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Programmed computer model of air infiltration in small residential
buildings with oil furnace
Konrad, A.; Larsen, B. T.; Shaw, C. Y.
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Ser
N21d
Conseil national
National Research
no.
860
"
;-'I
$
de recherches Canada
Council Canada
n 1
,,
.L kc*
PROGRAMMED COMPUTER MODEL OF
AIR INFILTRATION IN SMALL RESIDENTIAL
BUILDINGS
'WITH
OIL FURNACE
by
A.
Konrad,
B.T.
Larsen and
C.Y.
Shaw
Appeared
in
Proceedings, Third International Symposium on
The Use of Computers for Environmental Engineering
Related to Buildings
held in Banff, Alberta, 1 0
-
12 May
1978
p.
637
-
644
ANALYZEDDBR
Paper No. 860
Division
of
Building Research
This publication is being d i s t r i b u t e d by the Division of Building R e s e a r c h of the National R e s e a r c h Council of Canada. I t should not b e reproduced i n whole o r i n p a r t without p e r m i s s i o n of the o r i g i n a l publisher. The Di- vision would b e glad to b e of a s s i s t a n c e i n obtaining s u c h p e r m i s s i o n .
Publications of the Division m a y b e obtained by m a i l - ing the a p p r o p r i a t e r e m i t t a n c e ( a Bank, E x p r e s s , o r P o s t Office Money O r d e r , o r a cheque, m a d e payable to the R e c e i v e r G e n e r a l of Canada, c r e d i t NRC) t o the National R e s e a r c h Council of Canada, Ottawa. K1A OR6
.
S t a m p s a r e not acceptable.A l i s t of a l l publications of the Division is available and m a y b e obtained f r o m the Publications Section. Divieion of Building R e s e a r c h , National R e s e a r c h Council of Canada, Ottawa. KIA OR 6.
I
I
1111
3
IIIIII]I~II~II[IUI
9 0020
75
IIIII~I
1111
-PROGRAMMED COMPUTER MODEL OF AIR INFILTRATION IN SMALL RESIDENTIAL, BUILDINGS WITH OIL FURNACE
A . Konrad, B .'T. Larsen* and C .Y
.
ShawD 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 Research Council o f Canada Ottawa, Canada
"Norwegian Building Research I n s t i t u t e , Oslo, Norway (Guest worker w i t h DBR/NRC, 1975)
ABSTRACT
-
A computer program f o r t h e p r e d i c t i o n of t h e a i r i n f i l t r a t i o n l o a d i n s m a l l r e s i d e n t i b ? b u i l d i n g s i s d e s c r i b e d . The model r e p r e s e n t s an o i l - f i r e d f u r n a c e , a smoke p i p e w i t h b a r o m e t r i c damper, a chimney and a n o n - p a r t i t i o n e d b u i l d i n g w i t h l e a k a g e openings i n t h e b u i l d i n g envelope. T h i s envelope i n c l u d e s c e i l i n g , w a l l s , windows and d o o r s , t h e l e a k a g e opening of each b e i n g r e p r e s e n t e d by s e v e r a l h o l e s .The model can b e used t o p r e d i c t a i r f l o w through w a l l , window and door l e a k a g e openings a s w e l l a s t h e chimney, w i t h f u r n a c e on o r o f f . The e f f e c t s o f windspeed, wind d i r e c t i o n and i n d o o r / o u t d o o r t e m p e r a t u r e d i f f e r e n c e s a r e i n c o r p o r a t e d i n t h e model. The computer program p r e d i c t s t h e p o s i t i o n of t h e n e u t r a l p r e s s u r e l e v e l o f each w a l l , t o g e t h e r w i t h t h e o v e r - a l l a i r exchange r a t e and i n f i l t r a t i o n l o a d .
The program i s i n t e n d e d f o r s t u d y o f t h e dynamics o f a i r i n f i l t r a t i o n and f o r computer e x p e r i - m e n t a t i o n w i t h new d e s i g n i d e a s t o reduce t h e energy consumption o f s m a l l r e s i d e n t i a l t y p e b u i l d i n g s .
RESUME
-
Lss auteurs dgcrivent un progx-e inf'ormatique s e r v a n t 2 p r 6 d i r e l ' i n f i l t r a t i o n de l ' a i r dans dc p e t i t s immeubles r g s i d e n t i e l s . Le modsle r e p r E s e n t e une c h a u d i s r e2
l ' h u i l e , un c o n d u i t de fum6e munid'un r$$urateur de tirage baromi.trique, m e cheminge e t un bgtiment s a n s c l o i s o n s dont l ' e n v e l o p p e ccrmporte des o u v e ~ , u r e s de f u i t e . L'enveloppt; englobe p l a f o n d , murs, f e n f t r e s e t p o r t e s , l e s o u v e r t u r e s
de f u i t e de chacun 6 t a n t reprgsentges par p l u s i e u r s t r o u s .
Le modsle s e r t 5 p r g d i r e 1'6coulement de l ' a i r 2 t r a v e r s l e s o u v e r t u r e s d e s murs, d e s I
f e n f t r e s , des p o r t e s e t de l a cheminse, avec e t s a n s fonctionnement de l a c h a u d i s r e . Le modsle englobe l e s e f f e t s de l a v i t e s s e e t de l a d i r e c t i o n du v e n t e t l e s E c a r t s de t e m p g r a t u r e e n t r e l ' i n t g r i e u r e t I ' e x t E r i e u r . Le programme i n f o r m a t i q u e ~ r k d i t l a p o s i t i o n du n i v e a u de p r e s s i o n n e u t r e de chaque mur, a i n s i que l e t a u x d'6change g l o b a l de l ' a i r e t l a charge d ' i n f i l t r a t i o n .
