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Buildin9 and Environment, Vol. 29, No. 3, pp. 291-296, 1994Elsevier Science LtdPergamon Printed in Great Britain0360-1323/94 $7.00 + 0.000360-1323(94)E0029-Q

Ev aluat ion o f V ent i la t ion Perform ance forIndoor SpaceT O S H I A K I Y A M A M O T O *D A V I D S . E N S O R *L E S L I E E . S P A R K S t

Ventilation performance depends on room geometry, ventilation method, and operating conditionsas well as location and strength o f the source and types o f contaminants. A personal computerbased application of computational fluid dynamics was developed that is capable of determining theturbulent flo w ie ld and time-dependent/steady-state contaminant concentration distributions withinisothermal indoor space. The compu tational speed is extremely fast. The flo w field ca lculated fro mthis 2-D k -e turbulence model showed goo d agreement w ith results fro m the commercially availableF L U E N T code. Vent i lat ion performance was evaluated using the "vent ilation performance index."Effe cts o f room configurations, operating con ditions, and effective diffusion coefficient (or Pecletnumber) on ventilation performance were investigated.

I N T R O D U C T I O NI N C R E A S E D a w a r en e s s o f th e p o t e n t ia l h e a lt h r is k sa s s o c i a t e d w i th i n d o o r a i r p o l l u t a n t s h a s s t i m u l a t e d i n t e r -e s t in i m p r o v i n g o u r k n o w l e d g e o f h o w v e n t i l a ti o n a i r i sd i s t r i b u t e d a n d t r a n s p o r t e d i n i n d o o r s p a c e . I n t h e l a s ts e v e ra l y e a r s , c o m p u t a t i o n a l f l ui d d y n a m i c s ( C F D ) h a sb e e n a p p l i e d t o p r e d i c t i n g a ir f lo w a n d c o n t a m i n a n t d i s -p e r s i o n i n t h e i n d o o r e n v i r o n m e n t . T h i s i s a v e r y c h a l -l e n g in g a p p l i c a t i o n o f C F D b e c a u s e o f t h e c o m p l e x i t ie so f f u r n i t u r e ; je t s n e a r v e n t i l a ti o n d u c t s ; t h e t h e r m a lb u o y a n c y e f f e ct ; a n d p e r t u r b a t i o n s d u e t o u t i l i t ie s , f a n s ,a n d h u m a n a c t iv i ti e s.

I n p r a c t i c e , p o o r v e n t i l a ti o n a n d i n a d e q u a t e d e s i g n inf a c i l it i e s w i t h s i c k b u i l d i n g s y n d r o m e a r e w e l l d o c u -m e n t e d b y J o n e s [ 1 ] . T h e r e f o r e , a n e e d e x i s t s f o r p r a c -t i c i n g e n g i n e e r s t o h a v e a c c e s s to c o m p u t a t i o n a l t o o l s t od e m o n s t r a t e t h e m a j o r f e a t u r e s o f a ir f lo w a n d c o n -t a m i n a n t m o v e m e n t i n a r o o m .

C o m m e r c i a l l y a v a i la b l e , p u b l i c d o m a i n , a n d r e s e a rc hC F D s o f t w a r e u s i n g a w i d e r a n g e o f c o m p u t e r s i n c l u d i n gs u p e r c o m p u t e r s h a s b e e n a p p l i e d t o m o d e l i n d o o r a i rf lo w [ 2 - 5 ] . H o w e v e r , s t a t e - o f - t h e - a rt C F D i s v e r yc o m p l e x , t a k e s f r o m h o u r s t o d a y s t o r u n , i s v e r y e x p e n -s i v e, is n o t u s e r f r i e n d l y , a n d i s n o t a c c e s s i b l e t o m a n ye n g i n ee r s . U s u a l l y C F D s p e c ia l is t s m u s t r u n t h e C F Dm o d e l a n d i n t e r p r e t t h e r e s u l t s . I n a d d i t i o n , g i v e n t h ec o m p l e x i t y o f m a n y p r o b l e m s o f i n te r e s t, e v e n t h e m o s ts o p h i s t i c a t e d a p p r o a c h w i l l q u i t e l i k e l y b e v i e w e d a s a ni n a d e q u a t e a p p r o x i m a t i o n t o t h e a c t u a l s i tu a t i o n .

* Center f or A erosol Technology, Research Triangle Institute,P.O. B ox 12194, Research Triangle Pa rk, N C 27709, U.S.A.t A ir and Energy Engineering Research L aborato ry , U .S.Environmental P rotectio n Agency, Research Triangle Park , NC27711, U.S.A.291

O u r c o n c e p t i s to d e v e l o p a p r a c t i c a l a n d s i m p l e 2 - Da i r f lo w m o d e l t h a t c a n e a s il y a n d q u i c k l y b e u s e d o nw i d e l y a v a i la b l e p e r s o n a l c o m p u t e r s ( P C s ). E n g i n e e r sc o u l d t h e n u s e t h e s o f t w a r e t o c o m p u t e a r a n g e o f s ce n -a r i o s w i t h t h e p u r p o s e o f i d e n t if y i n g r e g i o n s o f p o o rv e n t i l a t i o n a n d s e l e c ti n g t h e b e s t l o c a t i o n s f o r v e n t i l a t i o nd u c t s .

