at the highest elevation to take care of the thermal

0 100 200 300 400 500 600 700 8000.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

Mas

s flo

w ra

te (k

g/s)

Heater power (W)

Model prediction Present experiment

Fig. 10. Comparison of loop mass ow rate predicted by model with experimentaldata.

0 100 200 300 400 500 600 700 8000

1

2

3

4

5

6

7

Tem

pera

ture

diff

eren

ce a

cros

s he

ater

(oC

)

Heater power (W)

Model predictions Present experiment

K. Naveen et al. / Progress in Nuclear Energy 75 (2014) 105e116112behavior. From Figs. 9e11 it is seen that model predictions madeusing the proposed friction factor correlation are in reasonablygood agreement with experimentally observed behavior.

5. Numerical investigations using the proposed friction factorcorrelation

5.1. Investigations on the loop addressed in Vijayan et al. (2001,2007)

The proposed correlation is applicable only for ow throughhorizontal pipes because it is based on steady state experimentaldata. Under steady state conditions, the wall and uid temperatureis expected to be same everywhere in the loop except in the heaterand cooler. Hence, the proposed correlation accounts for enhancedfriction only in horizontal section. Since, the proposed correlation isbased on the temperature drop across liquid lm; it is expected tobe applicable for all horizontal pipe ows. Hence, it is only logical totest the proposed correlation for the loop addressed by Vijayanet al. (2001). Vijayan et al. (2001) carried out experimental

1E7 1E8 1E9 1E1010

100

1000

10000

Re s

s

Grm/N

G

Model prediction made using proposed correlation

Present experimentFig. 9. Comparison of experimentally obtained loop mass ow rate with model pre-dictions made using proposed friction factor correlation.investigations in a rectangular single-phase natural circulationloop. The loop consists of a uniform diameter rectangular naturalcirculation loop. The details of the experimental set-up are given inVijayan et al. (2001, 2007). However, just for the sake ofcompleteness a brief description is given. It consists of borosilicateglass tubes of inside diameter 26.9 mm and outside diameter28.9 mm. The loop height and width are 2.2 m and 1.415 mrespectively. The horizontal and vertical sections are joined by 900

bends. The loop has two heaters and two coolers. One of the heatersis at lowest elevation and the other one is in vertical section. Thelengths of the horizontal and vertical heaters are 620 mm and730mm respectively. The heater consists of a nichromewire evenlywound on the outside of the glass tube. One of the coolers is placedin the horizontal section at the uppermost elevation and the othercooler is placed in vertical pipe section. Each cooler is 800 mm longwith outer tube having inside diameter of 49.2mm and 1.5mmwallthickness. The coolant ow to the secondary side of the cooler isprovided from an overhead tank. The loop also has an expansionFig. 11. Variation of steady state temperature difference across heater with heaterpower input.

expansion/shrinkage of water. The expansion tank consists of a97.3 mm internal diameter and 100.3 mm outer diameter cylin-drical tank. The tank is connected to the main loop through a21 mm outer diameter and 18 mm internal diameter tube of252 mm length. To minimize the heat loss to atmosphere, the loopwas insulated with ceramic wool.

The results of the numerical simulations carried out using pro-posed correlation are presented here. The following friction factorcorrelation has been used for predicting the loop transientbehavior:

ff Eq: 31 Horizontal pipes

16Re; 0:079

Re0:25

Vertical pipes

(36)

Figs. 12 and 13 show the comparisons of model predictionsmade using constant property forced convection friction factorcorrelation (also referred as conventional friction factor correla-tion) and the presently proposed friction factor correlation withexperimental data for a heater power input of 120 W and 220 Wrespectively. From Fig. 12, it is seen that the model predictions withconventional forced friction correlation show ow reversals during

heat sink temperature on dynamic behavior of a rectangular single-

6000 6500 7000 7500 8000-3

-2

-1

0

1

2

3

p (m

m o

f wat

er c

olum

n)

Time (s)

Experiment Model Prediction using friction factor,

f = ((64/Re)2+(0.316/Re0.25)2)0.5

Model Prediction using proposed friction factor correlation

Fig. 13. Model prediction for heater power of 220 W.

0 1000 2000 3000 4000 5000-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

Model prediction Experiment

p (m

m o

f wat

er c

olum

n)

Time (s)

K. Naveen et al. / Progress in Nuclear Energy 75 (2014) 105e116 113ow initiation whereas predictions with the proposed frictionfactor correlation show only unidirectional ow oscillation. How-ever, there is still mismatch between the observed and predictedfrequency and magnitude of oscillations. It is seen from Fig. 13 thatfor 220 W heater power, the model predictions made using pro-posed friction factor correlation are in close agreement with theexperimental data. It is worth noting here that the predictions withconventional friction factor correlation predict only unidirectionaloscillation while predictions made with proposed correlation pre-dict bidirectional oscillation. The difference between the predictedand experimentally observed behavior can be attributed to theinability of the expansion tank model to account for energy ex-change by natural convection.

