Infiltration models for multicellular structures — A literature review

Energy and Buildings, 8 (1985) 123 - 136

123

Infiltration Models for Multicellular Structures A Literature Review H. E. FEUSTEL and V. M. KENDON Applied Science Division, Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720 (U.S.A.) {Received December 11, 1984)

SUMMARY

Infiltration models are used to simulate the rates o f incoming and outgoing air flows for a building with known leakage under given weather and shielding conditions. Additional information about the flow paths and air-mass flows inside the building can only be made available by using multichamber infiltration models. Our review o f the literature revealed the existence o f 15 multichamber infiltration models, all developed between 1966 and 1983 and differing significantly in the number of cells they can handle, depending on the date of their development. In terms o f the flow equations these programs use, they are very similar; most o f the differences between them are in the description o f the building and the algorithm provided for solving the set o f nonlinear equations. In this literature review, we found that only a few of the 15 models are able to describe and simulate the ventilation system and the interrelation o f mechanical and natural ventilation.

INTRODUCTION The LBL infiltration model was developed in 1980 to simulate air infiltration of singlecell structures, such as single-family houses, under given weather conditions [1 ]. A high percentage of the existing buildings, however, have floor plans that characterize them more accurately as multichamber structures, which cannot be treated by single-cell models. This literature review is intended to be a first step in the development of a multichamber infiltration model. The advantage of multichamber models, besides being able to simulate infiltration in larger buildings, is their ability to calculate mass flow interactions between the different 0378-7788/85/$3.30

zones. Knowing a b o u t the air-mass flow in buildings is important for several reasons, significant among them are that: --exchange of outside air with the air inside the building is necessary for its ventilation; - - e n e r g y is consumed to heat or cool the incoming air to inside comfort temperature; -- air is needed for combustion and to exhaust gas for open fireplaces in different zones; - - a i r b o r n e particles and germs are transported by air flow in buildings. - - a i r flow determines smoke distribution in case of fire. The air-mass flow distribution for a given building is caused by pressure differences, whether evoked by wind, thermal buoyancy, mechanical ventilation systems or a combination of those. The distribution of openings in the building shell and the inner paths infuence the air flow too. The openings can be varied by the inhabitants, which can lead to significant differences in the pressure distribution inside the building. Figure 1 shows the influences on the air-mass flow distribution in detail. In terms of air-mass flow, buildings are complicated interlacing systems of flow paths. In this grid system the joints are the rooms of the building and the connections between the joints simulate the flow paths and include the flow resistances caused by open or closed doors and windows or air leakage through the walls. The boundary conditions for the pressure can be described by the grid points outside the building. The wind pressure distribution depends on the velocity and the direction of the wind, the terrain surrounding the building, and the shape of the building. If the physical interrelationship between the flow resistance and the air flow is known for all flow paths, the air flow distribution f o r the building can be calculated, as long as there is no temperature difference between outside © Elsevier Sequoia/Printed in The Netherlands

124

WIND -VELOCITY -DIRECTION

I

TEMPERATURE DIFFERENCES

t

I

SURROUNDINGS

I

I

MECHANICAL VENTILATION SYSTEMS

I

I VERTICAL FLOW

FAN AND DUCT CHARACTER ST CS

RESISTANCES !

SHAPE OF THE BUILDING

i

l

WINDPRESSURE DISTRIBUTION

I I

THERMAL BUOYANCY

_I --I INHABITANTS BERAVIOUR

i

~

BUILDING

IMPOSED PRESSURE I_ I-"

LEAKAGE CONFIGURATION

INSIDE PRESSURE D STR BUT ON

l AIR FLOW DISTRIBUTION Fig. 1. I n f l u e n c e s o n t h e air-mass flow d i s t r i b u t i o n .

and inside air. Differences in density of the air, due to differences between outside and inside air temperatures, cause further pressures in the vertical direction, again influencing the air-mass flow. Mechanical ventilation can also be included in this network. The duct system can be treated like the other flow paths in the building. The advantage for calculating air flow distribution effects of mechanical ventilation systems is that the duct pathways, as well as their connections with the building, are known. In the case of mechanical ventilation systems the fan can be described as the source of pressure differences, lifting the pressure level between two joints according to the characteristic curve of the fan. Because of the nonlinear dependency of the volume flow rate on the pressure differ-

ence, the pressure distribution for a building can be calculated only by using a m e t h o d of iterations. To describe buildings with arbitrary floor plans and to solve the set of nonlinear equations, large computer storage is necessary.

LITERATURE REVIEW

The Air Infiltration Centre (AIC) has recently published a review of ten mathematical infiltration models [2] that have been developed in five of the AIC participating countries. Only five of those described are multichamber infiltration models. The additional ten multichamber models described in this report show the necessity of a extended search. A literature survey produced 26 papers describing 15 different models developed in eight countries. In addition to the scarcity of computer programs for modelling infiltration in multicellular structures the descriptions of existing programs were not adequate for our purposes. Accordingly we developed a questionnaire and mailed it to all program authors, and completed one for our own model as well. In cases where the questionnaire was not returned, we answered the questions ourselves by using the reviewed literature. If, in these cases, the reviewed papers did not give us a reasonable answer to a certain problem, we entered a question mark in the questionnaire. The completed questionnaires are reproduced below. The addresses shown are the current addresses of the authors, rather than the addresses of the institution where the program was developed. Equations and references are reproduced separately in Appendix 1.

