081uMOM RI

BOUNDARY CON

ION a8

R.K.Singh H.S. Kushlwaha, B.Murali and A.KakodkarReactor Engineering Division

Bhabha Atomic Research CentreTrombay, Bombay - 400 085

INTRODUCTION

Knowledge of temperature fieldin composite tube shet geometriesis important from suitable andeffective thermal design aspect. Inseveral situations a number ofunknowns may be present at bounda­ries such as convective heat tran­sfer coefficient, and fluid bulktemperature. Since convective heattransfer coefficient is a functionof surface temperature for naturalconvection, it is desirable tocorrect the heat transfer coeffi­cient and surface temperature lite­ratively. In tube sheet problemsone has to obtain three dimensionaltemperature field for complex heatload and internal heat generation.At times an equipment is requiredto operate with only partial coo­ling water level due to eithernonavailability of cooling pumps ina system or due to failure of powersupply to cooling pumps. The desig­ner must ensure that the tempera­ture in the equipment is withinpermissible limits. In this problemthe temperature of cover gas trap~

ped above the water level becomesone additional unknown.

In the present paper the aboveproblem has been analysed at twostages. At first a simplified twodimensional model of composite tubesheet geometry is analysed by afinite element computer codeAXITEMP [1]. The heat transfercoefficients are corrected iterati­vely and the trapped cover gastemperature is obtained by ensuring

heat balance. A number of casesare analysed which include effectof water level fluctuation in theequipment, and effect of low flowor no flow from the cooling'pumps. In second stage a localpath of tube sheet with latticetube is used for study wi th athree dimensional finite elementcomputer code HEAT 5 [2]. In thisanalysis all the input such assurface tempera-ture at the patchedge, convective heat transfercoefficients and trapped covergas bulk temperature is takenfrom simpl ified two dimensionalanalysis.

MODELLING

In the simplified twodimen-sional analysis the tubesheets and the central slab withbuffle is first converted intoequivalent blocks with sameconduct ion vo I ume and convect ionsurface as shown in figure 1. Inthese models the lattice tubesand annular gap in baffle slabhave been replaced suitably toobtain overall temperature andthe cover gas temperature. Atright end of equipment the air

te perature is 271°C whil at the.left end air temperature is

82. 8°C. The water is upto a levelof G. Forced convection conditionis assumed in water portion. Foran assumed cover gas temperaturethe temperature distribution in

Re,g. J. Energy Heat Mass Transfer Vol. n No.3, pp .. j,g>7'-202 1989

.1.97

QSLAB

= heat from two slab faces

QTSR = heat from right tube sheet

to cover gas

where QTSL = heat from left tube

sheet to cover gas

ling water flow. The cover gastemperature is found to be

124.40C. The maximum temperature

on left tube sheet is 31. °C,(in cover gas portion) while themaximum temperature in right tube

sheet is 195° C. In case of powersupply failure to cooling pumpsthe water side temperature on

°left tube sheet is 141. C. Incover gas portion the maximumtemperature on left tube sheet is

11 °Cwhile on right side tube

sheet it is 200.SoC. Table 1represents the detail results forvarious cases. Fig.3 showstemperature in tube sheet by twoand three dimensional analysis.It may be noted that temperatureof different locations matcheswell.

( 1 )= 0

The cover gas temperature ischanged till the above equation issatisfied ..... (3).

two tube sheet sand the centralslab is obtained afteriteratively correcting the freeconvection heat transfercoefficients in cover gas and airportion. A heat balance as madefor the assumed temperature ofcover gas as follows:

The analysis was carried outfor two cases in which water levelin the equipment was changed from Grow to level between F and Grow(FG) and level between G and H row(FH). Outer cases which were stu­died by this method were shut downcase with normal cooling water flowin the equipment. In this case theinternal heat generation is reducedto 30%. Finally temperature distri­bution is obtained for a case whenpumps stop due to power failure. Inthis case the water temperature istaken to be 99°C with natural con­vection conditions. In phas~ 2analysis the heat transfer coeffi­cients in air and cover gas portionand the cover gas temperature ob­tained above are used as input fora detailed three dimensional tempe­rature distribution study. Here apatch of tube sheet and certainlength of lattice tube is modellednear water cover gas interfaceportion.

