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Inter-Zone convective heat transfer in buildings : a review
Barakat, S. A.
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Inter-Zone Convective Heat Transfer
in Buildings: A Review
by S.A. Barakat
Reprinted from
Heat Transfer in Buildings and Structures-HTD-Vol. 41
p. 45 -52
ASME-AIChE National Heat Transfer Conference
Denver, CO, August 4
-
7,1985
(DBR Paper No. 1323)
Price $2.00
NRCC 24953
On examine les travaux de recherche sur le transfert de chaleur
de convection inter-zone dans les batiments et on traite des
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INTER-ZONE CONVECTIVE HEAT TRANSFER I N BUILDINGS: A REVIEW
S.A. Barakat
Division of Building Research National Research Council of Canada
Ottawa, Ontario. Canada
ABSTRACT R e s e a r c h work on i n t e r - z o n e c o n v e c t i v e h e a t t r a n s f e r i n b u i l d i n g s is reviewed and t h e p a r a m e t e r s t h a t g o v e r n t h i s p r o c e s s a r e d i s c u s s e d . A l i m i t e d comparison between t h e h e a t t r a n s f e r r a t e s c a l c u l a t e d by e x i s t i n g c o r r e l a t i o n s and t h o s e o b t a i n e d i n a f u l l - s c a l e t e s t f a c i l i t y i s p r e s e n t e d . A number of r e s e a r c h a r e a s where more work i s needed a r e i d e n t i f i e d . NOMENCLATURE A p e r t u r e r a t i o (=D/H) Exponent of GrD i n E q u a t i o n ( 1 9 ) Room w i d t h S p e c i f i c h e a t of f l u i d C o e f f i c i e n t d e f i n e d i n E q u a t i o n ( 1 ) Opening h e i g h t H y d r a u l i c d i a m e t e r of doorway A c c e l e r a t i o n due t o g r a v i t y Heat t r a n s f e r c o e f f i c i e n t Room h e i g h t Thermal c o n d u c t i v i t y of f l u i d E n c l o s u r e l e n g t h ( d i s t a n c e between h o t and c o l d s u r f a c e s ) T o t a l h e a t t r a n s f e r r a t e t h r o u g h opening Power consumption i n c o l d room
Power consumption i n h o t room
R a d i a t i v e h e a t t r a n s f e r component t h r o u g h opening T h i c k n e s s of p a r t i t i o n Temperature Cold s u r f a c e ( o r room) t e m p e r a t u r e Hot s u r f a c e ( o r room) t e m p e r a t u r e Outdoor t e m p e r a t u r e Temperature d i f f e r e n c e
Temperature d i f f e r e n c e between t o p and bottom h a l v e s of t h e o p e n i n g Average t e m p e r a t u r e d i f f e r e n c e between z o n e s Loss c o e f f i c i e n t of c o l d room L o s s c o e f f i c i e n t of h o t room Width of o p e n i n g Dynamic v i s c o s i t y v K i n e m a t i c v i s c o s i t y P
-
F l u i d d e n s i t y P Average two-zone d e n s i t y o Stefan-Boltzmann c o n s t a n t D i m e n s i o n l e s s g r o u p s GrD Grashof number [ = g ~ p ~ 3 / p ~ 2 ] NuD N u s s e l t number [= hD/kl P r P r a n d t l number [ = c,v/kl ReD Reynolds number [= zVbD/vI INTRODUCTIONI n t e r - z o n e c o n v e c t i v e h e a t t r a n s f e r , o r t h e h e a t t r a n s f e r between zones ( o r rooms) i n a b u i l d i n g , c o u l d o c c u r s o l e l y due t o a t e m p e r a t u r e d i f f e r e n c e between t h e zones ( n a t u r a l c o n v e c t i o n ) , o r due t o t h e movement of a i r by m e c h a n i c a l means ( f o r c e d c o n v e c t i o n ) o r a c o m b i n a t i o n of b o t h . F o r c e d , c o n v e c t i o n c o u l d be g e n e r a t e d by i n t e n t i o n a l l y - u s e d c i r c u l a t i o n f a n s o r by a n u n b a l a n c e i n t h e a i r s u p p l y o r v e n t i l a t i o n system. Because of t h e f u n d a m e n t a l r o l e t h a t i n t e r - z o n e c o n v e c t i o n p l a y s i n b o t h c o n v e n t i o n a l and p a s s i v e s o l a r b u i l d i n g s , i t h a s r e c e n t l y r e c e i v e d i n c r e a s i n g a t t e n t i o n from t h e b u i l d i n g r e s e a r c h community. Convection i s r e s p o n s i b l e ( a l o n g w i t h t h e r m a l r a d i a t i o n ) f o r t h e d i s t r i b u t i o n of h e a t w i t h i n t h e o c c u p i e d s p a c e and between s p a c e s i n a multi-zone b u i l d i n g . T h i s h e l p s i n a c h i e v i n g a more u n i f o r m 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 a b u i l d i n g and r e d u c e s e x c e s s i v e o v e r h e a t i n g i n t h e s o u t h zone of a d i r e c t - g a i n b u i l d i n g .
Recent r e s e a r c h r e s u l t s have emphasized t h e i m p o r t a n c e of t h e i n t e r - z o n e c o n v e c t i o n p r o c e s s i n a b u i l d i n g and d e m o n s t r a t e d t h e need f o r a c c u r a t e a c c o u n t i n g of c o n v e c t i o n i n any a t t e m p t t o p r e d i c t t h e b u i l d i n g t h e r m a l performance. P r e v i o u s work h a s a l s o p o i n t e d o u t t h e s i g n i f i c a n t magnitude o f n a t u r a l c o n v e c t i o n a c r o s s d o o r o p e n i n g s . F o r example, h e a t f l o w r a t e s of more t h a n 1200 w a t t s h a v e b e e n f o u n d t o o c c u r t h r o u g h a 0.9x2.05 m doorway a s a r e s u l t of a
4
K t e m p e r a t u r e d i f f e r e n c e between t h e s p a c e s o n e i t h e r s i d e of t h e door. l o C o n v e c t i o n t h r o u g h s i n g l e doorwayswas a l s o found t o b e t h e major mecnanism f o r
d i s t r i b u t i n g h e a t from a s u n s p a c e t o t h e p a r e n t house. I n t e r - z o n e c o n v e c t i o n i s a l s o a n i m p o r t a n t f a c t o r a f f e c t i n g smoke movement and c o n t r o l i n b u i l d i n g s a s w e l l a s t h e t r a n s f e r of p o l l u t a n t s between s p a c e s . O t h e r a p p l i c a t i o n s r e l a t e t o t h e g e n e r a l movement of a i r w i t h i n a b u i l d i n g c r e a t i n g d r a u g h t s , l o s s of h e a t a t doorways of b u i l d i n g s where heavy p e d e s t r i a n t r a f f i c e x i s t s , and h e a t g a i n t h r o u g h t h e doorways of c o l d s t o r a g e rooms. The i n t e r - z o n e c o n v e c t i v e h e a t t r a n s f e r p r o c e s s is h i g h l y dependent on b o t h t h e g e o m e t r i c c o n f i g u r a t i o n of t h e s t r u c t u r e ( o p e n i n g h e i g h t and w i d t h , c e i l i n g h e i g h t , e t c . ) and on t h e boundary c o n d i t i o n s t h a t a r e e n c o u n t e r e d i n t h e s t r u c t u r e ( s u r f a c e t e m p e r a t u r e s and h e a t f l u x e s ) . T h i s p a p e r p r e s e n t s a d e t a i l e d r e v i e w of p r e v i o u s work on i n t e r - z o n e c o n v e c t i v e h e a t t r a n s f e r , p a r t i c u l a r l y a s r e l a t e d t o b u i l d i n g s , and d i s c u s s e s t h e p a r a m e t e r s t h a t g o v e r n t h i s p r o c e s s . I n t h e f o l l o w i n g p r e s e n t a t i o n some changes a r e made i n t h e t e r m i n o l o g y used by t h e o r i g i n a l a u t h o r s t o i n c r e a s e c l a r i t y and p e r m i t comparisons. For example, s u b s c r i p t s a r e added t o t h e N u s s e l t , G r a s h o f , and R a y l e i g h d i m e n s i o n l e s s numbers t o i n d i c a t e t h e c h a r a c t e r i s t i c l e n g t h u s e d i n t h e i r c a l c u l a t i o n . That is and RaD = GrD x P r F o r e x p l a n a t i o n s of a l l o t h e r t e r m s , t h e r e a d e r i s r e f e r r e d t o t h e Nomenclature.
