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Theoretical study of cooling load caused by lights
Kimura, K.; Stephenson, D. G.
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TH1 N21r2 no.394
c . 2 NATIONAL R E S E A R C H C O U N C I L O F CANADA C O N S E I L NATIONAL D E R E C H E R C H E S DU CANADA J 3 ; j $.\;-
v;;
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QT H E O R E T I C A L STUDY O F COOLING LOAD CAUSED BY L I G H T S
-
by K . Kimura a n d D.G. S t e p h e n s o n R e p r i n t e d from ASHRAE T R A N S A C T I O N S Vol. 7 4 , P a r t 11, 1 9 6 8 p. 189-197-
LIBRARY
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R e s e a r c h P a p e r No. 3 9 4 of 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 OTTAWA F e b r u a r y , 1 9 6 9 P r i c e 25 c e n t s NRC 1 0 6 3 0,(.--
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NATIONAL RESEARCH COUNCIL O F CANADA 'DIVISION O F BUILDING R E S E M C H
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" T h e o r e t i c a l Study of Cooling Load C a u s e d by L i g h t s " by K. K i m u r a a n d D. G. S t e p h e n s o n ( N R C 10630) F i g u r e 5
-
l a s t n u m b e r on o r d i n a t e s c a l e s h o u l d be 0. 7 5 . AppendixI
-
l a s t p a r a g r a p h should r e a d : T h e v a l u e s of r e s p o n s e f a c t o r s f o r f u r t h e r s t e p s of j which a r e n o t t a - b u l a t e d c a n b e obtained by nzultiply- ing t h e c o m m o n r a t i o by t h e r e s p e c - t i v e v a l u e s a t t h e s t e p j-
1 s u c c e s s i v e l yNo.
2087
D. G. STEPHENSON
Theoretical Study of Cooling Load
Caused by Lights
I
T h e m a j o r c o m p o n e n t of h e a t g a i n in t h e i n t e r i o r z o n e s of modern b u i l d i n g s i s t h e p o w e r s u p p l i e d t o t h e l i g h t s . A l t h o u g h t h i s e l e c t r i c a l e n e r g y i s a l l c o n v e r t e d t o h e a t , a l l t h e h e a t d o e s n o t a p p e a r im- m e d i a t e l y a s c o o l i n g l o a d . S o m e of t h e h e a t from t h e l i g h t s i s s t o r e d by t h e s t r u c t u r e , p a r t i c u l a r l y i n t h e floor s l a b , a n d o n l y c o n t r i b u t e s t o t h e s p a c e c o o l i n g l o a d a f t e r t h e l i g h t s a r e s w i t c h e d off. T h i s h e a t s t o r a g e e f f e c t s h o u l d b e t a k e n i n t o a c c o u n t in t h e c a l c u l a t i o n of c o o l i n g l o a d . S t o r a g e f a c t o r s h a v e b e e n p u b l i s h e d 1 for e x p o s e d a n d r e c e s s e d l i g h t f i x t u r e s , but t h e r e i s n o t h i n g in t h e l i t e r a t u r e t o s u p p o r t t h e s e d a t a . T h e c a l c u l a - t i o n s r e p o r t e d in t h i s p a p e r w e r e m a d e , i n t h e f i r s t i n s t a n c e , t o c h e c k t h e p u b l i s h e d d a t a . T h e y h a v e b e e n e x t e n d e d t o d e t e r m i n e t h e s e n s i t i v i t y of t h e s t o r a g e f a c t o r s t o c h a n g e s i n 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 s a t t h e room s u r f a c e s , t h e t h e r m a l c h a r a c t e r - i s t i c s of t h e f l o o r - c e i l i n g a r r a n g e m e n t , t h e propor- t i o n of t h e i n p u t p o w e r t h a t i s i n i t i a l l y t r a n s f e r r e d from t h e f i x t u r e t o t h e s p a c e a b o v e t h e c e i l i n g , a n d v e n t i l a t i o n of t h e c e i l i n g c a v i t y . T h i s t h e o r e t i c a l s t u d y of t h e s e n s i t i v i t y of t h e s t o r a g e f a c t o r s in- K . K i m u r a i s a P o s t D o c t o r a l F e l l o w , D i v i s i o n o f B u i l d i n g Research, 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, o n l e a v e f r o m t h e D e p a r t m e n t 0.f A r c h i t e c t u r e , Waseda U n i v e r s i t y , T o k y o , Japan. D. G. S t e p h e n s o n i s a R e s e a r c h O f f i c e r , B u i l d i n g S e r v i c e s Section, D i v i s i o n o f B u i l d i n g Research, 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, O t t a w a . T h i s paper i s o c o n t r i - b u t i o n from t h e D i v i s i o n o f B u i l d i n g Research, 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, and i s p u b l i s h e d w i t h t h e a p - ~ r o v a l of t h e D i r e c t o r o f the D i v i s i o n . T h i s paper was p r e p a r e d for p r e s e n t a t i o n a t t h e A S H R A E A n n u a l Meeting, L a k e P l a c i d , N e w York, J u n e 24 - 2 6 , 1968. d i c a t e s t h e n e e d for a d d i t i o n a l e x p e r i m e n t a l work. I t a l s o s h o w s h o w t h e e x p e r i m e n t a l r e s u l t s c a n b e a n a l y z e d t o o b t a i n t h e v a l u e s of t h e i m p o r t a n t p a r a m e t e r s . M E T H O D O F C A L C U L A T I N G C O O L I N G L O A D C o o l i n g l o a d s h a v e b e e n c a l c u l a t e d for f l u o r e s c e n t f i x t u r e s r e c e s s e d i n t o a s u s p e n d e d c e i l i n g a s s h o w n in F i g . 1. I t w a s a s s u m e d t h a t t h e r o o m s a b o v e a n d b e l o w w e r e i d e n t i c a l t o t h e room i n q u e s t i o n . T h e .--
L ( /h.