Fig. 14 shows the comparison of predicted ow initiation tran-sient with experimentally observed behavior for 220 W heaterpower. It is seen from Fig. 14 that initially only unidirectional os-cillations are observed both in model predictions and experimen-tally observed behavior. With the passage of time, the oscillationsbecome bidirectional. However, there is mismatch in the behaviorof initial oscillations. The differences in the initial amplitude ofoscillations can be attributed to use of constant property pureforced convection friction factor for vertical pipe sections. Saylor

0 1000 2000 3000 4000-3

-2

-1

0

1

2

3

p (m

m o

f wat

er c

olum

n)

Time (s)

Model prediction using proposed friction factor correlation

Model prediction using friction factor correlation, f = ((64/Re)2+(0.316/Re0.25)2)0.5

Experiment

Fig. 12. Model prediction for heater power of 120 W.and Joye (1991) studied pressure drop in mixed convection heattransfer in vertical tubes and observed that at low Reynoldsnumbers and high Grashof numbers, the pressure drop for aidingow (heating in up ow and cooling in down ow) through avertical tube under constant temperature conditions can be ordersof magnitude higher than that expected on the basis of forced owconsiderations. They also observed negative pressure drop fordownow heating in mixed convection zone. In a natural circula-tion loop, during start-up both aiding and opposing ow conditionsare encountered. However, as the ow picks up, themodel is able topredict the unidirectional and bidirectional oscillating behavior fora heater power of 120 W and 220 W respectively which is inagreement with the experimental data. It is hoped that once a moreprecise friction model is generated for vertical tubes, the overallprediction would be more precise.

5.2. Investigations on the loop addressed in Misale et al. (2011)

Misale et al. (2011) experimentally investigated the effect ofFig. 14. Comparison of ow initiation transient for 220 W heater power predictedusing proposed friction factor correlation with experimentally observed behavior.

0 1000 2000 3000 4000 5000 6000-40

-20

0

20

40

fD = ((64/Re)2+(0.316/Re0.25)2)0.5

Proposed correlation (Eq. 34)

T Hea

ter (

K)

Time (s)

Fig. 15. Model prediction for 500 W heater power input and 10 C heat sinktemperature.

1000 1200 1400 1600 1800 2000 2200 2400 2600 2800-40

-20

0

20

40

fD = ((64/Re)2+(0.316/Re0.25)2)0.5

Proposed correlation (Eq. 34)

T Hea

ter (

K)

Time (s)

Fig. 17. Model prediction for 500 W heater power input and 10 C heat sinktemperature.

K. Naveen et al. / Progress in Nuclear Energy 75 (2014) 105e116114phase natural circulation loop having horizontal heater and hori-zontal cooler. The loop consists of a 30 mm I.D. and 1.3 mm wallthickness pipe having 1112 mm width and 988 mm height. Thevertical legs and the four bends are made of SS and the cooler andheater are made of Cu. The heater and cooler lengths are respec-tively 960 mm and 900 mm. The heater in the experimental testfacility consists of a nichrome wire evenly wound on the outside ofthe Cu tube. The cooler is a double pipe heat exchanger havingouter tube I.D. of 102 mm (wall thickness 3 mm). Water and Glycolmixture having 40 C freezing temperature is used as coolant onthe cooler secondary side and cooler secondary ow rate wasmaintained at 0.61 kg/s throughout the experiments. In numericalsimulations for this loop, the cooler secondary heat transfer coef-cient is calculated using SiedereTate equation (with viscositycorrection) and the coolant temperature has been assumed to beconstant. To start with the loop is assumed to be lled with water at30 C temperature and the uid velocity is assumed to be zero. Inpresent study the loop behavior was simulated using the 1-Dmodeldescribed in Naveen (2013). Figs. 15e19 compare the model pre-

dictions made using the conventional friction factor correlation

1000 1200 1400 1600 1800 2000 2200 2400 2600 2800-40

-20

0

20

40

fD = ((64/Re)2+(0.316/Re0.25)2)0.5

Proposed correlation (Eq. 34)

T Hea

ter (

K)

Time (s)

Fig. 16. Model prediction for 500 W heater power input and 0 C heat sinktemperature.with that proposed in the present study (Eq. (36)). It is seen fromthese gures that the frequency of ow reversal increases whenpredicted with proposed friction factor correlation. The frequencyof oscillation predicted by the proposed friction factor correlation isqualitatively more closer to that observed experimentally. How-ever, both the correlations predict unstable behavior for all the heatsink temperatures.