REVIEW OF PREVIOUS WORK
Almost a l l p r e v i o u s p a p e r s on i n t e r - z o n e c o n v e c t i v e h e a t t r a n s f e r have f o c u s s e d on n a t u r a l c o n v e c t i o n o n l y i n s i m p l e and complex, o r d i v i d e d , e n c l o s u r e s ( s e e F i g u r e 1 ) . O s t r a c h l and C a t t o n Z p r e s e n t e d two comprehensive r e v i e w s of n a t u r a l c o n v e c t i o n i n s i m p l e e n c l o s u r e s . T h i s c a s e , however, i s o u t s i d e t h e s c o p e of t h i s p a p e r and w i l l n o t be d i s c u s s e d f u r t h e r .
A number of s t u d i e s have been performed f o r e n c l o s u r e s of d i f f e r e n t a s p e c t r a t i o s
(HIL),
w i t h b a f f l e s o r p a r t i t i o n s mounted i n t h e c a v i t y t o s t u d y t h e i r e f f e c t on r e d u c i n g t h e c o n v e c t i v e t r a n s f e r . F o r example, P r o b e r t and ward3 found t h a t t h e i n s e r t i o n of c o m p a r a t i v e l y s h o r t end-mounted v e r t i c a l b a f f l e s ( a t f l o o r and c e i l i n g ) r e d u c e s t h e t o t a l s t e a d y s t a t e h e a t t r a n s f e r a c r o s s t h e e n c l o s u r e ( i n c l u d i n g t h e r a d i a t i v e component) by 20 t o 30%.C t x
F i g u r e 1. E n c l o s u r e c o n f i g u r a t i o n I n a Mach-Zender i n t e r f e r o m e t r i c s t u d y , J a n i k o w s k i e t a 1 4 confirmed t h e above f i n d i n g i n a r e c t a n g u l a r e n c l o s u r e of h i g h a s p e c t r a t i o . They a l s o i n d i c a t e d t h a t t h e f r e e c o n v e c t i v e h e a t t r a n s f e r d e c r e a s e s a s t h e b a f f l e h e i h t i s i n c r e a s e d ( o p e n i n g h e i g h t d e c r e a s e d ) . Emeryf r e p o r t e d t h a t i f v e r t i c a l b a f f l e s a r e i n s e r t e d c e n t r a l l y ( i . e . l e a v i n g o p e n i n g s n e a r t h e f l o o r and c e i l i n g of t h e e n c l o s u r e ) , t h e i r p r e s e n c e d o e s not produce any s i g n i f i c a n t change i n c o n v e c t i v e h e a t t r a n s f e r from t h e u n b a f f l e d c o n d i t i o n . T h i s c a n b e e x p e c t e d s i n c e t h i s b a f f l e arrangement d o e s n o t a l t e r t h e buoyancy-induced f l o w which o c c u r s m a i n l y c l o s e t o t h e s u r f a c e s . Chang e t a 1 6 u n d e r t o o k a f i n i t e d i f f e r e n c e s t u d y of n a t u r a l c o n v e c t i o n i n 2-D e n c l o s u r e s , having a n a s p e c t r a t i o of 1 , w i t h a v e r t i c a l p a r t i t i o n mounted o n e i t h e r t h e c e i l i n g o r t h e f l o o r . The v e r t i c a l w a l l s , p a r a l l e l t o t h e p a r t i t i o n , were m a i n t a i n e d a t d i f f e r e n t u n i f o r m and c o n s t a n t t e m p e r a t u r e s w h i l e t h e r e s t of t h e s u r f a c e s were a d i a b a t i c . , They showed t h a t t h e e f f e c t of i n c r e a s i n g t h e p a r t i t i o n h e i g h t ( r e d u c i n g t h e opening h e i g h t ) , of i n c r e a s i n g t h e p a r t i t i o n t h i c k n e s s , and of moving t h e p a r t i t i o n away from t h e c e n t r e of t h e e n c l o s u r e i s t o r e d u c e t h e h e a t t r a n s f e r between t h e two s i d e s of t h e e n c l o s u r e . Changes i n p a r t i t i o n h e i g h t had t h e most s i g n i f i c a n t e f f e c t . T h e i r c o n c l u s i o n s o n t h e e f f e c t of t h e p a r t i t i o n t h i c k n e s s was based on r e s u l t s f o r a n o p e n i n g h a l f t h e e n c l o s u r e h e i g h t o n l y . No c o r r e l a t i o n was g i v e n f o r t h e h e a t t r a n s f e r r a t e s . I n r e l a t i o n t o b u i l d i n g s , t h e f i r s t e x t e n s i v e s t u d y of n a t u r a l c o n v e c t i o n t h r o u g h o p e n i n g s i n p a r t i t i o n s was c a r r i e d o u t by Brown and S o l v a s o n i n 1 9 6 2 . ~ They have t h e o r e t i c a l l y d e s c r i b e d t h e p r o c e s s i n t e r m s of t h e N u s s e l t number, NuD, t h e Grashof number, G r D , and t h e P r a n d t l number, P r , i n t h e formwhere t h e c o e f f i c i e n t C i s i n t h e r a n g e 0.2 t o 0.33. The development of E q u a t i o n ( 1 ) i s g i v e n i n
R e f e r e n c e ( 7 ) .
Brown and S o l v a s a n performed t h e i r e x p e r i m e n t s f o r
t h e c a s e of air f l o w between two l a r g e test chambers ( e a c h was 2.44 m s q u a r e and 1.2 m l o n g ) t h r o u g h s i n g l e r e c t a n g u l a r o p e n i n g s a t t h e c e n t r e of t h e p a r t i t i o n between t h e chambers. Opening s i z e s of 7 . 6 ~ 7 . 6 , 15.2x15.2, 1 5 . 2 ~ 3 0 . 5 , 2 2 . 9 ~ 2 2 . 9 , and 3 0 . 5 ~ 3 0 . 5 cm were examined f o r a i r t e m p e r a t u r e d i f f e r e n c e s from 8.3 t o 47.2
K.