R o o m S p a c e 1 F l o o r S l a b 2 h3 C e i l i n g P l e n u m S p a c e C e i l i n g ( \ R o o m S p a c e h3 C e i l i n g P l e n u m S p a c e C e i l i n gFig. 1 Thermal s y s t e m o / suspended ceiling with re- c e s s e d l i g h t s
power t o t h e l i g h t s w a s a s s u m e d t o be d i s s i p a t e d a s s h o w n in F i g . 1: a f r a c t i o n , p , of t h e i n p u t g o i n g up and (1-p) down i n t o the room. E a c h of t h e s e com- p o n e n t s w a s a s s u m e d t o b e d i v i d e d e q u a l l y b e t w e e n c o n v e c t i o n to the a i r a n d radiation a b s o r b e d by t h e floor s u r f a c e . T h e fraction (1-p)/2 of t h e input power that g o e s d i r e c t l y t o t h e room a i r a l l o w s for t h e h e a t t r a n s f e r by c o n v e c t i o n from t h e l i g h t f i x t u r e a n d t h e part of t h e r a d i a t i o n from t h e l i g h t s t h a t is a b s o r b e d by the furniture. T h i s p r e s u p p o s e s t h a t t h e r a d i a t i o n a b s o r b e d by t h e furniture a p p e a r s as c o o l i n g l o a d a l m o s t immediately b e c a u s e of t h e low h e a t s t o r a g e c a p a c i t y of t h e f u r n i s h i n g s . A l l of t h e h e a t s t o r a g e c a p a c i t y w a s a s s u m e d t o b e in t h e floor s l a b ; t h e s u s p e n d e d c e i l i n g being t r e a t e d as a thermal r e s i s - t a n c e . T h e h e a t f l u x e s through the upper and l o w e r s u r f a c e s of the floor s l a b w e r e computed by the re- s p o n s e f a c t o r m e t h ~ d ~ > ~ . T h e r e s p o n s e f a c t o r s for the floor s l a b w e r e e v a l u a t e d with the program g i v e n in R e f e r e n c e 4 using a time i n c r e m e n t of 1 5 mins. T h e y a r e t a b u l a t e d in Appendix I.
T h e t e m p e r a t u r e s a t e a c h s u r f a c e of the floor a n d c e i l i n g a n d i n t h e s p a c e a b o ~ e the c e i l i n g w e r e found by s o l v i n g t h e s e t of h e a t b a l a n c e e q u a t i o n s for t h e 4 s u r f a c e s a n d t h e c e i l i n g c a v i t y . T h i s s e t of e q u a t i o n s is g i v e n i n Appendix I1 i n matrix form.
T h e c o o l i n g l o a d a t e a c h time i s j u s t t h e s u m of the h e a t t r a n s f e r r e d t o t h e room a i r by c o n v e c t i o n from t h e floor and c e i l i n g p l u s t h e (1-p)/2 of t h e in- put power, which a c c o u n t s for c o n v e c t i o n from t h e light f i x t u r e s a n d furniture. 0 . 7 I I I I
I
I
N o P l e n u m V e n t i l a t i o n1
f
$
-
1-
0 . 7 4 9 e x p ( - 0 . 1 5 2 t )+
-
1-
0 . 7 5 5 e x p ( - 0 . 1 2 7 t )$
= 1 - 0 . 7 6 2 e x p ( - 0 . 0 9 6 t ) I I I II
1 2 3 4 5 T I M E , H R SFig. 2 Cooling load for unventzlated plenum, calculated using different convection coefficients
DISCUSSION O F R E S U L T S U n v e n t i l a t e d S p a c e A b o v e C e i l i n g
F i g . 2 s h o w s t h e c a l c u l a t e d c o o l i n g load v s time a f t e r l i g h t s a r e turned o n for a f l u o r e s c e n t fixture r e c e s s e d i n t o a n u n v e n t i l a t e d c e i l i n g s p a c e . T h e variation o f t h e l o a d with time i s r e p r e s e n t e d q u i t e w e l l by a n e x p r e s s i o n of t h e form - - q l - A e - B '
w -
(1) T h e r a t e a t w h i c h h e a t is being s t o r e d is W-
q = WAe-B' (2) T h u s , t h e t o t a l h e a t s t o r e d when s t e a d y - s t a t e c o n - d i t i o n s a r e r e a c h e d i s T h i s s t o r e d h e a t i s r e l e a s e d t o t h e room a i r o v e r q u i t e a long period a f t e r t h e l i g h t s a r e s w i t c h e d off. T h u s t h e c o o l i n g l o a d d o e s n o t s t o p e v e n though t h e p o w e r input h a s s t o p p e d . If i t i s a s s u m e d t h a t t h e h e a t t r a n s f e r c o e f f i c i e n t s remain the s a m e w h e t h e r the l i g h t s a r e on or off, the c o o l i n g l o a d a f t e r the l i g h t s a r e turned off i s g i v e n bywhere t h e l i g h t s w e r e o n from t=O t o t=M.
