Air Flow Scaling Parameters

8/2/2019 Air Flow Scaling Parameters

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Ene rgy and Bu i ld ings , 14 (199 0) 207 - 210 207

S c a l e E f f e c t i n R oom A i r f l ow S t ud i e sH. B. AWBID e p a r t m e n t o f C o n s t r u c ti o n M a n a g e m e n t , U n i v e r si t y o f R e a d i n g, W h i t en i g ht s , P .O . B o x 2 1 9 ,R e a d in g R G 6 2 B V ( U . K .)M. M. NEMRIM e c han ic a l and I ndus t r ia l Eng ine e r ing D e p ar tm e n t , N a p ie r Po ly t e c hn ic , C o | in ton Road , Ed inburgh ( U . K . )

ABSTRACTIn this paper, a numerical procedure isapplied for solving the two-dimensionalNavier-Stokes equations describing the flow

in an air-conditioned room using the finitevolume method. The effect of turbulence isdescribed by the K-e turbulence model. Therange of influence of Archimedes andReynolds numbers on the air velocity andtemperature distribution in the room is inves-tigated using the numerical solution. Compari-son of the numerical prediction is made withexperimental data. The results of the numeri-cal solutions can be used as a guide for thephysical modelling of air movement undermore complex thermal conditions.

INTRODUCTIONThe expected performance of an air dis-tribution system in some cases can be pre-dicted from past experience and establisheddesign procedure. However, in other cases andparticularly when non-conventional methodsof air distribution are employed, physicalmodelling and or mathematical modelling

must be used to evaluate the room environ-ment. Where the size of the building precludesa full-scale physical model (e.g., atria, indoorstadia, theatres, etc.), tests are carried outon a reduced-scale model. In practice, al-though a small-scale factor (a length ratio ofbuilding to model) is preferable, this may notbe realized due to the high cost of construct-ing large models.For the results from reduced scale-modeltests to be applicable to the prototype, geo-metric, kinematic and thermal similarity be-tween model and p roto type must be achieved[ 1 - 5 ]. Geometri c similarity is a p re-requisitefor any modelling investigation. For isother-

mal flows, geometric and kinematic similaritymust be present and these can be usuallyachieved without too much difficulty. How-ever, for non-isothermal flows all three simi-larity requirements should theoretically bepresent before a complete simulation of theflow in the building can be achieved. Inpractice, it is not possible to provide a com-plete similarity for non-isothermal flow and,as a result, difficulty in interpreting the modelresults may be experienced. Such problemsare naturally irrelevant in mathematicalmodelling, however, most available mathe-matical models have recently been developedand require validation.In this paper, the influence of kinematicand thermal similarities on the air velocityand temperature distribution in a room areinvestigated numerically using a finite volumecomputer program. The predicted results arecompared with measurements obtained in afull-scale test room.

PHYSICAL MODELLINGTo use the test data fr om a scaled model ofa room or a building for the air distribution

design of the p roto type, similarity of the flowpattern, velocity distribution and temperaturedistribution should be achieved in the model.Previous investigators [3, 5] have shown thatsuch similarity can only be achieved if geo-metric, kinemati c and thermal similarities be-tween the model and prototype exist. Withthe help of dimensional analysis, it can beshown, e.g., Roiloos [3], that complete simi-larity can only be attained if the Prandtlnumber , Pr, t he R eynolds number , Re, andthe Archimedes number, Ar, are equal forboth model and prototype and, in addition,geometric similarity and similarity of theboundary conditions are present. Assuming0378 -778 8/90/ $3.50 Elsevier Sequoia/ Printed in The Netherlands


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2 0 8t h a t g e o m e t r i c a n d b o u n d a r y s im i l ar it ie s e x is ta n d t h e s a m e f l ui d i s u s e d in th e m o d e l a n dt h e p r o t o t y p e ( a ir ) , i .e . , P r i s t h e s a m e , t h e ne q u a l i t y o f R e a n d A r m u s t b e o b t a i n e d t oa c h i e v e c o m p l e t e f l o w s i m i l a ri ty . A p p l y i n gt h i s s im i l a r i t y c r i t e r i o n t o t h e s u p p l y j e tm e a n s t h a t :

( a ) f o r R e e q u a l i t yR e = =

p m( 1 )

w i t h t h e s a m e f l u i d ( a ir ) u s e d i n m o d e l a n dp r o t o t y p e ,U m L p- - - - - - s ( 2 )U p L mw h e r e v i s t h e k i n e m a t i c v i s c o s i t y o f a ir , S i st h e s c al e f a c t o r , U is t h e s u p p l y v e l o c i t y a n dL i s a c h a r a c t e r i s t i c l e n g t h . E q u a t i o n ( 2 ) in d i -c a t es t h a t t h e v e l o c it y i n t h e m o d e l m u s t b eh i gh e r t h a n t h a t i n t h e p r o t o t y p e b y t h e f a c t o rl / S .( b ) f o r A r e q u a l i t y