T h e c e n t r a l t h r u s t o f t h e s o f t w a r e d e v e l o p m e n t i s t op r o v i d e c o m p u t a t i o n a l r e s u lt s w i t h in a f ew m i n u t e s s ot h a t a n e n g i n e e r c a n e v a l u a t e a n u m b e r o f c a s es i n o n es e s s io n . T h e c o m p r o m i s e s o f a 2 - D r a t h e r t h a n a 3 - Dg e o m e t r y , t h e n e g le c t o f th e r m a l b u o y a n c y , a n i m p r o v e da l g o r i t h m , a n d u s e o f a c o a r s e g r i d w e r e r e q u ir e d f o r af a s t s o l u t i o n t i m e . T h e s e l i m i t a t i o n s a r e b e l i e v e d t o b ec o n s i s t e n t w i t h t h e o b j e c t i v e s o f t h e e f f o r t . T h e a b i l i t y t ov i s u al i ze g r o s s a ir f lo w a n d c o n t a m i n a n t d i s t r i b u t i o n a n dt h e c o m p u t a t i o n o f a n i n t e g r a t e d v e n t i l a t io n i n d e x a sa n i n d i c a t o r o f e x p o s u r e s h o u l d b e u s e f u l to p r a c t i c in ge n g i n e e r s i n e v a l u a t i o n o f s e v e r a l d i f f e r e n t d e s i g n s .T h e r e a r e t r a d e o f f s b e t w e e n c o m p u t a t i o n a l a c c u r a c ya n d c o m p u t a t i o n a l s p e e d . B y m a k i n g s o m e c o m p r o m i s e sw i t h r e s p e c t t o t h e d e t a i l o f t h e c o m p u t a t i o n s , i t w a sp o s s i b le t o e n s u r e c o m p u t a t i o n a l a c c u r a c y w i t h in t h ec a p a c i t y o f P C s a n d y e t s t il l b e a b l e t o p r e d i c t t h e g e n e r a lb e h a v i o r o f c o n t a m i n a n t d i s p e r s i o n i n a r o o m a n d e v a l u -a t e t h e v e n t i l a t io n p e r f o r m a n c e .

W e d e v e l o p e d a u s e r f r i en d l y v e n t i la t i o n m o d e l s o l v e ra s a C F D t o o l f o r e n g i n ee r s w h o d o n o t h a v e k n o w l e d g eo f C F D . T h e s o f t w a r e a ll o w s o p e r a t in g a n d r o o m c o n -f i g u r a t i o n s t o b e c h a n g e d e a s i l y a n d p r o v i d e s a r a p i da n a l y s i s ( a f e w m i n u t e s i n c o m p u t a t i o n a l t i m e ) w i t hg r a p h i c a l o u t p u t s , i n c l u d i n g v e l o c i t y v e c t o r s , c o n t o u r so f s t r e a m l i n e s , k i n e t i c e n e r g y , d i s s i p a t i o n r a t e , e f f e c ti v ed i f f u s i o n c o e f f i c i e n t , a n d t i m e - d e p e n d e n t c o n c e n t r a t i o np r o f i l e s . A l s o , t h e c o n c e n t r a t i o n h i s t o r y , i t s p l a y b a c k ,l o c a l v e n t i la t i o n , a v e ra g e c o n t a m i n a n t c o n c e n t r a t i o n a t

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2 9 2 T . ) ~ # n a m o t o e t a l .

t h e b r e a t h i n g z o n e , a n d t h e v e n t i l a t i o n p e r f o r m a n c e o ft h e r o o m c a n b e e v a l u a t e d u s i n g t h e v e n t i l a t i o n p e r -f o r m a n c e i n d e x , w h i c h i s d e fi n e d l a t e r i n t h i s a r t i c le .

S e v e r a l c o n c e p t s i m p o r t a n t t o d e f i n i n g v e n t i l a t io n p e r -f o r m a n c e h a v e b e e n d i s c u s s e d i n t h e l i te r a t u r e . S a n d b e r ga n d S j o b e r g [ 6] i n t r o d u c e d t h e i d e a o f u s in g t h e " a g e - o f -a i r " i n a r o o m ( i. e. l o c a l - m e a n a g e - o f - a i r a n d r o o m -a v e r a g e a g e - o f - a i r ) t o e v a l u a t e v e n t i l a t i o n p e r f o r m a n c e .S e p p a n e n [ 7] d i s c u s s e d t h e v e n t i l a t i o n e f f ic i en c y u s in g a i r -e x c h a n g e e f fi c ie n c y a n d p o l l u t a n t r e m o v a l e f f e c ti v e n es s .K a t o e l a L [8] d i s cus sed t he s ca l e o f ven t i l a t i on e f f i c i ency .Y a m a m o t o e t a l . [ 9] p r o p o s e d t h r e e s c a l e s c a l l e d " v e n -t i l a t i o n p e r f o r m a n c e i n d i c e s " t h a t c o n s i s t o f : ( 1 ) a v e r a g ec o n t a m i n a n t c o n c e n t r a t i o n o r d e c a y r a t e , ( 2 ) a v e ra g ec o n t a m i n a n t d i f f u s i o n c o e f f ic i e n t, a n d ( 3 ) a v e r a g e c o n -t a m i n a n t c o n c e n t r a t i o n o r d e c a y r a t e a t t h e b r e a t h in glevel .