T h e u s u a l v a l u e s of B a r e s m a l l enough t h a t e-B'
i s n o t n e g l i g i b l e w h e n t = 2 4 hrs. T h u s , t h e r e i s a carry-over e f f e c t from d a y to d a y w h e n t h e l i g h t s a r e o p e r a t e d on a r e g u l a r d a i l y s c h e d u l e . A s s u m i n g t h a t t h e l i g h t s a r e o n for M hours a n d off for 24-M hours t h e c u m u l a t i v e c o o l i n g l o a d i s :
T h e s e i n f i n i t e g e o m e t r i c s e r i e s c a n b e summed t o g i v e
V a l u e s of given by t h e s e e q u a t i o n s with
d
M
= 10 h r s c a n b e compared with the published Stor- a g e L o a d F a c t o r s ( S L F ) mentioned earlier. T h e p o i n t s plotted in F i g .3
a r e t h e S L F for fluores- c e n t l i g h t s r e c e s s e d into a n unventilated plenum.-
-
c 0-
VI .- I I I I I I , 0 2 4 6 8 10 1 2 14 16 1 8 20 2 2 24 TIME. HR No P l e i i u m V e n t i l a t i o n - C a l c u l a t e d p = 0 . 6 L s = 0 . 5 , K c l L c = 1.0 h p = h 3 = 0 . 5 h i = h 4 = 1.5.
. C a r r i e r 1 0 0 l b l f t 2 , 24 h r O p e r a t i o n- -
-
I n f e r r e d C u r v e f o r C a r r i e r A = 0 . 5 2 5 , B = 0. 1 1 7 h r - lFig. 3 Storage load lactor /or unventilated plenum
T h e s e a r e for a room with 1 0 0 l b / f t 2 of floor a r e a and a cooling s y s t e m t h a t o p e r a t e s continuously. T h e dotted l i n e through the points r e p r e s e n t s the v a l u e s given by E q s 6 and 7 for A = 0.525 a n d B = 0.117 hr-l. T h e s o l i d l i n e r e p r e s e n t s t h e c a l - c u l a t e d r e s u l t s shown in F i g . 2 for h l = h 4 =
1.5
~ t u / f t ~ hr d e g
F
( i e : A = 0.754,B
= 0.127 hr'l). T h e s e c u r v e s show that the published S L F a r e s i g - nificantly higher than t h e c a l c u l a t e d v a l u e s for the times when the l i g h t s a r e on ( a n d consequently lower when the l i g h t s a r e off). T h e S L F c a n be rep- r e s e n t e d , however, by e q u a t i o n s of the form given inE q s 6 and 7, s o t h e s e e q u a t i o n s could be u s e d t o modify the ~ u b l i s h e d v a l u e s for any other v a l u e of
M.
A further s e t of c a l c u l a t i o n s w a s made to deter- mine the s e n s i t i v i t y of the r e s u l t s t o c h a n g e s in the a s s u m e d v a l u e s of t h e h e a t transfer c o e f f i c i e n t s , the fraction, p, of t h e power that i s d i s s i p a t e d into t h e plenum s p a c e , alld c h a n g e s in the thermal character- i s t i c s of the floor-ceiling combination. T h e l o a d s shown in F i g . 2 a r e b a s e d on a v a l u e of p = 0.6, which w a s c h o s e n on t h e b a s i s of d a t a in Reference 5; and h 2 = h 3 = 0.5, which s e e m e d reasonable for
natural convection in the plenum s p a c e . T h e v a l u e s of h a n d h d e p e n d on the r a t e of a i r movement in the room. A v a l u e of 1 . 5 w a s taken a s a rather con- s e r v a t i v e ( i e : high) e s t i m a t e of the v a l u e that might occur in a real building. T h e s e v a l u e s were taken a s t h e s t a n d a r d conditions when t h e various parameters were varied to determine the s e n s i t i v i t y of load to the parameters. T h e r e s u l t a n t c h a n g e s in the A and B v a l u e s a r e shown in F i g . 4. T h e main conclusion
Fig.