A r = I g{JLAOo ] [g{JLAO o][J~ p = [ ~ - - - - J , ,

w h e r e /3 is t h e c u b i c e x p a n s i o n c o e f f ic i e n t( l / K ) , a n d A 0 o is t h e t e m p e r a t u r e d i f f e re n c eb e t w e e n s u p p ly a n d r o o m ( K ) .A s s u m i n g s i m i la r t h e r m a l c o n d i t i o n s b e -t w e e n t h e m o d e l a n d t h e p r o t o t y p e a n d u s in gt h e s a m e f l u i d ,U r n _ L V ~ 1 (3 )

F r o m e q n s . ( 2 ) a n d ( 3 ) , it i s c l e a r t h a t t h er e q u i r e m e n t s f o r th e e q u a l i t y o f R e a r e q u i t ed i f f e r e n t f r o m t h e r e q u i r e m e n t s f o r t h e e q ua l -i t y o f A r a n d t h e t w o e q u a l i t i e s c a n n e v e r b ea c h i e v e d c o n c u r r e n t l y i n a m o d e l s t u d y . I nt h e c a s e o f i s o t h e r m a l f l o w s , s i m i la r it y c a n b ea c h i e v e d w i t h c o n s t a n t R e . H o w e v e r , c o m -p l e t e s i m i la r it y f o r n o n - i s o t h e r m a l f l o w s c a n-n o t b e a c h i e v e d i n p r a c t i c e . I n t h i s c a s e t h er a n g e s o f R e a n d A r o v e r w h i c h t h e a i r d i st ri -b u t i o n s y s t e m i n t h e p r o t o t y p e is r e q u i re d t oo p e r a t e c a n p r o v i d e a n i n s i g h t i n t o d e c i d i n gw h e t h e r e q u a l i t y o f R e o r A r i s m o s t r e l ev a n tf o r m o d e l i n v e s t ig a t io n .

N U M E R I C A L S O L U T IO NT h e g e n e r a l e q u a t i o n s d e s c r i b i n g t h e s t e a d yi n c o m p r e s s i b l e f l o w i n a r o o m a r e s o l v e d i n a

f i n it e d i f f e r e n c e f o r m . T h e f l u c t u a t i n g v e lo c i -t ie s a n d t e m p e r a t u r e t e r m s a re r e p r e s e n t e d b ye q u i v a l e n t t i m e - a v e r a g e t e r m s u s i n g t h e K - et u r b u l e n c e m o d e l . T h e e f f e c t s o f b u o y a n c yo n t h e v e rt ic a l c o m p o n e n t o f v e l o c i ty a n d t h ek i n e t i c e n e r g y o f t u r b u l e n c e , K , a n d i t s d i ss i-p a t i o n r a t e , e , a r e a l s o i n c l u d e d i n t h e s o l u -t i o n p r o c e d u r e , s e e A w b i [ 6 , 7 ] f o r fu r t h e rd e t a i l s .

T E S T R O O MT h e r o o m b e i n g i n v e s t ig a t e d f o r th i s p u r-

p o s e h a s a s q u a r e f l o o r o f l e n g t h L = 4 . 2 ma n d c e i li n g h e i g h t H = 2 . 8 m . T h e a i r is s u p -p l i e d f r o m a c o n t i n u o u s s l o t in t h e c e i li n gs p a n n in g t h e w i d t h o f t h e r o o m a n d a t a d is -t a n c e 1 . 2 m f r o m t h e w a l l . T h e r o o m l o a d w a sp r o d u c e d b y e l e c t ri c a l ly h e a t e d t a p e s l ai do v e r t h e f l o o r a r e a t o p r o d u c e a u n i f o r m l o a dd i s t r i b u t io n . T h e a ir v e l o c i t e s w e r e m e a s u r e dw i t h T S I 1 6 1 0 l o w v e l o c i ty a n e m o m e t e r sw h i c h g iv e t h e m a g n i t u d e o f t h e v e l o c i t y a tt h e m e a s u ri n g p o i n t . T h e t h e r m o c o u p l e s w e r ep r o v i d e d w i t h a r a d i a t io n s h i e l d t o r e d u c e t h ee f f e c t o f r a d i a n t t e m p e r a t u r e . T h e m e a s u r e -m e n t s w e r e c a r r ie d o u t u s i n g s q u a r e g ri d s o f1 . 0 a n d 0 . 5 m a t d i s t a n c e s o f 0 . 1 5 , 0 . 6 , 1 . 2a n d 1 . 8 m a b o v e t h e f l o o r .