RESULTS

CONCLUSIONThe temperature distribution

in a complex geometry such ascomposite tube sheet can beobtained by simplified twodimensional and detailed threedimensional fini te elementanalysis. The effect of heattransfer coefficient ontemperature distribution can beiteratively corrected. Simplifiedanalysis helps to arrive atvarious boundary conditions interms of temperature bulk fluidbulk fluid temperature and heattransfer coefftcients fordetailed three dimensional analy­sis.

REFERENCES

1. H.S. Kushwaha, .K.Singh,B.Murali 'AXITEMP' A finiteelement computer code for twodimensional and asimsymmetricstructures thermal analysis ­RED, BARC, Bombay .

Fig. 2 shows temperature dis­tribution in left and right tubesheet and the baffle slab withwater level at GG with normal coo-

2. H.S. Kushwaha 'HEA 5 - Afinite element computer codefor three dimensional thermalanalysis - RED, BARC'

198

3. Heat transfer and fluid flowdata book by General ElectricCompany.

- -199 .

Table - 1

---------------------------------------------------------------------SR CASE COVER GAS MAX.TSR MAX.TSR MAX. BAFFLER

NO. TEMP. (DC) l:EMP. (DC) l:EMP. (DC) SLAB TEMP.(1,2) (1,2) (DC)

•(1,2)---------------------------------------------------------------------1. Water level FG 118.3 120 (E) 191. 1 (B) 98.9(B)

normal flow 127.8 111. 7 73.9

2. Water level GG 124.4 127.8 111. 7 73.9

normal flow 127.8 111. 7 73.9

3. Water level GH 132.4 148.3 200(B) 115.6(B)

normal flow 127.8 111. 7 73.9

4. Shut down water 113.1 103.3(E) 190(B) 90.6(B)

level GG normal 110 111. 7 73.9

flow

5. Shut down waterlevel GG low 135.2 118.9(F) 200.6(B) 119.4(B)

due to power 141. 7 140 103.3

supply failureto pumps

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

Legend •1 First temp.in cover gas portion Second temp. inwater portion.

•2 Letters in bracket show location of the tubesheet.

TYPICAL LATTICE TUBE

~ \ COV~ ~

82.SoC 1=0-\ L- -----;d _~=,= 2.,,° C hIllAI n W ATEH LEVEL

--t----I----l---'--~'G'

T!.iL }

T5H

TUllr-: SIHU>:TS

TSL SLAB

SLAB - FOil BAFFLEAnnANGE.MENT

SLAB MODEL EOUIVLENT SOLIO BLOCK

CONDUCT ION VOI..uME=VOLUME OF SLAIJ VOl.UMg OF

OPElU!OHATIONS

CONVECTION AnEA

O--1- -. J:1 __ =SUIUlACE AIlEA DE FACES

~ I _ AnCA OF PEIlI!UIlAT ION S

II

I

AREA EQU IVA LENCE

TUDE SHEET MODEL

CIRCULAR

I" FOR ALL MODELS• MODEL A MODEL hA

FIG .1

H [J __~_2_ 10-RES':I1.!i 30- RESUl TS

130 126.7 126.7

TSL SL\B TSR

)15 ,105.5 1;5

m.9 131.7 121.7lib,7 105.3

DeaVER GAS

1812) 121.7 102.5 112UI 1;0 (271.11 130 COVER GASAIR AIR

120.3 99.4 150

131.7 92.2 lS6.7 120.3 111.7 111.7

m.o 71.9 ~27 .2123.9

us.s ii.1 1:3.3

126.1 75.6 110 m.B -SL 91.1 91.1 G .si:

126.1 75.• 11011~,1. WATER

126.1 75.• 110

125.1 75.• WATER 110 117.2 109.973.9 10M

1~6.1 75.6 110

121.1126.1 75.6 110

126.1 75.6 110 123.9 152.2 152.2 H

126.1 75.6 110

126.1 75.6 110

CENTM~ TEMPERATUREOF TUBE SHEETS AIm SLAB re) 1 .26.1 132.2 132.2153.9

CASE. WATEn lEVEL GG1I0RMAlFLOW TEMPERATUnE DISTRIBUTION AT WATER COVERGAS ~lTeRFACe rCI

FIG.2 CASE. WATER LEVEL GGNORMAL FLOW

FIG. 3

.202

TRANSIENT TEMPERATURE COMPUTATIONS INDIFFERENT SIZES OF C-COUPlINGS DUE TO

REACTOR START-UP AND SH·UT-DOWN

D.S.Chawla, B.K.Dutta, H.S.Kushwaha and A.Kakodkar

Reactor Engineering DivisionBhabha Atomic Research Ce~tre

Trombay, BOMBAY-400 085

Abstract

The procedure. for computing temperature transients in twodifferent sizes of C-cuplings, used in nuclear rea c tors isdescribed. Finite element numerical solution technique is used forthis purpose. Imposed transient flux is due to fuell i rig machineoperation as well as reactor startup and shutdown. Considerationof various convective boundary conditions and calculation ofassociated h values are shown.

INTRODUCTION

C-couplings are becomingmore and m9re popular compo­nents in nuclear power plantsand are used in place of con­ventional flanges because oftheir compactness, easy main­tenance and more reliability.They are used in large numbersin Pressurised Heavy WaterReac~ors (PHWR) such as at thejoint between feeder pipes andEnd-fiting, in F/M housingetc. Integrity of thes~ clampshave direct effect on overallsafety of the nuclear powerplants.

This necessitates properdesign, fabrication, installa­tion and maintenance of thesecomponents.

The temperature transientcomputation of these couplingsduring reactor start-up andshut-down are found to benecessary to che~k whethermaximum thermal stresses arewithin codal limit and also to

compute allowable fatiguecycles. The irregular outerprofile of the couplingnecessitates the use of apowerful numerical techniquesuch as finite elements fortemperature computational pur­poses. The coupling with itshub may very well be simulatedas an axisymmetric body whenmounted~ from heat transferpoint of view. The inner sur­face of the coupling is incontact with its hubs, whichis exposed to channel flowingwater. The temperature of thewater changes during variousreactor operations. Hence heattransfer coefficient of thissurface changes. Heat lossthrough outer surface of thecoupling is due to naturalconvection and hence again afunction of varying surfacetemperature.

In the present work tran­sient temperatures are com­puted in two different sizesof C-couplings. The next Sec-

Reg. J. Energy Heat and Mass Transfer vol. 11, No.4, pp. 2?:~···7-'/H .1';>H9-

273

Table 1: N~e.riGal»~9n~t~ts ~nEq (1) based on Teja and RiceMethocFfor 'viscosit iesofl iqutd mixtures,

R21-DMF

aD 0.3878E+01a1 -0. 1122E+04a2 0.9738E+03a3 O. 1391E+03a4 0.4348E+03a5 -0. 1727E+02a6 0.1220E-02

R21-DMETEG

01f 4396E+Oli '.:-0. 1777E+04

'O'~:1371E+030.'1.1210E;':0 2

-0. 3294E-020.1216E-02

R22-DMF

0.3270E+Ol-0.1033E+04

0.1430E+030.1333E+02

-0. 3561E-020.1257E-02

R22-DMETEG

0.3773E+01-0. 1672E+04

0.1538E+030.2134E-02

-0. 5240E-020.1355E-02

Table ?: ,. Nt.U1leri8arcon~t~I}tsin EQ. (5) based on Ely and HanleyMeth()d .. fof.fh~rm8:1;qonductiVi ties. of liquid mixtures

R21-DMf'

bO -0.3647E+o.Ob1 -0.2043E+03b2 -0.6911E+02b3 -0.3943E+02b4 ....0.3257E-02b5 -0.6224E-03b6 -0. 1o32E:"'02

R21-DMETEG

""0. 3201E-01-0.2077E+03-0. 4568E+02

0.9777E+02-0. 2623E-02-0~8038E""03

~O.2048E--02

R22-DMF

-0.2018E+00-0.2009E+03-0.1460£+01

0.1263E+03-0. 3539E-02~0.3880E-03

-0.. 3126E-02

R22-DMETEG

-0. 8961E-01""0. 1881E+03-0. 2560E+02

0.1117E+03""0. 3201E+02-0 ..1416£,....02-0.2058£-02

R21 =CHCI F; R22 =CHCIF2 ; DMF = Dimethyl formamide;DMETEG = Dimethyl; ether of tetraethylene glycol.

