Indi an Jouma l 01' Engineeri ng & Mate ri als Sc iences Vol. '). Dece ill ber :2002. pp . .. U2-·nY

Flow distribution in spherical header of a liquid metal-cooled fast breeder reactort

K atcs<ln. K Vc lusa lllY. P Sclvaraj & P Chcllapandi

Mecha nics a III I Hydraul ics Di vision. Indir;l G;lndhi Centre for Atom ic Research. Kalpakkalll 603 102. India

/? I'Ceil 'l' i/ /3 Dccell/ber 200 /: ({cccpled 2 Ocwber 20()2

Liquid ,odi um fro lll prilllary pUIllP o f a typi ca l Liquid Metal -coo led Fast Breeder Reactor (LMFBR ) reaches a , pheri cal header through a ve rtical pipe and fl ows to the inlet plenum of the reactor through two di scharge pipes. whi ch co nnctt thc heackr to the plenuill. T he header is prov ided with a ce ntral cone ;lIld rI ow di recting barnes fo r the purpose of having ;1 s illooth prop;lga tion of sodium fl ow and hence a red uced pressure drop. 3D hydrauli c analyses of sodium flo w in the header for va rio us des ign co nfi gurati ons ha ve been carri ed out to in ves ti gate the crfect iveness of fl ow ba lTles and to a"css the prc"lIre drop in the header. It kls been found th at a confi gurati on of 3D bartl e co mbined wit h a cen tral cone red uces the pressure drop in the header to the desirabl e leve l ( 1.7 mlc) .

Sodium now in the primary circuit of an LMFBR I is mai nrai ned by t \VO centri fu gal pumps, known as primary sod ium pumps (PSP). operating in parall el. Each pump is des igned to supply a nominal sod ium flow rate of 4. I 3 m1/s against a head of 75 mlc at 590 rpm. The pressuri sed sodium from each pump reaches a spherical header of I A I m diameter throu gh a 0.9 m diameter verti ca l pipe. Sodium from the header is then supplied to the inlet plenum through two 0.6 m diameter ptpes. Schematic of the header-pipe assembly is shown in Fig. I . It is we ll known that whenever there is a sudden change either in the flow area or in th e direction of the fl ow, large rec irculations are induced in the ducts~ .. l . These rec ircul ations are the potential sources of large pressure drop in the system. Large pressure drop leads to high operating cost, which is unwarranted. Hence, one of th e obj ec ti" es o f the hyd rauli c design of the components is to c ntour the duct, carrying the fluid , to avo id sudden changes in the fl ow area and direction . Achi ev ing thi s objective is becoming increas ingly si mpler due to the advancement in the computational flui d dynamics and development of computer technolog/. With thi s in view, the primary sodium header is provided with a central cone of 0.69 m diameter base and I. 102 m height as well as fl ow directing baffl es . However, the effectiveness of these dev ices needs to be inves ti gated in detail.

' Prese nted at the 281h Nati onal Co nference on Fl uid Mechani cs & rluid Power, he ld at Punjab Engineering Coll ege. Chandigarh , during 13- 15 December 200 I

I n order to assess the effec t o f' cenlral cone and now banks in the PSP header, the following four confi gurations of the header have been considered and the flow/pressure distribution in each configuration assessed: (i) Simple header (Fig. 2); ( ii ) Header with the central cone alone (Fig. 3); (iii ) Header w i th the central cone and a simple ax isymmetric baffl e (Fig. 4); and, (iv) Header with the central cone and a non axisymmetric 3D baffle (Fig. 5).

In the present inves ti gations, comparison of flow distributions in the various design configurations o f the header (Figs 2-5) has been made and effecti veness of various dev ices has been assessed from th e poi nt of v iew of pressure drop in the header.

Flow from PSP I Flow frOll 1 I'SI"!

t;r id plntl'

Fig. I- Schematic of the header to primal'y pipe co nnecti on

NATESAN el (II.: FLOW DISTRIBUTION IN SPHERICAL HEADER OF A FAST BREEDER REACTOR 433

Section A-A

Section B-B

Fig. 2-Simple header

Section A-A

Section B-B

rig .. 1- Header with a central cone

Section A-A

Section B-B

Fig. 4- Header with a central cone and an axi symmetri c barne

Section A-A

Section B-B

Fig. 5-Header with a central cone and a non-axisymmetric 3D baffle

434 INDI AN J. ENG. MATER. SCI. , DECEMBER 2002

Modelling Details Governing equations

Sodi um fl ow process in the header is governed by 3-D conservati on eq uati ons of mass and momentums. For a steady incompressible flow in Cartesian co­ord inates (x, y, z) with velocity components (u, v, w) , pressure (p) and density (p), the eq uations are:

~ (pII ) + ~ (pv) + ~ (pw) = 0 ax ay az

a () a - (pIIII ) + - (pII V ) + - (pII W )

ax ay az

= _ ap + ~(T.rJ+~(r I'J+~(r~t) ax ax ay ' az

~ (pVl!)+ -~ (pvv)+ ~ (pvw) ax ay az

= _ up + ~(rn. )+~(r \'I' )+~(r : \ , ) ay a.x . ay' . az .

a a a - (pwu ) + - (pwv) + - (pww) ax ay az

= - ~p +~(rt_ )+~(r\'_ )+~(L) az ax ' ay , az "

where, l' represents the viscous and turbulent stresses. The turbulent stresses are evaluated from the eddy viscosi ty based k-E turbulence model6 . The governing equations for the turbulent kineti c energy (k) and its dissipation rate (E) are:

-(puk) +- (pvk)+-(pwk) = - l k -a a a a ( ak) ax ay az ax ax

+ ~( lk ak )+ ~( lk ak)+ S k ay ay az l az

- (plI E) +-(pVE )+ - (pWE ) = - rE -a a a a ( aE) ax ay az ax ax

+lJ r ~J +~( r aE) +s aA E ay az E az E

where 1 and S are respectively diffusion coefficient and source terms. Si nce the geometry of the header docs not fit in to the regular Cartesian or cylindrical

co-ordinate system, a boundary fitted co-ordinate system (~ . ry . n IS used, where,

~=~(x.y.z ). 17=ry(x, y.z ) and ~=~(x.y , z ). All these governing equations can be represented by a single general eq uation of the following form, in the

(~ ,17 , (') co-ord i nates as 7 ,

a a a - (pU¢)+ -- (pV¢)+ - (pW¢ ) a~ ary . a~

In ·the above general equation 1 41 is the diffusion

coefficient and S¢ (~. ry . ~ ) is the source term for the

scalar variable <I> and J is the Jacobian of transformation with :

J = x~ YlJ zs + XS Y~Z 'l + xIJ Ysz~

-xSYSZ'l - XSY'l ZS -X'lY~Z(

Cf" = (y'l ZS - YsZ'1)2 + (XSZ IJ -X'l Zs )2

+ (xlJ Ys -xsYlJr

Cf22 = (Y s z .; - YsZsr+ (x~zs -xsz~ r +(x( y ~ -xsYs r

Cf 33 = (ys Z'l .- Y'l Zs )2 + (xlJ z~ - Xs Z,J 2

+(x~ YIJ - X'lYS)2

Q'2 = en 1 = b'(Z,; - Ys~) (Y1)~ - Y(Z,))

+ (x~z( - x(z,;) (x(Z1) - A;)Z( )+(x(Ys - xsY() (A;lY( - x(YIJ)

Q13 =ql1 = (YSZ'1-Y,l'; )(YIJZ( - Y(Z'1)

-t{X(~l-'try2( ) (A;l,; - XS~) )+(X';Y'I- A;lY'; )('~lY( - x(y,J

NATESAN e/ al.: FLOW DISTRI BUTION IN SPHERICAL HEADER OF A FAST BREEDER REACTOR 435

q23 = q32 = (Y~Z11 - y,)Z; )(Y(Z~ - Y~Z( )

+ (\2{ -X( Z~ ) (X,)Z,; - ,\~ Z,) )+ (X';YI) - X1)Y'; ) (X(Y.; - X.;Y( )

The above set o f equati ons are solved by the finite vo lume method us ing the PHO ENI CS8 code .

Computational deta ils

The spheri cal header with a sing le circular inle t and

two sy mmetric outlet pipes (included angle as 136°) and fl ow defl ecting cone and baffl es has 180°

sy mmetry . Hence, 180° symmetry sector of the header with one di scharge pipe one half inlet pipe is taken for analys is. The general purpose C FD code PHOENICS has been used for the analys is. A grid pattern

co mpri si ng 15x 36x65 grids in the radi al ax ial and circum fe rential coordinate direc tions has been used in the analys is. In the various configurati ons studied (Fi gs 2-5 ), sodium in the regions below the cone and baffles are considered to be stagnant and hence they do not form a part of the calculation domain .

y.

U.

II J .

2

1-: 1{ = ).' 11

= 1.67

x. lJ

Outlot

Fig. 6- Schemati c o f backward fac ing step

. _ . PHOEN ICS Result s

C Experi menta l Res ults of Eato n "nu johnso n

1.5

:r:: -.... > .