Various r a t i o s of p a r t i t i o n t h i c k n e s s t o o p e n i n g h e i g h t , t / D , were a l s o t e s t e d o v e r t h e r a n g e 0.19 t o 0.75. The a i r t e m p e r a t u r e d i f f e r e n c e between t h e warm and c o l d s i d e s was u s e d t o d e t e r m i n e t h e Nuand G r numbers. The a i r t e m p e r a t u r e was measured a s t h e a v e r a g e on a v e r t i c a l g r i d ( f l o o r t o c e i l i n g ) l o c a t e d 38 and 20 cm away from t h e p a r t i t i o n w a l l o n t h e warm and c o l d s i d e s , r e s p e c t i v e l y , and 61 cm from t h e c e n t r e of t h e o p e n i n g p a r a l l e l t o t h e w a l l . The o p e n i n g h e i g h t , D, was u s e d a s t h e c h a r a c t e r i s t i c l e n g t h . T h e i r e x p e r i m e n t a l r e s u l t s i n d i c a t e d t h a t t h e e x p o n e n t of t h e Grashof number i n E q u a t i o n (1) i s s l i g h t l y g r e a t e r t h a n 0.5. The r e s u l t s a l s o i n d i c a t e d a dependance of t h e h e a t t r a n s f e r r a t e ( o r Nu) on t / D . At l o 7
<
G r D<
l o 8 , v e r y l i t t l e i n f l u e n c e of t / D was n o t e d f o r t h e r a n g e t / D = 0.19 t o 0.38, however f o r G r D<
l o 7 and t / D = 0.38 t o 0.75, t h e e f f e c t of t / D was s i g n i f i c a n t . I n a n o t h e r p u b l i c a t i o n , Brown e t a18 p r e s e n t e d e q u a t i o n s and c h a r t s t o c a l c u l a t e h e a t and m o i s t u r e t r a n s f e r due t o n a t u r a l c o n v e c t i o n t h r o u g h o p e n i n g s i n v e r t i c a l and h o r i z o n t a l p a r t i t i o n s s e p a r a t i n g s p a c e s a td i f f e r e n t c o n d i t i o n s . F o r v e r t i c a l p a r t i t i o n s t h e f o l l o w i n g c o r r e l a t i o n s were g i v e n : f o r l o 6
<
G r D<
l o 8 and 0.19<
t / D<
0.75, and f o r G r D,
10'. ~ r o w n ~ a l s o examined t h e c a s e of o p e n i n g s i n a h o r i z o n t a l p a r t i t i o n when t h e c o l d e r a i r i s a t t h e t o p . I n a d d i t i o n , Brown and s o l v a s o n 7 performed l i m i t e d e x p e r i m e n t s t o examine t h e e f f e c t of f o r c e d a i r f l o w i n g h o r i z o n t a l l y p a r a l l e l t o t h e v e r t i c a l p a r t i t i o n o n t h e n a t u r a l c o n v e c t i o n r a t e s . Such f o r c e d c o n v e c t i o n was found t o h a v e a n e f f e c t ( i n c r e a s e o r d e c r e a s e ) on t h e n e t i n t e r c h a n g e a c r o s s t h e opening depending on t h e f o r c e d a i r v e l o c i t y . No c o r r e l a t i o n was g i v e n f o r t h e s e c a s e s . I n 1971, shawl0 r e p o r t e d on a s t u d y of h e a t t r a n s f e r by n a t u r a l c o n v e c t i o n and combined n a t u r a l and f o r c e d c o n v e c t i o n t h r o u g h l a r g e r e c t a n g u l a r o p e n i n g s i n a v e r t i c a l p a r t i t i o n . S i n c e h i s work a d d r e s s e d t h e problem of c o n t a m i n a n t exchange between h o s p i t a l rooms, t h e e x p e r i m e n t s were a c t u a l l y performed i n a h o s p i t a l and measured a i r exchange between a n i s o l a t i o n room and a v e s t i b u l e . The rooms were v e n t i l a t e d by a c e n t r a l s y s t e m w i t h a i r s u p p l y and e x t r a c t i o n o p e n i n g s i n e a c h room. For n a t u r a l c o n v e c t i o n , e a c h room had b a l a n c e d a i r s u p p l y and e x t r a c t volumes. For combined n a t u r a l and f o r c e d c o n v e c t i o n , t h e c o l d room had a i r s u p p l y o n l y .The doorway opening between t h e rooms was 2.05 m
h i g h and ranged from 0.1 t o 0.9 m wide. The t e m p e r a t u r e d i f f e r e n c e between t h e rooms was v a r i e d from 0 t o 12 K, and t / D was c o n s t a n t a t 0.05. The measured t e m p e r a t u r e d i f f e r e n c e between t h e t o p and bottom of t h e opening was u s e d t o c a l c u l a t e Nu and G r , and t h e o p e n i n g h e i g h t was u s e d a s t h e c h a r a c t e r i s t i c l e n g t h a l t h o u g h t h e e f f e c t o f t h i s l a t t e r v a r i a b l e was n o t s t u d i e d . F o r t h e n a t u r a l c o n v e c t i o n c a s e and 10'
<
GrD<
1011, Shaw r e p o r t e d t h a t t h e c o e f f i c i e n t C of E q u a t i o n ( 1 ) i s a f u n c t i o n of t h e magnitude of t h e t e m p e r a t u r e d i f f e r e n c e , AT, and t h e r e f o r e c a l l e d i t t h e c o e f f i c i e n t of t e m p e r a t u r e . Between a t e m p e r a t u r e d i f f e r e n c e AT of4
and 10 K, C had a v a l u e of 0.22 and i n c r e a s e d f o r AT below 4 K. T h i s i n c r e a s e wasa t t r i b u t e d t o t h e a i r v e l o c i t y o r t u r b u l e n c e w i t h i n t h e v e n t i l a t e d rooms, which was found by measurement t o be of t h e same o r d e r of magnitude a s t h e v e l o c i t y t h r o u g h t h e opening. F o r AT above 10 K, C was o b s e r v e d t o r i s e v e r y s l o w l y . Some of t h e r e s u l t s were a f f e c t e d by p r o x i m i t y of two doorways c a u s i n g a n i n t e r a c t i o n between t h e a i r f l o w t h r o u g h them when f u l l y opened.
F o r t h e c a s e of combined n a t u r a l and f o r c e d c o n v e c t i o n , e x c e s s a i r was s u p p l i e d t o t h e i s o l a t i o n room ( c o l d s i d e ) t o c o u n t e r a c t t h e a i r motion by n a t u r a l c o n v e c t i o n . For t h i s c a s e , Shaw e x p r e s s e d t h e N u e s e l t number a s a f u n c t i o n of a d i m e n s i o n l e s s g r o u p , Sw, t h a t i n c l u d e d b o t h t h e Reynolds and Grashof numbers. Shaw's t h e o r e t i c a l development i s p r e s e n t e d i n R e f e r e n c e (10). The f i n a l e x p r e s s i o n was g i v e n a s ~e~~
D
'
where
Sw = G r ~~2
2WD and D = h y d r a u l i c d i a m e t e r of t h e opening =-
h W+
D I t c a n be noted t h a t t h e t e r m D ~ / would d i s a p p e a r D ~ ~ i f t h e same c h a r a c t e r i s t i c l e n g t h , D, was u s e d i n b o t h Re and G r .The c o e f f i c i e n t C' i n E q u a t i o n ( 4 ) was found t o be a p r o d u c t of t h e c o e f f i c i e n t C ( o f t h e n a t u r a l
c o n v e c t i o n c a s e ) and a f o r c e d v e l o c i t y c o e f f i c i e n t C V which i s a f u n c t i o n of t h e f o r c e d a i r f l o w .
I n a l a t e r s t u d y , Shaw and whytel l i n d i c a t e d t h a t t h e t e m p e r a t u r e d i f f e r e n c e t h a t l e d t o t h e most a c c u r a t e c o r r e l a t i o n of h e a t f l o w was t h e d i f f e r e n c e between t h e mean t e m p e r a t u r e of t h e a i r f l o w i n g o u t o f t h e warm room and t h a t f l o w i n g i n t o t h e warm room measured on a g r i d a t t h e opening. Next b e s t was t h e t e m p e r a t u r e d i f f e r e n c e between t h e t o p and bottom of t h e opening. S i n c e t h e s e were n o t r e a d i l y a v a i l a b l e i n p r a c t i c e , t h e t h i r d c h o i c e was p i c k e d , which was t h e d i f f e r e n c e between t h e room a i r t e m p e r a t u r e s a t t h e c e n t r e of e a c h room a t a l e v e l h a l f t h e d o o r ' s h e i g h t . The c h o i c e of a d i f f e r e n t t e m p e r a t u r e d i f f e r e n c e from t h a t u s e d i n t h e p r e v i o u s s t u d y l e d t o a change i n t h e c a l c u l a t e d v a l u e of t h e c o e f f i c i e n t C. That i s , a C v a l u e of 0.27 was found ( i n s t e a d of 0.22) f o r AT between 1 and 10 K. To i n d i c a t e t h e s i g n i f i c a n c e of n a t u r a l c o n v e c t i o n , Shaw and Whyte p o i n t e d o u t t h a t a t e m p e r a t u r e d i f f e r e n c e of 4 K r e s u l t s i n a n a i r t r a n s f e r r a t e , e a c h way t h r o u g h a 0.9x2.05 m doorway, of 0.25 m3/s ( i . e . a h e a t t r a n s f e r r a t e o v e r
1200 w a t t s ) .