274

3.53.01000/ T ---------=-

c

x: 2280 285 290 2.9 5 300 305

T ,..

FIG.1

54

13

2

11

1 ·00·8

0.6

0.4

I4

0.. 3o

f1G.2

0.20,...---------------------.

no. 3

275

sis of high pressure pipecoupling (feeder Gray lock)for KAPP, RED internal reportno. RED/AK/1393/86 (1986).

TABLE...! MATERIAL AND HEAT TRANSFER DATA FOR FUELLING MACHINE C'"COUPLI NG ANALYSIS

MATERIAL DATA HEAT TRANSFER COEFFICIENT DATA

° 2Surface temp. ( C)h(kcal/mm HroC)38 0.050 5.466810 1.643

100 9.1891

DensitySp.Heat

Material - 403 SS InnerAv.Conductivity- 0.01462 Kcal/mm Outer

Hr°C- 1.811E-06Kg/mm2

- 0.11 Kcal/Kg°C

Surface-525Surface -

2 °Kcal/mm Hr C

TABLE ...2 MATERIAL AND HEAT TRANSFER DATA FOR FEEDER PIPE C ...COUPLING ANALYSIS

MATERIAL DATA HEAT TRANSFER COEFFICIENT DATA

Material - 403 SS Inner SurfaceAv. Conductivity - 0.01542Kcall

002mm Hr C Surface temp. ( C)h(kcal/mm

HroC)Sp.Heat - O.llKcal/KgOC 50 0.0111124

10' 0.01322100 0.016108200 0.021642250 0.021642316 0.019419

Outer surface-assumed insulated

F

III 11/11 111~

N III 11111 111

Ie:t 1!l£i1; !3:ti

"-1111111 ' T

I- " _I I l.l!H'.lJ I 1111.-=:>

r--r--. I "Ce~L--I-~~

ee:l=: '"....

:-

IG: . FINITE ELEMENT MESH OF THE STRUCTURE

80 1 - - - - - - - - - - - - - - - - - -

FIO.211 TEMPERATURE TRANSiENT ALONG TIlE TfIiCKNESS'AT SECTION1-1

FIG,2A TEMPERATURE TRANSIENT ALONG TUE TfIICKNESS AT SECTION.-.

e '

20 30 LOl",ClnESS III ...,..--

JOIrt----f::---~:__--_b_--~:----~--Iso10 3D 40tHICKNESS IN toelot----.

.10JOll---;;;-----:~---±---~:-----,L,-----1

FIG,JA TEMPERATURE TRANSIENT ALONG THE THICKNESS AT SECTION2-2

FlG..:lIl TEMPeRATURETRANSIE~'l" AlONG WE 7HICKNESS AT SECTlON2·2

277

FIG. 4- OISCRETlZATION OF KAPP FEEDER PIPE COUPLING

FIG.50 TEMPEflATUflE TnANSI"NTINKAPPPIPE FEEDERCOUPLINO AT5I!CTIONl-l DUflIIIG­COOllIIG.

G56055\0

-.-....----,---------

------- ..._-------

......- ... _--- ..._-'-------

1.0 loStlA~l!....!!lm-~_·';'

11I-tlIIUIE

l/.r.tIIlUI~

50 _.

100

nG.SA TEMPEnATUnET",,115IENTINKAPPPIPE FEED"n COUPLIIIOAT5ECTIONl-l DunlNOIIEATIIiG.

1>0

100

FIG.6A TEIoIPERAlURE 'TRA1lS1ENlIN KAPPPIPEFEEDERCOUPlIlIG AT5ECT101I2·2DURING

HEATING.

FIG.ao TEMPEflAlURE TRANSIENT INKArp PIPE FEEDEn COUPl.INGATSECTION2·2OUfIINOCOOLING. ' ,

278

0·8G4 MIIiUIE

300

N4MltlUIE

350 ---,u JOO9'44 MINUIE

.6

1150 15'/.5MINUIE

100lH5MINUIE

SO -----I

015 3D 35 /.0 45

'5f1adlUI In mm -teo

LC·GIMINUTE

;4P-IINUTE

12MINUTE

I30

-----tOC

so

15

30

t10

··~ISO~~