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Annals of Nuclear Energy 34 (2007) 679–686

annals of

NUCLEAR ENERGY

Technical Note

Cellular convection in vertical annuli of fast breeder reactors

M.G. Hemanath *, C. Meikandamurthy, V. Ramakrishnan, K.K. Rajan,M. Rajan, G. Vaidyanathan

Fast Reactor Technology Group, Indira Gandhi Center for Atomic Research, Kalpakkam, India

Received 21 August 2006; received in revised form 28 February 2007; accepted 2 March 2007Available online 11 May 2007

Abstract

In the pool type fast reactors the roof structure is penetrated by a number of pumps and heat exchangers that are cylindrical in shape.Sandwiched between the free surface of sodium and the roof structure, is stagnant argon gas, which can flow in the annular spacebetween the components and roof structure, as a thermosyphon. These thermosyphons not only transport heat from sodium to roofstructure, but also result in cellular convection in vertical annuli resulting in circumferential temperature asymmetry of the penetratingcomponents. There is need to know the temperature asymmetry as it can cause tilting of the components. Experiments were carried out inan annulus model to predict the circumferential temperature difference with and without sodium in the test vessel. Three-dimensionalanalysis was also carried out using PHOENICS CFD code and compared with the experiment. This paper describes the experimentaldetails, the theoretical analysis and their comparison.� 2007 Elsevier Ltd. All rights reserved.

1. Introduction

In Fast Breeder Reactors, many mechanical componentssuch as Pump, Intermediate Heat Exchanger (IHX), Rotat-ing plugs, etc. penetrate the top closures of the reactor withargon as cover gas above free sodium level at 803 K. Thesepenetrations form vertical annular gaps, which are open atthe bottom to hot cover gas and closed at the top (Fig. 1a).The top closure is cooled by air through an external circuitto maintain its temperature at 393 K to minimize sodiumdeposition in the annuli (melting point of sodium�370 K). Due to the temperature differences between thetop closure and bottom entrance of annulus, there is natu-ral convection of argon gas in the annuli. As the hot gasmoves up it loses heat to the annuli wall, becomes denserand slowly starts coming down and exits through anothercircumferential location (Fig. 1b). This phenomenon resultin setting up of natural convection cells in the annulus andis also referred to as Cellular Convection. This results innon-uniform circumferential temperature distribution in

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* Corresponding author. Tel./fax: +91 44 27480311.E-mail address: hemanath@igcar.gov.in (M.G. Hemanath).

the penetrating component, leading to deflection due touneven expansion and impacting their functional require-ment. This type of phenomena is noticed even for annulifilled with liquids such as water (Vijayan et al., 1986) andsodium (Timo, 1954).

Studies carried out in different countries have indicatedthat the non-uniformity of circumferential temperature dis-tribution is a function of temperature of the cover gas,aspect ratio (L/d), the temperature of the walls of the annu-lus. Timo (1954) have reported on free convection in nar-row sodium filled annuli resulting in large circumferentialtemperature difference and deduced a simple correlationfor Nu in terms of Gr and Pr. He has also suggested amethod of determining the number of natural convectioncells based on the aspect ratio. In the PHENIX fast reactorin France, the Intermediate Heat Exchanger (IHX) annulihad a temperature asymmetry of 80 K (Kung and Gama,1975). Goldstein et al. (1979) have carried out a two-dimensional analysis of the same. Their analysis involvestwo codes, one dealing with convection in the annuli cou-pled to another conduction code for the wall. Large-scaleexperiments namely GULLIVER (Baldassari et al., 1984)and LILLIPUT (Roux et al., 1988) were set up in France

Nomenclature

Cp specific heat (J/kg K)D diameter of the vessel (m)g gravitational acceleration (m/s2)k thermal conductivity (W/m K)L length of the annular gap in axial direction (m)P pressure (kg/cm2)Gr Grashoff number, Gr ¼ gbDTL3

c2

Pr Prandtl number, Pr ¼ CplK

Ra Rayleigh number, Ra = Gr Æ Pr

T mean temperature of the annulus (K)u velocity (m/s)

Greek

DT axial temperature difference of the annulus(K)

DTc circumferential temperature difference of theannulus (K)

c kinematic viscosity (m2/s)l dynamic viscosity (kg/m s)d annular gap (m)e aspect ratio ðe ¼ L

dÞb thermal expansion coefficient, 1/Tq density (kg/m3)

Fig. 1a. Component penetration in roof slab.

