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Journal of Shanghai University (English Edit ion) , 2006, 10(4) : 362 - 365Article ID: 1007-6417(2006)04-0362-04

3 D s i m u l a t i o n o n t h e u n i t d u c t i n t h e s h e ll s id e o ft h e R O D b a f f l e h e a t e x c h a n g e rWUJin- x /ng( ~ : ,~ ) 1 ~, DONG Q/- wu( ~) 1 2, LIUMin -sha n(~J ~) ~, W EIXin - l i (~ ~]) ~1. School of Chemical Engineering, Zhongzhou University , Zhongzhou 450002, P. R . China2. School of Mechanical and Power Engineering, East China University of Science and Technology, Shanghai 200237, P .R . Chinab s t r a c t T h e R O D b a f fl e h e a t e x c h a n g e r c a n s l ig h tl y e n h a n c e t h e s h e l l s i d e h e at t r a n s f e r c o ef f i ci e nt i t h t h e s i gn i fi c an t e d u c t i on o f

p r e s s u re l o s s d u e t o t h e s he l l s i d e f l u id l o w i n g l o ng i tu d in a ll y h r o u g h t u b e b u n d l e w h i c h l e a d s t o t h e r e d uc t i o n o f t he m a n u f a c t u r e a n drunning cost and in some cases to the dimensions reduction of the heat exchangers. Because of the complexities of fluid dynamicsequations and the stxucture of heat exchangers, few theoretical researches have been accomplished to specify the shell side chaxacteris-tics of the ROD baffle heat exchanger. A unit duct model in the shell side of the longitudinal flow type heat exchanger has been deve-loped based on suitable simplification. A numerical analysis on shell side of the ROD baffle heat exchanger has been carried out at con-stant wall temperature to obtain the characteristics of heat transfer and pressure drop. The numerical results show that the ROD bafflesplaced vertically and horizontally in the unit duct continue to shear and comminute the streamline flow when the fluid crosses over theROD-baffles, and change the fluid flow directions, and then the coni2nuity and stability of the fluid are destroyed. The effect of disturb-ing flow can promote fluid turbulent intensity and effectively enhance heat transfer. The numerical analyses can provide the theoreticalbases for op tuuizing the structure of ROD baffle heat exchanger and improving its performance.Key words ROD baffle heat exchanger, uni t duct, numerical simulation, shell side characteristics.

IntroductionThe traditional segmental baffle heat exchangers

(SHE) can be simply manufactured and run reliably,but they are mainly suitable for the situation of lowerflow velocity. When fluid velocity become s higher inthe shell side, the pressure drop increases more quick-ly, and the fluid-induced vibration will probably hap-pen, and even the heat exchanger will be destroyed.In order to prevent the tube bundle from vibration, theROD baffle heat exc hange r ( RHE ) was firstly deve-lope d by the Phillips Pet role um Co. C1~ with the seg-mented baffles replaced by ROD baffle, which areinserted between tubes and normal to the tubes in theRHE. The shell side fluid flows entirely in an axialdirection along the shell, and fluid flows essentiallyparallel to the tubes rather than across them . Thisarrangement claims to eliminate tube failure resultingfrom the vibration of the tubes in the holes of the seg-mental baffles.

Rceived Dec. 25, 2004; Revised un. 20, 2005WU Jin-~dng, Ph.D., Assoc. Prof., E-mall: wtljx@zzu.edu.cn

The RHE can slightly enhance the shell side heattransfer coefficient with the significant reduction ofpressure loss due to the shell side fluid flowing longitu-dinally through tube bundle, whic h leads to the co streduction and in some cases to the reduction of themeasurement of heat exchangers. However the collo-cation of heat transfer tubes in the RHE is convention-ally square, which leads to less heat transfer area inunit volume. The RHE is superior to the SHE onlywhe n the Reyno lds nu mbe r is high er ~2~. So th e inte-grated pe rforma nce of the RIlE is not optimal yet. Be-cause of complexities of fluid dynamics equations andthe structure of heat exchangers, few theoretical re-searches can specify the shell side heat transfer char-acteristics of the RHE. The experimental me thods ar e.often used to investigate the performance of heat ex-changers and can obtain overall pressure drop and totalheat transfer coefficients, but they are often expensiveand difficult. Howeve r the detailed field values of fluidvelocity, pressure, temperature and turbulence inten-sity are crucial for better understanding the operationof heat exchangers and for the design of heat exchang-ers.