Questionnaires received from authors o f computer programs N a m e a n d address:

D. W. Etheridge, British Gas C o r p o r a t i o n , W a t s o n House, Peterborough Road, L o n d o n $W6 3HN, United Kingdom.

References:

3 -6

125 E q u a t i o n used for - - flow t h r o u g h cracks: flow t r o u g h large o p e n i n g s : - - flow t h r o u g h d u c t w o r k : - - fan flow characteristics: w i n d pressure: -- thermal buoyancy : o u t s i d e pressure f l u c t u a t i o n : circulation flow o n large o p e n i n g s : - -

1 (D) 2 (D) constant

- -

5 (c)

- -

6 (B) 7 (h)

- -

A l g o r i t h m t o solve t h e n o n l i n e a r set o f e q u a t i o n s -- name of algorithm: -- equation :

Maximal n u m b e r o f r o o m s : (including shafts, corridors, etc.) Limits o n n u m b e r o f - - o p e n i n g s per r o o m : - - shafts, corridors, floors: ventilation systems: -

-

m

e

c

h

a

n

i

c

a

l

Program language: Program available: Written for c o m p u t e r t y p e :

Internal r e f e r e n c e pressure adjusted until flow errors negligible ? VENT1 40

VENT2 2

n o limits per r o o m 40/40/40 o n e flow per o p e n i n g

40 0 1

F O R T R A N 77 limited availability H A R R I S and CAI A L P H A

BASIC limited availability T E K T R O N I K 4 0 / 5 HP 87

N a m e and address:

P. R. Warren and M. D. A. E. S. Perera, Building Research E s t a b l i s h m e n t , Bucknalls Lane, G a r s t o n , Watford WD2 7JR, United Kingdom.

References:

7

E q u a t i o n used for - - flow t h r o u g h cracks : flow t h r o u g h large o p e n i n g s : - - flow t h r o u g h d u c t w o r k : - - fan flow characteristics: wind pressure: -- thermal buoyancy: o u t s i d e pressure f l u c t u a t i o n : c i r c u l a t i o n flow o n large o p e n i n g s : - -

- -

1 (H) 2(D) 3 (D) 4(D) 5 (B) 6 (F)

- -

- -

A l g o r i t h m to solve t h e n o n l i n e a r set o f e q u a t i o n s name of algorithm : equation : - -

- -

Maximal n u m b e r o f r o o m s : (including shafts, corridors, etc.) Limits o n n u m b e r o f - - o p e n i n g s per r o o m : - - shafts, c o r r i d o r s , floors: ventilation systems: -

-

m

e

c

h

a

n

i

c

a

l

Program language: Program available: Written for c o m p u t e r t y p e :

BREEZE Iterative technique using linear approximation to a set of nonlinear equations including Q and P 60

n o t r e s t r i c t e d ; o n e cell can be j o i n t e d t o a n o t h e r b y o n l y o n e flow p a t h max. no. o f r o o m s ; 10 floors no r e s t r i c t i o n e x c e p t t h a t t h e y c o n f o r m t o an overall size r e s t r i c t i o n o f 60 z o n e s

FORTRAN 77 Yes, but not user-friendly V A X ; it also has been implemented on T E L 1904S

126 Name and address:

P. J. J a c k m a n , Building Services Research and I n f o r m a t i o n Association, Old Bracknetl Lane West, Bracknell, Berkshire RG12 4AH, United Kingdom.

References :

8, 9

E q u a t i o n used for - - flow t h r o u g h cracks: - - flow t h r o u g h large o p e n i n g s : - - flow t h r o u g h d u c t w o r k : - - fan flow characteristics: - - w i n d pressure: -- thermal buoyancy : - - o u t s i d e pressure f l u c t u a t i o n : - - c i r c u l a t i o n flow o n large o p e n i n g s : A l g o r i t h m to solve t h e n o n l i n e a r set o f e q u a t i o n s - - n a m e o f algorithm : - -

equation:

1 (c) 2(c)

not applicable not applicable 5 (B) 6 (C) not applicable not applicable H a r d y Cross t o establish reasonable first e s t i m a t e f o l l o w e d by Cholesky triangular f a c t o r i z a t i o n 8 (C)

Maximal n u m b e r o f r o o m s : (including shafts, corridors, etc.) Limits o n n u m b e r o f - - o p e n i n g s per r o o m : - - shafts, corridors, floors: m e c h a n i c a l ventilation s y s t e m s :

limited by available c o m p u t e r m e m o r y size

Program language: Program available : Written for c o m p u t e r t y p e :

FORTRAN for use b y B S R I A s t a f f o n l y P R I M E 300

- -

no particular limit no particular limit no particular limit; mechanical v e n t i l a t i o n is s i m u l a t e d as specified air flow rate per r o o m

Name and address:

J. Gabrielsson, E k o n o A s s o c i a t i o n for P o w e r and Fuel E c o n o m y , P.O. Box 27, 00131 Helsinki 13, Finland.

