Simulation of air movement in multi-storey buildings

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Simulation of air movement in multi-storey buildings

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National Research

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Council Canada

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SIMULATION

OF

AIR MOVEMENT IN

MULTI-STOREY BUILDINGS

by

D.M.

Sander and

G.T. Tamura

//

Reprinted, with permission,

from

Vol. 1, Proceedings 2nd Symposium on Use of Computers for Thermal Environmental Engineering, Paris, 1974 p.

1 6 5 . 1 7 1

DBR

Paper No.

815

Division of Building Research

SOMMAIRE

Les f u i t e s d ' a i r 1 t r a v e r s l ' e n v e l o p p e e x t 6 r i e u r e d'un E d i f i c e s o n t un dl6ment i m p o r t a n t d e s c h a r g e s c a l o r i f i q u e s , de r e f r o i d i s s e m e n t e t d1humidit6 des systgmes de c h a u f f a g e , de v e n t i l a t i o n e t de c l i m a t i s a t i o n . La p r 6 d i c t i o n d e s v o i e s de d6placement d e l ' a i r e t d e s v i t e s s e s d16coulement 1 l V i n t 6 r i e u r d'un 6 d i f i c e joue 6galement un r81e i m p o r t a n t dans l a l u t t e c o n t r e l e s Gldments p o l l u a n t s cornme l a fum6e e t les o d e u r s . Le p r 6 s e n t a r t i c l e d 6 c r i t une m6thode d e c a l c u l des 6coulements d ' a i r e t des d i f f s r e n c e s d e p r e s s i o n que peuvent p r o d u i r e dans un d d i f i c e 1 p l u s i e u r s 6 t a g e s l e s e f f e t s combin6s du v e n t , d e l ' a p p e l d ' a i r e t de l ' e x p l o i t a - t i o n d e s s y s t s m e s d e t r a i t e m e n t d e l ' a i r .

ABSTRACT

Air t h a t l e a k s t h r o u g h t h e e x t e r i o r envelope of a building i s a s i g - n i f i c a n t c o m p o n e n t of t h e h e a t i n g , cooling and m o i s t u r e l o a d s of heating, ventilating, and a i r - c o n d i t i o n i n g s y s t e m s . T h e p r e d i c t i o n of a i r m i g r a - tion r o u t e s and flow r a t e s within a building i s a l s o i m p o r t a n t in r e l a t i o n t o t h e c o n t r o l of c o n t a m i n a n t s , s u c h a s s m o k e and o d o u r s . T h i s p a p e r d e s c r i b e s a p r o c e d u r e f o r c a l c u l a t i n g a i r flows and p r e s s u r e d i f f e r e n t i a l s t h a t will o c c u r in a m u l t i - s t o r e y building a s a r e s u l t of a combination of wind e f f e c t , s t a c k e f f e c t , and o p e r a t i o n of a i r - h a n d l i n g s y s t e m s .

MATHEMATICAL MODEL O F BUILDING

A i r l e a k a g e t h r o u g h t h e e x t e r n a l w a l l s and i n t e r n a l s e p a r a t i o n s of a building can be s i m u l a t e d with a r e l a t i v e l y s i m p l e m a t h e m a t i c a l m o d e l . Its b a s i c c o m p o n e n t s a r e i l l u s t r a t e d in F i g u r e 1 f o r a t y p i c a l s t o r e y of a m u l t i - s t o r e y building. T h e m a i n b a r - r i e r s t o a i r m o v e m e n t a r e e x t e r i o r w a l l s , w a l l s of v e r t i c a l s h a f t s , s u c h a s e l e v a t o r s h a f t s and s t a i r w e l l s , and t h e f l o o r c o n s t r u c t i o n . T h e m o d e l h a s been s i m p l i f i e d in t h a t i t n e g l e c t s i n t e r n a l p a r t i t i o n s on t h e f l o o r s p a c e s .

1

SIMULATION OF AIR MOVEMENT IN MULTI-STOREY BUILDINGS

SANDER

D.M.,

TAMURA

G.T.,

;r

Building Services Section

,

Division of Building Research, National Research Council of Canada Ottawa

-

CANADA

M e c h a n i c a l a i r s u p p l y and e x h a u s t d u c t s h a v e a n i m p o r t a n t effect on t h e m a s s a i r b a l a n c e a t e a c h f l o o r ; when t h e y a r e not in o p e r a t i o n t h e y p r o v i d e a d d i t i o n a l i n t e r

-

c o n n e c t i o n s between f l o o r s . T h e e f f e c t s of a i r - h a n d l i n g s y s t e m s a r e taken into

a c c o u n t by s p e c i f y i n g e i t h e r t h e e x c e s s a m o u n t of s u p p l y o v e r e x h a u s t a i r t o e a c h floor s p a c e o r t h e r a t e s of s u p p l y o r e x h a u s t a i r in t h e v e r t i c a l s h a f t s t h a t have openings in t h e i r w a l l s t o f l o o r spac e s . E a c h s h a f t m a y h a v e v e n t s t o t h e o u t s i d e located a t a n y f l o o r l e v e l . 165