With the development of computational fluid dyna-

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Vol. 10 No. 4 Aug. 2006 WU J X, eta/. : 3D simulation on the unit duc t in the shell side . .. 363m i c s C F D ) , t h e m e t h o d o f n u m e r i c a l s i m u la t io n i se x t e n s i v e l y a p p l i e d i n t h e s t u d y o f h e a t e x c h a n g e r s .N o w a d a y s , t h e r e a x e m a i n l y t w o m e t h o d s t o s i m u l a t ef l o w a n d h e a t t r a n s f e r i n h e a t e x c h a n g e r s . T h e f i r stm e t h o d , r e f e r r e d t o a s t h e d i s tr i b u t e d r e s i s t a n c e a p -pro ach I3~ , a s sum es tha t t he she l l i s f i l l ed wi th por ousm e d i u m t h r o u g h w h i c h a f i n e - sc a l e r e s i s ta n c e t o t h ef lu id mo t ion i s d i s t r ibu ted . Thi s a l lows the she l l c ros ss e c t i o n t o b e m o d e l e d b y a r e l a t i v e l y c o a r s e g r i d w h e r ea s i n g l e c o m p u t a t i o n a l c e l l m a y h a v e m u l t i p l e t u b e sp r e s e n t . S o t h i s m e t h o d c a n n o t p r e d i c t th e d e t a i l e df l o w , p r e s s u r e , t e m p e r a t u r e a n d t u r b u l e n c e i n fo r m a -t i o n i n a h e a t e x c h a n g e r . T h e s e c o n d i s t h e d e t a i l e dr e p r e s e n t a t i o n o f a l l t h e t u b e s i n t h e h e a t e x c h a n g e r .H o w e v e r t hi s m e t h o d i s c o m p u t at i o n a U y v er y e x p e n -s i v e . A s m a l l h e a t e x c h a n g e r w i t h 5 0 0 t u b e s a n d 1 0b a f f l e s w o u l d r e q u i r e a t l e a s t 1 50 m i l li o n c o m p u t a t i o n a lce l l s t o re so lve the geo me t ry ISj . In th i s p ap e r a n ewk i n d o f n u m e r i c a l m o d e l , c a l l e d a s t h e u n i t d u c t m o -d e l , i s p r e s e n t e d o n t h e b a s i s o f t h e s e c o n d m e t h o d f o rpred ic t in g the de ta i l ed d i s t r ibu t ion of the she l l s ide f lu -i d f l o w , p r e s s u r e a n d t e m p e r a t u r e o f t h e R H E .2 U n i t d u c t m o d e l a n d n u m e r i c a l m e t h

o d s2.1 Unit duct modelD u e t o t h e s q u a r e c o l l o c a t i o n o f t h e h e a t t r a n s f e rt u b e s i n th e R H E , a n d i n t h e l ig h t o f th e s y m m e t r y o ft h e h e a t t r a n s f e r t u b e s i n t h e s h e ll o f t h e R H E , e x c e p tf o r o n e s a d j a c e n t t o s h e ll w a l l , t h e f l u i d f lo w r e g i o na m o n g t h e a d j a c e n t f o u r t u b e s i s r e g a r d e d a s a u n i td u c t o f t h e s h e l l s i d e o f th e R H E , a s s h o w n i n F i g . 1 .S o it c a n b e r e g a r d e d t h a t t h e s h e ll s i d e o f t h e R H E i sm a d e u p o f m a n y id e n t i c a l a n d p a ra l l el u n i t d u c t s , a n dthe f lu id ma in ly f lows in tube ax ia l d i rec t ion in the un i tduc t C41 . Suppo s ing tha t t he inne r d i am ete r o f hea tt r a n s f e r t u b e i s 0 . 0 2 m , a n d t h e d i s t a n c e b e t w e e n t h et w o a d j a c e n t t u b e s c e n t e r i s 0 . 0 32 m , a n d t h e l e n g t ho f t h e u n i t d u c t i s 0 . 1 6 m . T h e r e a r e t w o R O D b a f f l e sw h i c h a r e r e s p e c t i v e l y a r r a n g e d i n h o r i z o n t al a n d v e r t i -c a l d i r e c t i o n s a t t h e d i s t a n c e o f 0 . 0 8 m i n a u n i t d u c t ,a n d t h e d i a m e t e r o f th e R O D i s 0 . 0 0 6 m .