References:

10

E q u a t i o n used for - - flow t h r o u g h cracks: flow t h r o u g h large openings: - - flow t h r o u g h d u c t w o r k : fan flow characteristics: w i n d pressure : -- thermal buoyancy : o u t s i d e pressure f l u c t u a t i o n :

1 (G)

- -

- -

- -

- -

3 (A) i n t e r p o l a t e d f r o m fan curve 5 (E)

6 (B) as in ASHRAE procedure for determining heating and cooling loads for computerized energy calculations. Algorithms for building's heat transfer subroutines, New York 1971

- - c i r c u l a t i o n flow o n large o p e n i n g s : A l g o r i t h m t o solve t h e n o n l i n e a r set o f e q u a t i o n s o f algorithm equation: - -

n

a

m

e

:

- -

Maximal n u m b e r o f r o o m s : (including shafts, corridors, etc.) Limits o n n u m b e r o f - - o p e n i n g s per r o o m : - - shafts, corridors, floors: m e c h a n i c a l ventilation s y s t e m s : - -

8 (A) 725

unlimited 5; 720; 720 20

127 Program language : Program available: Written for c o m p u t e r t y p e :

F O R T R A N 77 limited ( F i n n i s h manuals o n l y ) V A X 11/780

N a m e and address:

C. Y. Shaw, Bldg. M-24 Division o f Building Research, NRC, M o n t r e a l R o a d , Ottawa KIA OR6, Canada.

References:

11 - 13

E q u a t i o n used for - - flow t h r o u g h cracks: - - flow t h r o u g h large o p e n i n g s : - - flow t h r o u g h d u c t w o r k : - - fan f l o w characteristics: -w i n d pressure: -- thermal buoyancy: - - o u t s i d e pressure f l u c t u a t i o n : - - c i r c u l a t i o n flow on large o p e n i n g s : A l g o r i t h m to solve t h e n o n l i n e a r set o f e q u a t i o n s -n a m e o f algorithm : -- equation: Maximal n u m b e r o f r o o m s : (including shafts, corridors, etc.) Limits o n n u m b e r o f - - o p e n i n g s per r o o m : - - s h a f t s , corridors, floors: -mechanical ventilation systems: Program language : Program available : Written for c o m p u t e r t y p e :

N a m e and address:

Walton, National Bureau o f Standards, BR/B114, Washington DC 20234, U n i t e d States o f America.

References:

14

1 (F) 2 (E) constant cp ( w i n d t u n n e l m e a s u r e m e n t s ) 6 (D)

CP 45 8 (D) 25 c o m p o n e n t s and 8 shafts

4 1

up to 8 F O R T R A N IV yes IBM 360

G . N .

E q u a t i o n used for - - f l o w t h r o u g h cracks: - - flow t h r o u g h large o p e n i n g s : - - flow t h r o u g h d u c t w o r k : - - fan flow characteristics: -w i n d pressure: -- thermal buoyancy : - - o u t s i d e pressure f l u c t u a t i o n : - - c i r c u l a t i o n flow o n large o p e n i n g s :

5 (A) 6 (A) user input by multiple large openings

A l g o r i t h m t o solve t h e n o n l i n e a r set o f e q u a t i o n s -n a m e o f algorithm : -equation :

Newton (modified) 8 (E)

Maximal n u m b e r o f r o o m s : (including shafts, corridors, etc.) Limits o n n u m b e r o f - - o p e n i n g s per r o o m : - - shafts, corridors, floors : -mechanical ventilation systems:

1 (A)

2 (A)

it is i n t e n d e d t h a t t h e p r o g r a m be c o m p i l e d w i t h t h e a p p r o p r i a t e values o f a f e w p a r a m e t e r s t a t e m e n t s t o m a t c h t h e p r o g r a m to t h e p r o b l e m

128 Program language : Program available : Written for c o m p u t e r t y p e :

F O R T R A N 77 yes S P E R R Y 1100 (also running o n V A X and IBM)

Name and address:

S. J. Irving, The Oscar F a b e r s h i p M a r l b o r o u g h House, Upper Marlborough Road, St. Albans, Hefts. A L l 3UT, United Kingdom.

References :

15, 16

E q u a t i o n used for - - flow t h r o u g h cracks : - - flow t h r o u g h large openings: - - flow t h r o u g h d u c t w o r k : - - fan flow characteristics: wind pressure: -- thermal buoyancy: -- o u t s i d e pressure f l u c t u a t i o n : - - c i r c u l a t i o n flow o n large o p e n i n g s : -

-

A l g o r i t h m t o solve t h e nonlinear set o f e q u a t i o n s name of algorithm: equation : -

-

-

-

1 (U) 2(B) 4 (A)

5 (B) 6 (B)

Newton-Raphson 8 (B)

Maximal n u m b e r o f r o o m s : (including shafts, corridors, etc.) Limits o n n u m b e r of - - o p e n i n g s per r o o m : -- shafts, corridors, floors: mechanical ventilation s y s t e m s :

300

Program language : Program available : Written for c o m p u t e r t y p e :

F O R T R A N IV limited availability P R I M E 50 series m a c h i n e

-

120 no limits w i t h i n t h e above c o n s t r a i n t s

-

Name and address:

Ch. F. Pedersen, Statens Byggeforskningsinstitut, P o s t b o k 113, DK-2970 H o r s h o l m , Denmark.