4
S e n s i t i v i t y o/ A and B to the changes o/ para- meters /or unventilated plenumthat c a n be drawn from t h e s e r e s u l t s is t h a t t h e value of A i s q u i t e s e n s i t i v e to c h a n g e s in p w h i l e
B
i s unaffected by c h a n g e s i n p. On the o t h e r h a n d ,B
i s much more s e n s i t i v e thanA
to c h a n g e s in the convective h e a t t r a n s f e r c o e f f i c i e n t s a t t h e floor and c e i l i n g s u r f a c e s . Neither A norB
i s very s e n s i - tive to c h a n g e s in the c o n v e c t i v e h e a t transfer c o e f - f i c i e n t s in the s p a c e above t h e ceiling. F i g . 4 a l s os h o w s t h a t t h e v a l u e s of both A a n d B depend on the thermal r e s i s t a n c e of the c e i l i n g a n d the t h i c k n e s s of the floor. Changing the t h i c k n e s s of the floor ( i e : the h e a t s t o r a g e c a p a c i t y of t h e room) h a s the g r e a t e s t e f f e c t on B.
All t h e r e s u l t s p r e s e n t e d in F i g s . 2,
3
and4
w e r e obtained by u s i n g the rather arbitrary a s s u m p t i o n that the power d i s s i p a t e d from t h e l i g h t s is e q u a l l y divided between radiation and c o n v e c t i o n . Some a d - d i t i o n a l c a l c u l a t i o n s w e r e made a s s u m i n g that i t w a s divided i n t o 30% c o n v e c t i o n a n d 70% radiation, a n d ,vice v e r s a . It made very l i t t l e d i f f e r e n c e which a s -sumption w a s u s e d for t h e component of the h e a t that w a s transferred upward, but t h e c o o l i n g l o a d w a s in- c r e a s e d when more of t h e downward component w a s a s s u m e d to b e c o n v e c t e d d i r e c t l y t o the room a i r . E x p e r i m e n t a l work i s required t o e s t a b l i s h t h e a p - propriate r a t i o of c o n v e c t i o n t o radiation for rooms with t y p i c a l l i g h t fixtures and a r r a n g e m e n t s of furni- ture. A l l of t h e downward component would h a v e t o be c o n v e c t e d to t h e room a i r t o make c a l c u l a t e d re- s u l t s a g r e e with t h e published s t o r a g e l o a d f a c t o r s . It s e e m s s a f e t o c o n c l u d e , therefore, t h a t t h e pub- l i s h e d d a t a a r e q u i t e c o n s e r v a t i v e .
Ventilated S p a c e Above C e i l i n g
When room a i r is e x h a u s t e d through the s p a c e a b o v e the c e i l i n g , part of the h e a t from t h e l i g h t s is re- moved before i t c a n e n t e r t h e room. T h i s e f f e c t is taken i n t o a c c o u n t i n the c a l c u l a t i o n of room c o o l i n g load by introducing the f i n a l term in the h e a t b a l a n c e e q u a t i o n for the plenum g i v e n in Appendix 11. With t h i s c h a n g e t h e c o o l i n g l o a d of the room a p p r o a c h e s a s t e a d y - s t a t e v a l u e q, t h a t is l e s s t h a n W, and t h e h e a t e x t r a c t e d from t h e plenum a p p r o a c h e s W - q,. F i g .
5
s h o w s t h a t the room c o o l i n g l o a d c a n b e r e p r e s e n t e d by a n d the h e a t e x t r a c t i o n from t h e c e i l i n g s p a c e , q,, c a n be r e p r e s e n t e d by V a l u e s of A, B , C a n d q,/W a r e given in F i g .6
for s e v e r a l different v a l u e s of the v a r i a b l e parameters. T h e computed v a l u e s of q / W a n d qc/W a r e for t h e0.1 0
1 2 3 4 5
TIME. H R S
Fig. 5 Cooling load and heal removed by exhnust air
I I I I
I
- --
1 - 0 . 7 2 0 e x p l - 0 . 1 4 6 11 1- - , 0 0-
0 0-
0 '0 0 -./
W i t h P l e n u m V e n t i l a t i o n-
V = 10 ft31ft2 h L S = 0.5, k c / L , = 1.0-
p = 0.6 - h 2 = h3 = 1.0, h i = h4 = 1.5 --
-
I I I I s a m e s t a n d a r d c o n d i t i o n s a s the r e s u l t s in F i g . 2 for h , = h 4 = 1.5 e x c e p t t h a t plenum ventilation of 1 0 c f h per f t 2 of floor a r e a h a s b e e n introduced.- P - h i . h 4 -h2. h j - k c l L , - L ,
Fig. 6 S e n s i t i v i t y o f A , B , C and q , t o / h e c h a n g e s of parameters for ventilated plenum
T h e p u b l i s h e d S L F d a t a for a v e n t i l a t e d c e i l i n g plenum approach a v a l u e of 1 a s t becomes large, just a s for the c a s e s with n o v e n t i l a t i o n . It s e e m s , therefore, t h a t t h e s e d a t a a r e for ( q ,
+
q)/W rather than just q/W. T h e c a l c u l a t e d v a l u e s of q/W and (q+
qC)/W, modified t o a l l o w for a 10-hr p e r d a y s c h e d u l e of o p e r a t i o n , a r e plotted in F i g . 7 along with the p u b l i s h e d d a t a . H e r e the e a r l i e r d a t a a r e0 2 4 6 8 1 0 1 2 1 4 1 6 1 8 20 22 24 T I M E . H R S W i t h P l e n u m V e n t i l a t i o n
-
C a l c u l a t e d-
i f P l e n u m A i r R e c i r c u l a t e d-
C a l c u l a t e d - i f P l e n u m A i r E x h a u s t e d p = 0. 6. V = 10 L s = 0.5. K c l L c = 1. 0 h ? = h 3 = 1.0. h i = h4 = 1 . 5 9.