I n 1979, Wray and weber12 and Weber e t a l l 3 r e p o r t e d t h e r e s u l t s of a n i n t e r - z o n e c o n v e c t i o n s i m i l a r i t y s t u d y . The e x p e r i m e n t s were performed i n a s m a l l two-zone scaled-down e n c l o s u r e (L = 71 cm, H = 30 cm, B = 4 3 cm) w i t h Freon a s t h e working f l u i d . The t e m p e r a t u r e d i f f e r e n c e between zones was m a i n t a i n e d by k e e p i n g t h e o p p o s i t e end w a l l s a t d i f f e r e n t
t e m p e r a t u r e s ( o n e w a l l was h e a t e d and t h e o t h e r c o o l e d ) . They p r e s e n t e d t h e i r r e s u l t s i n t h e form
where NuH and GrH a r e c a l c u l a t e u s i n g t h e e n c l o s u r e h e i g h t , H, a s a c h a r a c t e r i s t i c l e n g t h ( a n d n o t t h e d o o r h e i g h t a s i n p r e v i o u s s t u d i e s ) . As a r e s u l t t h e v a l u e of K was found t o be a f u n c t i o n of t h e r a t i o of t h e d o o r t o c e i l i n g h e i g h t s ( o r a p e r t u r e r a t + o Ap = D/H), w i t h v a l u e s of 0.19 and 0.29 f o r Ap of 0.82 and 1.0 r e s p e c t i v e l y . (These v a l u e s were r e p o r t e d e r r o n e o u s l y i n t h e o r i g i n a l p a p e r a s 1.9 and 2.9; t h e new v a l u e s a r e c a l c u l a t e d from t h e p r e s e n t e d d a t a . ) The t e m p e r a t u r e d i f f e r e n c e used t o d e v e l o p E q u a t i o n ( 5 ) was t a k e n a s t h e d i f f e r e n c e between t h e a v e r a g e h o t and c o l d s i d e t e m p e r a t u r e s measured by a v e r t i c a l g r i d of movable thermocouples i n s i d e t h e s p a c e . I f E q u a t i o n ( 5 ) i s changed t o t h e form of E q u a t i o n ( I ) , t h a t i s t h e n c o e f f i c i e n t C would have t h e v a l u e of 0.29 a n d 0.41 f o r A of 0.82 and 1.0, r e s p e c t i v e l y .
I n a
!allow-up
s t u d y , Weber and b a r n e y 1 4c o n c l u d e d t h a t t h e o p e n i n g h e i g h t i s more s u i t a b l e a s a c h a r a c t e r i s t i c l e n g t h . When combined w i t h an
a p p r o p r i a t e t e m p e r a t u r e d i f f e r e n c e , a n e x p r e s s i o n of t h e form of E q u a t i o n ( 1 ) . i n d e p e n d e n t of t h e room and doorway g e o m e t r i e s , c a n b e found.
Two t e m p e r a t u r e d i f f e r e n c e s were used. The f i r s t , ATa, was d e f i n e d a s t h e d i f f e r e n c e between t h e a v e r a g e t e m p e r a t u r e of t h e t o p and bottom h a l v e s of t h e doorway. The s e c o n d , ATr, i s t h e d i f f e r e n c e between a volume-weighted a v e r a g e t e m p e r a t u r e c a l c u l a t e d from
v e r t i c a l l y s p a c e d t h e r m o c o u p l e s l o c a t e d t o t h e s i d e of t h e opening n e a r t h e p a r t i t i o n w a l l .
1 n a d d i t i o n t o t h e model r e s u l t s , Weber and f o r a c o n d u c t i n g p a r t i t i o n , and Kearnev u s e d t h e r e s u l t s o b t a i n e d from two f u l l - s c a l e
t e s t s i o d e t e r m i n e t h e c o e f f i c i e n t and t h e exponent of E q u a t i o n ( 1 ) u n d e r v a r i a t i o n s of h e a t s o u r c e and h e a t s i n k c o n f i g u r a t i o n s .
They c o r r e l a t e d t h e i r r e s u l t s i n t h e form f o r a non-conducting p a r t i t i o n . The a p p e a r a n c e of A, i n t h e e q u a t i o n and a
(7)
d i f f e r e n t v a l u e of t h e ~L exponent ( i . e . G r and P rNuD/Pr = 0.26 G r D o s 5 AT = ATa e x p o n e n t s ) from t h a t i n E q u a t i o n ( 1 ) r e f l e c t t h e p a r t i c u l a r d e f i n i t i o n of AT and t h e c h a r a c t e r i s t i c and l e n e t h and t h e u s e of l i q u i d s w i t h h i g h P r a n d t l number.
-
-( P r e f f e c t was n o t c o n s i d e r e d i n p r e v i o u s s t u d i e s u s i n g ( 8 a i r . )
Some d i f f e r e n c e s o b s e r v e d between t h e c o r r e l a t i o n of t h e l a b o r a t o r y r e s u l t s and t h e f u l l - s c a l e r e s u l t s were a t t r i b u t e d t o d i f f e r e n t c o n v e c t i o n p a t t e r n s t h a t might have developed due t o d i f f e r e n c e s i n
c o n f i g u r a t i o n and boundary c o n d i t i o n s .