References:

17

E q u a t i o n used for - - flow t h r o u g h cracks: - - flow t h r o u g h large openings: - - flow t h r o u g h d u c t w o r k : fan flow characteristics : wind pressure: -- thermal buoyancy : o u t s i d e pressure f l u c t u a t i o n : circulation flow o n large o p e n i n g s -

-

-

-

-

-

-

-

A l g o r i t h m t o solve t h e n o n l i n e a r set o f e q u a t i o n s name of algorithm : equation : -

-

-

-

Maximal n u m b e r o f r o o m s : (including shafts, corridors, etc.) Limits o n n u m b e r of o p e n i n g s per r o o m : - - shafts, corridors, floors : mechanical ventilation systems : -

-

-

-

(i) 9 ? 9 9 9 9

n o d e s and l o o p s ~ la K i r c h h o f f ?

100

129 Program language: Program available: Written for c o m p u t e r t y p e :

N a m e and address:

W. F. deGids, I n s t i t u t e for E n v i r o n m e n t a l Hygiene - - TNO, P.O. Box 214, NE-2600 AE Delft, Netherlands.

References:

18

E q u a t i o n used for - - flow t h r o u g h cracks: flow t h r o u g h large o p e n i n g s : - - flow t h r o u g h d u c t w o r k : - - fan flow characteristics: wind pressure: -- thermal buoyancy : o u t s i d e pressure f l u c t u a t i o n : circulation flow on large o p e n i n g s : -

-

-

-

-

-

-

-

A l g o r i t h m t o solve the n o n l i n e a r set o f e q u a t i o n s n a m e o f algorithm : equation : -

-

-

-

Maximal n u m b e r o f r o o m s : (including shafts, corridors, etc.) Limits o n n u m b e r o f - - o p e n i n g s per r o o m : - - shafts, corridors, floors : m e c h a n i c a l ventilation s y s t e m s : -

N a m e and address:

W. B r i n k m a n n , B u n d e s b a u d i r e k t i o n Berlin, F a s a n e n s t r a s s e 87, D-1000 Berlin 12, Federal R e p u b l i c o f G e r m a n y .

References :

19

E q u a t i o n used for - - flow t h r o u g h cracks: flow t h r o u g h large o p e n i n g s : - - flow t h r o u g h d u c t w o r k : - - fan flow characteristics : w i n d pressure: -- thermal buoyancy : o u t s i d e pressure f l u c t u a t i o n : flow on large o p e n i n g s : -

-

-

-

K-Newton 8 (D) 50

total n u m b e r o f c o n n e c t i o n s smaller t h a n 200

HPL no

HP 9 8 2 5 / H P 9816

1 (E)

5 (D) 6 (B)

-

-

-

c

i

r

c

u

l

a

t

i

o

n

A l g o r i t h m to solve the nonlinear set o f e q u a t i o n s n a m e o f algorithm : -- equation: -

5 (B) 6 (G) 7 (B)

-

Program language : Program available: Written for c o m p u t e r t y p e :

-

1 (E) 2 (F) 3 (E) 4 (E)

-

Maximal n u m b e r o f r o o m s : (including shafts, corridors, etc.)

t h e e x a c t n o n l i n e a r e q u a t i o n s were solved to d e t e r m i n e the volume flow rate: t h e balance o f in- and o u t f l o w i n g air was d e t e r m i n e d by iteration (variation o f t h e neutral pressure level N P L ) in h o r i z o n t a l direction (per floor) 3 groups o f r o o m s ; outside g r o u p divided in w i n d w a r d a n d leeward flats, inner

130 group (shafts), m i d d l e group (corridors) c o m b i n e t h e d i f f e r e n t groups: in vertical d i r e c t i o n ; 30 Limits o n n u m b e r o f - - o p e n i n g s per r o o m : - - shafts, corridors, floors: - - m e c h a n i c a l ventilation s y s t e m s :

o n e to each a t t a c h e d region u n l i m i t e d ; o n e per floor; 30 n o m e c h a n i c a l ventilation

Program language: Program available: Written for c o m p u t e r t y p e :

HP-Special only in parts HP

N a m e and address:

H . E . Feustel, L a w r e n c e Berkeley L a b o r a t o r y , Building 90, R o o m 3074, Berkeley, CA 94720, U n i t e d States o f America.