T h e t h r e e v e n t il a t i o n p e r f o r m a n c e i n d ic e s ( V P l s ) p r o -p o s e d b y Y a m a m o t o e t a l . [ 9] h a v e b e e n s h o w n t o p r o v i d es i m i l a r tr e n d s f o r a w i d e r a n g e o f p r a c t i c a l c as e s , l e a d i n gu s t o c o n c l u d e t h a t o n e V P I i s su f f ic i en t t o desc r i be ven -t i l a ti o n p e r f o r m a n c e . V P I i s d e s c r i b e d a s t h e a v e r a g ec o n t a m i n a n t c o n c e n t r a t i o n e v a l u a t e d a t t = r ,C~,,.~(t = z), c o m p a r e d w i t h th e c o n c e n t r a t i o n w i t h a p e r -f e c t m i x i n g a s s u m p t i o n a t t = z ( n o w a l l a b s o r p t i o na s s u m e d ) , C ~ , , ( t = r ) , a n d i s n o w c o n v e n i e n t l y d e f i n e d a sV P I = C e , ,( t = z ) / C , v ~ ( t = ~ ) . The h ighe r t he V P I , th eb e t t e r t h e v e n t i l a t i o n p e r f o r m a n c e . V P I i s s im i l a r t o t he" a g e - o f - a i r " c o n c e p t b u t r e q u i r e s a f i n i t e t i m e s c a l e ( r)t o e v a l u a t e v e n t i l a t i o n e f fe c t iv e n e s s.

I n t h i s s t u d y , t o d e m o n s t r a t e t h e a p p l i c a t i o n o f t h es o f t w a r e , w e s e le c t e d a s i m p l e r o o m c o n f i g u r a t i o n a n di n v e s t i g a t e d t h e e ff e c ts o f th e r o o m c o n f i g u r a t i o n , o p e r a -t i n g c o n d i t i o n s , a n d e f fe c t iv e d if f u s i o n t u r b u l e n c ec o e f f i c i e n t ( o r P e c l e t n u m b e r , d e f i n e d b e l o w ) o n v e n -t i l a t i o n p e r f o r m a n c e . I n a c t u a l a p p l i c a t i o n , a n e n g i n e e rc o u l d u s e a r o o m c o n f i g u r a t i o n o f in t e r e s t .

V E N T I L A T I O N E F F E C T I V E N E S S M O D E LN u m e r i c a l s c h e m e

T y p i c a l r o o m a i r f l o w is l o c a l l y t u r b u l e n t , t r a n s i t i o n a l ,o r f u l ly tu r b u l e n t . H o w e v e r , v e r y f ew r o o m a i r f lo w s a r el a m i n a r . T h e r e f o r e , i t i s a p p r o p r i a t e t o u s e a s t a n d a r d k -e, m o d e l . T h e d e v e l o p m e n t o f t h e P C - b a s e d m o d e l w a si n i t i a t e d w i t h t h e 2 - D s t a n d a r d k - e , t u r b u l e n c e f o r -m u l a t i o n u n d e r i s o t h e r m a l c o n d i t i o n s w h i c h w a s d e r i v e db y i n t r o d u c i n g a g r a d i e n t - d i f f u s i o n a n d a n e d d y v i s c o s i tyh y p o t h e s i s . I t i s n e c e s s a r y t o m o d e l t h e R e y n o l d s s t r e s st e r m i n t h e f u n c t i o n a l f o r m . T h e R e y n o l d s s t r e s s m o d e lp r o b a b l y p r o v i d e s t h e o p t i m u m l ev e l o f c l o s u re i n t e r m so f p h y s i c a l i n t e r p r e t a t i o n a n d h a s t h e p o t e n t i a l t o b eg e n e r a l l y a p p l i c a b l e t o a w i d e r a n g e o f fl o w s .

T o r e d u c e c o m p u t a t i o n a l t i m e , t h e N a v i e r - S t o k e se q u a t i o n s a n d R e y n o l d s s t r e ss e q u a t i o n s c a n b e e x p r e s s e di n t h e f o r m o f a v o r t i c i t y - s t r e a m f u n c t i o n , w h i c h r e q u i r e so n l y f o u r f u n d a m e n t a l e q u a t i o n s : a c o n t i n u i t y e q u a t i o n ,a v o r t i c i t y e q u a t i o n , a k i n e t i c e n e r g y e q u a t i o n , a n d a ne n e r g y d i s s i p a ti o n r a t e e q u a t i o n . T h e v a r i a b l e s a re n o n -d i m e n s i o n a l i z ed a s :

~?v* ~u* ~B W~* _ _ _ q , , = _ _8 x * B y * U

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E v a l u a t io n o f V e n t i la t io n P e r f o r m a n c e 2 9 3

O Cat

w h e r eC =G =

Deer =

a x \ O y }/ a c \ a a c+ (7 )

n o n - d i m e n s i o n a l i z e d p a r t i c l e c o n c e n t r a t i o nn o n - d i m e n s i o n a l i z e d p a r t i c l e g e n e r a t i o n r a t eI / ( R e S c ) + vitro = n o n - d i m e n s i o n a l i z e d e f f ec t iv et u r b u l e n t d i f f u s i o n c o e f fi c i e n t

D~+fr = (Uo B) De rf = d i m e n s i o n a l e ff e c ti v e t u r b u l e n t d i f -fu s ion coe f f i c i en t (m 2 /s )

v, = tr,k2/e = n o n - d i m e n s i o n a l i z e d t u r b u l e n t k i n e t ice n e r g y

S c = v /D = S c h m i d t n u m b e r .tr,. = 0.9 .