E q u a t i o n ( 8 ) was s u b s e q u e n t l y u s e d by ~ a l c o m b l ~ and Balcomb and yamaguchi16 t o produce a f o r m u l a t h a t c a n b e u s e d a s a d e s i g n a i d f o r d e t e r m i n i n g t h e n e c e s s a r y d o o r s i z e f o r p a r t i c u l a r i n t e r - z o n e and i n s i d e - o u t s i d e t e m p e r a t u r e d i f f e r e n c e s u n d e r s t e a d y s t a t e c o n d i t i o n s . That i s From d e t a i l e d s i m u l a t i o n s of a d i r e c t - g a i n h o u s e , Balcomb concluded t h a t AT p r e d i c t e d by E q u a t i o n
(9)
i s q u i t e c l o s e t o t h e a v e r a g e room-to-room AT f o r c a s e s of m o d e r a t e t e m p e r a t u r e swings i n t h e s o u t h zone ( a b o u t 4 K). However, t h e e q u a t i o n t e n d s t o o v e r p r e d i c t t h e a v e r a g e AT f o r l a r g e t e m p e r a t u r e swings. R e c e n t l y , e x t e n s i v e work i n t h e g e n e r a l a r e a of c o n v e c t i v e h e a t t r a n s f e r i n b u i l d i n g s was r e p o r t e d by i n v e s t i g a t o r s a t t h e Lawrence B e r k e l e y L a b o r a t o r y . T h e i r work r e l e v a n t t o i n t e r - z o n e c o n v e c t i o n i s summarized below. I n 1979, G a d g i l 1 7 d e v e l o p e d a n u m e r i c a l code f o r modeling n a t u r a l c o n v e c t i o n i n r e c t a n g u l a r e n c l o s u r e s a t R a y l e i g h numbers, RaL, u p t o 1 0 l 0 . He p r e s e n t e d a l i m i t e d comparison between t h e n u m e r i c a l s o l u t i o n and a c t u a l measurements produced by ~ u b e r ~ l ~ f o r t h e c a s e of c o n v e c t i o n from a h e a t e d f l o o r .Bauman e t a 1 l 9 performed n a t u r a l c o n v e c t i o n e x p e r i m e n t s i n a s m a l l model (L = 31 cm, H = 17 cm, B = 84 cm) s i m i l a r i n c o n f i g u r a t i o n t o t h e one u s e d by Weber. The model was, however, b u i l t t o a p p r o x i m a t e 2-dimensional f l o w and u t i l i z e s w a t e r t o a c h i e v e h i g h Ra. T h e i r l i m i t e d d a t a on t h e two-zone c o n f i g u r a t i o n i n d i c a t e d t h e e x p e c t e d b e h a v i o u r of d e c r e a s i n g
c o n v e c t i v e h e a t t r a n s f e r r a t e s w i t h d e c r e a s i n g opening h e i g h t . I n t h e i r p r e s e n t a t i o n t h e e n c l o s u r e l e n g t h , L, and t h e t e m p e r a t u r e d i f f e r e n c e between t h e h o t and c o l d s u r f a c e s were u s e d i n c a l c u l a t i n g t h e Nu and Ra. The c h o i c e of L a s a c h a r a c t e r i s t i c l e n g t h was n o t d i s c u s s e d . The h e i g h t of t h e v e r t i c a l h o t and c o l d s u r f a c e s would b e e x p e c t e d t o be t h e dimension most r e l e v a n t t o t h e buoyancy-induced f l o w i n t h i s e n c l o s u r e geometry. N a n s t e e l and G r e i f Z O c a r r i e d o u t e x p e r i m e n t s i n a s m a l l 2-D e n c l o s u r e ( s i m i l a r t o t h e one d e s c r i b e d above) w i t h w a t e r ( 3
<
P r<
4.3) a t R a y l e i g h numbers o v e r t h e range 2.3x101°<
Ra<
1 . l x l O l l ( e n c l o s u r e l e n g t h ) and a p e r t u r e r a t i o s A-
D/H) of 1 , 314, 112, P -and 114. Two p a r t i t i o n w a l l m a t e r i a l s were u s e d , t h e r m a l l y c o n d u c t i n g and non-conducting. Flow v i s u a l i z a t i o n s were a l s o performed. The r e s u l t s were c o r r e l a t e d u s i n g t h e f o l l o w i n g r e l a t i o n s h i p s : The f l o w v i s u a l i z a t i o n e x p e r i m e n t s r e v e a l e d t h e e x i s t e n c e of t h r e e r e l a t i v e l y d i s t i n c t r e g i o n s a t RaL a p p r o x i m a t i n g 1 0 l l . As shown i n F i g u r e 2 , t h e y a r e : a n i n a c t i v e c o r e r e g i o n ; a r e g i o n of weak c i r c u l a t i o n i n t h e u p p e r c o r n e r on t h e warm s i d e of t h e p a r t i t i o n ; and a p e r i p h e r a l boundary l a y e r flow. The p r e s e n c e of t h e p a r t i t i o n was found t o markedly s u p p r e s s t h e l a m i n a r - t u r b u l e n t t r a n s i t i o n on t h e e n c l o s u r e v e r t i c a l s u r f a c e s t o t h e e x t e n t t h a t t u r b u l e n t f l o w d i d n o t e x i s t anywhere w i t h i n t h e e n c l o s u r e f o r RaL up t o 1011. The a u t h o r s p o i n t e d o u t t h e d i f f e r e n c e between t h e exponent of A i n E q u a t i o n ( 1 0 ) and t h a t f o u n d f o r d a t a produced i n a P s i m i l a r s t u d y by DuxburyZ1 f o r e n c l o s u r e s w i t h c o n d u c t i n g p a r t i t i o n s . F o r t h e l a t t e r , a n e x p o n e n t of 0.41 was o b t a i n e d f o r a i r a t RaL i n t h e r a n g e of l o 6 and A = 518. N a n s t e e l and G r e i f q u e s t i o n e d t h e Duxgury f i n d i n g b e c a u s e of e r r o r s t h a t might h a v e o c c u r r e d i n h i s r e s u l t s due t o t h e l a r g e h e a t l o s s from h i s t e s t c e l l ( 1 5 t o 40%). I n a n e x t e n s i o n t o t h e i r work, N a n s t e e l and
rei if^^
c a r r i e d o u t s i m i l a r e x p e r i m e n t s u s i n g s i l i c o n o i l (620<
P r<
920) o v e r t h e range 1 . 5 5 ~ 1 0 ~<
RaL<
5 . 8 6 ~ 1 0 ~ and u s i n g a low c o n d u c t i v i t y p a r t i t i o n . The f o l l o w i n g c o r r e l a t i o n was developed:The d i f f e r e n c e between t h e a p e r t u r e r a t i o dependence i n E q u a t i o n s ( 1 1 ) and ( 1 2 ) was a t t r i b u t e d p a r t i a l l y t o t h e d i f f e r e n c e i n P r a n d t l number b u t m a i n l y t o t h e d i f f e r e n c e s i n t h e c o n d u c t a n c e of t h e p a r t i t i o n . They o b s e r v e d a r e d u c t i o n i n r e c i r c u l a t i o n s t r e n g t h i n t h e upper warm q u a d r a n t of t h e e n c l o s u r e a s t h e p a r t i t i o n c o n d u c t a n c e d e c r e a s e d c a u s i n g reduced c o n v e c t i o n a d j a c e n t t o t h e u p p e r p a r t of t h e h o t w a l l . They c o n c l u d e d t h a t i n s u l a t i n g p a r t i t i o n s r e p r e s e n t a n A K CLOCKWISE C I R C U L A T I O N F i g u r e 2. Flow a t t e r n o b s e r v e d by N a n s t e e l and GreifJlo f o r 1 0 l 0
<
RaL<
1011i n c r e a s e d r e s i s t a n c e t o t h e h e a t t r a n s f e r between t h e h o t and c o l d z o n e s w i t h a g r e a t e r r e s u l t i n g s e n s i t i v i t y t o t h e a p e r t u r e r a t i o .