C a r r i e r 1 0 0 l b l f t ? 24 h r O p e r a t i o nFig. 7 Storage l o a d factor for v e n t i l a t e d p l e r ~ u m
s o m e w h a t s m a l l e r t h a n t h e c a l c u l a t e d (q
+
q,)/W d u r i n g t h e t i m e w h i l e t h e l i g h t s a r e on a n d l a r g e r w h i l e l i g h t s a r e off. T h e y a r e a l w a y s l a r g e r , h o w - e v e r , t h a n q / W f o r t h e room. C O O L I N G L O A D W E I G H T I N G F A C T O R S F O R L I G H T S T h e c o o l i n g l o a d d u e to l i g h t s c a n b e c a l c u l a t e d e a s i l y by t h e w e i g h t i n g f a c t o r m e t h o d d e s c r i b e d i n R e f e r e n c e 2 e v e n t h o u g h t h e l i g h t s a r e o p e r a t e d on a n i r r e g u l a r s c h e d u l e . T h e c o o l i n g l o a d a t a n y time, t, is: w h e r e W t - j ~ is t h e a v e r a g e p o w e r i n p u t t o t h e l i g h t s d u r i n g t h e i n t e r v a l b e t w e e n t-jA a n d t-(j + 1 ) A . T h e w e i g h t i n g f a c t o r s r j a r e s i m p l y t h e v a l u e s of q/W a t t = ( j+
1 ) A f o r t h e case w h e r e t h e l i g h t s w e r e o n from t = 0 t o t = A a n d a r e off t h e r e a f t e r : f o r j = O r , = l - ~ e - ~ ~ ( l l a ) for j 2 1 r j = A ( 1 - e - ~ ~ ) e- jBA (lib)T h e v a l u e s of r j g e t p r o g r e s s i v e l y s m a l l e r a s j in- c r e a s e s s o t h a t t h e y b e c o m e n e g l i g i b l e f o r l a r g e v a l u e s o f j . T h u s t h e s u m m a t i o n for q c a n b e s t o p p e d a f t e r a f i n i t e n u m b e r of t e r m s ; t h e a c t u a l n u m b e r of t e r m s d e p e n d i n g on t h e m a g n i t u d e of B A a n d t h e p r e c i s i o n r e q u i r e d . C O N C L U S I O N T h i s s t u d y h a s s h o w n t h a t t h e c o o l i n g l o a d a s s o - c i a t e d w i t h p o w e r i n p u t t o l i g h t s d e p e n d s o n t h 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 e f f i c i e n t s a t t h e c e i l i n g a n d f l o o r s u r f a c e s , t h e t h e r m a l r e s i s t a n c e of t h e c e i l i n g , t h e p r o p o r t i o n s of t h e i n p u t p o w e r t h a t a r e d i s s i p a t e d u p w a r d a n d d o w n w a r d from t h e l i g h t f i x t u r e , a n d t h e h e a t s t o r a g e c a p a c i t y of t h e f l o o r s l a b . C a l c u l a t e d v a l u e s of s t o r a g e l o a d f a c t o r s b a s e d on e s t i m a t e d v a l u e s 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 s a r e i n f a i r a g r e e m e n t w i t h p u b l i s h e d v a l u e s : t h e p u b l i s h e d v a l u e s a p p e a r i n g t o b e c o n s e r v a t i v e . E x p e r i m e n t a l w o r k is n e e d e d t o e s t a b l i s h t h e a p - p r o p r i a t e v a l u e s of t h 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 - e f f i c i e n t s in r o o m s w i t h v a r i o u s a i r s u p p l y a n d e x h a u s t a r r a n g e m e n t s . An e x p e r i m e n t a l d e t e r m i n a t i o n of c o o l i n g l o a d d u e t o l i g h t s w i l l y i e l d v a l u e s of t h e t w o c o n s t a n t s A a n d B i n E q 1. An a n a l y s i s s i m i l a r t o t h e o n e r e p o r t e d i n t h i s p a p e r c a n e s t a b l i s h t h e c u r v e of B v s h f o r t h e s p e c i f i c c a s e u n d e r t e s t ; t h e n t h e e x p e r i m e n t a l v a l u e of B c a n b e u s e d t o f i n d t h e a p p r o p r i a t e v a l u e of h. S i m i l a r l y , t h e e x p e r i - m e n t a l v a l u e of A c a n b e u s e d t o f i n d t h e p r o p o r t i o n of t h e i n p u t p o w e r t h a t is t r a n s f e r r e d d i r e c t l y t o t h e room. When t h e s e d a t a a r e k n o w n , t h e e q u a t i o n s p r e s e n t e d i n t h i s p a p e r c a n b e u s e d t o e v a l u a t e t h e c o o l i n g l o a d w e i g h t i n g f a c t o r s o r t h e s t o r a g e l o a d f a c t o r s for r o o m s w i t h s i m i l a r v e n t i l a t i o n a r r a n g e - m e n t s b u t d i f f e r e n t floor
-
c e i l i n g a r r a n g e m e n t s . R E F E R E N C E S1. Carrier Air Conditioning Company, Handbook of Air Conditioning S y s t e m D e s i g n , McGraw-Hill, Inc., 1965.