F o r s i m p l i f i c a t io n o f c o m p u t a t i o n o f f l o w fi e l d , t h ef o l l o w i n g s u p p o s i t i o n s a r e p u t f o r w a r d . 1 ) T h e f l o wa n d h e a t t r a n s f e r c h a r a c t e r i s t i c s o f th e t w o a d j a c e n tu n i t d u c t s d o n o t i n t e r a c t w i th e a c h o t h e r . 2 ) T h et h e r m o p h y s i c a l p a r a m e t e r s o f t h e f l u i d i n th e u n i t

Fig.1 Unit duct model of the RHEd u c t , s u c h a s d e n s i t y p , v i s c o s i t y / ~ a n d s p e c i f ic h e a tC p e t c . , a r e c o n s t a n t f o r g i v e n s i t u a t io n . 3 ) T h e fl u i di s i n c o m p r e s s i b l e a n d f l o w s s t e a d i l y . 4 ) T h e f l o w i sp e r i o d i c a ll y f u l ly d e v e l o p e d . 5 ) T h e fl u id b o u n d a r i e sb e t w e e n e v e r y t w o a d j a c e n t u n it d u c t s a r e t h e s y m m e -t r i c a l b o u n d a r i e s .2. 2 Boundary conditions and numerical meth

odsA c c o r di n g t o t h e a b o v e p h y s i c a l m o d e l s a n d a s s u m p -

t i o ns o f t h e s he l l s i de o f t h e R H E , t h e m a s s , m o m e n -t u m a n d e n e r g y c o n s e r v a t i o n e q u a t i o n s f o r t u r b u l e n tf l u id f l o w a n d h e a t t r a n s f e r a t s t e a d y s t a t e c a n a p p l yt h e n o r m a l g o v e r n i n g e q u a t i o n s . T h e b o u n d a r y c o n d i -t i o n s o f t h e f l u id in t h e u n i t d u c t a r e a s f o l l o w s . 1 )T h e f l u i d m e d i u m o f sh e l l s id e i s a i r a t c e r t a i n t e m p e r -a t u r e , i . e . , T m = 3 0 0 K . 2 ) T h e h e a t t r a n s f e r t u b ew a l l t e m p e r a t u r e i s c o n s t a n t , i . e . , Tw = 40 0 K . 3 )S u p p o s e t h a t f lu i d m a s s f l o w r a t e M i s 0 . 0 0 5 k g / s . 4 )T h e f l u i d a d j a c e n t t o a ll o f so l i d w a l l h a s n o s l i p p a g e ,i . e . U = O .

D u r i n g t h e n u m e r i c a l c o m p u t a t i o n t h e c o m m e r c i a lF L U E N T s o f t w a r e i s u s e d , t h e s t a n d a r d k - e t u r b u -l e n t m o d e l i s a p p l i e d t o s i m u l a t e t h e f u l l y d e v e l o p e dt u r b u l e n t f l o w a n d h e a t t r a n s f e r o f t h e u n it d u c t . T h ea lgor i thm of S IMPL E pr op ose d by Pa ta nka r ~61 i s em -p l o y e d t o s o l v e c o u p l i n g r e l a t io n s o f p r e s s u r e a n d v e -l o c i t y . T h e s h e l l a n d R O D b a f f l e w a l l s a re m o d e l e d u s -i n g t h e w a ll f u n c t io n a p p r o a c h . T h e c o n s e r v a t i o ne q u a t i o n s a r e s o l v e d b y t h e f i n i te v o l u m e m e t h o d .

3 Re s u l t s a n d d i s c u s s io n sA c c o r d i n g t o a b o v e p h y s i c a l m o d e l s a n d c o m p u t a -

t i o n a l m e t h o d s , t h e f l o w f i e l d , p r e s s u r e f i e l d a n d t e m -p e r a t u r e f i e l d , a n d t h e i r d i s t r i b u t i n g c h a r a c t e r i s t i c s i nt h e u n i t d u e t a r e o b t a i n e d .3 . 1 Velocity contour and turbulence intensity

contour plotsFig . 2 and F ig . 3 sho w the X = 0 ax ia l s ec t ion ve lo c i -

t y c o n t o u r a n d t u r b u l e n c e i n t e n s i t y c o n t o u r p l o t s r e -s p e c t i v e ly . T h e p l o t s i n d i c a t e t h a t t h e R O D b a f f l e sh a v e g r e a t i n f l u e n c e o n t h e f l o w f i e ld o f th e u n i t d u c t