Le programme s e r t
2
6 t u d i e r l a dynamique de l ' i n f i l t r a t i o n de l ' a i r e t 2 s i m u l e r p a r o r d i n a t e u r de nouveaux modsles v i s a n t 2 r 6 d u i r e l a consommation d r k n e r g i e des p e t i t s immeubles r g s i d e n t i e l s .INTRODUCTION
I t i s known from a i r leakage and p r e s s u r e measurements on houses (Tamura and Wilson, 1963; ~ u n t and Burch, 1975; B a h n f l e t h , Moseley and H a r r i s , 1957 ( a ) ( b ) ) t h a t a i r i n f i l t r a t i o n may a c c o u n t f o r a s i g n i f i c a n t f r a c t i o n o f t h e h e a t i n g
l o a d . With t h e growing importance o f energy con. s e r v a t i o n , t h e v a l u e o f computer s i m u l a t i o n o f a i r i n f i l t r a t i o n f o r p r e d i c t i n g t h e a i r exchange r a t e h a s become more and more i m p o r t a n t .
on o r o f f f o r any combination o f windspeed, wind d i r e c t i o n and i n d o o r / o u t d o o r t e m p e r a t u r e s . The program comprises a MAIN and t h e f o l l o w i n g s u b r o u t i n e s (Larsen, 1977) .
INFILT f o r t h e s i m u l a t i o n o f a i r i n f i l t r a t i o n / e x f i l t r a t i o n through t h e l e a k a g e openings i n t h e b u i l d i n g envelope;
FLOWS f o r t h e computation o f a i r f l o w through t h e h o l e s r e p r e s e n t i n g leakage openings; T h i s p a p e r d e s c r i b e s a computer model f o r t h e PCDEF f o r o b t a i n i n g wind p r e s s u r e c o e f f i c i e n t s s t u d y of a i r i n f i l t r a t i o n i n s m a l l r e s i d e n t i a l t y p e a t t h e b u i l d i n g e x t e r i o r s u r f a c e s ; b u i l d i n g s . The model c o n s i s t s o f a f o r c e d - a i r
h e a t i n g system w i t h o i l - f i r e d f u r n a c e and a non- WIND f o r c o n v e r t i n g windspeed measured a t t h e p a r t i t i o n e d b u i l d i n g (Larsen, 19 76) . The computer m e t e o r o l o g i c a l s i t e t o windspeed a t t h e program p r e d i c t s t h e a i r exchange r a t e w i t h f u r n a c e b u i l d i n g s i t e ;
CHMNEY f o r t h e s i m u l a t i o n of t h e g a s flow i n t h e c = wind p r e s s u r e c o e f f i c i e n t a t j - t h h o l e smoke p i p e , b a r o m e t r i c damper and chimney; j ( d e f i n e d a s t h e r a t i o of a v e r a g e s u r f a c e
wind p r e s s u r e t o v e l o c i t y p r e s s u r e due t o FFACT f o r t h e computation o f f r i c t i o n f a c t o r s f o r wind a t t h e same h e i g h t ) ;
gas flow i n t h e smoke p i p e and chimney;
r = d e n s i t y of o u t s i d e a i r ;
0
PRESSR f o r t h e computation o f t h e p r e s s u r e w = windspeed a t t h e b u i l d i n g s i t e ; d i f f e r e n c e a c r o s s t h e b a r o m e t r i c damper;
g = g r a v i t a t i o n a l a c c e l e r a t i o n ;
FRNACE f o r t h e s i m u l a t i o n o f t h e g a s flow from t h e h . = h e i g h t o f j - t h h o l e above t h e ground l e v e l .
o i l f u r n a c e . J
The f o l l o w i n g s e c t i o n s d e s c r i b e t h e mathematical P r e s s u r e , Pij, i s g i v e n by t h e a l g e b r a i c sum o f model and t h e v a r i o u s a l g o r i t h m s implemented i n t h e t h e i n t e r i o r p r e s s u r e a t ground l e v e l and t h e computer program, s t a t i c p r e s s u r e of t h e a i r column i n s i d e t h e
b u i l d i n g from ground l e v e l t o t h e j - t h c r a c k . AIR LEAKAGE MODEL
C o n s i d e r t h e b u i l d i n g shown i n F i g . 1 . Assume t h a t t h e r e a r e no i n t e r n a l p a r t i t i o n s . Every e x t e r i o r w a l l , window and door i s assumed t o have l e a k a g e o p e n i n g s . I n t h e model t h e s e leakage openings a r e r e p l a c e d w i t h N number o f h o l e s e q u a l l y spaced a l o n g t h e h e i g h t o f t h e component. I f t h e combined r e s i s t a n c e i s Rt and t h e flow exponent i s n, each o f t h e N h o l e s has a r e s i s t a n c e o f
The flow r e s i s t a n c e Rt i s i n SI u n i t s , i . e . , i n pa/ (m3/s) l / n .
where P1 i s t h e i n t e r i o r p r e s s u r e a t t h e ground l e v e l and ri i s t h e d e n s i t y o f indoor a i r . When indoor t e m p e r a t u r e i s T i , ri i s g i v e n by t h e e q u a t i o n of s t a t e f o r i d e a l g a s
where R i s t h e g a s c o n s t a n t f o r a i r . The d e n s i t y o f outdoor a i r ro when t h e outdoor t e m p e r a t u r e i s
To c a n b e o b t a i n e d from a n e q u a t i o n s i m i l a r t o ( 5 ) . The volume flow of a i r through t h e j - t h h o l e i n By s u b s t i t u t i n g e q u a t i o n s (1) and ( 3 ) t o (5) t h e b u i l d i n g envelope i s g i v e n by i n e q u a t i o n (2) and m u l t i p l y i n g by t h e d e n s i t y r ,
one o b t a i n s t h e mass flow r a t e o f a i r through t h e n j - t h h o l e a s ( 2) w 2 where G . J = s r R n
1.