Fig. 1b. Natural convection of argon in annulus.

680 M.G. Hemanath et al. / Annals of Nuclear Energy 34 (2007) 679–686

M.G. Hemanath et al. / Annals of Nuclear Energy 34 (2007) 679–686 681

for their Super Phenix and European Fast reactor pro-grams. In the earlier one, the top closure was kept at313 K, while in the latter it was kept at 393 K. The highertemperature in the upper closure of the second-generationfast reactors is to avoid sodium vapor deposition in theannular gaps. Yamakawa and Sakai (1986) performedexperiments for a typical IHX penetration with water asthe fluid and compared with three-dimensional codeTHERVIS III. They studied the effect of different aspectratios of the gap (L/d = 50–210). This type of phenomenonhas also been encountered in the sodium cooled Fast Bree-der Test Reactor (FBTR) in India. Tilting of the reactorvessel by about 8 mm occurred due to a circumferentialtemperature difference of 80 K in the rotating plug annuli(Srinivasan et al., 1988). If the tilt is more than 10 mm, itwould affect movement of control rods. To reduce the nat-ural convection helium gas was injected into the annulusfrom top and maintaining a stable helium layer above alayer of argon, this resulted in reducing the circumferentialtemperature difference.

Considering the absence of generalized relationships andthe impact of geometry on the temperature asymmetry,theoretical and experimental studies were undertaken. Ear-lier an experiment was conducted in a small test vesselCOBA containing sodium with vertical annuli in the topclosure (Fig. 2) (Meikandamurthi et al., 1991). The analysiswas carried out by a combination of THYC-2D solving theconvection in the annulus and a conduction programCOND-2D which solves the conduction equation in thestructures around the annulus. It also took care of radia-tion heat transfer between the structures (Velusamy et al.,1998). It was felt that a single three-dimensional codeshould be employed for analyzing both the phenomenatogether. It was also thought that the impact of sodiumaerosols in the cover gas above sodium would have moreimpact on the heat flux in the annulus and not on the tem-perature asymmetry. In case of no impact on the asymme-

Fig. 2. Experiment with sodium, Model I.

try, simple experiments without sodium could beconducted for validating design.

This paper presents the experimental studies carried outin COBA model with and without sodium and their effecton maximum circumferential temperature variation. Forthe studies without sodium, a heated plate is kept at thelocation of the sodium level. This paper also presents theinfluence of different sodium temperature, helium as covergas and effect of depression of cellular convection by cool-ing the annulus wall. A three-dimensional analysis usingPHOENICS CFD is also presented and compared withexperiments in COBA.

2. Experimental results

The COBA model (Model I) has two parts, the lowerand upper vessel. Sodium is contained in the lower vesseland the annulus is formed in the upper vessel as shownin Fig. 2. The upper vessel annulus height is 1000 mmand the upper vessel can be dismantled into inner and outershell. The upper vessel simulates the penetration of apump/intermediate heat exchanger. To achieve differentaxial temperature difference in the annulus wall, a surfaceheater is put in the top of upper vessel outer shell. Stainlesssteel sheathed chromel alumel thermocouples are used tomeasure the upper vessel outer shell circumferential tem-perature of the annulus at the top, middle and bottom.Eight numbers of thermocouples are distributed radiallyat each height. An immersion heater in the lower vesselmaintains sodium at 803 K. A 3/4 in. 40 pipe is used for fill-ing and draining of sodium in the vessel. The sodium levelin the lower vessel is maintained such that cover gas heightis 800 mm above the sodium free level as in the reactor. Theargon cover gas pressure inside the test vessel is maintainedat 100 millibar above atmosphere as in the reactor. Fibreglass wool insulation is provided over the circumferenceof the upper and lower vessel and upper vessel inner shellto minimize the heat loss. Fig. 3a shows the circumferential

430

440

450

460

470

480

490

500

510

0 45 90 135 180 225 270 315 360

Angle (deg)

Circ

umfe

rent

ial t

empe

ratu

re d

istr

ibut

ion

K Axial diff 68 K

Axial diff 63 K

Axial diff 35 K

Axial diff 22 K

Fig. 3a. Circumferential temperature distribution at the bottom of annulifor sodium at 803 K at different axial temperature difference.