V a r i o u s b o u n d a r y c o n d i t i o n s w e r e p r o p o s e d t oi m p r o v e n u m e r i c a l a c c u r ac y . A l t h o u g h t h e u s e o f a f in e rm e s h , e s p e c i a l l y n e a r t h e w a l l , w h e r e t h e s t e e p e s t g r a d i e n to f v e l o c i t ie s ex i st s , im p r o v e s t h e c o m p u t a t i o n a l a c c u r a c y ,c o m p u t a t i o n a l t i m e b e c o m e s e x c e s s iv e f o r m o s t c a s e s .T h e r e f o r e , s t a n d a r d b o u n d a r y c o n d i t i o n s w e r e u se d f o rt h i s s i m u l a t i o n : n o n s l i p b o u n d a r y c o n d i t i o n s a l o n g t h es o l i d w a l l , u n i f o r m f l o w a l o n g t h e f l o w i n l e t , p a r a l l e l f l o wa t f lo w , a n d z e r o c o n t a m i n a n t g r a d i e n t a l o n g t h e w a l l.Us e r f r i e nd l y mode l

A m e n u - d r i v e n v e n t i l a ti o n m o d e l d i s p l a y s t h e c h o i c e so f r o o m c o n f i g u r a t io n s a n d o p e r a t i n g p a r a m e t e r s , p e r -m i t t i n g t h e u s e r t o c o n t r o l t h e f l ow o f t h e p r o g r a m . C o m -p u t a t i o n a l t i m e i s v e ry s h o r t ( 1 - 2 m i n u t e s w i t h a 4 8 6 / 50p e r s o n a l c o m p u t e r ) f o r a g r i d m e s h o f 2 5 x 21 a n d a g r i dcel l s ize of 15.24 x 15.24 cm (6 x 6 in . ) .

W h e n e v a l u a t i n g v e n t i l a t io n p e r f o r m a n c e o f a r o o m ,a p o i n t s o u r c e c a n n o t b e u s e d b e c a u s e v e n t i l a ti o n p e r -f o r m a n c e o f a r o o m d e p e n d s o n t h e f lo w f ie l d a n dl o c a t i o n o f t h e s o u r c e . O n e w a y t o e v a l u a t e v e n t il a t i o np e r f o r m a n c e i s t o a s s u m e t h a t t h e r o o m g e n e r a te s c o n -t i n u o u s c o n t a m i n a n t u n i f o r m l y t h r o u g h o u t t h e r o o m .T h e s t e a d y - s t a te c o n c e n t r a t i o n p r o f i l e a n d v e n t i l a ti o np e r f o r m a n c e c a n b e o b t a i n e d [ 9] . T h e o t h e r w a y i s t oa s s u m e t h a t t h e r o o m i s i n i ti a l ly u n i f o r m l y c o n t a m i n a t e da n d n o o t h e r s o u r c e i s p r e s e n t t h e r e a f t e r . I n a d d i t i o n , n op a r t i c l e s a r e a s s u m e d t o a b s o r b i n t o t h e w a l l s . T h e t i m e -d e p e n d e n t c o n c e n t r a t i o n a n d v e n t i l at i o n p e r f o r m a n c ec a n t h e n b e c o m p u t e d . W e s e l e c t e d t h e l a t t e r c a s e . F o rt h e c a s e o f th e 2 - D v e n t i l a t i o n m o d e l , t h e c h a r a c t e r i s t i ct i m e c o n s t a n t u s e d w a s r = W H / B U o .

M o s t i n d o o r e n v i r o n m e n t s a r e n o t p e r f e c t ly m i xe d .T h e r e f o r e , i t i s i m p o r t a n t t o u n d e r s t a n d t h e s p a c i a l d i s -t r i b u t i o n o f t h e d e g r e e o f m i x i n g in t h e r o o m . T h e c o n -t a m i n a n t d i f f u s i o n c o e ff i c ie n t c o n s i s t s o f t h e d i f f u s i o n d u et o B r o w n i a n m o t i o n ( D ) , w h i c h is a f u n c t io n o f p a r t i c l es i z e o r t y p e o f g a s e s , a n d t h e d i f f u s i o n d u e t o t u r b u l e n tk i n e t i c e n e r g y ( D , = vj~rc), w h i c h i s a f u n c t io n o f r o o mc o n f i g u r a t io n a n d t u r b u l e n t i n t e n s i ty a t t h e s u p p l y d u c t .Thu s , t he e f f ec t i ve t u rb u l e n t d i f fu s ion coe f f i c i en t (D ~+fr) sa s u m m a t i o n o f t h o s e t w o [ D { f r - - - D + D , o r

De~ = 1 / ( Re S c ) + v , / a~ ] a n d r e p r e s e n t s a i r m i x i n g . T h eeff ec t o f D~+ffo n v e n t i l a t i o n p e r fo r m a n c e c a n b e e v a l u a t e db y t h e n o n - d i m e n s i o n a l p a r a m e t e r , t h e P e c le t n u m b e r( P c ) , g i v e n b y P e = BUo/D~+ff = 1~D eft.