+;k
+ s = +1 i f (Poj-
Pi j ) > 0 ( a i r i n f i l t r a t i o n ) = -1 i f (Poj-
P i j ) < 0 ( a i r e x f i l t r a t i o n ) ; Poj = p r e s s u r e o u t s i d e b u i l d i n g a t j - t h h o l e ; P i j = p r e s s u r e i n s i d e b u i l d i n g a t j - t h h o l e ; Rj = v a l u e o f r e s i s t a n c e t o a i r l e a k a g e o f j - t h where = ri if = and = ro if = h o l e i n b u i l d i n g e n c l o s u r e a s d e f i n e d by ( 1 ) ; (Larsen,
1976).n j = flow exponent f o r j - t h h o l e i n b u i l d i n g I f t h e r e a r e m h o l e s i n t h e b u i l d i n g envelope e n c l o s u r e . and t h e mass flow r a t e of a i r t o t h e o u t s i d e
t h r o u g h t h e chimney i s -Gc, then mass b a l a n c e P r e s s u r e , P OJ
.,
i s g i v e n by t h e a l g e b r a i c sum o f t h e r e q u i r e s t h a tatmospheric p r e s s u r e a t ground l e v e l , t h e dynamic
wind p r e s s u r e and t h e s t a t i c p r e s s u r e o f t h e a i r m
column o u t s i d e t h e b u i l d i n g from t h e ground t o t h e
1
G . - G = Oj - t h h o l e . J C
j =1 w
P = P + c r - -
0 j j o 2 r o g h j ( 3 ) The s u b r o u t i n e WIND f i n d s t h e c o n v e r s i o n f a c t o r f o r changing windspeed a t t h e weather s t a t i o n where b u i l d i n g h e i g h t o v e r a f l a t , suburban o r c i t y 10 m above a f l a t t e r r a i n t o windspeed a t t h e
PCOEF f i n d s t h e wind p r e s s u r e c o e f f i c i e n g c j f o r any g i v e n s u r f a c e o r i e n t a t i o n and wind d i r e c t i o n and f o r one of t h e f o l l o w i n g e i g h t b u i l d i n g dimen- s i o n s
Height Length
NO. Width Width
The p r e s s u r e c o e f f i c i e n t c j r e p r e s e n t s an a v e r a g e v a l u e over t h e s u r f a c e and i s o b t a i n e d by averaging and i n t e r p o l a t i n g t h e r e s u l t s p r e s e n t e d by Chien e t a 1
.,
1951. The s u b r o u t i n e FLOWS computes Gj f o r any assumed v a l u e o f t h e i n t e r n a l p r e s s u r e P i . S i m i l a r l y , t h e s u b r o u t i n e CHMNEY r e t u r n s a v a l u e f o r Gc depending on t h e o p e r a t i o n of t h e f u r n a c e . F i n a l l y , i n s u b r o u t i n e INFILT a n i t e r a t i v e procedure based on t h e R e g u l a - F a l s i method (Rektorys, 1969)i s s e t up t o f i n d an approximation t o Ply t h e r o o t of t h e n o n - l i n e a r a l g e b r a i c e q u a t i o n ( 7 ) .
F i g . 1 . I t c o n s i s t s of a chimney and a horizon- t a l smoke p i p e with b a r o m e t r i c damper (Larsen, 1976; Colborne and M o f f a t t , 1959; M o f f a t t and Colborne, 1959). The mathematical model a l l o w s t h e computation of t h e gas flow Gc i n t h e chimney, g i v e n t h e p r e s s u r e P1 a t t h e ground l e v e l i n s i d e t h e house and t h e g a s flow Gf from t h e f u r n a c e . The model does n o t t a k e h e a t l o s s e s from t h e smoke p i p e and chimney i n t o a c c o u n t . The chimney c r o s s - s e c t i o n i s r e c t a n g u l a r , t h e smoke p i p e c r o s s - s e c t i o n c i r c u l a r .
P r e s s u r e , Pb, a t t h e barometric damper opening j u s t o u t s i d e t h e smoke p i p e i s g i v e n i n terms of p r e s s u r e P1 a s
where hz i s t h e d i s t a n c e between t h e ground l e v e l and t h e a x i s o f t h e smoke p i p e (h2 is n e g a t i v e i f t h e smoke p i p e i s l o c a t e d below ground l e v e l ) .
P r e s s u r e , P3, a t t h e chimney opening i s , th e a l g e b r a i c sum o f atmospheric p r e s s u r e a t ground l e v e l , wind p r e s s u r e , and t h e weight o f a column of outdoor a i r p e r u n i t a r e a extending from t h e chimney t o p t o ground l e v e l
Once t h e indoor p r e s s u r e P1 a t ground l e v e l i s
known, t h e h e i g h t of t h e n e u t r a l p r e s s u r e l e v e l a t P = P + c r - - r o g h 3 w2
3 0 2 (1 2)
each s u r f a c e o r w a l l of t h e b u i l d i n g c a n be d e t e r - mined. The indoor p r e s s u r e P i a t any given h e i g h t h i s g i v e n b y
where c i s t h e wind p r e s s u r e c o e f f i c i e n t a t t h e chimney t o p (a v a l u e of -0.5 was used) and hs i s P. = P - r . g h (8) t h e d i s t a n c e between ground l e v e l and t h e t o p o f
1 1 1 t h e chimney.