References:

20, 21

E q u a t i o n used for - - flow t h r o u g h cracks: flow t h r o u g h large o p e n i n g s : - - flow t h r o u g h d u c t w o r k : - - fan flow characteristics: w i n d pressure: -- thermal buoyancy : o u t s i d e pressure f l u c t u a t i o n : - - c i r c u l a t i o n flow o n large o p e n i n g s :

1 (E)

- -

- -

3 (B)

4 (B) 5(D)

6 (B)

- -

A l g o r i t h m t o solve t h e nonlinear set o f e q u a t i o n s n a m e o f algorithm : equation : - -

- -

Maximal n u m b e r o f r o o m s : (including shafts, corridors, etc.) Limits o n n u m b e r o f - - o p e n i n g s per r o o m : - - shafts, corridors, floors : ventilation systems: - - m e c h a n i c a l

Program language : Program available : Written for computer type:

N a m e and address:

G. Hausladen, Schiedel G m b H & Co., L e r c h e n s t r a s s e 9, P o s t f a c h 50 05 65, D-8000 Munich 50, Federal R e p u b l i c o f G e r m a n y .

References:

22 - 24

E q u a t i o n used for - - flow t h r o u g h cracks : flow t h r o u g h large o p e n i n g s : -- flow through duct work: fan flow characteristics : w i n d pressure : -- thermal buoyancy : o u t s i d e pressure f l u c t u a t i o n : flow o n large openings:

Newton 8 (B) 200

unlimited no limit w i t h i n t h e above c o n s t r a i n t s 6 F O R T R A N IV no

CDC C Y B E R

1 (E)

- -

- -

- -

- -

- - c i r c u l a t i o n

3 (C) 4 (c) 5 (B) 6(E)

131 A l g o r i t h m t o solve t h e n o n l i n e a r set of e q u a t i o n s name of algorithm: equation: - -

- -

Maximal n u m b e r of r o o m s : ( i n c l u d i n g shafts, corridors, etc.) Limits o n n u m b e r of -- o p e n i n g s p e r r o o m : - - shafts, corridors, floors: mechanical ventilation systems: - -

4

1;0;? ?

P r o g r a m language: P r o g r a m available : W r i t t e n for c o m p u t e r t y p e :

N a m e a n d address:

References :

J.P. Cockroft, Building Services R e s e a r c h Unit, U n i v e r s i t y of Glasgow, 3 Lillybank Gardens, Glasgow G 1 2 8 R Z , United Kingdom. 2 5 ,

2 6

E q u a t i o n used for - - flow t h r o u g h cracks: -- flow t h r o u g h large o p e n i n g s : - - flow t h r o u g h d u c t w o r k : fan flow c h a r a c t e r i s t i c s : wind pressure: -- thermal buoyancy: o u t s i d e pressure f l u c t u a t i o n : c i r c u l a t i o n flow o n large o p e n i n g s : - -

1 (E) n o t specified ? ? ?

- -

? ?

- -

- -

n o t specified

A l g o r i t h m to solve t h e n o n l i n e a r set o f e q u a t i o n s n a m e of a l g o r i t h m : equation : - -

- -

M a x i m a l n u m b e r of r o o m s : (including shafts, corridors, etc.) Limits o n n u m b e r of -- openings per room: - - shafts, corridors, floors: mechanical ventilation systems : - -

P r o g r a m language: P r o g r a m available : W r i t t e n for c o m p u t e r t y p e :

Name and address:

R. E. Bilsborrow, D e p a r t m e n t of Building Science, F a c u l t y o f t h e A r c h i t e c t u r a l Studies, University o f Sheffield, Sheffield $10 2TN, United Kingdom.

References:

27, 28

E q u a t i o n used for - - flow t h r o u g h cracks: flow t h r o u g h large o p e n i n g s : - - flow t h r o u g h d u c t w o r k : fan flow c h a r a c t e r i s t i c s : wind pressure: - -

- -

- -

1 (E) ? ? ? ?

132 -- t h e r m a l b u o y a n c y : outside pressure f l u c t u a t i o n : c i r c u l a t i o n flow o n large o p e n i n g s : -

-

-

-

A l g o r i t h m to solve t h e n o n l i n e a r set o f e q u a t i o n s n a m e of a l g o r i t h m : equation : -

-

-

-

Maximal n u m b e r of r o o m s : ( i n c l u d i n g shafts, corridors, etc.) Limits o n n u m b e r of -- o p e n i n g s per r o o m : -- shafts, corridors, floors: mechanical ventilation systems:

4 1 ; ?; 10 ?

P r o g r a m language : Program available : W r i t t e n for c o m p u t e r t y p e :

FORTRAN yes ICL 1907

-

-

N a m e a n d address:

K . S . Swetlov, Soviet U n i o n .

References :

29

E q u a t i o n used for -- flow t h r o u g h cracks: flow t h r o u g h large o p e n i n g s : -- flow t h r o u g h d u c t w o r k : fan flow c h a r a c t e r i s t i c s : -- w i n d pressure: -- t h e r m a l b u o y a n c y : o u t s i d e pressure f l u c t u a t i o n : c i r c u l a t i o n flow o n large o p e n i n g s : -

-

-

-

-

-

-

-

A l g o r i t h m t o solve t h e n o n l i n e a r set of e q u a t i o n s n a m e of a l g o r i t h m : equation: -

-

-

-

Maximal n u m b e r o f r o o m s : (including shafts, corridors, etc.) Limits o n n u m b e r of -- o p e n i n g s per r o o m : -- shafts, corridors, floors : ventilation systems: -

-

m

e

c

h

a

n

i

c

a

211

1 (D) 2 (G)

2(G) ? ? ? ? ?