T o d e m o n s t r a t e t h e u t i l it y o f t h e a p p r o a c h , t h e f o l-l o w i n g r o o m c o n f i g u r a t io n a n d d i m e n s i o n s w e r e s e le c -ted : W = 3 .66 m (12 f t ) , H = 3 .05 m (10 f t ) , B = 0 .61 m(2 f t) , and T = 0 .61 m (2 f t) . The d im ens ion o f i n l e to f f s e t , A , w as va r i ed a s 0 . 30 m (1 ft ) f o r t he l e f t en t ry(LE ) , 1 . 52 m (5 f t ) f o r t he cen t e r en t ry (C E) , an d 2 . 74 m( 9 f t ) f o r t h e r i g h t e n t r y ( R E ) , a s s h o w n i n F i g . 1 . T oe v a l u a t e t h e e f f e ct o f a i r e x c h a n g e r a t e , w e v a r i e d i n f lo wv e l o c i t y (Uo) t o hav e t he va lues 0 .05 m / s (10 f t /m in ) , 0 .15m /s (30 f t /m in ) , and 0 . 25 m / s (50 f t /m in ) .

N U M E R I C A L R E S U L T S A N D D I S C U S S IO NF i g u r e 2 s h o w s t h e t i m e - a v e r a g e d v e l o c i ty v e c t o r s i n a

r o o m w h e n a s u p p l y d u c t i s a t t h e c e n t e r ( a ) , le f t ( b ) , a n dr igh t ( c ) . I n a l l f i gu re s , Uo = 0 . 15 m / s (30 f t /m in ) . Thec e n t e r e n t r y s h o w s t w o l a r g e r e c i r c u l a t i o n z o n e s , o n e o ne a c h s i d e o f t h e m a i n a i r f lo w p a t h w h e r e t h e p o o r m i x i n go r v e n t i l a t i o n o c c u r s . T h e l e f t e n t r y s h o w s o n e m a j o rr e c i rc u l a t io n a t t h e u p p e r c e n t e r o f t h e r o o m . T h e a i rm o t i o n i n t h e u p p e r r i g h t s e c t i o n i s r a t h e r s m a l l , i n d i -c a t i n g p o o r m i x i n g o r v e n t i l a ti o n z o n es . W h e n t h e s u p p l ya i r d u c t i s a t t h e r i g h t s i d e, a l a r g e p o r t i o n o f t h e r o o mi s o c c u p i e d w i t h f l o w r e c i r c u l a t i o n a n d t h e m a j o r f l o wa c t i v i t y is s h i f te d r i g h t . T h i s f l o w b y p a s s c a u s e s t h e l a r g ea r e a o f p o o r m i x i n g z o n e , r e s u lt i n g in t h e p o o r e s t v e n t i -l a t i o n . T h e n o r m a l i z e d a i r f l o w d i s t r i b u t i o n s f o rUo = 0 . 05 m / s (10 f t /m in ) and Uo = 0 . 25 m / s (50 f t /m in )w e r e a l m o s t i d e n t i c a l.I n o r d e r t o v a l i d a t e th e d e v e l o p e d m o d e l , a i r f lo w d i s -t r i b u t io n s i n a s i m p l e i n d o o r s p a c e w e r e c o m p a r e d w i t ht h e r e s u l ts o b t a i n e d f r o m t h e c o m m e r c i a l l y a v a i la b l eF L U E N T c o d e u s in g a F u ji t su ( S U N ) -4 / 3 30 G X P w o r ks t a ti o n , T h e c o m p u t a t i o n a l r e s u l ts f o r b o t h c a s e s a p p e a rt o a g r e e r e a s o n a b l y w e l l [ 11 ]. H o w e v e r , t h e c o m p u t a t i o nt i m e f o r t h i s n e w l y d e v e l o p e d m o d e l w a s a t l e a s t o n eo r d e r o f m a g n i t u d e l es s t h a n t h e t im e r e q u i r e d t o r u n t h eF L U E N T c o d e u s i n g t h e s a m e c o n v e r si o n c ri t e ri a .

W h e n t h e r o o m i s i n i ti a l ly u n i f o r m l y c o n t a m i n a t e da n d t h e f r e s h a i r i s i n t r o d u c e d a t t h e s u p p l y d u c t , t h et i m e - d e p e n d e n t c o n c e n t r a t i o n p r o f il e a n d v e n t i l a ti o n p e r -f o r m a n c e a r e e v a l u a t e d u s i n g VP1 = Cp, ,( t = r ) /C avo(t = Z) . W he n U o = 0 . 05 m / s , t he co nce n t r a t i on h i s -

W

Fig, 1. Room outline and variables.T

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2 9 4 T . Y a m a m o t o e t a l .