The outdoor p r e s s u r e Po a t h e i g h t h i s given by P r e s s u r e , P2, i n s i d e t h e smoke p i p e a t t h e barometric damper (on t h e s i d e n e a r e s t t h e f u r n a c e ) i s given, by B e r n o u l l i ' s e q u a t i o n , a s P = P + c r o w -
rag
h (9 t h e a l g e b r a i c sum o f P3, t h e weight of a columno f a i r p e r u n i t a r e a i n t h e chimney, t h e p r e s s u r e l o s s due t o f r i c t i o n a t t h e smoke p i p e and
By e q u a t i n g indoor and outdoor p r e s s u r e s , one can chimney w a l l s , and p r e s s u r e l o s s due t o a change o b t a i n a n e q u a t i o n t h a t can be s o l v e d f o r h e i g h t h i n f l u e - g a s v e l o c i t y w Z v C
'
v L P I - P - c r-
f 0 2 h = (10) i-
0 where For each w a l l , h i s computed i n t h e MAIN programa c c o r d i n g t o e q u a t i o n ( 1 0 ) . Note t h a t a ) i n t h e absence of wind e f f e c t s t h e n e u t r a l l e v e l i s t h e same f o r e v e r y w a l l of a b u i l d i n g , and b) when indoor/outdoor a i r d e n s i t i e s a r e e q u a l ( i - e . , i n t h e absence of s t a c k e f f e c t ) , h becomes i n d e t e r - minate [when such a c o n d i t i o n a r i s e s . t h e Droeram
rc = d e n s i t y of f l u e g a s e s i n t h e chimney; DE = p r e s s u r e drop due t o f r i c t i o n l o s s e s i n
t h e smoke p i p e and chimney;
vc = v e l o c i t y o f f l u e g a s e s i n t h e chimney; rf = d e n s i t y o f f l u e g a s e s l e a v i n g t h e furnace;
.
-
computes a f i n i t e b u t v e r y l a r g e h ).
vf = v e l o c i t y o f f l u e g a s e s e n t e r i n g t h e smoke p i p e .MODEL FOR FLUE-GAS EXHAUST SYSTEM
The p r e s s u r e drop DE due t o f r i c t i o n l o s s e s i s The f l u e - g a s exhaust system i s i l l u s t r a t e d i n given by t h e following e x p r e s s i o n
where
Z = p r e s s u r e l o s s c o e f f i c i e n t f o r t h e branch from t h e smoke p i p e t o t h e b a r o m e t r i c damper;
B = number of elbows i n t h e smoke p i p e ;
A = smoke p i p e c r o s s - s e c t i o n a l a r e a ; S f = Darcy's f r i c t i o n f a c t o r f o r flow i n t h e S smoke pipe; L = smoke p i p e l e n g t h ; s D s = smoke p i p e diameter; f = Darcy's f r i c t i o n f a c t o r f o r flow i n t h e C chimney; L = chimney l e n g t h = h s - h n ; C
D = chimney h y d r a u l i c diameter = 4Ac/Pc;
C A = chimney c r o s s - s e c t i o n a l a r e a ; C P = chimney c r o s s - s e c t i o n a l p e r i m e t e r . C d i f f e r e n c e P4 - P2 a c r o s s t h e damper opening i s I
compared with t h e barometric damper d r a f t s e t t i n g . I f P4
-
P2 exceeds t h e d r a f t s e t t i n g D ( 7 . 5 Pa wasu s e d ) , t h e n t h e damper opens and t h e mass flow
1
r a t e of f l u e g a s e s Gc i n t h e chimney i n c r e a s e s byGd, t h e mass flow r a t e of a i r through t h e b a r o - m e t r i c damper. An i t e r a t i v e procedure based on
t h e simple method of b i s e c t i o n (Rectorys, 1969) i s I used i n t h e s u b r o u t i n e C W E Y t o f i n d t h e flow I
r a t e Gc f o r which t h e p r e s s u r e d i f f e r e n c e P4 - P2 e q u a l s ( o r j u s t b a r e l y exceeds) t h e d r a f t s e t t i n g
D . In o r d e r t o s t a r t t h e i t e r a t i v e procedure, t h e flow r a t e G f of t h e g a s e s from t h e f u r n a c e must be g i v e n . Gf i s computed by t h e s u b r o u t i n e FRNACE.
OIL FURNACE MODEL
I
Consider a f o r c e d - a i r h e a t i n g system w i t h a n o i l - f i r e d f u r n a c e t h a t u s e s No. 2 f u e l o i l . T h i s f u e l o i l h a s an average s p e c i f i c g r a v i t y (SG) of 0.856 a t a temperature o f 15.56"C. I t s Higher Heating Value (HHV) i n J / k g i s e s t i m a t e d from
(ASHRAE, 1977)
HHV = 2,326 (22,320
-
3,780 SG) = 44,390,128 (16) The p r e s s u r e l o s s c o e f f i c i e n t , Z, f o r t h e branchfrom t h e smoke p i p e t o t h e b a r o m e t r i c damper can b e computed from t h e f o l l o w i n g e x p r e s s i o n i f t h e b a r o - m e t r i c damper d r a f t s e t t i n g , D, t h e mass flow r a t e Gf o f f l u e g a s e s l e a v i n g t h e f u r n a c e , and t h e i r a v e r a g e temperature Tf a r e known (Daugherty and F r a n z i n i , 1965). I t s composition according t o t h e d a t a p u b l i s h e d b y ASHRAE (1977) i s I Carbon (C) : 85 p e r c e n t (average) Hydrogen (H): (26
-
1 5 SG) = 13 p e r c e n t Sulphur (S) : 0 . 5 p e r c e n t (maximum)The remaining 1 . 5 p e r c e n t i s assumed t o be 2D n 2 D: P D miscellaneous contaminants with no h e a t v a l u e .