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364 ournal of Shanghai Universitye x c e p t f o r s u p p o r t i n g t u b e b a n k . W h e n t h e fl u id c r o s s -e s o v e r th e R O D b a f f l e s t h e R O D b a f f l e s c o n t i n u e s t os h e a r a n d c o m m i n u t e t h e s t r e a m l i n e f l o w a l o n g t h eh o r i z o n t a l a n d v e r t ic a l d i re c t i o n s i n t h e u n it d u c t a n dt h e f l u i d f l o w d i r e c t i o n c h a n g e s a n d t h e c o n t i n u i t y a n ds t a b i li t y o f t h e f l u i d a x e d e s t r o y e d . T h e c i r c u l a t i o na r e a a t t h e l o c a t i o n o f R O D b a f f le is d e c r e a s e d s o t h a tt h e f l u i d i s a c c e l e r a t e d a t t h e s e c t i o n s v e r t i c a l t o R O D

b a f fl e a n d t u r b u le n c e i n t en s i ty b e c o m e s m o r e a n dm o r e s t r e n u o u s a s s h o w n i n F i g . 4 . T h e h i g h v e l o c i t yf l u i d c o n t i n u o u s l y s c o u r s t h e t u b e w a l l s o t h a t t h e l i q -u i d b o u n d a r y l a y e r o n t h e t u b e w a l l b e c o m e s v e r y t h in -n e r w h i c h i s v e r y b e n e f i c i a l t o h e a t t r a n s f e r e n h a n c e -m e n t . B u t t h e r e is a r e s i d e n c e r e g i o n a t t h e b a c k s i d eo f e v e r y R O D b af f le t h a t r e d u c e s h e a t t r a n s f e r e s p e -c i a ll y i n t h e g a p o f th e t w o a d j a c e n t t u b e s .

x * Z: " ~ : "- ' ~ : . .. .. .. .. .. .. .. .. .. .. :::::: ................. : " ~ - '~ ~ ' " ~ ~ F " ~

.. . . . : . . . . . . . . . . . . . . . . . . . .7..: :- .. ~. . . . . . . . . . . ~ ~ ~ : : - ' , . . . . . . . . . . . . ~.

Fig.2 X = 0 axial section velocity contours plots in a periodic domain

xtF i g 3 X = 0 axial section turbulence in~nsity contours plots in a periodic domain

Y

*z

Fig.4 X = 0 axial section pressur e contours plots in a periodic domain3 . 2 P r e s s u r e c o n t o u r p l o t

P i g . 4 s h o w s t h e X = 0 a x ia l s e c t i o n p r e s s u r e c o n t o u rd i s t ri b u t i o n i n a p e r i o d i c d o m a i n . I t c a n b e s e e n t h a tt h e p r e s s u r e d r o p i s p e r i o d i c a n d s y m m e t r i c a l a b o u tcen te r ax i s i n the she l l s ide of RHE. Due to the in f lu -e n c e o f R OD b a f f le t h e p r e s s u r e l if ts a t w i n d w a r d s i d eo f R O D b a f f l e i n u n i t d u c t a n d m e a n w h i l e t h e p r e s -s u r e d e c a y s a t l e e w a r d s i d e o f R OD b a f f l e . T h i s is t h em a i n re a s o n o f i n c r e a s e o f d y n a m i c c o n s u m p t i o n . O nt h e o t h e r w i s e t h e h i g h p r e s s u r e i n f o r e p a r t o f t h eR O D b a f f l e m a k e s t h e f l u i d v e l o c i t y i n c r e a s e a t t h e t w os i d e o f th e R O D b a f f l e . T h i s is t h e m a i n s o u r c e o f h e a tt r a n s f e r e n h a n c e m e n t .3 . 3 T e m p e r a t u r e c o n t o u r p l ot s

T h e t e m p e r a t u r e c o n t o u r p l o t s o f c r e s s s e c t io n s a r es h o w n i n F i g . 5 . T h e p l o t s i n d i c a t e t h a t t h e f l u i d t e m -p e r a t u r e i s b e c o m i n g h i g h e r a n d h i g h e r a l o n g t h e f l o w

d i r e c t i o n . T h e Z = - 0 . 0 6 m c r o s s s e c t i o n i s n e a r t of lu i d i n l e t o f t h e u n i t d u c t h e n c e t h e i n d i s t i n c t t e m -p e r a t u r e d i f f e r en c e h a p p e n s . T h e Z = - 0 . 0 4 m c r o s ss e c t i o n i s j u s t t h e l o c a t i o n o f R O D b a f f l e t h e f l u idt e m p e r a t u r e o f t h i s s e c t i o n s t il l c h a n g e s l i t t l e b u t t h eR O D b a f f l e m a k e s t h e f lu i d t e m p e r a t u r e o f t h e Z =- 0 . 0 2 m c r o s s s e c t i o n g e t o b v i o u s l y h i g h e r . T h e t e m -

p e r a t u r e d i f f e r e n c e a t t h e Z = 0 . 0 2 m c r o s s s e c t i o n i sg e t t in g s m a l l b e t w e e n i n t e r i o r a n d e x t e r i o r r e g i o n s o ft h e u n i t d u c t . U n t il th e f l u i d e n c o u n t e r s t h e n e x t R O Db a f f l e t h e a b r u p t c h a n g e o f f l ui d t e m p e r a t u r e d o e s n o th a p p e n . T h a t i s t o s a y i f n o R O D b a f f le is p l a c e d i nt h e u n it d u c t t h e c h a n g e o f t h e f lu i d t e m p e r a t u r e w i lla l w a y s b e s m a l l e r a l o n g w h o l e d u c t li k e t h e Z =