I n a f u r t h e r development, N a n s t e e l and
c re if^^
examined t h e l o c a t i o n of t h e p a r t i t i o n on t h ei n t e r - z o n e h e a t t r a n s f e r . They a l s o e x t e n d e d t h e work t o cover 3-dimensional c a s e s by d i v i d i n g t h e e n c l o s u r e i n t o two zones u s i n g a v e r t i c a l p a r t i t i o n w i t h a s i n g l e opening a t t h e c e n t r e . The o p e n i n g w i d t h was
m a i n t a i n e d c o n s t a n t a t 0.093 of t h e e n c l o s u r e wi-Tth, w h i l e t h e h e i g h t was v a r i e d between 114, 112, 314, and 1 of t h e e n c l o s u r e h e i h t . Measurements were c a r r i e d o v e r t h e r a n g e 2 . 4 ~ 1 0 1 1
<
RaL<
1 . 1 ~ 1 0 ~ ~ u s i n g w a t e r (3.0<
P r<
4.3). N a n s t e e l and G r e i f found t h a t t h e b a s i c f l o w p a t t e r n o b s e r v e d i n t h e c e n t r a l l y - d i v i d e d 2-D e n c l o s u r e p e r s i s t s f o r o t h e r p a r t i t i o n l o c a t i o n s i n t h e r a n g e examined ( p a r t i t i o n l o c a t i o n s , x/L, between 0.25 and 0.75). S i m i l a r l y , t h e t e m p e r a t u r e f i e l d remained q u a l i t a t i v e l y t h e same. The i n t e r - z o n e h e a t t r a n s f e r was shown t o depend o n l y s l i g h t l y on t h e p a r t i t i o n l o c a t i o n .The f l o w p a t t e r n i n t h e 3-D e n c l o s u r e ( w i t h D
<
H), however, was found t o be very d i f f e r e n t from t h a t i n t h e 2-D c a s e . F o r t h e 3-D c o n f i g u r a t i o n , t h e f l o w a t t h e e n c l o s u r e mid p l a n e , W/2, r e s e m b l e d t h e f l o w i n t h e 2-D c a s e o n l y when D/H = 1 ( n o s o f f i t ) . The p r e s e n c e of a s o f f i t had a s u b s t a n t i a l e f f e c t i n t h e 3-D c a s e , c a u s i n g r e g i o n s of l o c a l i z e d t u r b u l e n c e , i n s t a b i l i t y , boundary l a y e r s e p a r a t i o n and r e a t t a c h e m e n t , and a h i g h d e g r e e of R a y l e i g h number dependence. The h e a t t r a n s f e r r a t e was c o r r e l a t e d u s i n g t h e e q u a t i o n L i t t l e d i f f e r e n c e was o b s e r v e d i n t h e h e a t t r a n s f e r between t h e 2-D r e s u l t s from t h e i r e a r l i e r work ( E q u a t i o n ( 1 I ) ) , and t h e 3-D r e s u l t s ( E q u a t i o n ( 1 3 ) ) f o r t h e same opening h e i g h t . T h i s o b s e r v a t i o n i s s u r p r i s i n g b e c a u s e of t h e s u b s t a n t . i a 1 d i f f e r e n c e s between t h e two f l o w a t t e r n s .I n a r e p o r t by Bauman e t a12' summarizing r e c e n t LBL work, t h e a u t h o r s u s e d a method s i m i l a r t o t h a t d e v e l o p e d by C h u r c h i l l and ~ s at o a d j u s t t h e h e a t ~ i ~ ~ t r a n s f e r e q u a t i o n s t o c o n d i t i o n s i n a i r ( P r = 0 . 7 ) . They a l s o r e f o r m a t t e d t h e r e s u l t s and p r e s e n t e d them i n t e r m s of GrH and NuH. The i n t e r - z o n 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 n W/m K was g i v e n a s f o r t h e 2-D c a s e , where H i s i n m e t r e s and AT i s i n K e l v i n , and f o r t h e 3-D c a s e . I n b o t h c a s e s AT was b a s e d on t h e s u r f a c e t e m p e r a t u r e s of t h e v e r t i c a l end w a l l s ( h o t and c o l d ) and c a l c u l a t e d a s The a u t h o r s i n d i c a t e d t t , f o r s i m p l i c i t y , a n a d d i t i o n a l f a c t o r of ( ~ / H ) o ' ~ ' , c a l c u l a t e d f o r H = 2.74 m, was a b s o r b e d i n t o t h e c o n s t a n t s of E q u a t i o n s ( 1 4 ) and ( 1 5 ) . T h i s c a u s e s a s m a l l e r r o r ( l e s s t h a n 5 % ) when t h e s e e q u a t i o n s a r e a p p l i e d f o r room h e i g h t s between 2 and 4 m. Taking t h i s f a c t o r i n t o c o n s i d e r a t i o n , t h e c o r r e l a t i o n ( i n d i m e n s i o n l e s s form and f o r a i r ) t a k e s t h e form
where t h e e x p o n e n t ' a ' h a s t h e v a l u e of 0.47 and 0.25 f o r 2-D and 3-D c a s e s , r e s p e c t i v e l y . It s h o u l d b e noted t h a t E q u a t i o n s ( 1 4 ) and ( 1 5 ) e x h i b i t a d i f f e r e n t f u n c t i o n a l dependence of h on t h e t e m p e r a t u r e d i f f e r e n . ? compared t o E q u a t i o n s ( 3 ) . ( 7 ) and ( 8 ) . T h i s i s du- t o t h e u s e of s u r f a c e t e m p e r a t u r e s (and n o t room a i r t e m p e r a t u r e s ) i n d e v e l o p i n g t h e co!.-elation. While t h e s u r f a c e t e m p e r a t u r e s may be e a s i e r t o measure e x p e r i m e n t a l l y , t h e y a r e n o t w e l l d e f i n e d o r a v a i l a b l e i n most r e a l s i t u a t i o n s . Room a i r t e m p e r a t u r e , however, i s more p r a c t i c a l t o u s e f o r d e s i g n a s w e l l a s e n e r g y a n a l y s i s p u r p o s e s . For t h i s r e a s o n , c o r r e l a t i o n s s u c h a s t h o s e of E q u a t i o n s (14) and (15) may n o t be d i r e c t l y u s e f u l .
I n a most r e c e n t development yamaguchiP6
e x p e r i m e n t a l l y examined t h e e f f e c t s of a p e r t u r e h e i g h t , w i d t h and v e r t i c a l p o s i t i o n on t h e i n t e r - z o n e n a t u r a l c o n v e c t i v e h e a t t r a n s f e r . He u s e d a o n e - f i f t h s i m i l i t u d e model of a two-room b u i l d i n g , f i l l e d w i t h F r e o n , s i m i l a r t o t h a t u s e d by weber.14 F o r t h e s e v e n d i f f e r e n t a p e r t u r e c o n f i g u r a t i o n s u s e d , t h e r e s u l t i n g h e a t t r a n s f e r c o r r e l a t i o n was found t o be g e n e r a l l y c o n s i s t a n t w i t h p r e v i o u s work by Brown and ~ o l v a s o n ' and by Weber and ~ e a r n e ~ . l 4 The c o e f f i c i e n t of E q u a t i o n ( 1 ) was r e p o r t e d t o r a n g e between 0.l.9 and 0.21 depending on t h e a p e r t u r e c o n f i g u r a t i o n . The a v e r a g e t e m p e r a t u r e s 15 cm away from t h e v e r t i c a l h o t and c o l d s u r f a c e s were used t o produce t h e c o r r e l a t i o n . Yarnaguchi r e p o r t e d , however, t h a t t h e r e s u l t s were much a f f e c t e d by t h e d e f i n i t i o n of t h e t e m p e r a t u r e
d i f f e r e n c e .
Summary of P r e v i o u s R e s u l t s
The work d e s c r i b e d above on i n t e r - z o n e c o n v e c t i v e h e a t t r a n s f e r i s summarized i n T a b l e 1. The main c o n c l u s i o n s a r e :
1. It i s a p p a r e n t , b o t h from t h e o r y and e x p e r i m e n t s , t h a t t h e h e a t t r a n s f e r a c r o s s o p e n i n g s i n p a r t i t i o n s between two zones a t d i f f e r e n t
t e m p e r a t u r e s c a n be e x p r e s s e d by a c o r r e l a t i o n of t h e g e n e r a l form
Nu = c o n s t .
~r~
p r C ( 1 7 ) 2. The e x p e r i m e n t a l r e s u l t s i n d i c a t e t h a t , f o ri n t e r - z o n e c o n v e c t i o n i n b u i l d i n g s (where a i r i s t h e t r a n s f e r medium) and when t h e o p e n i n g h e i g h t , D , i s used a s t h e c h a r a c t e r i s t i c l e n g t h i n b o t h Nu and G r , t h e dependence of 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 on A d i s a p p e a r s and E q u a t i o n ( 1 7 ) r e d u c e s t o P
3. The v a l u e of t h e c o e f f i c i e n t C and t h e exponent b depend on t h e c h o i c e of t h e t e m p e r a t u r e d i f f e r e n c e . When AT i s t a k e n a s t h e d i f f e r e n c e between t h e a v e r a g e room a i r t e m p e r a t u r e s , C i s i n t h e range 0.22 t o 0.33 and t h e exponent b i s a b o u t 0.5. There was a l s o some i n d i c a t i o n t h a t t h e v a l u e of C may b e a f u n c t i o n of t h e magnitude of AT.