2. D. G. S t e p h e n s o n , a n d G. P . Mitalas, Cooling Load C a l c u l a t i o n s by Thermal R e s p o n s e F a c t o r Method, ASHRAE TRANS., Vol. 7 3 , P a r t I , 1967.
3. G. P . Mitalas, a n d D. G. Stephenson, Room Thermal R e s p o n s e F a c t o r s , ASHRAE TRANS., Vol. 7 3 , P a r t I , 1967.
4. G. P . M i t a l a s , a n d J . G. Arseneault, Fortran IV Program t o C a l c u l a t e H e a t F l u x R e s p o n s e F a c t o r s f o r
Canada, Division of Building Research, Computer Progfam No. 26, June 1767.
5. J . E. Flynn, and S. M. Mills, Architectural Lighting Graphics, Reinhold Publishing Corp., 1962.
NOMENCLATURE
01,, = upper s u r f a c e temperature of floor s l a b
0 2 , n = l o w e r s u r f a c e temperature of floor s l a b 03,, = upper s u r f a c e temperature of c e i l i n g p a n e l 0 4 , n = l o w e r s u r f a c e temperature of c e i l i n g p a n e l O,,, = a v e r a g e a i r temperature i n c e i l i n g plenum q = outward c o n d u c t i v e h e a t flux to s u r f a c e 1 qz,, = outward c o n d u c t i v e h e a t flux t o s u r f a c e 2 S e c o n d s u b s c r i p t n d e n o t e s time a f t e r l i g h t s a r e s w i t c h e d o n i n u n i t s of 1 / 4 h r h = 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 a t s u r f a c e 1 h 2 = 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 a t s u r f a c e 2 h 3 = 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 a t s u r f a c e
3
h q = 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 a t s u r f a c e4
hr32 = r a d i a 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 b e t w e e n s u r f a c e3
a n d 2 h , 4 = r a d i a 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 b e t w e e n s u r f a c e4
a n d 1 k,,k, = thermal c o n d u c t i v i t y of c e i l i n g p a n e l a n d floor s l a b r e s p e c t i v e l y L,,L, = t h i c k n e s s of c e i l i n g p a n e l a n d floor s l a b r e s p e c t i v e l y C,,y = s p e c i f i c h e a t a n d s p e c i f i c w e i g h t of return a i r r e s p e c t i v e l y p = f r a c t i o n of power input t h a t i s t r a n s f e r r e d t o plenum W = power s u p p l i e d t o l i g h t s p e r s q u a r e foot of floor a r e aq = room c o o l i n g l o a d per s q u a r e foot of f l o o r a r e a a f t e r l i g h t s turned on q , = r a t e of h e a t removal by v e n t i l a t e d a i r through plenum a f t e r l i g h t s turned on q, = toom c o o l i n g l o a d d u e t o l i g h t s a t s t e a d y s t a t e c o n d i t i o n when plenum i s v e n t i l a t e d A , B , C , = c o n s t a n t s d e p e n d e n t on p a r a m e t e r s i n t h e a p p r o x i m a t e r e p r e s e n t a t i o n of t h e c o o l i n g l o a d ( E q s 1 a n d
9)
t = time a f t e r l i g h t s turned on i n h o u r s A = time i n c r e m e n t d = number of s u c c e s s i v e d a y s of i d e n t i c a l o p e r a t i o nV = r a t e of v e n t i l a t e d a i r flow through plenum i n
c u b i c foot p e r h o u r per s q u a r e foot of floor a r e a
r i = c o o l i n g l o a d w e i g h t i n g f a c t o r s for l i g h t s a t
t = ( j
+
1)AX j Y , Z j = thermal r e s p o n s e f a c t o r s for a homoge- n e o u s s l a b (Appendix I a n d 11)
A P P E N D I X I
R E S P O N S E F A C T O R S F O R C O N C R E T E S L A B A program for c a l c u l a t i n g t h e thermal r e s p o n s e f a c t o r s for a h o m o g e n e o u s s l a b o r a multi-layer s l a b made up of h o m o g e n e o u s l a y e r s is p r e s e n t e d in
R e f e r e n c e
4.