C 2

Air leakages occur through any c r e v i c e s between windows and walls, c r a c k s of openable windows, joints of curtain walls, and in s o m e instances through e x t e r i d r walls. Air aleo leaks through the walls of v e r t i c a l shafts, through c r a c k s formed by elevator and s t a i r w e l l doors, joints of m a s o n r y walls and s p a c e s between pipes a r ducts and the wall. Air leakages through the floor construction occur through openings around the various s e r v i c e pipes and i n t e r s t i c e s formed by the e x t e r i o r wall and the floor constructian. In the mathematical model, t h e leakage a r e a s in the major v e r t i - c a l separations have been combined and a r e represented by equivalent openings located a t mid-height of each storey.

The value of outside p r e s s u r e at mid-height of the f i r s t s t o r e y i s taken a s the r e f e r e a c e p r e s s u r e . h t s i d e a i r p r e s s u r e s a t other levels depend on the density of outside a i r and on wind speed and direction. P r e s s u r e a inside the building a t various levels a r e interrelated by the weight of the column of inside a i r between levels and the p r e s s u r e d r o p a c r o s s intervening f l o o f s . The p r e s s u r e g r d t e n f ih the v e r t i c a l shafts can usually be taken t o be just the weight of the a i r in the shbft. P r e s s u r e l o s s e s can be mignificant, holkever, when a shaft with a relatively high r e s i s t a n c e t o a i r flow, such a s a s t a i r ehaft, i s supplied with a l a r g e amount of a i r t o keep it p r e s s u r i z e d . The mathematical model for this cage is given in Appendix A.

CAIKULATION

PROCEDURE

The simulation entails determining the p r e s s u r e in e a c h space s o that the resultant flows produce a m a s s balance in e v e r y space.

The equation for the r a t e of a i r flow through the m a j o r separations can be e x p r e s - sed a s

where

F = flow r a t e a t standard condition

K

=

flow coefficient at standard condition

A P

=

p r e s s u r e difference

x = flow exponent (0. 5 s x r I . 0 ) .

The coefficient K i s determined for a i r a t standard t e m p e r a t u r e . A c o r r e c t i o n factor C needs to be used when the t e m p e r a t u r e is f a r f r o m n o r m a l a s in the c a s e of a

w h e r e P

=

d e n s i t y of e n t e r i n g a i r po = d e n s i t y of a i r a t s t a n d a r d t e m p e r a t u r e CI _{= v i s c o s i t y of e n t e r i n g a i r}

%

= v i s c o s i t y of a i r at standard t e m p e r a t u r e . T h e r e is no need t o c o r r e c t f o r v a r i a t i o n s of a few d e g r e e s in a i r t e m p e r a t u r e . The s e t of equations t o r e p r e s e n t t h e building a r e obtained by w r i t i n g m a s s balance equations for e a c h floor s p a c e and e a c h s h a f t .

F o r t h e i t h f l o o r , I Fo ( i s k) + F

-

F a ( i )

-

,

7 Fs (i, j) + ( i )

=

0 k = 1 b ( i ) and f o r t h e jth s h a f t , w h e r e

Fo (i, k) = flow f r o m outside through e x t e r i o r wall of s i d e k t o f l o o r ( i ) F = flow f r o m f l o o r below t o floor ( i )

b ( i )

F = flow f r o m f l o o r (i) t o floor above a ( i )

Fs (i, j)

=

flow f r o m f l o o r ( i ) t o s h a f t (j)

(i)

=

flow of a i r supplied t o floor ( i ) by a i r - h a n d l i n g s y s t e m

F

= flow f r o m outside into shaft ( j ) through vent opening v ( j l

F

=

flow of o u t s i d e a i r supplied i n t o s h a f t (j) by air-handling s h ( j ) s y s t e m

=

n u m b e r of s i d e s of e x t e r i o r w a l l = n u m b e r of f l o o r s

T h e flows a p p e a r i n g in Equations ( 3 a ) and (3b)

are

indicated i n F i g u r e 1. C o m - bining m a s s balance Equations (nos. 3a and 3b) with t h e flow Equation (no. 1 )

r e s u l t s in a s e t of s i m u l t a n e o u s n o n - l i n e a r equations. T h e o u t s i d e p r e s s u r e s and t h e p r e s s u r e d i f f e r e n c e s d u e t o column weight c a n be c a l c u l a t e d f o r a given condition; t h e unknown v a r i a b l e s a r e t h e n t h e f l o o r and s h a f t p r e s s u r e s . F o r

N

f l o o r s and J s h a f t s t h e r e a r e N

+

J equations.