490

500

510

520

530

540

550

560

570

0 45 90 135 180 225 270 315 360Angle (deg)

Circ

umfe

rent

ial t

empe

ratu

re d

istr

ibut

ion

K Axial diff 68 K

Axial diff 63 K

Axial diff 35 K

Axial diff 23 K

Fig. 5. Circumferential temperature distribution at the bottom of annulifor heated plate at 803 K at different axial temperature difference.

520

540

560

580

600

erat

ure

dist

ribut

ion

K

Model-II

682 M.G. Hemanath et al. / Annals of Nuclear Energy 34 (2007) 679–686

temperature distribution at the bottom of the annuli for asodium temperature of 803 K at different axial temperaturedifference. The increase in circumferential temperature dif-ference increases the natural circulation.

The circumferential temperature difference is plottedagainst the logarithm of the Rayleigh number as shownin Fig. 3b and it is a straight line.

After carrying out the test with sodium, the test vesselwas drained and a heated plate was kept at the sodium levelas shown in Fig. 4 and is referred as Model II. The bottomplate is heated by using surface heater closely wound at thebottom surface. The temperature of bottom plate is main-tained at 803 K equal to sodium temperature. Fig. 5 showsthe circumferential temperature distribution at the bottomof the annuli for a sodium temperature of 803 K at differentaxial temperature difference. Fig. 6a shows the circumfer-ential temperature distribution between sodium and heatedplate at 803 K for 68 K axial temperature difference. It canbe seen that the average temperature has gone up but thecircumferential difference is of the same order �60 K.Fig. 6b shows the comparison of circumferential tempera-ture difference plotted against the logarithm of the Ray-leigh number between sodium and heated plate.

10

20

30

40

50

60

70

80

1.0E+07 1.0E+08 1.0E+09 1.0E+10

Rayleigh no.

Circ

umfe

rent

ial t

emp

diff

K

Fig. 3b. Circumferential temperature difference vs. Rayleigh number.

Fig. 4. Experiment without sodium, Model II.

400

420

440

460

480

500

0 45 90 135 180 225 270 315 360

Angle, deg

Circ

umfe

rent

ial t

emp

Model-I

Fig. 6a. Comparison of circumferential temperature distribution betweensodium and heated plate at 803 K for 68 K axial temperature difference.

10

20

30

40

50

60

70

80

1.0E+07 1.0E+08 1.0E+09 1.0E+10

Rayleigh no.

Circ

umfe

rent

ial t

emp

diff

K

Model-II

Model-I

Fig. 6b. Comparison of circumferential temperature difference vs Ray-leigh number between sodium and heated plate.

To assess the effect of cooling of the annulus walls on thecircumferential asymmetry, studies were conducted in a lar-ger scale model with sodium free level maintained 800 mmbelow the top closure bottom, (Model III) with the sameaspect ratio (height of annulus/width of annulus) as inother two models. Fig. 7 shows the model, referred to as

Fig. 7. Rotatable plug annulus in test vessel, Model III.

Angle, deg

300

350

400

450

500

0 45 90 135 180 225 270 315 360

Circ

umfe

rent

ial t

empe

ratu

re d

istr

ibut

ion

K

sodium temp. 673K sodium temp. 723K

sodium temp. 773K sodium temp. 803K

Fig. 9. Comparison of circumferential temperature distribution for ModelIII, with cooling at various sodium temperatures.

300

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340

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400

420

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460

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500

0 45 90 135 180 225 270 315 360Angle (deg)

Circ

umfe

rent

ial t

empe

ratu

re d

istr

ibut

ion

K Argon Helium

Fig. 10. Comparison of circumferential temperature distribution forModel III, with argon and with helium as cover gas.

M.G. Hemanath et al. / Annals of Nuclear Energy 34 (2007) 679–686 683

the rotatable plug annulus model. It comprises a coolingduct in the wall of the annulus. Experiments wereconducted in this model with and without cooling. Fig. 8shows the comparison of circumferential temperature dis-tribution for sodium temperature at 803 K without cooling.Without cooling the maximum circumferential difference is87 K and with cooling it has come down to 15 K. Fig. 9shows the results of experiments with cooling at differentsodium temperatures.