(a )

4 4 4 ~ e ~4 4 4 4 ~ t

= ~ . 4 4 4 ~ 1

I

. . . . . : : - . \ -

(b )

( c )

44 ~p4

X

I

I

Fig . 2 . T ime-averaged ve loc i ty vectors in a room for U, , = 0 .15m / s (30 f t /min ) . ( a ) C en ter en try ; (b) l e f t en try : (c) right entry.

t o r y u p t o t = 2 . 5 ~ i s a s s h o w n i n F i g . 3 a f o r t h e c e n t e re n t r y , F i g . 3 b f o r t h e le f t e n t r y , a n d F i g . 3 c f o r t h e r i g h te n t r y . T h e p a r t i c l e d i f fu s i o n c o e f f ic i e n t w a s a s s u m e d t ob e D = 0 . 6 8 4 x 1 0 - 9 m 2 / s f o r a l l c a s e s t h a t c o r r e s p o n d t o0 . 1 - p m p a r t i cl e s . T h e t i m e c o n s t a n t i s v = 6 . 0 m i n f o r t h isc a s e . H e r e , C , ve i s t h e a v e r a g e c o n t a m i n a n t c o n c e n t r a t i o ni n t h e r o o m , C ~ b i s t h e a v e r a g e c o n t a m i n a n t a t th eb r e a t h i n g l e v e l b e t w e e n 1 . 0 5 a n d 1 .8 m ( 3 . 5 a n d 6 . 0 f t )f r o m t h e f l o o r , Cp, , i s th e c o n c e n t r a t i o n c o m p u t e d w i t ht h e a s s u m p t i o n o f p e r f e c t m i x i n g , a n d C ~ 0, ( 53 0 , a n d C s0a r e th e f r a c t i o n s o f t h e c o n c e n t r a t i o n l e s s t h a n 1 0 , 3 0 ,a n d 5 0 % o f t h e in i t i a l c o n c e n t r a t i o n , r e s p e c t i v e ly . N o t et h a t C ~ ve b i s l o w e r t h a n C a ~ f o r a l l c a s e s . T h e b e s t v e n -

1( a )

I 0 . 8 '0 . 6~ 0 . 4 "~ 0 . 2

; c p m", , c a v e

~ ' ' l l . . . 1

" n i n e ( r n in )(b ) '

r r n e ( ra n )(c) I

. . . . . . . . . . . . . . . .

o ~ ~ ~ ~ 1 '2l in w ( m i n )Fig . 3 . C on ce n tra t ion h i s tory for Uo = 0 .05 m/s (10 f t /min ) . ( a )Center e ntry ; (b) lef t entry ; (c) right entry.

t i l a t io n p e r f o r m a n c e a c h i e v e d w a s f o r t h e l e f t e n t r y( D ,+ ff = 0 . 4 0 9 x 1 0 3 m 2 / s , P e = 7 6 , a n d V P I = 0 . 9 8 5 ) ,f o l l o w e d b y t h e c e n t e r e n t r y ( D ~+ , = 0 . 3 1 9 x 1 0 - 3 m 2 / s ,P e = 9 7 , a n d V P I = 0 . 6 4 4 ) , a n d t h e r i g h t e n t r y (D ~+ fr= 0 . 2 2 6 x 1 0 - 3 m 2 / s , P e = 1 3 7 , a n d V P I = 0 . 4 9 5 ) . T h e

h i g h e r v e n t i l a t i o n p e r f o r m a n c e i s a c h i e v e d w i t h i n c r e a s e dV P L D ~ , o r P e , i n d i c a t in g t h a t o n l y o n e p e r f o r m a n c ep a r a m e t e r , V P I , i s a d e q u a t e i n s t e a d o f t h e t h r e e V P I sp r o p o s e d e a r l i e r [ 9 ] .

I n t h e i n i ti a l s t a g e o f v e n t i l a t i o n , t h e c o n t a m i n a n td e c a y r a t e ( o r s l o p e ) f o r C a vo s s i g n i f i c a n t l y h i g h e r t h a nt h a t f o r C p , , f o r a l l t h r e e c a s e s . C , v ,g s t a y s a t 1 . 0 u n t i l t h ef r e s h a i r a r r i v e s a t t h e b r e a t h i n g z o n e a n d f a s t e r z o n ec l e a r i n g f o l l o w s . C av ~ b e c o m e s t h e s a m e a s C p , , at t = z /2( 3 r a in ) f o r t h e c e n t e r e n t r y , t = r ( 6 m i n ) f o r t h e l e f te n t r y , a n d t = ~ / 4 ( 1 . 5 m i n ) f o r t h e r i g h t e n t r y . T h e n , C , v ee x c e e d s Cp, , b e y o n d t h e s e t i m e s . T h e r e a r e t w o d i s t i n c ts l o p e s f o r C ~ v a n d C , v, b: t h e i n i t i a l s t e e p s l o p e ( f a s te rc l e a r i n g ) a n d t h e s e c o n d g r a d u a l s l o p e ( s l o w e r c l e a r in g ) .T h i s i n d i c a t e s t h a t t h e v e n t i l a t i o n i s e x t r e m e l y e f f e c t i v ei n i t i a l l y b u t e f f e c t i v e n e s s i s s i g n i f i c a n t l y r e d u c e d i n t h el a t e r s ta g e . T h e s a m e t r e n d i s s h o w n f o r C l o , C 3 o , a n d C s 0.T h e w o r s t v e n t i l a t i o n w a s f o r t h e r i g h t e n t r y , w h e r e t h e

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E v a lu a t io n o f V e n t il a t io n P e r fo rm a n c e 2 9 5s e c o n d ( g r a d u a l ) s l o p e w a s 0 . 00 7 9 m i n - t a f t e r 1 . 5 m i n ,i n d i c a t i n g n o e f fe c t iv e v e n t i l a t i o n . T h e v e n t i l a t i o n a t t h el e ft s i d e o f t h e r o o m w a s c o n t r i b u t e d b y D ~+ff, w h i c hi m p l i es t h a t t h e r o o m c o n f i g u r a t i o n is n o t a d e q u a t e .