z = -
-1 = - 12 (1 5)
r f f 8 R Tf Gf The mass flow r a t e of f l u e gases Gf l e a v i n g t h e
f u r n a c e when t h e f u r n a c e i s on can b e computed
2 is computed i n t h e s u b r o u t i n e FRNACE. from (ASHRAE, 1977)
The Darcy's f r i c t i o n f a c t o r s f s and f c a r e f u n c t i o n s of Reynolds number, a b s o l u t e roughness and h y d r a u l i c d i a m e t e r of p i p e . They can be computed from t h e Hagen-Poiseuille formula f o r Reynolds number l e s s t h a n 3000 and from t h e Colebrook and Karman formulae f o r h i g h e r Reynolds numbers (Daugherty and F r a n z i n i , 1965). The Reynolds number can be c a l c u l a t e d from t h e h y d r a u l i c diameter of t h e p i p e , t h e v e l o c i t y , and t h e dynamic v i s c o s i t y of t h e g a s e s ( t h e l a t t e r was taken a s t h e same a s f o r a i r ( K r e i t h , 1965). The Reynolds numbers and t h e v i s c o s i t i e s a r e computed i n t h e s u b r o u t i n e PRESSR. The f u n c t i o n s u b r o u t i n e FFACT computes t h e Darcy's f r i c t i o n f a c t o r s and p a s s e s them t o PRESSR, which i n t u r n c a l c u l a t e s t h e p r e s s u r e drop DE due t o f r i c t i o n l o s s e s and
p r e s s u r e P2 a t t h e damper i n s i d e t h e smoke p i p e , assuming t h a t t h e b a r o m e t r i c damper i s c l o s e d ( i . e . assuming t h a t t h e g a s flow Gc i n th e chimney e q u a l s t h e g a s flow Gf from t h e f u r n a c e ) . P2 i s passed on
to t h e s u b r o u t i n e CHMNEY.
The p r e s s u r e , Pq, a t t h e damper o u t s i d e t h e smoke p i p e i s computed i n t h e s u b r o u t i n e INFILT and i s passed on t o CHFgNEY where t h e p r e s s u r e
where t h e 1 on t h e r i g h t a c c o u n t s f o r a u n i t mass of f u e l o i l burned, A s t a n d s f o r t h e r a t i o of mass of a i r s u p p l i e d f o r combustion t o mass o f a i r t h e o r e t i c a l l y n e c e s s a r y f o r combustion (1.75 was u s e d ) , and F i s t h e b u r n e r c a p a c i t y ( i . e . , mass o f f u e l o i l burned p e r u n i t t i m e ) . I t should be noted h e r e t h a t t h e p o r t i o n of Gf t h a t i s w a t e r vapour i s given by 0.085 IIF. For power b u r n e r s , t h e mass flow r a t e of g a s e s l e a v i n g t h e f u r n a c e during t h e o f f - c y c l e period i s approximately 45 p e r c e n t of t h e mass flow r a t e Gf d u r i n g t h e on- c y c l e p e r i o d .
The number of on/off b u r n e r c y c l e s p e r hour (Nc) v a r i e s a c c o r d i n g t o t h e f u r n a c e load f a c t o r ( f )
.
I t i s obvious t h a t a t no load (f = 0.0)Nc = 0.0 and a t f u l l l o a d ( f = 1.0) Nc = 1 . 0 . Between t h e s e two extremes, a t 50 p e r c e n t l o a d
(f = 0 . 5 ) , Nc a t t a i n s i t s maximum v a l u e M ( t y p i c a l l y 6) (Bonne and Johnson, 1974; Bonne, Torborg and J a n s s e n , 1975). Thus, Nc can b e expressed a s a q u a d r a t i c polynomial i n f
N = 2(1
-
2M) f 2 + (4M-
1) f (18) Provided t h a t an e s t i m a t e o f t h e c o n s t a n t a may be computed from OStart can be found,I A complete c y c l e c o n s i s t s of a n on-cycle period and
an o f f - c y c l e p e r i o d . T h e i r d u r a t i o n i n seconds i s
given by a = - T on loge [ : o n s : % t a r t ] (251 ons ' o f f s
f ton = 3,600 -
Nc The temperature a t t h e end o f t h e on-cycle period, and
estop,
can be o b t a i n e d by e v a l u a t i n g e q u a t i o n(24) a t time t = ton. 1
toff = 3,600 -
-
ton (20)
Nc period has two d i s t i n c t p a r t s , each d e s c r i b e d by The temperature f a l l d u r i n g a n o f f - c y c l e a decaying e x p o n e n t i a l . During t h e f i r s t p a r t o f r e s p e c t i v e l y . I f t h e s t e a d y - s t a t e o f f - c y c l e tem- a n o f f - c y c l e period t h e a i r c i r c u l a t i o n f a n i s on p e r a t u r e of t h e f l u e gases l e a v i n g t h e furnace i s and t h e temperature i s given by
( t y p i c a l l y 21°C), t h e average on-cycle f l u e gas temperature i s Ton and t h e average o f f - c y c l e f l u e gas temperature i s Toff, t h e n t h e h e a t l o s s
during one on-cycle p e r i o d i s given by 'off1 ( t
'1
= 'ons - ['ons-
'offs]+ 0.085 H E F]ton (21) t' + b Lon = rGfCpf (Ton - 'offs)
where Cpf i s t h e s p e c i f i c h e a t of t h e f l u e g a s e s
I
I - e
-E]
(26)(taken a s t h e same a s t h e s p e c i f i c h e a t of a i r a t temperature Ton) and E i s t h e h e a t of v a p o r i z a t i o n of water a t temperature S i m i l a r l y , t h e h e a t