360

380

400

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460

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500

520

540

0 45 90 135 180 225 270 315 360

Angle, deg

Circ

umfe

rent

ial t

empe

ratu

re d

istr

ibut

ion

K

with cooling

without cooling

Fig. 8. Comparison of circumferential temperature distribution for ModelIII, with and without cooling the annulus.

To study the influence of cover gas in the heat transferargon gas is replaced with helium as cover gas in ModelIII. Experiments were conducted in this study with cooling.Fig. 10 shows the comparison of circumferential tempera-ture distribution between argon and helium as cover gaswith cooling. The various parameters of Models I, II andIII are shown in Table 1.

3. Discussion

3.1. Influence of sodium aerosol

Experiment in Model II was carried out with hot plate at803 K and argon as cover gas without sodium. In thisexperiment there was no sodium aerosol. At steady statethe annulus temperature were measured and comparedwith that obtained with sodium aerosol (Model I) as shownin Fig. 6a. The mean temperature of the pure argon is more

Table 1The various parameters of Models I, II and III

Sl. no Parameter Annulus model (Experimental) FBR annulus (prototype)

Model I Model II Model III

1 Heat source at 803 K Using sodium Using hot plate Using sodium Using sodium2 Cover gas at 100 millibar (g) Argon Argon Argon/helium Argon3 Cover gas height, mm 800 800 800 8004 Annulus height, mm 1000 1000 2300 23005 Annulus width d, mm 20 20 40 406 Rayleigh number, Ra 108–1010 108–1010 1010 1010

7 Aspect ratio e ¼ Ld

� �50 50 57.5 57.5

8 Heat sink To surrounding asheat loss throughinsulation

To surrounding asheat loss throughinsulation

Biological sheildinglike concrete/iron ore

Biological sheildinglike concrete/iron ore

684 M.G. Hemanath et al. / Annals of Nuclear Energy 34 (2007) 679–686

by about 40 K, while circumferential temperature differ-ence has gone up slightly. Furukawa et al. (1984) hadestablished that the presence of sodium aerosols in covergas attenuates the radiation heat transfer to closures. Inthe experiment with sodium, the sodium aerosol in thecover gas argon attenuates the radiation heat transfer,reducing the mean temperature of the cover gas.

3.2. Influence of sodium temperature

It can be seen from Fig. 9 that the circumferential differ-ence comes down with sodium temperature. It is also inter-esting to note that the points of maximum and minimumtemperature are not same for all sodium temperatures. Thisshows that the convection patterns are not stable withrespect to position and vary with temperature. This phe-nomenon is also referred to as rolling convection.

3.3. Influence of wall cooling

With annulus wall cooling the circumferential tempera-ture difference were reduced from 87 K to 15 K as seen inFig. 8. This is one of the best way to keep the temperaturedifference under control.

3.4. Influence of cover gas

With helium as cover gas there is no significant changein the circumferential temperature distribution. The cir-cumferential temperature difference is about 10 K in bothcases. The mean temperature observed in Fig. 10 is higherin argon than in helium. This may be due to high operatingtemperature of air-cooling circuit.

4. Numerical model

Computational fluid dynamic analysis for Model IIexperiment (without sodium) was carried out using thecomputer code PHOENICS Ver. 3.2. The ratio of annulusgap to its radius is small and thereby the curvature effectsare negligible. Hence the flow analysis is carried out in

developed space of Cartesian coordinate in x, y and z planeas shown in Fig. 11. A grid pattern of 100 * 19 * 129 wasconsidered. The developed space represents the annulus,the boundary conditions on the left and right sides of theslab is imposed with cyclic boundary conditions. ThePHOENICS code solves the continuity, Navier–Stokesand energy equation for argon in three-dimensions takingthe temperature boundary conditions of heated plate tem-perature of 803 K. Boussinesq approximation was used toaccount for buoyancy effects in the momentum equation.The global equations are given below:

Conservation of mass:

r � �u ¼ 0

�u ¼ ðu; v;wÞ

Conservation of momentum with Boussinesq approxi-mation:

r � ð�u�uÞ ¼ cr2�u�rP þ gbðDT Þdi3

di3 ¼ 0 ðif i 6¼ 3Þ¼ 1 ðif i ¼ 3Þ

Conservation of energy:

r � ð�uT Þ ¼ kqCpr2T þ Qv

qCp

For simulating turbulence, the k–e model proposed byLaunder and Spalding (1974) is employed. The transportequations for k and e are

rð�ukÞ ¼ ð�ukr2kÞ þ Sk

rð�ueÞ ¼ ð�uer2eÞ þ Se

where

r ¼ io

oX; j

o

oY; k

o

oZ

� �

r2 ¼ o2

oX 2þ o2

oY 2þ o2

oZ2

� �

ut ¼Clk2

e

Fig. 11. Developed space of annulus and test section for thermal hydraulic analysis.