F i g u r e 4 a s h o w s c o n c e n t r a t i o n c o n t o u r s a t t = z = 6m i n f o r t h e c e n t e r e n t r y w h e n Uo = 0 . 0 5 m / s . T h e c o n -t a m i n a n t c o n c e n t r a t i o n i s h i g h e r o n t h e u p p e r l ef t a n dr i g h t s i d es o f th e r o o m . P l a c i n g t h e s u p p l y a i r d u c t a t t h el e ft s id e o f t h e r o o m c r ea t es t h e c o n t a m i n a n t c o n -c e n t r a t i o n d i s t r i b u t i o n s a t t = z s h o w n i n F i g . 4 b . T h ea v e r a g e c o n t a m i n a n t c o n c e n t r a t i o n i s s ig n i fi c a n tl yi m p r o v e d . S h o w n i n F i g . 4 c i s t h e c o n t a m i n a n t d i s -

(a )

(b)

( c )

Fig. 4. Con cen trat io n profile at t = z for Uo= 0.05 m/s (10ft /min). (a) Cente r entry ; (b) left entry ; (c) r ight entry.

t r i b u t i o n a t t = z f o r t h e r i g h t e n t r y . T h e a v e r a g e c o n -c e n t r a t i o n i s t h e w o r s t a m o n g t h e t h r e e c a s e s b e c a u s e al a rg e f r a c t i o n o f t h e r o o m i s u n m i x e d d u e t o f l ow b y p a s s .

A t a h i g h e r v e l o c i t y , Uo = 0 . 2 5 m / s ( 5 0 f t / m i n ) , t h ec o n c e n t r a t i o n h i s t o r y is as s h o w n i n F i g . 5 a f o r c e n t e re n t r y a n d F i g . 5 b f o r l e f t e n t ry . A l l t h e r e s t o f t h e p a r -a m e t e r s a r e t h e s a m e a s i n t h e e a r l i e r c a s e. T h e t i m ec o n s t a n t f o r t h i s c a s e i s z = 1 .2 ra i n . T h e c o n c e n t r a t i o nh i s t o r y f o r a l l c a s e s i s a l m o s t t h e s a m e ( s e e F i g . 3 ) ,a l t h o u g h t h e t i m e s c a l e i s c h a n g e d . T h e b e s t v e n t i l a t i o np e r f o r m a n c e a c h i e v e d i s a g a i n f o r t h e l e f t e n t r y( V P I = 0 .974) wh ere De~r i s the h igh es t (D~+fr= 0 .2 0 3 x 1 0 - 2 m 2 / s ) o r P e i s t h e l o w e s t ( P e = 7 6 ) . T h e

w o r s t p e r f o r m a n c e i s f o r t h e r i g h t e n t r y ( V P I = 0 .4 9 4 )wh ere De~r i s the low es t (D~+rr - - -0 .114x 10 -2 m ~/s ) o rP e = 1 35 . T a b l e 1 s u m m a r i z e s t h e v a l u e s o f Cave(t = Z),C a v c b ( / = T ) , O + f f , P e , th e s e c o n d s l op e ( m i n - l ) , a n d V P If o r Uo = 0 .0 5 , 0 .1 5 , a n d 0 .2 5 m / s .

T a b l e 1 i n d i c a t e s t h a t V I I b e c o m e s s l i g h t l y h i g h e r a sUo b e c o m e s s m a l l e r , p r o b a b l y d u e t o h i g h e r t u r b u l e n td i f f u s i o n i n t h e r o o m . T h e s e c o n d s l o p e d i v i d e d b y Uob e c o m e s c o n s t a n t , i n d i c a t in g t h a t t h e v e n t i l a t i o n p e r-f o r m a n c e i s s o l e l y a f u n c t i o n o f D ~+ffo r P e w h e n t h e r o o ml a y o u t a n d o p e r a t i n g c o n d i t i o n s a r e s et . T h e v a l u e o fD~+fr o r P e c a n b e d e t e r m i n e d b y t h e t u r b u l e n t i n t e n s i t ya t t h e f l o w i n l e t .

F i g u r e 6 i l l u s t r a t e s t h e e f f e c t o f D ~+rf o n c o n c e n t r a t i o nh i s t o r y f o r t h e c e n t e r e n t r y f o r Uo = 0.05 m/s. D~+f~v a r y -i n g f r o m 1 0 6 t o 1 0 - 9 m 2 /s d o e s n o t m a k e a p p r e c i a b l ed i ff e r en c e . H o w e v e r , t h e i n c r e a s e o f t u r b u l e n c e t o D e af= 10 -3 m2/s ( P e = 3 2 ) a n d 2 .0 1 0 - 3 m 2 / s ( t h e l a t t e r i s

h i g h l y t u r b u l e n t ) p r o d u c e s a s i g n i f i c a n t e f fe c t o n t h e c o n -c e n t r a t i o n h i s t o r y .