° o

0.5 °

° U - X direc tion veloc it y Uo - mean inlet velocit y

( r-hc~~~nononTnTnTnTrrrrrrTnonTnTnnorrr o 0. 1 0.2 0 .3 0 .4 0.5 0 .6 0 .7 0 .8 0.9

U/UO

Fig. 7- Comparison of now di stri bution in the backward fac ing step at xlh=8 and ER= 1.67

Validation

Although PHOENICS is a commercial soft ware, its usage needs to be validated . For this purpose, the standard test problem of turbulent fl ow in a backward facing step (Fig. 6) at a Reynolds number of 38000 and expansion ratio of 1.67 is sol ved using PHOENICS. The numerical results are compared against the experimental results of Eaton and ]ohnston9 and the numerical results of Abe e! aLi a

The PHOENICS prediction of x-velocity di stribution at a hori zontal di stance of 8H from the step location is shown in Fig. 7. Also shown in the same figure are the measured data of Eaton and Johnston. It can be seen that the predi cted distributi on matches sati sfac toril y with the measurements . Similar compari son was seen in the velocity di stri bution at other locations also. Likewise, the reattachment point computed by PHOENICS is 7 .5 H and it compares well with the prediction of Abe et al. tO

, viz. 7.9 H.

--~> 18 m/s

Fig. 8- Flow distribution without any devices In the c ircumferential planes at 0=00 and 0= 1800

436 INDI AN 1. ENG. MATER. SCI., DECEMBER 2002

Results and DisclIssion Afte r the validatio n exerci se, fl ow and pressure

di stributi ons in the spherical header of the LMFBR were ana lysed for vario us geo metrical config urations as al ready ex plained. Fl ow di stributi on o f sodium in

two r-z planes viz. 8 = 0° and 8 = 180° of the simple header (wi thout any flow directing devices) is shown in Fi g . 8 . Flow disLributi on in the pe ripheral radi a l plane adjacent to tk inner surface of the spherical header is shown in Fig. 9. It is ev iden t from these fi g ures that the re are stro ng rec ircul ati ons of sodium \V ith in the header. The fl ow recirculati o n can be seen at the inle t to the di scharge pipes also. It may be noted

that discharge pipe is located at 8=68°. The maximum veloci ty at the di scharge pipe location is 12.3 m/s. From the computed press ure di stributi o ns, the press ure drop in the header has been es timated to be 5 .7 m of sod ium column . This va lue o f press ure drop bei ng high , flow-d irect in g devices are necessary fo r

- - __ )t 18 m/s

rig . 9- Flow distributi on witho ut any devices in the peripheral radial plane

the smooth propagati on of sodi um flow within the header.

To start with, a central verti cal cone is fi xed to the bottom of the header as shown in Fig. 3. The

computed fl ow di stributio n in the r-z planes at 8=0°

and 8= 180° and the periphera l radia l pl anes of the header are shown in Figs 10 and I I, respecti ve ly. It can be seen that in thi s case also, there are stro ng recirculati ons in the sodium fl ow. Rec irculati o n can a lso be seen at the inlet to the discharge pipe. The maximum velocity at the inle t to the di scharge pipe is 11 .9 m/s . The pressure dro p in the header has been es timated to be 5 .28 m of sodium. Thus, there is no sig nificant improve ment in the sodium fl ow and pressure drop within the header due to the introductio n of a central cone alone. He nce, it was decided to introduce an axisymmetric baffle along with the central cone as shown in Fig. 4. T he radius o f curvature of the baffle considered is 1.35 m. The

0=0° 0 = IROo

--__ • 19 Ill/"

Fig. 10-Flow di stributi on with a central cone alone in the c ircumferential planes a t 0=00 and 8= 1800

NATESAN el 01. : 1'1 . ," ," DISTRIBUTION IN SPHERICAL HEADER OF A FAST BREEDER REACTOR 437

---+. 1 9 m/s

Fig. II - Flow di stributio n with a ceillral cone alone In the peripheral radial plane

1Il/ ..

Fig. 12- Flow distribution with a cone and axisymmetric baffle in the ci rcumferelllial planes at 0=00 and 8= 180 0

••. Axi - tY!;':!neLr-:,; udtf.~

- _ :.., m/ ..

Fig . 13- Flow di stribution with a cone and axisy mmetric baftle in the peripheral radial plane

·L·l.·.hlLl.L_'~ __ __ _ Cone

'~ii~~-- - Non-ax i symlT\etric ~ baf fle

_ J, 4 . 4 m/s

Fig . I4--Flow di stribution with a cone and non axi sy mmetri c

baflle in the c ircumferential planes at 0=00 and 0= 180 0

baffle joins the central cone at the central horizo ntal plane of header and it joins the header at the bottom of the discharge pipe.