R E S U L T S A N D D I S C U S S IO NE f f e c t o f R e y n o l d s n u m b e r ( is o t he r m a l f l o w )F i g u r e l ( a ) s h o w s r e s u l t a n t v e l o c i t y p r o -f il e s in t h e o c c u p i e d z o n e o f t h e r o o m f o r di f-f e r e n t a i r f l o w r a t e s i . e . , d i f f e r e n t R e . T h e s ep r o f i le s r e p r e s e n t t h e r a t io o f t h e m e a n v e l o c i-t ie s i n h o r i z o n t a l p l a n e s o f t h e o c c u p i e d z o n e

n2.0 am,~ r P red ic ted, ~ -o - Re=2400~ ' -e - Re =3 1001.5, J f -~ - Re =4000i~m Exper imental~ i L R e =2 4 00"E 1.0. - ~ Re =3100

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0.0 , ~ .1~" r0 . 0 0 0 . 0 4 0 . 0 8 0 . 1 2 0 . 1 8v /U oF i g . l ( a ) . C o m p u t e d a n d m e a s u r e d i s o t h e r m a l v e l o -c i t y prof i l e s .


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t o t h e s u p p l y v e l o c it y . A s c a n b e s e en f r o m F ig .l ( a ) t h e p r e d i c t e d v e l o c i t y p r o f il e s a re c l o s et o t h e e x p e r i m e n t a l v a lu e s , e x c e p t n e a r th ef l o o r w h e r e t h e p r e d i c t e d v a l u e s a re h i g h e r i ns o m e c a s e s. T h i s c an b e a t t r i b u t e d , e s p e c i a l lyi n t h e l o w R e y n o l d s n u m b e r c a se s , t o t h ed i r e c t i o n a l s e n s i t i v i ty o f t h e a n e m o m e t e r s .T h e a n e m o m e t e r h a d a c y l i n d r i c a l s e n s o rw h i c h m e a s u r e s t h e c o m p o n e n t o f v el o c i tyn o r m a l t o t h e c y l i n d e r a xi s. T h e s e n s o r i sn o r m a l l y s e t w i t h i ts a x i s p a ra l le l t o t h e f l o o ro f t h e r o o m . T h e m e a s u r i n g p l a n e a t 1 5 0 m ma b o v e t h e f l o o r is w i t h i n t h e b o u n d a r y l a y e rr e g i o n o f t h e r e v e r se f l o w a n d u n l e s s t h e a xi so f t h e a n e m o m e t e r is p e r p e n d i c u l a r t o t h ed i r e c t i o n o f t h e f l o w , a l o w v e l o c i t y r e a d i n gw i ll b e o b t a i n e d a t t h i s h e ig h t . A t h ig h e rl e ve l s a b o v e t h e f l o o r , t h e a n e m o m e t e r w i l l b em e a s u r i n g f l o w i n t h e s h e a r l a y e r a n d t h e v o r-t e x r e g i o n s w h e r e t h e f l o w h a s n o d e f i n e dd i r e c t i o n . In d e e d , m e a s u r e m e n t s a t h i g h e rl ev e ls p r o d u c e d g o o d c o r r e l a t i o n w i t h p r e d i c -t i o n s . A n o t h e r c a u s e o f d i s c r e p a n c y a t l o wl e ve l s m a y b e a t t r i b u t e d t o t h e K - e m o d e l ' sf a i lu r e i n n o t d e s c r i b i n g t h e e f f e c t o f w a llp r o x i m i t y a c c u r a t e l y a n d a ls o th e e f f e c t o fl o w R e ( t r a n s it i o n ) f l o w s n e a r t h e w a l l. T h ew a l l e f f e c t h a s b e e n i n c l u d e d i n t h e p r e s e n tc o m p u t a t i o n u s in g L a u n d e r a n d S p a ld i n g 's[ 8 ] w a l l f u n c t i o n e x p r e s s i o n , h o w e v e r , N a g a n oa n d H i s h id a [ 9 ] h a v e r e p o r t e d a n i m p r o v e m e n tt o t h e K - e m o d e l b y t h e i nc l u s io n o f b o t h e f -f e c t s a n d h a v e a t t a i n e d b e t t e r re s u l ts . T h e p re s -e n t a u t h o r s a n t i c ip a t e t h e u s e o f i m p r o v e df o r m s o f th e K - e m o d e l i n t h e n e a r f u t u re .

A s s h o w n i n F ig . l ( a ) t h e e f f e c t o f i n cr e a s-i n g R e o n t h e v e l o c i t y p r o f il e is m o s t p r o m i -n e n t n e a r t h e f l o o r . F ig u r e l ( b ) s h o w s t h is ef -f e c t e x t e n d e d t o i n c lu d e h ig h e r R e , a n d b yi n c r e a s i n g R e t h e m a x i m u m r e c i r c u l a t i n g f l o w2.0 , .~

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V / U oF i g. l ( b ) . C o m p u t e d i s o t h e r m a l v e l o c i t y p r o fi le s .