l o s s d u r i n g one o f f - c y c l e period i s given by where t ' i s t h e time measured from t h e s t a r t of t h e o f f - c y c l e and r o f f l i s a time c o n s t a n t
( t y p i c a l l y 150 s ) . The c o n s t a n t b r e p r e s e n t s t h e Loff = 0.45 G €
(Toff - 'of f s ) tof f (22) time i n t e r v a l t h a t corresponds t o t h e temperature
f P drop from t h e s t e a d y - s t a t e on-cycle f l u e g a s
temperature
eons
t o t h e temperature a t t h e where C i s t h e s p e c i f i c h e a t of a i r a t temperature end of t h e on-cycle ( s e e F i g . 2 ) . I t 1s g i v e n by T o f f Fhus t h e f u r n a c e e f f i c i e n c y Ef can becomputed from
b = - T 'st0 'offs (271 CLon + Loff)
Nc
o f f 1 l o g e[eOn1
1
iOffiJE f = 1 -
3,600 F HHV f (23)
The average on- and o f f - c y c l e temperatures Ton Assuming t h a t t h e a i r c i r c u l a t i o n f a n i s and Toff needed t o f i n d t h e l o s s e s Lon and Loff can c o n t r o l l e d by thermostat and t h a t t h e f a n s t o p s be c a l c u l a t e d i f one assumes t h a t t h e f l u e gas tem- when t h e f l u e g a s temperature f a l l s t o Ofan p e r a t u r e d u r i n g t h e on- and o f f - c y c l e s can be r e p r e - ( t y p i c a l l y 55"C), t h e l e n g t h o f time t h e f a n i s s e n t e d by r i s i n g o r decaying e x p o n e n t i a l f u n c t i o n s on ( t f a n ) can be o b t a i n e d from e q u a t i o n s (26) and of time ( t ) , r e s p e c t i v e l y (Larsen, 1976; Bonne and (27) a s
Johnson, 1974; Bonne, e t a 1 1975). A t y p i c a l s i t u a - t i o n i s i l l u s t r a t e d i n Fig. 2. In t h e g e n e r a l case, t h e on-cycle f l u e gas temperature e o n ( t ) can be
expressed a s t f a n = - T ("fan
:
%ffs'; (28)+ a o f f 1 l o g e 'stop ' o f f s
[
-5
eon
( t ) = (eons-
e o f f s ) 1-
e + Ooffs (24)During t h e second p a r t o f t h e o f f - c y c l e , when t h e a i r c i r c u l a t i o n f a n i s t u r n e d o f f , t h e temperature i s given by
where
eons
i s t h e s t e a d y - s t a t e on-cycle f l u e g a stemperature ( t y p i c a l l y 3 0 0 ' ~ ) and T~~ i s a time 'off2 ( t ' ) = 'fan - ['fan - e o f f s
c o n s t a n t ( t y p i c a l l y 100 s )
.
The c o n s t a n t , a, r e p r e - s e n t s t h e time i n t e r v a l t h a t corresponds t o t h e1
temperature r i s e from t h e s t e a d y - s t a t e o f f - c y c l e
I
-
t'-
tfan f l u e g a s temperature t o t h e temperature642
where ~ ~ f f 2 i s a time c o n s t a n t ( t y p i c a l l y 500 s ) . The computer program p r e d i c t i o n s o f t h e The temperature a t t h e end o f t h e o f f - c y c l e , n e u t r a l l e v e l s a t each e x t e r i o r w a l l o f t h e house
eend
= O o f f 2 ( t t = t o f f ) must equal t h e temperature a r e u s e f u l f o r v i s u a l i z i n g t h e e f f e c t s on a i r1
estart
a t t h e beginning of t h e next o n - c y c l e . i n f i l t r a t i o n of indoor/outdoor temperatured i f f e r e n c e s , windspeed, wind d i r e c t i o n and I n t h e s u b r o u t i n e FRNACE, a n i t e r a t i v e furnace o p e r a t i o n . For example, t h e computed
'
procedure based on s u c c e s s i v e e v a l u a t i o n s o f n e u t r a l l e v e l s a t a f u r n a c e load f a c t o r of 0 . 5e q u a t i o n s (24) through (29) is s e t up t o match f o r t e s t No. 2 a r e
BStart t o eend. TO begin t h e i t e r a t i o n s , t h e
i n i t i a l v a l u e of
estart
i s computed from equation(24) by s e t t i n g t = 0 and a = 0. When Wall o r i e n t a t i o n NE SE SW
NW
estart
andeend
match w i t h i n 0.55 c e n t i g r a d e deg,t h e i t e r a t i o n s t o p s and t h e average temperatures Furnace on, h 4.80 m 1 . 5 3 m 2.33 m 1 . 5 3 Rt Furnace o f f , h 4.57 m 1 . 3 1 m 2.11 m 1.31 m
Ton and Toff a r e computed. Ton i s found by
i n t e g r a t i n g Oon(t) between t h e l i m i t s t = 0 and Wind speed: 1 6 . 3 km/h
t = ton and then d i v i d i n g t h e r e s u l t o f t h e Windfrom: NE
i n t e g r a t i o n by ton. Toff i s found by i n t e g r a t i n g Indoor temp: 21.1 "C
eOffl
( t ' ) from t ' = 0 t o t ' = t f a n andeoff2
( t ' ) Outdoor temp: - 3 . 9 " ~from t ' = t f a n t o t ' = toff and then d i v i d i n g t h e i r
sum by t o f f . Ton and Toff a r e needed t o compute
t h e e f f i c i e n c y given by equation (23) and, t h e The house i s 3.05 m h i g h . I t i s e v i d e n t p r e s s u r e l o s s c o e f f i c i e n t Z given by e q u a t i o n (15). t h a t when t h e f u r n a c e i s on, t h e n e u t r a l l e v e l s
a r e r a i s e d ( h i g h e s t on t h e upwind w a l l ) . Below t h e n e u t r a l l e v e l s a i r flow is i n t o t h e