The flow distribution in the r-z planes at 8=00 and 8= 1800 and peripheral radial plane (8-z plane) of the header, having a central cone and an axisymmetric baffle, are shown in Figs 12 and 13, respectively. It is seen from the figures that the strength of recirculation has reduced in this case compared to that in the earlier cases. The maximum velocity at the inlet of the discharge pipe is 10.8 mls. The pressure drop in the

438 INDIAN J. ENG. MATER. SCI. , DECEMBER 2002

_-- - - - - Cone

_ 1 4 . 4 rn/ ..

- Non axisymmetric baffle

ri g. l .'i- Flow di stri but io n with a co ile and 1l0 1l ax isy mmetric bafne ill the peripheral rad ial plane

heJder is 3 m of sodium, which is s igni fica ntl y less th an that seen in the earlier cases.

Since the baffl e is seen to intluence the tlow and pressure drop fav ourably, in the nex t case, the baffle configurati on has been altered. In thi s case, the baffl e is made non-ax isy mmetric as depicted in Fig. 5. The profile of the baffle changes both rad ially as we ll as circumferentiall y. At 8=0° and 8=1 80°, the baffles on either side of symmetry plane form two wedges. The elevation of these wedges with reference to the central cone is simi lar. At the angular location of the di scharge pipes (8=68°), the profile changes to that of the axisymmetric baffle discussed in the previous paragraph. The tlow distributions for thi s case are shown in Figs 14 and IS , respectively. It is evident that wi th mod ificat ions in the bartle geometry, the rec ircul ations within the header have nearl y vanished and sodium is drawn smoothl y towards the outlet pipes. The maximum velocity at the inlet to the di scharge pipe is 9.4 m/s. The pressure drop in the header in this case is 1.74 m of sodium. This shows the necessity/usefulness of the 3D non-axi sy mmetric bartle in the header for hav ing a smooth velocity field and hence low pressure drop.

In the investigations di scussed so far, the rad ial domain of the computational model was taken to end at the periphery of the header. No part of the di scharge pipe is considered in the model with a view to reduce the computational time. In order to assess the impact this simplification, the case of 3D baffle

_1.35E ... Olll1/"

Fig. 16-Flow di stributi on w ith o utlet pipe considered in the model in the peripheral radial plane

with central cone is re-analysed by considering a 200 mm length of the discharge pi pe. The predicted tlow distribution in the peripheral radial plane within the header for this case is shown in Fi g. 16. Comparing this with the tlow distribution obtained for the corresponding case without the outle t pipe (Fig. IS), it can be seen that exclusion of outlet pipe in the model does not affect the tlow distribution in the header. The maximum value of velocity at the inlet to the discharge pipe is same in both the cases (9.4 m/s) . The pressure distributions in the header are also similar in both the cases . Similarly, the pressure drop in both the cases were found to be the same. Thus, it can be concluded that modeling of di scharge pipe is not essential in the numerical predi ct ion of tlow di stributi on and pressure drop in the header.

It may also be mentioned that the hydrau lic analyses of the header have also been carried out for various other geometrical configurations, which are marg inally different from that of the 3D bartle. The configurations studied are: (i) Raising the elevation of the wedges (at 8=0° and 8=180°) from the nominal position by 1 SO mm, (ii) rai sing the e levation of the baffle-cone junction at the location of outlet by 100 mm and (iii) rai sing the elevations of the wedges as well as that of baffle-cone junction by 150 mm. It is found that the pressure drop in all these configurations is in the range of 1.8 m to 1.9 m, which is higher than that in the reference geometry . Thus,

NATESAN el al.: FLOW DISTRIBUTION IN SPHERI CAL HEADER OF A FAST BREEDER REACTOR 439

the reference geometry of the baffle (Fig. 5) offers the minimum pressure drop in the header.

Conclusions 3D hydrauli c analys is of the primary sod ium header

has been carried out for the vari ous des ign configurations such as: a simple header, header with a central cone alone, header with central cone and an ax isy mmetric curved baffle and header with central cone and a non-axisymmetric 3D baffle. It has been found that the pressure drop in the header for the above mentioned confi gurati ons is: 5.7 m, 5.28 m, 3 m and 1.74 m of sod ium, respectively. The configurati on of the header with central cone and 3D baffle gives a smoother tl ow profile in the header with minimum rec irculations and pressure drop.

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