0 . 0 6 m c r o s s s e c t io n . T h e r e f o r e it c a n b e c o n c l u d e dt h a t i t i s t h e R O D b a f f l e t h a t h a s e n h a n c e d c o n v e c t i v eh e a t t r a n s f e r o f f lu i d i n t h e u n i t d u c t .

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Vol. 10 No. 4 Aug. 2006 WU J X, et al. : 3D simulation on the unit duct in the shell side . . . 365

Y

Fig.5 Cross sections temperature contours in the unit duct3. 4 The heat transfer and pressure drop char

acteristicsF i g . 6 s h o w s t h a t t h e h e a t t r a n s f e r c o e f f i c i e n t h i s

a l w a y s a s c e n d i n g w i t h a u g m e n t a t i o n o f R e n u m b e r i nt h e u n i t d u c t . T h i s is b e c a u s e o f t h e i n f l u e n ce o f R O Db a f f l e s o n t h e f l o w f i e l d a n d t e m p e r a t u r e f i e l d i n u n i td u c t . T h e R O D b a f f l e s f i r s tl y b r e a k s t r e a m l i n e f l o w ,a n d t h e c i r c u l a t i o n a r e a a t t h e l o c a t i o n o f R O D b a f f l e i sa b r u p t l y r e d u c e d s o t h a t f l u id i s a c c e l e r a t e d , a n d t h e nf l ui d s c o u r s a n d d i s tu r b s t h e b o u n d a r y l a y e r , a n d i m -p r o v e s t u r b u l e n t f l o w i n t e n s i ty . A l l t h e t r a n s f o r m a t i o no f t h e f l u id f l o w c o n f o r m a t i o n i s a d v a n t a g e o u s t o h e a tt r a n s f e r e n h a n c e m e n t . H o w e v e r t h e p r e s s u r e g r a d i e n to f f l u id i n c r e a s e s d i s ti n c tl y w i t h a u g m e n t a t i o n o f R en u m b e r i n t h e u n i t d u c t , a s s h o w n i n F i g . 7 .

100

20 t ~ ~ ~ ~0 0.5 1.0 1.5 2.0 2.5 3.0Re xl0 -4)Relation of h and Re number

Re xl0 -4)Relation of pressure gradient and Re num ber

~,~ 8O

6

~ 4O

Fig 7

Fig 60

-200.-. -400B

-600-800

-1 000

-1 200 0

a t Z = - 0 . 0 6 m , - 0 . 0 4 m , - 0 . 0 2 m , 0.0 2 m , 0 .0 4 m , 0 . 0 6 m

4 C o n c l u s i o n sI n o r d e r t o f u l l y u n d e r s t a n d t h e s h e l l s i d e c h a r a c t e r -

i s ti c s o f t h e R H E , a n e w k i n d o f n u m e r i c a l m o d e l o ft h e s h el l a n d t u b e h e a t e x c h a n g e r i s p r e s e n t e d , w h i c hi s c a l l e d a s th e u n i t d u c t m o d e l . T h e n u m e r i c a l s i m u -l a t i o n h a s a c h i e v e d t h e f o l l o w i n g c o n c l u s i o n s . T h es h e ll s i de s t r u c t u r e o f t h e R H E i s v e r y c o m p l i c a t e d ,b u t t h e u n i t d u c t m o d e l c a n p e r f e c t l y p r e d i c t t h e d i st r i-b u t i o n s o f t h e f l o w , p r e s s u r e a n d t e m p e r a t u r e f i e l d ,w h i c h i s a d v a n t a g e o u s t o a n a l y z e t h e e n h a n c e d h e a tt r a n s f e r m e c h a n i s m o f t h e R O D b af f l e s . T h e R O D b a f -f l e c a n c h a n g e t h e f l u i d f l o w d i r e c t i o n a n d s t r o n g l y i n -c r e a s e t h e f l o w v e l o c i t y . T h i s f u n c t i o n o f d i s t u r b i n gf l o w c a n a u g m e n t t u r b u l e n c e i n t e n s i t y , c o n s e q u e n t l ye n h a n c e c o n v e c t i v e h e a t t r a n s f e r o f s h el l s i d e f l ui d .

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Editor YAO Yne-yuan)