M.G. Hemanath et al. / Annals of Nuclear Energy 34 (2007) 679–686 685

where Cl is considered as 0.09.

at ¼ut

Prt

Prt is taken to be 1 as the enhancement in the heat transferdue to turbulence would be in the same as the enhancementin the momentum transport.

The boundary conditions are shown in Table 2. Theupper vessel inner shell was assumed adiabatic. The heat

transferred to the outer annulus wall is by convection,and is dissipated to the surrounding by conductionthrough wall and convection to atmosphere air outsidethe insulation cladding. Since the annular gap area facingthe heat source at the bottom is relatively less andannulus wall are at the temperature of about 373 K,radiation was not considered in the thermal hydraulicanalysis.

Table 2Boundary conditions

No. Geometry Boundary conditions

1 Heat source Fixed surface temperature, 803 K2 Annulus outer

shellHeat loss to atmosphere through wall andinsulation

3 Top plate Adiabatic4 Annulus inner

shellAdiabatic

400

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580

0 45 90 135 180 225 270 315 360

Angle, Deg.

Ann

ulus

tem

p. K

Model IIexperimentThermal hydraulicanalysis

Fig. 12. Comparison of Model II experiment and thermal hydraulicanalysis at heated plate temperature of 803 K.

686 M.G. Hemanath et al. / Annals of Nuclear Energy 34 (2007) 679–686

5. Analysis results

Initially coarse grid analysis was done and achieved theapproximate temperature distribution. By having fine grids(100 · 19 · 129), grid independent values of temperaturedistribution were obtained. The comparison of analysisand experimental results for Model II at 803 K are depictedin Fig. 12. The magnitude of Rayleigh number is 7.5 · 108.

Considering the uncertainty in the experiments andassumptions in the theoretical analysis, the comparison issatisfactory.

6. Conclusion

Experiments on the circumferential temperature differ-ence in vertical annuli open at the bottom and closed atthe top have been studied for application to sodium cooledfast breeder reactors. To evaluate the impact of sodiumaerosol on the circumferential temperature difference, anexperiment was conducted with sodium surface replacedby a stainless steel plate at the same temperature. It was

seen that the circumferential temperature difference werecomparable and were more (+10 K) for the later experi-ments without sodium. Influence of sodium temperatureand annulus wall cooling has been studied and wall coolingis found to be a good method to keep the circumferentialtemperature difference within limits.

Analysis with PHOENICS code has also shown a gooddegree of matching with experimental measurements. It isfelt that the future estimation of circumferential tempera-ture difference for other components penetrating the upperclosure can be carried out without sodium. The resultswould be conservative.

References

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Furukawa, O., 1984. Experimental study of heat transfer through covergas in the LMFBR. In: International Conference on Liquid MetalEngineering and Technology, pp. 451–458.

Goldstein, S., Joly, J., 1979. Thermal analysis of penetrations of aLMFBR. Fifth SMIRT.

Kung, Jean-Pierre, Gama, Jean-Michel, 1975. Fluid flow and heattransfer. In: European Nuclear Conference, vol. 20. American NuclearSociety.

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Roux, S., Elie, D., 1988. Comparison between measurement and compu-tational analysis on open azimuthal thermosyphons in annular spaceof LILIPUT model. In: Fourth International Conference on LiquidMetal Engineering and Technology, France.

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Timo, D.P., 1954. Free convection in narrow vertical sodium annuliKAPL-1082 Knolls Atomic power laboratory, Scenectady, New York .

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Vijayan, P.K. et al., 1986. Studies on natural convection in vertical annuliheated from below. In: Proceedings of Eighth International HeatTransfer Conference, San Fransisco,California, USA, vol. 4, pp. 1563–1568.

Yamakawa, M., Sakai, T., 1986. Analysis of natural convection in narrowannular gaps of LMFBR. Journal of Nuclear Science of Technology 23(5), 451–460.