Newton 0

150

l

Program language: Program available : Written for c o m p u t e r t y p e :

DISCUSSION Whereas single-cell models are somewhat more variable in their performance [2], the

investigated multichamber models were, with regard to the equations used, very similar to each other. The flow equation used to describe the air flow characteristics of the

133

buildings is similar to the one describing measured results for air flow through building components [30 - 36]. Twelve of the 15 programs use this empirical power-law expression t y p e of equation; even though the pressure e x p o n e n t m a y differ from 0.5 to 1.0, depending on the nature of flow. A comparison of air leakage measurements conducted in 196 houses by means of the blower door technique showed, f o r the whole house, a mean value for the exponent of 0.66 [37], which is in good agreement with the measured flow characteristics of building components. A second commonality among program authors {six of the fifteen) was their use of Newton's m e t h o d of iteration for solving the set of nonl.inear equations. However, the m e t h o d of solving this problem varied from simple one-dimensional methods [23] to the two-dimensional methods described above. The differences are seen in the necessary storage and the quality of convergence. Unfortunately, the programs reviewed here have one negative point in c o m m o n : most of them are available only to a limited number of users. The programs differ most in their ability to simulate mechanical ventilation systems. Eight of them are n o t able to simulate forced ventilation at all, or at least the references do n o t indicate any handling of ventilation systems; two use the simplified m e t h o d of setting a fixed air-mass flow for unbalanced mechanical ventilation systems, and only five describe mechanical ventilation systems by means of fan and duct characteristics. The latter are able to simulate the interaction of mechanical and natural ventilation. The difficulties of measuring infiltration in multichamber structures means that few such models have been validated properly, if at all. The possibility of doing piecemeal validations of certain algorithms has been considered; e.g. the algorithms for air flow through open doorways or air flow through cracks have been tested separately [38]. Even though infiltration cannot be measured for an entire building at once, measuring a few cells of the whole structure could still provide a severe test for existing models. These data are important not only for validation purposes but also as a means of further understanding of air m o v e m e n t in large multizoned buildings. We need to

identify the critical variables in different building types in order to develop more accurate input data, and u l t i m a t e l y , more accurate models. Wind pressure coefficients, for example, represent a factor that needs further study, and collating of existing data should help our efforts to simplify data requirements.

CONCLUSION

Multichamber infiltration models treat the true complexity of flows in a building in recognizing effects of internal flow restrictions. They require extensive information a b o u t flow characteristics and pressure distributions, and, in many cases, are t o o complex to justify their use to predict flow for simple structures, such as single-family residences [39]. Most multicellular models presently in use are n o t available to the public or are written as research tools, rather than for the use of professional engineers or architects. There is an obvious need for a simplified multichamber infiltration model capable of providing the same accuracy as the established single-cell models.

ACKNOWLEDGEMENTS

This work was supported by the Assistant Secretary for Conservation and Renewable Energy, Office of Building Energy Research and Development, Building Systems Division of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098. We should like to acknowledge the cooperation of the program authors in responding to our questionnaires, for without this information the different programs could not have been compared. We must also acknowledge Peter Cleary and Laural Cook for their critical review and helpful comments. No undertaking of this kind escapes the welcome scrutiny of all our colleagues at the Energy Performance of Buildings Group. In particular we appreciate the valuable comments of Richard Diamond during the writing process.