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v e l o c i t y n e a r t h e f l o o r a l s o i n c r e a s e s . T h er a n g e o f R e c o n s i d e r e d h e r e c o v e r s m o s tr a n g e s u s e d i n m o d e l i n v e s t i ga t i o n .E f f e c t o f A r c h im e d e s n u m b e r( n o n - i s o t h e r m a l f l o w )

F i g u re 2 s h o w s t h e e f f e c t o f A r c h i m e d e sn u m b e r o n t h e m e a n v e l o c i ty i n t h e o c c u p i e dz o n e . A s A r ( i .e . , c o o l i n g l o a d ) i n c r e a s e s , t h er o o m v e l o c i t y i n c r e a s es a s a r e s u l t o f t h ed o w n w a r d b u o y a n c y a c ti n g o n a c o o l j e t . T h ea g r e e m e n t b e t w e e n t h e p r e d i c t e d r e su l ts a n dm e a s u r e m e n t i s c l o s e fo r m o s t p r a c ti c a l p u r -p o s e s . T h i s i n d i c a t e s t h a t e s p e c i a ll y f o r h i g h e rA r v a l u es , m o d e l l i n g a t r e d u c e d s c al e s h o u l db e b a s e d o n t h e e q u a l i t y o f A r b e t w e e n m o d e la n d p r o t o t y p e .

F i g u re 3 s h o w s t h e n o n ~ l i m e n s i o n a l t e m p e r -a t u r e d i s t r i b u t i o n A 0 / A 0 o in t h e o c c u p i e d z o n ef o r t w o d i f f e r e n t v a lu e s o f A r . A 0 r e p r e s e n t st h e d i f f e r e n c e i n t h e a v e r a g e t e m p e r a t u r e i n ah o r i z o n t a l p l a n e a n d a ir s u p p l y t e m p e r a t u r ea n d A 0 o i s t h e d i f f e r e n c e b e t w e e n t h e a v e r a ge

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l o g A rF i g. 2 . E f f e c t o f A r c h i m e d e s n u m b e r o n t h e a v e r a g ev e l o c i t y .

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0 . 5 1 . 0 1 . 5 2 . 0 2 . 5T e m p e r a t u r e R a t i oF i g . 3 . T e m p e r a t u r e d i s t r i b u t i o n i n o c c u p i e d z o n e f md i f f e r e n t A t .


4/4

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t e m p e r a t u r e i n t h e o c c u p i e d z o n e a n d t h es u p p l y t e m p e ra t u r e. A s c a n b e s e e n f r o m t hi sFigure, t he effect of A r o n t h e t e m p e r a t u r eg r a d i e n t i s v e r y s m a l l w h i c h i n di c at e s a g o o dm i x i n g o f t h e f lo w. S i n c e t h e r o o m l o a d w a ss i tu a te d o n t h e f l o or , t h e t e m p e r a t u r e r a ti oi n c r ea s e s t o w a r d s t h e f l o o r w i t h A S / A ~ o > 1 .

C O N C L U S I O N S

T h e r e su l ts f r o m t h i s s t u d y s h o w t h a t w h e nm o d e l l i n g i s o t h e r m a l f l o w s in a r o o m , i t i s i m -p o r t a n t t o p e r f o r m t h e m o d e l t e s t a t t h e s a m eRe as in the p r o t o t y p e , s i n c e R e w a s f o u n d t oi n f l u e n c e t h e v e l o c i t y in th e o c c u p i e d z o n e .I n t h e c a s e o f a r e d u c e d - s c a l e m o d e l t h i sm e a n s a s u p p l y v e l o c i t y e q u a l t o t h a t i n t h ep r o t o t y p e m u l t i p l i e d b y t h e s c al e f a c t o r 8 , i .e . ,a h i g h e r v e l o c i t y . I n t h e c a s e o f n o n - i s o -t h e r m a l f l o w s , t h e v e l o c i t y d i s t r i b u t i o n i n t h eo c c u p i e d z o n e i s a f f e c t e d b y b o t h Re and At ,b u t i t h a s b e e n f o u n d t h a t i t i s m o r e i m p o r -t a n t t o p e r f o r m t h e m o d e l t e s t a t t h e ~ m ev a l u e o f Ar as in the p r o t o t y p e w h e n A r ~>1 1 0 - a a n d t o p e r f o r m t h e m o d e l t e s t a t th esame Re as in t h e p r o t o t y p e w h e n A r

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Air Flow Scaling Parameters