4. A l l p r e v i o u s r e s u l t s i n d i c a t e l i t t l e e f f e c t of opening w i d t h on 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 . Even w i t h t h e l a r g e d i f f e r e n c e s o b s e r v e d i n f l o w p a t t e r n s between t h e 2-D and 3-D c a s e s ( a f u l l w i d t h o p e n i n g and a s t a n d a r d doorway, r e s p e c t i v e l y ) t h e r e were s u r p r i s i n g l y small o b s e r v e d d i f f e r e n c e s i n h e a t t r a n s f e r c o e f f i c i e n t s .
TABLE 1 Summary of I n t e r - Z o n e N a t u r a l C o n v e c t i v e Heat T r a n s f e r i n B u i l d i n g s 5. T h e r e i s an i n d i c a t i o n t h a t p a r t i t i o n t h i c k n e s s h a s some e f f e c t on 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 f o r s m a l l opening s i z e s a s g i v e n by E q u a t i o n s ( 2 ) and ( 3 ) . No e x p e r i m e n t a l e v i d e n c e e x i s t s t o c o n f i r m s u c h c o r r e l a t i o n s f o r l a r g e r ( d o o r s i z e ) openings. 6. There i s some i n d i c a t i o n t h a t t h e n a t u r a l c o n v e c t i v e h e a t t r a n s f e r c o e f f i c i e n t i s a f f e c t e d by t h e p a r t i t i o n conductance. T h i s e f f e c t , however, was o b s e r v e d f o r 2-D c a s e s w i t h h i g h P r a n d t l number f l u i d s and was n o t t e s t e d f o r o t h e r c a s e s w i t h p a r a m e t e r r a n g e s s i m i l a r t o t h o s e i n r e a l b u i l d i n g s . 7. P r e s e n t i n t e r - z o n e c o n v e c t i v e h e a t t r a n s f e r c o r r e l a t i o n s a r e l i m i t e d t o t h e boundary c o n d i t i o n u s e d i n t h e e x p e r i m e n t s and a r e n o t t e s t e d f o r o t h e r boundary c o n d i t i o n s . There is a l a r g e number of boundary c o n d i t i o n s and b u i l d i n g c o n f i g u r a t i o n s p o t e n t i a l l y of i n t e r e s t ; f o r example, a two-zone c o n f i g u r a t i o n w i t h a warm f l o o r i n one of t h e zones, a c o n d i t i o n t h a t o c c u r s i n d i r e c t g a i n b u i l d i n g s . I n g e n e r a l , t h e e x t e n t t o which e x i s t i n g c o r r e l a t i o n s c a n be a p p l i e d t o o t h e r c o n f i g u r a t i o n s i s unknown.
8. Most of t h e r e c e n t e x p e r i m e n t s were performed i n s m a l l - s c a l e t e s t e n c l o s u r e s u t i l i z i n g f l u i d s o t h e r t h a n a i r a n d , i n some c a s e s , w i t h o u t f u l l hydrodynamic s i m i l a r i t y . F u r t h e r , l i t t l e c o n f i r m a t i o n of t h e h e a t t r a n s f e r c o r r e l a t i o n s was produced u s i n g d a t a from f u l l - s c a l e b u i l d i n g s u n d e r v a r i o u s boundary c o n d i t i o n s .
9. Very few s t u d i e s examined i n t e r - z o n e h e a t t r a n s f e r u n d e r combined n a t u r a l and f o r c e d c o n v e c t i o n s i t u a t i o n s . Forced c o n v e c t i o n i n a b u i l d i n g c o u l d be g e n e r a t e d by f o r c e d v e n t i l a t i o n o r u n b a l a n c e s i n t h e f o r c e d a i r h e a t i n g and v e n t i l a t i o n s y s t e m s . L i m i t e d Comparison Between N a t u r a l C o n v e c t i o n C o r r e l a t i o n s The i n t e r - z o n e h e a t f l o w c a l c u l a t e d u s i n g p r e v i o u s - - - - ~- - -c o r r e l a t i o n s i n t h e form of E q u a t i o n ( 1 8 ) a r e -compared t o e a c h o t h e r a s w e l l a s t o t h e r e s u l t s of a t e s t o b t a i n e d i n a f u l l - s i z e b u i l d i n g . The c o r r e l a t i o n d e v e l o p e d by N a n s t e e l ( E q u a t i o n ( 1 5 ) ) i s e x c l u d e d s i n c e i t i s b a s e d on s u r f a c e t e m p e r a t u r e d i f f e r e n c e s and d o e s n o t r e l a t e t o t h e c o n f i g u r a t i o n examined. E x p e r i m e n t a l r e s u l t s were o b t a i n e d i n a two-zone t e s t u n i t of t h e p a s s i v e s o l a r t e s t f a c i l i t y a t t h e D i v i s i o n o f . B u i l d i n R e s e a r c h , N a t i o n a l R e s e a r c h C o u n c i l of C a n a d a . ~ ~ The u n i t c o n s i s t s of two rooms 3 . 0 5 ~ 4 . 5 8 ~ 2 . 4 4 m e a c h , c o n n e c t e d by a 0 . 8 ~ 2 . 0 3 m doorway i n t h e i n s u l a t e d p a r t i t i o n s e p a r a t i n g t h e rooms. S i n c e t h e h e a t l o s s c h a r a c t e r i s t i c s of t h e s e rooms were d e t e r m i n e d p r e v i o u s l y , 2 8 i t i s p o s s i b l e , by p e r f o r m i n g a s t e a d y - s t a t e h e a t b a l a n c e f o r e a c h room, t o c a l c u l a t e t h e amount of h e a t t r a n s f e r r e d t h r o u g h t h e doorway by c o n v e c t i o n and r a d i a t i o n a s
where q h and q c a r e t h e h e a t i n g power consumption i n t h e warm and c o l d rooms, r e s p e c t i v e l y , and To i s t h e o u t d o o r t e m p e r a t u r e .
The c o n v e c t i v e h e a t f l o w r a t e c a n t h e n be
c a l c u l a t e d by s u b t r a c t i n g t h e r a d i a t i v e component, qr. Assuming t h a t b o t h room c a v i t i e s behave l i k e b l a c k b o d i e s , t h e r a d i a t i o n h e a t t r a n s f e r t h r o u g h t h e doorway i s c a l c u l a t e d a s
To a p p r o x i m a t e a s t e a d y - s t a t e c o n d i t i o n , a p e r i o d of 6 h o u r s was chosen d u r i n g a n i g h t when t h e o u t d o o r t e m p e r a t u r e remained f a i r l y c o n s t a n t a t a b o u t O . S 0 C . A l l windows were s h a d e d b e f o r e and d u r i n g t h e t e s t p e r i o d t o e l i m i n a t e t h e dynamic e f f e c t a s s o c i a t e d w i t h t h e s t o r a g e of eolar e n e r g y i n t h e room. Rooms were k e p t a t 21.6-C and 20.1'6 (50.1
K).