T h e downward h e a t f l u x e s a t t h e upper s u r f a c e of s l a b a n d t h e l o w e r s u r f a c e of s l a b a t e v e r y time s t e p j d u e t o a triangle u n i t p u l s e t o the u p p e r s u r f a c e a t j = o a r e d e f i n e d a s t h e r e s p o n s e f a c t o r s X j a n d Y , a n d t h e upward h e a t f l u x e s a t t h e lower a n d upper s u r f a c e s of s l a b , d u e to the u n i t p u l s e t o t h e l o w e r s u r f a c e , a sZ , a n d
Y ,
r e s p e c - t i v e l y . F o r a h o m o g e n e o u s s l a b a s u s e d h e r e X , = Z j b e c a u s e of symmetry.T h e v a l u e s o f X i , Y a n d Z i t a b u l a t e d i n T a b l e A for 0.3, 0.5 a n d 0.7 f t of c o n c r e t e s l a b w e r e c a l c u - l a t e d with t h e time i n t e r v a l of 1 5 m i n s , which w a s s h o r t enough to be q u i t e a c c u r a t e a s d i s c u s s e d in R e f e r e n c e
3.
T h e v a l u e s of r e s p o n s e f a c t o r s for further s t e p s of n which a r e n o t t a b u l a t e d c a n b e o b t a i n e d by multiplying t h e common r a t i o by the r e s p e c t i v e v a l u e s a t t h e s t e p j; 1 s u c c e s s i v e l y .
A P P E N D I X I1
H E A T B A L A N C E EQUATIONS AND SOLUTION P R O C E D U R E
Referring t o F i g . 1 , t h e h e a t b a l a n c e e q u a t i o n s c a n be set u p a s f o l l o w s , u s i n g the room a i r temperature a s t h e z e r o b a s e :
'
- 'W - h l e l , n q l , n+2
+ h r 4 1 ( e 4 , n-
= 0 ( A l ) w h e r e 2. A t t h e l o w e r s u r f a c e of f l o o r s l a b P q2.n+?W
+ h2(0C7n - 02,n) w h e r e3.
A t t h e u p p e r s u r f a c e o f c e i l i n g p a n e lk
-C ~ ~ ( 0 4 , n-
03,n) + h3(0Cyn - 03,,,) - hr32(03,n - 02,.> = 0 ( A 3 )4.
A t t h e l o w e r s u r f a c e of c e i l i n g p a n e l - h,41(04,n - d l y n ) = 0 ( A d )5 .
A t t h e c e i l i n g p l e n u m h 2 ( 0 2 , n - Oc,,-,) + h3(03,n-
O c , n ) P + -W - 2 C p y V 0 c , n = 0 ( A 5 ) 2 T h e a b o v e h e a t b a l a n c e e q u a t i o n s c a n b e c o n - v e r t e d i n t o t h e f o l l o w i n g s i m u l t a n e o u s e q u a t i o n s e x p r e s s e d i n m a t r i x forms to b e s o l v e d for 0 l , n , 0 ~ , n , 0 3 , n , 0 4 , n a n d 8 c , n .T h e n the c o o l i n g l o a d d u e to l i g h t s a f t e r s w i t c h e d on c a n be o b t a i n e d by t h e formula
T A B L E A
R E S P O N S E F A C T O R S F O R A HOMOGENEOUS C O N C R E T E S L A B
fer from the u p p e r s u r f a c e of floor s l a b t o the room a i r ; the s e c o n d term, the t r a n s f e r from t h e lower s u r - 1 - P w
q n = h1e1," + h494.n +T
T h e f i r s t term r e p r e s e n t s t h e c o n v e c t i v e h e a t t r a n s -
C o n s t a n t s u s e d :
f a c e of c e i l i n g to t h e room a i r ; a n d t h e third term, the i n s t a n t a n e o u s h e a t g a i n from f i x t u r e s . T h e r m a l c o n d u c t i v i t y k , = 1 . 0 ~ t u / f t
*
h r OF/ft S l a b t h i c k n e s s L , = 0.3, 0.5, 0.7 ft S p e c i f i c w e i g h t D = 1 4 0 1b/ft3 S p e c i f i c h e a t C = 0 . 2 0 B t u / l b O F T h e i n t e r v a l At = 0 . 2 5 hour Common Ratio 0.3756387234 0.7029384971 0.8354040384DISCUSSION
R. H. T U L L (Morristown, N. J.): T h e a u t h o r s a r e t o b e commended for c a r r y i n g t h e i r work on more a c - c u r a t e c a l c u l a t i o n of c o o l i n g l o a d s , i n t o the problem of the c o o l i n g l o a d c a u s e d by l i g h t s . T h i s p a p e r ex- t e n d s t h e i r work on the a p p l i c a t i o n of the r e s p o n s ef a c t o r methodology i n t o a m o s t important a r e a of l o a d c a l c u l a t i o n . T h i s method h a s been a d o p t e d by the ASHRAE T a s k Group o n E n e r g y R e q u i r e m e n t s a s the b a s i s for t h e p r o p o s e d new c a l c u l a t i o n procedure f o r d e t e r m i n i n g h e a t i n g a n d c o o l i n g l o a d s . C o n s e -
q u e n t l y , w e f e e l t h a t t h i s p a p e r m a k e s a s i g n i f i c a n t c o n t r i b u t i o n t o our k n o w l e d g e in t h i s field.