6. Conclusions

Numerical and experimental investigations have been carriedout to study the effect of constitutive laws for wall friction on loopsteady state behavior. The results presented in this paper havehelped in gaining more insight into the role of friction factor insingle-phase natural circulation loop dynamics. The following in-sights are obtained from this study:

1. The role of constitutive laws for wall friction derived fromsteady state forced convection experiments in predicting thesteady state single-phase loop dynamics has been investigated.

Literature survey fails to give a satisfactory answer for the

1000 1200 1400 1600 1800 2000 2200 2400 2600 2800-40

-20

0

20

40

fD = ((64/Re)2+(0.316/Re0.25)2)0.5

Proposed correlation (Eq. 34)

T Hea

ter (

K)

Time (s)

Fig. 18. Model prediction for 500 W heater power input and 20 C heat sinktemperature.

Appendix A

Table A.1Steady state data for different experimental runs.

Runno.

Power(W)

Tavg(C)

DTacrossheater

Coolersecondaryinlet watertemp. (C)

Loopmass owrate, W(kg/s)

Expandeduncertainty(%)

1 40 30.2 1.4342 27.0 0.0067 12.632 40 33.8 1.4711 30.4 0.0065 12.603 40 34.4 1.5253 31.2 0.0063 12.584 40 35.0 1.5297 31.6 0.0063 12.595 40 34.3 1.5730 31.1 0.0061 12.586 60 35.2 2.1932 29.7 0.0065 8.467 60 33.0 2.2543 28.3 0.0064 8.458 60 35.0 1.8718 30.8 0.0077 8.489 60 35.9 1.7793 31.1 0.0081 8.5110 60 36.1 2.0457 31.6 0.0070 8.4611 60 35.7 1.9573 31.3 0.0073 8.4312 80 36.0 2.3941 30.3 0.0080 6.4213 80 34.0 2.5779 28.3 0.0074 6.4414 80 36.7 2.2727 31.0 0.0084 6.4815 80 37.2 2.3923 31.5 0.0080 6.3916 80 36.9 2.2680 31.2 0.0084 6.4217 100 35.2 2.7226 27.6 0.0088 5.5018 100 34.4 2.0448 27.8 0.0117 5.3619 100 38.2 2.9057 31.1 0.0082 5.1920 100 37.5 2.5976 31.0 0.0092 5.2821 100 38.2 2.5623 31.1 0.0093 5.2122 100 38.7 2.8447 31.6 0.0084 5.1423 100 38.3 2.6670 31.2 0.0090 5.1824 150 39.7 2.8864 30.5 0.0124 3.6625 150 41.0 2.9467 31.4 0.0122 3.6426 200 40.5 3.4244 28.1 0.0140 3.3627 200 42.0 3.3936 29.7 0.0141 2.8528 200 41.2 3.0938 30.2 0.0155 2.9529 200 42.7 3.4404 31.1 0.0139 2.7930 200 42.1 3.6244 30.4 0.0132 2.8331 200 42.0 3.3797 30.9 0.0142 2.8332 200 43.3 3.3393 30.9 0.0143 2.7533 200 43.1 3.2227 31.0 0.0148 2.7534 200 42.8 3.3297 31.6 0.0144 2.7435 200 43.0 3.3010 31.1 0.0145 2.7436 240 44.8 3.6313 30.9 0.0158 2.3437 250 45.0 3.4195 31.0 0.0175 2.3138 300 46.9 4.1354 30.8 0.0174 2.0039 300 47.8 3.9700 30.9 0.0181 1.9840 300 47.6 3.7023 31.4 0.0194 2.0841 300 47.2 3.9723 31.3 0.0181 1.95

uclear Energy 75 (2014) 105e116 115problem at hand. Based on the curve tting, different correla-tions have been obtained for different heater and cooler orien-tations. These correlations give different values of friction factorfor the same Reynolds number. This brings out the inherentinadequacy of the above approach used for deriving frictionfactor correlations from steady state experimental data. Theabove approach based on straight line t clearly fails to bring outthe physics of the process and correlation derived in this way arehighly specic to the loop and the heater and the cooler orien-tation. Hence, these correlations have a limited applicability.

2. The steady state experimental investigations have been carriedout in a natural circulation loop having horizontal heater andhorizontal cooler orientation. These investigations clearly showthat the conventional wall constitutive laws derived from con-stant property steady state forced convection experimental datafail to predict the observed experimental behavior.