PRESENTATION OF RESULTS AND house, above it, o u t o f t h e house. For compari-
COMPARISON WITH MEASUREMENTS son, t h e r e s u l t s f o r t e s t No. 5 a r e a s f o l l o w s The computer program was t e s t e d a g a i n s t a i r
i n f i l t r a t i o n measurements on a o n e - s t o r e y house Wall o r i e n t a t i o n NE SE SW NW
(Tamura and Wilson, 1963) u s i n g t h e t r a c e r gas Furnace on, h 2.27 m 2.75 m 2.08 m 4.20 m
t e c h n i q u e (Dick, 1950). The a i r leakage c h a r a c t e r - F u r n a c e o f f , h 2.11m 2 . 6 0 m 1 . 9 2 m 4 . 0 4 m i s t i c s of t h e same house were measured by t h e
method of p r e s s u r i z a t i o n (Tamura, 1975). Thus, Wind speed: 1 6 . 6 km/h
leakage r e s i s t a n c e s of t h e roof and e x t e r i o r w a l l s , Wind from: NW
windows and doors were c a l c u l a t e d from a i r flow Indoor temp: 23.9"C
r a t e s measured by Tamura (1975; s e e T a b l e s 1, 2, Outdoor temp: -9.4"C
5, House No. 4) by applying e q u a t i o n s (1) and ( 2 ) . I n t h e program t h e leakage openings of each
component were r e p r e s e n t e d a r b i t r a r i l y by f o u r The computer program r e t u r n s many more d e t a i l s h o l e s (N = 4 ) . The flow exponent used f o r roof and than i t i s p o s s i b l e t o reproduce h e r e (e.g., a i r w a l l s was 0.65, and f o r d o o r s and windows 0 . 5 . flow r a t e s f o r t h e chimney and f o r each h o l e when
t h e f u r n a c e i s on and when it i s o f f ; t h e The computer program was r u n f o r a l l t h i r t y p r e s s u r e a t ground l e v e l r e l a t i v e t o outdoor combinations of indoor/outdoor temperature, wind- p r e s s u r e a t t h e same l e v e l ; f u r n a c e e f f i c i e n c y )
.
speed and wind d i r e c t i o n given by Tamura and Wilson,(1963; s e e Table 111). The c o r r e l a t i o n of computed
and measured a i r exchange r a t e s i s p r e s e n t e d i n Fig. CONCLUSIONS
3. Some of t h e measurements were taken with t h e
f u r n a c e t u r n e d o f f ; some were t a k e n with i t A mathematical model f o r a i r i n f i l t r a t i o n i n o p e r a t i n g . A s f u r n a c e load f a c t o r s a r e not known, small houses has been p r e s e n t e d i n d e t a i l and a t h e computations were c a r r i e d o u t f o r load f a c t o r s computer program implementation b r i e f l y o u t l i n e d . of 0, 0.25, 0.5, 0.75 and 1 . The r e s u l t s i n d i c a t e The program i s capable of p r e d i c t i n g t h e a i r a f a i r l y s t r o n g v a r i a t i o n i n a i r leakage r a t e s with exchange r a t e of a small house under v a r i o u s f u r n a c e load f a c t o r . For example, f o r t e s t No. 2 combinations of indoor/outdoor temperature, wind- (Tamura and Wilson, 1963) t h e computed a i r exchange speed, wind d i r e c t i o n and o p e r a t i o n o f a n o i l - r a t e s were 0.551, 0.564, 0.578, 0.597 and 0.612, f i r e d f u r n a c e .
r e s p e c t i v e l y .
The program h a s been t e s t e d a g a i n s t a i r F i g u r e 3 shows t h a t p r e d i c t e d and measured a i r exchange r a t e s measured by t h e t r a c e r g a s t e c h - exchange r a t e s may d i f f e r by a s much a s 225 p e r nique on a o n e - s t o r e y house under v a r i o u s indoor/ c e n t , save f o r t e s t p o i n t No. 12, which can be outdoor c l i m a t i c c o n d i t i o n s . For t h i s p a r t i c u l a r
ignored because t h e measurements were taken with t e s t house it was found t h a t agreement between
t h e f i r e p l a c e damper open. The p o i n t s p l o t t e d i n c a l c u l a t e d and measured a i r exchange r a t e s i s Fig. 3 a r e f a i r l y evenly d i s t r i b u t e d about t h e l i n e w i t h i n 25 p e r c e n t .
of agreement. Taking a l l t h e u n c e r t a i n t i e s i n
both t h e mathematical model and t h e experimental ACKNOWLEDGEMENTS
r e s u l t s i n t o c o n s i d e r a t i o n , t h e agreement between The a u t h o r s a r e i n d e b t e d t o G . P . M i t a l a s f o r t h e measured and c a l c u l a t e d a i r changes may be h i s generous a s s i s t a n c e during t h e c o u r s e of t h i s
r e g a r d e d a s good. r e s e a r c h work; and t o R . L . Q u i r o u e t t e f o r
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 o f B u i l d i n g Research, National Research Council o f Canada and i s p u b l i s h e d w i t h t h e approval of t h e D i r e c t o r of t h e D i v i s i o n .
REFERENCES
ASHRAE, 1977. Handbook and Product D i r e c t o r y . Fundamentals, New Nork: A .S .H .R .A. E
.