T h e a u t h o r s p o i n t o u t the n e e d for e x p e r i m e n t a l work to provide an e m p i r i c a l b a s e for the mathe- m a t i c a l a n a l y s i s a n d for e s t a b l i s h i n g S t o r a g e L o a d F a c t o r s ( S L F ) for t y p i c a l l i g h t i n g fixture a p p l i c a - t i o n s . A r e q u e s t for s u c h a n e x p e r i m e n t a l s t u d y h a s been i n i t i a t e d by t h e T a s k Group. We f e e l t h a t i t is highly d e s i r a b l e for ASHRAE to u p g r a d e its informa- tion on t h i s s u b j e c t . T h e p r e s e n t ASHRAE HAND- BOOK O F FUNDAMENTALS g i v e s r e c o m m e n d a t i o n s t h a t c o m p a r e w i t h t h e a u t h o r s ' c a l c u l a t i o n s ( F i g s . 1 & 2).
F i g u r e 1 s h o w s t h e c o m p a r i s o n for a r e c e s s e d fixture i n a n o n - v e n t i l a t e d plenum. Note t h a t t h e ASHRAE recommendation g i v e s much h i g h e r i n s t a n - t a n e o u s c o o l i n g l o a d s during the period when t h e l i g h t s a r e on and g i v e s n o information on t h e c o o l i n g l o a d r e s u l t i n g from t h e s t o r e d h e a t a f t e r the l i g h t s a r e turned off. F i g u r e 2 s h o w s a s i m i l a r c o m p a r i s o n with a v e n t i l a t e d plenum. T h e m a t h e m a t i c a l a n a l y s i s d e v e l o p e d in t h i s p a p e r c e r t a i n l y i n d i c a t e s a n e e d for a r e v i s i o n i n t h i s ASHRAE information. We h o p e
COOLING LOAD FROM LIGHTS STORAGE LOAD FACTORS
RECESSED FLUORESCENT LIGHTS-ON 10 HOURS/24 HRS.
NO PLENUM EXHAUST
LIGHTING INPUT = 15 BTUH/FT'
UPWARD FRACTION P = 0.75
STORAGE LOAD FACTOR
t-
LIGHTS ON-
LIGHTS OFF_I
HOURS
Fig. 1 Comparison of Storage Load Factors ( S L F) for a recessed fixture in a non-ventilated plenum
a n d t r u s t that i t may o p e n the way for further re- s e a r c h in d e t e r m i n i n g the i n s t a n t a n e o u s c o o l i n g l o a d s from a l l t y p e s of a p p l i c a t i o n s of l i g h t i n g equipment.
MR. KIMURA: T h e comment by Mr. T u l l is v e r y much a p p r e c i a t e d . We a r e now making p l a n s for e x p e r i - m e n t a l work to d e t e r m i n e t h e unknown f a c t o r s a s d e s c r i b e d i n t h e p a p e r , a n d h o p e t h a t t h e r e s u l t s w i l l s u p p l e m e n t t h i s t h e o r e t i c a l s t u d y .
T h e s t o r a g e l o a d f a c t o r c u r v e s d e s i g n a t e d a s N . R . C . i n F i g . 1 of Mr. T u l l ' s comment for unven- t i l a t e d plenum c o r r e s p o n d s to t h e c u r v e i n F i g .
3
i n t h e p a p e r , w h i l e t h e N.R.C. c u r v e s i n F i g . 2 of Mr. T u l l ' s comment for v e n t i l a t e d plenum s h o w only t h e s p a c e c o o l i n g l o a d w h i c h c o r r e s p o n d s to the l o w e r c u r v e i n F i g . 7 of t h e p a p e r . T h e s l i g h t d i f f e r e n c e s b e t w e e n the c u r v e s in t h e f i g u r e s of Mr. T u l l ' s com- m e n t a n d t h o s e i n the p a p e r a r e d u e to t h e d i f f e r e n t v a l u e s of p a r a m e t e r s a s s u m e d i n the c a l c u l a t i o n s . T h e computer program d e v e l o p e d at N.R.C. c a l c u l a t e s e i t h e r s t o r a g e l o a d f a c t o r o r v a l u e s of A, B, C , a n d q,/W for any c o m b i n a t i o n s of p a r a m e t e r s i n c l u d i n g t h e period of l i g h t s on a n d off.COOLING LOAD FROM LIGHTS
STORAGE LOAD FACTORS
RECESSED FLUORESCENT LIGHTS-ON 10 HOURS/24 HRS.
RETURN AIR EXHAUST THROUGH PLENUM V = 15 F T ' / F T ~ H
LIGHTING INPUT = 15 BTUH / FT2
UPWARD FRACTION P = 0.75 STORAGE LOAD FACTOR 0 0 2 4 6 8 10 12 14 16 18 20 22 24 HOURS
Fig. 2 Comparison of Storage Load Factors ( S L F) for a recessed fixture in a ventilated plenum