3. The present experimental data for HHHC orientation is inagreement with the experimental data reported in the literaturefor the same heater and cooler orientations.

4. The experimental results show that loop mass ow rate in-creases with increase in heater power. Model predictions madeusing conventional friction factor laws overpredict the mass

1000 1200 1400 1600 1800 2000 2200 2400 2600 2800-40

-20

0

20

40

fD = ((64/Re)2+(0.316/Re0.25)2)0.5

Proposed correlation (Eq. 34)

T Hea

ter (

K)

Time (s)

Fig. 19. Model prediction for 500 W heater power input and 30 C heat sinktemperature.

K. Naveen et al. / Progress in Now rate at all heater power inputs.5. A new correlation has been proposed for friction factor in hor-

izontal pipes under mixed convection. The proposed correlationis a modication of friction factor correlations proposed byMorcos and Bergles (1975) and Meyer et al. (2008). The pro-posed correlation predicts the loop steady state behavior quitewell. However, similar correlations need to be developed forow through vertical pipes also for predicting the loop dy-namics more accurately.

6. The proposed friction factor correlation has been used to predictthe transient behavior of the loop addressed by Vijayan et al.(2001, 2007). A comparison of model prediction made usingthe conventional forced ow friction factor correlation with theproposed correlation shows that the proposed correlation pre-dicts the loop behavior more closely.

7. Model application to the loop addressed by Misale et al. (2011)show that the proposed correlation predicts the loop behaviorbetter than that predicted using conventional forced ow fric-tion factor correlation. However, the model predictions showunstable behavior for all heat sink temperatures while theexperimental observations show stable loop behavior for a heatsink temperature of 10 C.

42 310 45.3 4.3887 28.3 0.0169 2.6743 350 48.6 3.9987 30.7 0.0209 1.8444 350 49.5 4.0067 31.5 0.0209 1.8245 350 49.7 4.0433 31.0 0.0207 1.8146 350 49.6 4.1893 31.0 0.0200 1.7747 350 49.9 3.8537 31.1 0.0217 1.7648 370 51.0 4.3020 30.3 0.0206 1.7549 400 50.3 4.3496 29.9 0.0220 1.7350 400 45.2 3.4048 25.6 0.0281 1.9251 400 51.1 4.3146 31.1 0.0222 1.6652 400 51.4 4.3157 31.3 0.0222 1.6853 400 51.8 4.4427 30.9 0.0215 1.5854 400 51.6 4.3483 31.3 0.0220 1.6555 450 53.3 4.7307 31.2 0.0227 1.5756 450 53.5 4.5150 31.1 0.0238 1.5757 450 54.1 4.3203 31.3 0.0249 1.4958 500 55.7 4.7217 31.6 0.0253 1.4059 500 55.9 4.7800 30.6 0.0250 1.4660 500 55.4 4.8467 30.7 0.0247 1.4661 500 55.9 4.8250 31.4 0.0248 1.3762 550 57.6 4.9253 31.2 0.0267 1.47

63 580 55.3 5.4259 28.8 0.0256 1.3664 600 52.6 4.6342 25.6 0.0310 1.4865 600 57.2 5.2366 30.0 0.0274 1.3566 600 55.6 4.5838 28.0 0.0313 1.49(continued on next page)

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Table A.1 (continued )

Runno.

Power(W)

Tavg(C)

DTacrossheater

Coolersecondaryinlet watertemp. (C)

Loopmass owrate, W(kg/s)

Expandeduncertainty(%)

67 600 59.8 5.1940 31.5 0.0276 1.2668 600 59.9 5.3243 30.7 0.0269 1.3069 600 60.3 5.1737 31.6 0.0277 1.2770 620 58.1 5.2991 29.1 0.0280 2.2671 640 58.0 5.2691 29.1 0.0290 2.4572 700 63.4 5.5520 31.4 0.0301 1.1873 700 63.3 5.7153 30.9 0.0293 1.21

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Investigations on single-phase natural circulation loop dynamics. Part 2: Role of wall constitutive laws1 Introduction2 Previous research on wall constitutive laws for natural circulation loops3 Overview of the experiments3.1 Description of the experimental loop3.2 Experimental procedure3.3 Data reduction and uncertainty analysis

4 Development of friction factor correlation5 Numerical investigations using the proposed friction factor correlation5.1 Investigations on the loop addressed in Vijayan et al. (2001, 2007)5.2 Investigations on the loop addressed in Misale et al. (2011)

6 ConclusionsAppendix AReferences