134 REFERENCES

1 M. H. Sherman and D. T. Grimsrud, Measurement of infiltration using fan pressurization and weather data, Proc. 1st AIC Conference, Windsor, England, 1980. 2 M. Liddament and C. Allen, The Validation and Comparison o f Mathematical Models o f Air Infiltration, Technical Note AIC 11, Air Infiltration Centre, 1983. 3 D. W. Etheridge and D. K. Alexander, The British Gas Multicell Model for Calculating Ventilation, A S H R A E Trans., 86 (II) (1980) 808 - 821. 4 D. W. Etheridge, Crack flow equation and scale effect, Build. Environ., 12 {1977) 181 - 189. 5 D. W. Etheridge and J. A. Nolan, Ventilation measurements at model scale in a turbulent flow, Build. Environ., 14 (1979) 53 - 64. 6 D. W. Etheridge and P. Phillips, The prediction of ventilation rates in houses and the implications for energy conservation, Proc. C.I.B. Steering Group $17 Meeting, Holzkirchen, 1977, pp. 46 - 67. 7 E. Evers and A. Waterhouse, A Computer Model for Analysing Smoke Movement in Buildings, CP 69/78, Building Research Establishment, 1978. 8 P. J. Jackman, A study of the natural ventilation of tall office buildings, JIHVE, 38 (1970) 103 118. 9 P. J. Jackman, Heat loss in buildings as a result of infiltration, Building Services Eng., 42 (1974) 6-15. 10 J. Gabrielsson and P. Porra, Calculation of infiltration and transmission heat loss in residential buildings by digital computers, J. Inst. Heat. Vent. Eng., 35 (1968) 357 - 368. 11 D. M. Sander and G. T. Tamura, A F O R T R A N IV Program to Simulate Air Movements in Multistorey Buildings, DBR Computer Program No. 35, National Research Council of Canada, 1973. 12 D. M. Sander, A F O R T R A N IV Program to Calculate Air Infiltration in Buildings, DBR Computer Program No. 37, National Research Council of Canada, 1974. 13 C. Y. Shaw, D. M. Sander and G. T. Tamura, A F O R T R A N I V Program to Simulate StairShaft Pressurization System in Multi-storey Buildings, DBR Computer Program No. 38, National Research Council of Canada, 1974. 14 G. N. Walton, Thermal Analysis Research Program Reference Manual, NBSIR 83-2655, U.S. Department of Commerce, 1983. 15 S. J. Irving and A. P. Wilson, Validation of a smoke movement program, Building Services Engineering Res. & Technol., 2 (4) (1981) 151 159. 16 S. J. Irving, The computer simulation of smoke movement during building fires, Fire Prev. Sci. Technol., 22 (1979) 3 - 8. 17 Ch. F. Pedersen, Datamatberegning af Luftstromninger i Bygninger, Statens Byggeforskningsinstitut, Notat 72, 1977.

18 W. F. deGids, Calculation Method for the Natural Ventilation o f Buildings, Publ. No. 632, TNO Research Institute for Environmental Hygiene, Delft, 1977. 19 W. Brinkmann, Zur Bestimmung des Liiftungsw~irmebedarfs hoher Geb~iude, Dissertation, Technische Universit~it Berlin, 1980. 20 H. E. Feustel, Beitrag zur theoretischen Beschreibung der Druck und Luftmassenstromverteilung in natfrlich und maschinell geliifteten Geb~iuden, Fortschritt-Berichte der VDI-Zeitschriften, 1984, Reihe 6, Nr. 151. 21 H. E. Feustel and H. Esdorn, Mass flow distribution in high-rise buildings with forced ventilation systems, Proc. Int. Conf. on System Simulation in Buildings, Lidge, 1982, University of Li6ge. 22 G. Hausladen, WohnungsliJftung, Untersuchung der verschiedenen L/iftungsarten bzw. Liiftungspraktiken unter hygienischen, bauphysikalischen und energetischen Gesichtspunkten, Dissertation Technische Universit~it MiJnchen, FortschrittBerichte der VDI Zeitschriften, 1980, Reihe 6, Nr. 73. 23 G. Hausladen, Luftwechsel in Wohnungen, Heizung Liiftung Haustechnik, 1 (1978) 21 - 28. 24 W. Krueger and G. Hausladen, Einfluss yon Windund thermischen Kr~iften auf das Betriebsverhalten yon mechanisch betriebenen Entliiftungsanlagen in mehrgeschossigen Wohngeba'uden, Forschungsbericht des Instituts fiir Haustechnik, Technische Universit~it Miinchen, 1979. 25 J. P. Cockroft, Air flows in buildings, Proc. The Environment Inside Buildings Symposium, Southend on Sea, 1979. 26 J. P. Cockroft, Validation of buildings and systems energy prediction using real measurements, Computer Aided Design, 14 (1) (1982) 39 - 43. 27 R. E. Bilsborrow, Digital Analogue for Natural Ventilation Calculations, Report No. BS 6, Department of Buildings Science, University of Sheffield, 1973. 28 A. C. Pitts and I. C. Wards, A Review o f the Prediction and Investigation o f Air Movement in Buildings, Report No. BS 69, Department of Buildings Science, University of Sheffield, 1983. 29 K. S. Swetlov, Calculations of Air Infiltration in Multi-story Buildings using Electronic Computers, Vodosnabzie i Sanitarna Tekhnika, 11 (1966), HVRA-Translation 122. 30 L. P. Hopkins and B. Hansford, Air flow through cracks, Building Services Eng., 42 (1974) 123 131. 31 D. Holz, Zusammenhang zwischen der Fugendurchllissigkeit yon Fenstern und dem Luftwechsel im Haus, Forschungsbericht T80-075, Bundesministerium fiir Forschung und Technologie, 1980. 32 F. Peterson, On flow in narrow slots applied to infiltration, Proc. 3rd AIC Conference, London, 1982. 33 E. Raisch, Die W~irme- und Luftdurchl~/ssigkeit yon Fenstern versehiedener Konstruktion, GI Gesundheits-lngenieur, 45 (1922) 99 - 105. 34 H. Reiher, K. Fraass and E. Settle, Ober die

135

35 36 37

38

39

Frage der Luft- und W~'rmedurchl~issigkeit von Fenstern, 1. Teilbericht, Wa'rmewirtschaftliche Nachrichten, 6 (1932/1933) 45 - 52 and 55 - 59. W. Schuele, Luftdurchl~issigkeit yon Fenstern, GI Gesundheits-Ingenieur, 83(b) (1962) 181 184. K. Sigwart, Luftdurchl~issigkeit yon Holz- und Stahlfenstern, GI Gesundheits-Ingenieur, 55 (1932) 515 - 517. M. H. Sherman, D. J. Wilson and D. E. Kiel, Variability in residential air leakage, Proc. A S T M Symposium on Measured Air Leakage Performance o f Buildings, Philadelphia, 1984. B. H. Shaw and W. Whyte, Air movement through doorways -- the influence of temperature and its control by forced air flow, Building Services Eng., 42 (12) (1974) 210 - 218. A S H R A E Handbook o f Fundamentals, Ch. 22, to be published in 1985.