I n c . , Ch. 1 4 .BAHNFLE'IH, D .R., MOSELEY, T . D . , and HARRIS, W .S. 1 9 5 7 ( a ) . Measurements of i n f i l t r a t i o n i n two r e s i d e n c e s , P a r t I : Technique and Measured
I n f i l t r a t i o n , ASHRAE T r a n s . , 63, 439-452. BAHNFLETH, D . R . MOSELEY, T .D
.
,
and HARRIS, W .S.1 9 5 7 ( b ) . Measurements o f i n f i l t r a t i o n i n two r e s i d e n c e s , P a r t I I : Comparison o f v a r i a b l e s a f f e c t i n g i n f i l t r a t i o n , ASHRAE T r a n s . , 63, 453-476.
BONNE, U . , and JOHNSON, A . E . 1974. Thermal
e f f i c i e n c y i n non-modulating combustion systems, Proc. o f Conference on Improving E f f i c i e n c y i n HVAC Equipment and Components i n R e s i d e n t i a l and Small Commercial B u i l d i n g s , Sponsored by NBS and ASHRAE, Purdue Univ., W . L a f a y e t t e , Ind. BONNE, U., TORBORG, R . H . , and JANSSEN, J . E . 1975.
D i g i t a l s i m u l a t i o n o f t h e performance of combus- t i o n h e a t i n g systems, A.1.Ch.E. 1 5 t h Annual Regional Symposium, Twin C i t y S e c t i o n , Bloomington, Minnesota.
CHIEN, N . , FENG, Y., WANG, H . - J . , and SIAO, T.-T. 1951. Wind t u n n e l s t u d i e s o f p r e s s u r e d i s t r i b u - t i o n on e l e m e n t a r y b u i l d i n g forms, P r o j e c t sponsored by t h e O f f i c e o f Naval Research under c o n t r a c t N80NR-500, Iowa I n s t i t u t e o f Hydraulic Research, S t a t e Univ. o f Iowa, Iowa C i t y , U.S.A. COLBORNE, W .G
.
,
and MOFFATT, W .C.
1959. A fundamen-t a l a n a l y s i s of chimney performance, P r e s e n t e d a t ASHRAE Annual Meeting, Lake P l a c i d , N . Y .
DALGLIESH, W.A., and BOYD, D.W. 1962. Wind on b u i l d i n g s , D i v i s i o n of Building Research, N a t i o n a l Research Council of Canada, CBD 28. DAUQIERTY, R.L., and FRANZINI, J . B . 1965. F l u i d
mechanics w i t h e n g i n e e r i n g a p p l i c a t i o n s , New York. McGraw-Hill
.
DICK, J . B . 1950. Measurement o f v e n t i l a t i o n u s i n g t r a c e r g a s technique, ASHRAE J o u r n a l , Heating
,
P i p i n g and A i r - C o n d i t i o n i n g , p.
131.HUNT, C . M . , and BURCH, D . M . 1975. A i r i n f i l t r a t i o n measurements i n a four-bedroom townhouse u s i n g s u l f u r h e x a f l u o r i d e a s a t r a c e r g a s , ASHRAE T r a n s . , 81, P a r t I , 186-201. KREITH, F . 1965. P r i n c i p l e s of h e a t t r a n s f e r , S c r a n t o n , Pennsylvania: I n t e r n a t i o n a l Textbook Co., Table A - 3 , p . 595. LARSEN, B.T. 1976. D i g i t a l s i m u l a t i o n of e n e r g y consumption i n r e s i d e n t i a l b u i l d i n g s , P r e s e ~ t e d a t I n t e r n a t i o n a l CIB Symposium on Energy
C o n s e r v a t i o n i n t h e B u i l t Environment, B u i l d i n g Research S t a t i o n , Garston, England, A p r i l 6-8. LARSEN, B.T. 1977. Energy consumption o f r e s i d e n -
t i a l b u i l d i n g s ; The computer program ENCO*, P a r t 2, Documentation, Norwegian Building Research I n s t i t u t e , Computer Program L i b r a r y , Program No. 12, O s l o .
MOFFATT, W.C., and COLBORNE, W.G. 1959. New method o f chimney d e s i g n and performance e v a l u a t i o n , P r e s e n t e d a t ASHRAE Annual Meeting, Lake P l a c i d
N . Y .
REKTORYS, K . (Ed.) 1969. Survey o f A p p l i c a b l e Mathematics, Cambridge, Massachusetts, The M.I.T. P r e s s .
TAMURA, G.T. 1975. Measurement o f a i r l e a k a g e c h a r a c t e r i s t i c s of house e n c l o s u r e s , ASHRAE T r a n s . , 81, I , 202-211.
TAMURA, G.T. and WILSON, A . G . 1963. A i r l e a k a g e and p r e s s u r e measurements on two occupied houses, ASHRAE J o u r n a l , 5, No. 12, 65-73.
3 I C h i m n e y C e i l i n g j - t h h o l e I R j ) I 1 I P I I Figure 1 Diagram showing c r o s s - s e c t i o n of b u i l d i n g used i n a i r leakage model
F U R N A C E EXHAUST GAS T E M P E R A T U R E ( 8 ) 4
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' o n 'on+'off T I M E (11 F i g u r e 2Typical v a r i a t i o n o f f u r n a c e exhaust gas temperature w i t h time; n o t i c e t h a t t ' = t
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t on 0 W i n t e r - s p r i n g t e s t I f - 0 ) S u m m e r t e s t ( f - 0 14
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0 . 3 4: F l r e n p l a c e w d a m p e r I- open 3 u L i n e of a g r e e m e n t 4 u 0 . 1M E A S U R E D A I R CHANGE PER HOUR
Figure 3
C o r r e l a t i o n of measured and c a l c u l a t e d a i r exchange r a t e s