M u l t i - p o i n t a v e r a g i n g t h e r m o p i l e s , w i t h s e n s o r s p l a c e d a t room mid-height, were u s e d f o r t e m p e r a t u r e c o n t r o l a n d measurement. Under t h e c o n d i t i o n s d e s c r i b e d above, t h e t o t a l h e a t f l o w r a t e t h r o u g h t h e doorway ( c a l c u l a t e d f r o m E q u a t i o n ( 1 9 ) ) was 322 w a t t s ('10 W), of which 14 w a t t s was e s t i m a t e d t o b e due t o r a d i a t i o n . The c o n v e c t i v e h e a t t r a n s f e r r a t e o b t a i n e d from measurements i s compared w i t h t h a t p r e d i c t e d by c o r r e l a t i o n s i n T a b l e 2. Values i n t h e t a b l e c o r r e s p o n d t o G r D = 1 . 9 ~ 1 0 ~ and P r = 0.7. Although v e r y l i m i t e d , t h e comparison i n d i c a t e s t h a t c o r r e l a t i o n s i n t h e form of E q u a t i o n ( 1 ) would p r e d i c t t h e i n t e r - z o n e n a t u r a l c o n v e c t i v e h e a t t r a n s f e r r a t e p r o v i d e d t h a t t h e t e m p e r a t u r e d i f f e r e n c e i s p r o p e r l y d e f i n e d and t h e c o r r e s p o n d i n g c o e f f i c i e n t C i s d e t e r m i n e d . I t s h o u l d be n o t e d t h a t the t e m p e r a t u r e d i f f e r e n c e used t o a r r i v e a t t h e e x p e r i m e n t a l v a l u e was t h e d i f f e r e n c e between t h e a v e r a g e r i d - h e i g h t room a i r t e m p e r a t u r e s . T h i s does not c o r r e s p o n d t o a n y of t h e t e m p e r a t u r e d i f f e r e n c e s used i n t h e c o r r e l a t i o n s . FUTURE RESEARCH REQUIREMENTSA d d i t i o n a l r e s e a r c h
is
needed b e f o r e r e l i a b l e c o n v e c t i o n c o r r e l a t i o n s and d e s i g n g u i d e l i n e s c a n b e made a v a i l a b l e t o t h e b u i l d i n g d e s i g n e r o r energy a n a l y s t . T h i s work s h o u l d c o v e r : 1. Examination o f t h e a p p l i c a b i l i t y o f r e c e n t l y developed c o r r e l a t i o n s t o f u l l - s c a l e c o n d i t i o n si n
a c t u a l buildings. A l s o m o d i f y i n g t h e c o r r s l a t i o n e , i f needed, t o accommodate t e m p e r a t u r e d i f f e r e n c e s t h e t can be r e a d i l y measured o r c a l c u l a t e d and a r e t h e r e f o r e of p r a c t i c a l s i g n i f f c a n c e t o d e s i g n e r s .C o r r e l a t i o n
N a t u r a l c o n v e c t i v e r a t e , w a t t s Brown e t a l , E q u a t i o n ( 3 ) 318
Shaw and Whyte, E q u a t i o n ( 1 8 ) (C = 0.27, b = 0.5) J e b e r and Kearney, E q u a t i o n ( 8 ) (C = 0.3, b = 0.5) Sxperimental v a l u e 308 TABLE 2 Comparison of N a t u r a l C o n v e c t i v e Heat T r a n s f e r R a t e s
2 . Examination of a wide v a r i e t y of two-zone
c o n f i g u r a t i o n s and boundary c o n d i t i o n s t o t e s t t h e g e n e r a l i t y of t h e c o r r e l a t i o n s o r d e v e l o p more g e n e r a l c o r r e l a t i o n s f o r zone c o u p l i n g . 3. S t u d y of i n t e r - z o n e c o n v e c t i o n u n d e r combined n a t u r a l and f o r c e d c o n v e c t i o n s i t u a t i o n s . F o r example, t h e i n t e r a c t i o n between n a t u r a l c o n v e c t i o n , due t o t e m p e r a t u r e d i f f e r e n c e s between s p a c e s , and f o r c e d v e n t i l a t i o n o r a i r d i s t r i b u t i o n i n t h e b u i l d i n g . 4. Examination of t h e e f f e c t of p a r t i t i o n t h i c k n e s s and conductance on i n t e r - z o n e c o n v e c t i v e h e a t t r a n s f e r w i t h l a r g e o p e n i n g s i z e s f o r c a s e s w h e r e t h e y may have s i g n i f i c a n t impact; f o r example, n a t u r a l c o n v e c t i o n between a s u n s p a c e and t h e p a r e n t b u i l d i n g t h r o u g h m u l t i p l e openings. 5. Study of t h e e f f e c t of t h e P r a n d t l number on 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 t o e n a b l e f u t u r e u s e of s m a l l e x p e r i m e n t a l models u n d e r s i m i l a r c o n d i t i o n s . 6. I m p l e m e n t a t i o n of d e v e l o p e d c o r r e l a t i o n s i n e n e r g y a n a l y s i s programs and a s s e s s i n g t h e a b i l i t y of t h e improved models t o p r e d i c t e n e r g y consumption and i n d o o r t e m p e r a t u r e s i n multi-zone b u i l d i n g s . SUMMARY A review of p r e v i o u s r e s e a r c h work on i n t e r - z o n e c o n v e c t i v e h e a t t r a n s f e r i s p r e s e n t e d . The p u r e n a t u r a l c o n v e c t i o n c a s e h a s r e c e i v e d t h e most a t t e n t i o n compared t o o t h e r c a s e s of n a t u r a l c o n v e c t i o n combined w i t h f o r c e d a i r movement between t h e s p a c e s . P r e v i o u s work h a s p o i n t e d o u t t h e s i g n i f i c a n t magnitude of t h e n a t u r a l c o n v e c t i v e h e a t f l o w t h r o u g h i n t e r - z o n e o p e n i n g s . I t i n d i c a t e d t h a t f o r t h i s c a s e , t h e h e a t t r a n s f e r c a n be c o r r e l a t e d by a n e q u a t i o n of t h e f o r m
where b i s a p p r o x i m a t e l y 0.5 and C l i e s between 0.22 and 0.33 depending on t h e t e m p e r a t u r e d i f f e r e n c e u s e d f o r t h e c o r r e l a t i o n . Work i s s t i l l needed t o d e f i n e t h e most a p p r o p r i a t e t e m p e r a t u r e d i f f e r e n c e and t o d e t e r m i n e t h e a s s o c i a t e d v a l u e o f t h e c o e f f i c i e n t C. A need f o r a d d i t i o n a l work i s i d e n t i f i e d t o d e v e l o p h e a t t r a n s f e r c o r r e l a t i o n s f o r o t h e r multi-zone c o n f i g u r a t i o n s and boundary c o n d i t i o n s , a s w e l l a s f o r c o n d i t i o n s of mixed n a t u r a l and f o r c e d c o n v e c t i o n . The r e s e a r c h s h o u l d l e a d t o methods and c o r r e l a t i o n s t h a t c a n b e u s e d by t h e b u i l d i n g d e s i g n e r and e n e r g y a n a l y s t t o e n a b l e them t o t a k e t h i s s i g n i f i c a n t h e a t t r a n s f e r component i n t o a c c o u n t . ACKNOWLEDGEMENTS T h i s p a p e r i s a c o n t r i b u t i o n from t h e D i v i s i o n of B u i l d i n g R e s e a r c h , N a t i o n a l R e s e a r c h C o u n c i l Canada. REFERENCES 1. O s t r a c h , S., " N a t u r a l Convection i n E n c l o s u r e s " , Advances i n Heat T r a n s f e r , Vol. 8 , pp. 161-227, Academic P r e s s , New York, 1972.
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27. B a r a k a t , S.A., "NRCC P a s s i v e S o l a r T e s t F a c i l i t y : D e s c r i p t i o n and Data R e d u c t i o n " , B u i l d i n g R e s e a r c h Note No. 214, D i v i s i o n of B u i l d i n g R e s e a r c h , N a t i o n a l R e s e a r c h C o u n c i l o f Canada, Ottawa, 1984. 28. B a r a k a t , S.A., "NRCC P a s s i v e S o l a r T e s t F a c i l i t y : Performance of D i r e c t Gain U n i t s " , B u i l d i n g R e s e a r c h Note No. 215, D i v i s i o n of B u i l d i n g R e s e a r c h , N a t i o n a l R e s e a r c h C o u n c i l of Canada, Ottawa, 1984. reprinted from
Heat Transfer in Buildings and Structures
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