Subscripts o outside f, i, r, s l o c a t i o n s in t h e d u c t s y s t e m i inside ] iteration step j + 1 iteration step + 1 s stack v velocity 0 reference NET inside

TABLE 1 Equations used for flow through cracks APPENDIX 1

List of symbols A area B constant C crack flow coefficient CR correction term D flow coefficient E effective leakage area F mass f l o w r a t e H height K constant L crack length N number of storeys P pressure Q volume flow rate S resistance T temperature X considered storey a, b, c coefficients Cp surface pressure coefficient f function of g gravity i, m number of ductwork components n flow exponent t temperature

m

2

F=DxApn

1 (B)

Q = D x AP n

1 (C)

Q

D -

3600

m a / m h Pa n Pa m a / h Pan cm 2 kg/h m m Pa ma/h h Pa/m a K

X

Apl/n

3600

I(D)

A P = a x Q2+b x O

1 (E)

Q=CXLXAP n

1 (F)

F=KxApx

I(G)

Q=CxA

l(H)

AP = (~--~) n

1 (I)

AP=0.5X L

x AP n

xpx

Q2

TABLE 2 Equations used for flow through large openings -m/s 2

2 (A)

F = D x Apn

2 (B)

Q = D × hp" Q

--

v

wind speed

°C m/s

z p p X

depth of crack air d e n s i t y v i s c o s i t y o f air friction factor f i t t i n g loss c o e f f i c i e n t absolute temperature

m kg/m a m2/s --K

0

I(A)

D -

x AP l/n

2 (C)

3600

3600

2(D)

Q=AXCX(~-~)

2(E)

F=KxZAP x

2 (F)

Q =A

2(G)

AP=SxQ2

X

(2 ~tP) I/n

,/:

X

(I/p) I/2

136 TABLE 3

TABLE 6

E q u a t i o n s used for flow t h r o u g h d u c t w o r k

E q u a t i o n s used for t h e r m a l b u o y a n c y

3(A)

6 (A)

Ap=p

xgxAH

6(B)

A p = (Po - - P i ) x g x ( H - - H o )

6 (C)

A p = 3462 X ( H - - H o ) x

6 (D)

Ap=(po--Pi)XgxH

6 (E)

Ap=(po--pi)

Q=CxA[Pf--pfxg

X Hr-Hf

x

+ -2

-- H s

--Pi +pi xg

•

Hs -×gxttx(X-0.5-N/2)

xb+e

i=1 3 (C)

P - - -- x v 2x 2

i

1 +~

3(D)

AP= K+~-

3 (E)

O = ANE w X (2 A p ) l

( 0 )

6(F)

Q = (CD X A / n ) X AO x g x -

6 (G)

'Ti -- To 1 AP=po XiTiXTo XT o xgxH

1/2

+APvE--PD=0

\~/

l

\__

TABLE 4 E q u a t i o n s used for fan flow characteristics

TABLE 7 E q u a t i o n s used for o u t s i d e pressure f l u c t u a t i o n s

4(A)

Q=KI+K2X

AP+K 3XAP 2

4(B)

AP=KI+K2×Q+K3xQ2

7 (A)

( A P ' 2 ) 0"s = 0.5 X (Po'2) 0.s

4(C)

Ap=Ap o-KI×Q-K2XQ2

7 (B)

Qv = 1/2

4(D)

AP=Bxn

4 (E)

A p = f(Qv)

Q2 2XD 2

×

ANE w × (0.001V 2 + 0.0035

X H X AT + 0.01) I/2

+ A 2 XD 4

TABLE 5 E q u a t i o n s used for wind pressure TABLE 8 5 (A)

P A p = _ X v2 2

5(B)

AP=Cx

Po -- xv 2

A l g o r i t h m t o solve t h e nonlinear set of e q u a t i o n s

8(A)

ej+~=pj+( QJ] "j

XVo 2

8(B)

Pj+~=ey----

Xv(H) 2

8 (C)

CR =

\ C~A/ ~Q

2 5(C)

AP=CX_

P 2

5(D)

AP=CX--

P

~ D × A P wn

2 5 (E) with

~

-- X A P ( ( l / n ) - l )

I° n

P A p = _ X v2 2

8 (D)

~F

v = v0 x 2334 x (1 + 2.8 l n ( H + 4.75))

8 (E)

Pj + l = PJ - - C o r r e c t i o n

= 0

[