I n s u m m a r y , t h is u s e r f r ie n d l y, P C b a s e d C F D v e n -t i l a t i o n e ff e c ti v e n es s m o d e l w a s d e m o n s t r a t e d u s i n g a

(a)o.1~

O ~ '0 ~ 6 1 '.2 1 '.8 d 4" r ~ ( rn~ )( b ) 1

I 0 . 8 -0 . 6 -~

.4-02- '

~ ' 1 / ", ro~ o'.e f~ I' .8 2'.4Vlmo r~)Fig. 5. Conce ntrat io n history for Uo = 0.25 m/s (50 f t /min). (a)Cen ter entry ; (b) left entry.

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29 6 T . Y a m a m o t o et al.

Table 1. Summary of C~vo(t = O, Caw~(t = 3) , D~r , Pc, slope, and VP 1 for U,, = 0.05, 0.15, and 0.25 m/sC~,~(t= v) C~,v~(t = r) D~I (me/s) Pe Slope (rain I) V P I

U,, = 0.05 m/s (z = 6.0 min)LE 0.373 0.257 0.409 x l0 ~ 76 0.0090 0.985CE 0.571 0.517 0.319 x l0 3 97 0.0135 0.644RE 0.743 0.747 0.226 x 10 3 137 0.0079 0.495U,, = 0.15 m/s (z = 2.0 min)LE 0.378 0.262 0.122 x 10 : 76 0.0265 0.974CE 0.572 0.519 0.958 x l0 3 97 0.0402 0.643RE 0.744 0.749 0.683 x 10 3 135 0.0234 0.495U,, = 0.25 m/s (3 = 1.2 rain)LE 0.378 0.263 0.203 x 10 2 76 0.0441 0.974CE 0.573 0.520 0.160x 10 2 97 0.0669 0.642RE 0.744 0.749 0.114 x 10 2 135 0.0389 0.494

i0 .8

r ' ~ ( r r ~ )Fig. 6. The effect of DA on concen tration history for the centerentry when Uo = 0.05 m/s (10 ft/min ).

simple indoor case. The ventilation model provides notonly a detailed flow field and contaminant distribution,but also a ventilation strategy. The ventilation per-formance is uniquely defined using V P I a n d only becomesa function of Pe once the room c onfiguration and op era-ting conditions are given. Incorpora tion of thermal buoy-ancy effects and draftiness into the model will be our nextstep.

Acknowledgment--This work was supported by the U.S.Environmental Prot ection Agency under cooperative agreementCR817083-01-0.

R E F E R E N C E S1. D. J. Jones, Room air distribution and vent ilation effectiveness in air conditi oned offices, in Pro-

ceedings o f lndoor A i r '90, Volume 4, pp. 133-138 (1990).2. H.B. Awbi, Application of computatio nal fluid dynamics in room ventilation. B ui ld ing and Envi ron-m e n t 2 4 , 73-84 (1989).3. Q. Chen and Z. Jiang, Significant questions in predicting room air motion. A S H R A E T r an s ac ti o ns :S y m p o s i a AN-92-9-1,929-939 (1992).4. J. W. Weathers and J. D. Spitler, A comparative study of room airflow : numerical prediction usingcomputatio nal fluid dynamics and full-scale experimental measurements.A S H R A E T r an s ac ti o ns 3705(1993).5. P. V. Nielsen and P. Heiselberg, P r o c e ed i n y s o f R O O M V E N T ' 9 2 - - A i r D i st r ib u t io n in R o o m s , 3 r dInternational Conference, Volumes 1-3, Aalborg, Denm ark (1992).6. M. Sandberg and M. Sjoberg, The use of moments for assessing air quality in a ventilated room.B ui ld in9 and Envi ronm e nt lg, 181-197 (1983).7. O. Seppanen, Ventilation efficiency in practice, in P r o c e ed i n g s o f l A Q '86, pp. 559-567 (1986).8. S. Kato, S. Murakami and H. Kobayashi, New scales for evaluating venti lation efficiency as affectedby supply and exhaust opening based on spacial distributio n of contaminant, in Int . Syrup. on RoomAir Convection and Vent i la t ion E f fec t i venes s , pp. 321-332, University of Tokyo (22-24 July 1992).9. T. Yamamoto, D. S. Enso r and L. E. Sparks, Evalua tion of venti lation effectiveness using an IAQmodel, in P r o c e ed i n g s o f R O O M V E N T ' 9 2 - - A i r D i s t r ib u t io n i n R o o m s , 3 r d In t e r n a ti o n a l C o n fe re n ce ,Volume 1, pp. 437-446, Aalborg, Denmark (1992).10. B.E. Laun der and D. B. Spaulding, The numerical computa tion of turbulent flows. C o m p u t e r M e t h o d sin Appl i ed Mech anica l Engineer in 9 3, 269-289 (1974).11. T. Yamamoto, D. S. Ensor, L. E. Sparks, M. Inokuchi, M. Koganei and Z. Li, Ventilation model:comparison of PC and work station, in Proceedings o f I ndoor A i r Q ual i t y , Vent i la t ion and EnergyConservat ion, The 5th Intern ationa l Jacq ues Cart ier ConJbrence, pp. 326-333, Montreal, Canada (7 -9 October 1992).