T h e s e s i m u l t a n e o u s n o n - l i n e a r equatidns a r e solved by a method of s u c c e s s i v e l i n e a r a p p r o x i m a t i o n s . T h e n o n - l i n e a r function d e s c r i b e d by Equation (1) i s shown in F i g u r e 2.

In

t h e r e g i o n n e a r t h e paint (LIP F )

,

t h i s function m a y be a p p r o x i -

t ' t

mated by a s t r a i g h t l i n e that i s tangent t o t h e c u r v e a t t h i s point. T h e equation of t h i s tangent i s

w h e r e

E a c h l e a k a g e flow in Equations ( 3 a ) and (3b) c a n be a p p r o x i m a t e d by t h i s type of l i n e a r e x p r e s s i o n . The r e s u l t i n g s e t of l i n e a r equations c a n then be solved by s t a n d a r d m e t h o d s .

The i t e r a t i o n p r o c e d u r e i s a s follows. An i n i t i a l l i n e a r a p p r o x i m a t i o n i s m a d e f o r e a c h e l e m e n t and t h e r e s u l t i n g equations solved f o r floor and s h a f t p r e s s u r e s . T h e flows c o r r e s p o n d i n g t o t h e s e p r e s s u r e s a r e t h e n c a l c u l a t e d u s i n g Equation (1) and t h e flow through e a c h e l e m e n t i s c o m p a r e d with t h e flow used f o r t h e l i n e a r i z a t i o n of that e l e m e n t . If t h e d i f f e r e n c e i s g r e a t e r than t h e c o n v e r g e n c e c r i t e r i o n , t h a t e l e m e n t i s r e l i n e a r i z e d about t h e m o s t r e c e n t l y d e t e r m i n e d flow, and t h e l i n e a r s i m u l t a n e o u s equations a r e solved again. T h i s p r o c e d u r e i s r e p e a t e d until t h e flow t h r o u g h e v e r y e l e m e n t s a t i s f i e s t h e c o n v e r g e n c e c r i t e r i o n .

APPLICATION

A c o m p u t e r p r o g r a m b a s e d on t h e m a t h e m a t i c a l m o d e l t o s i m u l a t e a i r m o v e m e n t in m u l t i - s t o r e y buildings h a s been published (1) a s w e l l a s p r o g r a m s for o t h e r s p e c i f i c a p p l i c a t i o n s (2, 3). Air leakage values f o r w a l l s and i n t e r n a l s e p a r a t i o n s r e q u i r e d f o r t h e m o d e l a r e given in R e f s . 4, 5 and 6. S o m e of t h e s e d a t a h a v e been obtained by conducting m e a s u r e m e n t s in s e v e r a l r e a l buildings. T h e m a t h e m a t i c a l m o d e l h a s been applied t o t h e s t u d y of a i r and e m o k e m o v e m e n t and ways t o c o n t r o l t h e m in m u l t i - s t o r e y buildings (6, 7 and 8). It h a s a l s o b e e n used t o d e t e r m i n e i n f i l t r a t i o n r a t e s f o r t h e c a l c u l a t i o n of heating, cooling and m o i s t u r e l o a d s in a building.

R E F E R E N C E S

1. S a n d e r , D. M. and T a m u r a , G. T. A F o r t r a n IV P r o g r a m t o S i m u l a t e A i r Move- m e n t i n Multi-Storey Buildings. National R e s e a r c h Council of Canada,

Division of Building R e s e a r c h , DBR C o m p u t e r P r o g r a m No. 35, M a r c h 1973.

2. Shaw, C. Y., D. M. S a n d e r and G. T. T a m u r a . A F o r t r a n IV P r o g r a m t o S i m u l a t e S t a i r -Shaft P r e s s u r i z a t i o n S y s t e m i n Multi-Storey Buildings, DBR C o m p u t e r P r o g r a m No. 38, 1974.

3. Sander, D. M. A F o r t r a n IV P r o g r a m t o C a l c u l a t e A i r I n f i l t r a t i o n in Buildings, DBR C o m p u t e r P r o g r a m No. 37, 1974.

4. ASHRAE Handbook of F u n d a m e n t a l s , C h a p t e r 19, Infiltration and N a t u r a l Ventila- tion 1972.

5. Shaw, C. Y., D. M. S a n d e r and G. T. T a m u r a . A i r L e a k a g e M e a s u r e m e n t s of t h e E x t e r i o r Walls of T a l l Buildings, p r e s e n t e d a t t h e S p r i n g C o n f e r e n c e of

ASHRAE, Minneapolis, USA, 1973, J a n u a r y and F e b r u a r y .

6. T a m u r a , G. T. C o m p u t e r A n a l y s i s of S m o k e Movement i n Buildings, ASHRAE T r a n s a c t i o n s , Vol. 75, P a r t 11, 1969. (NRCC 11542)

7. T a m u r a , G. T. and A. G. Wilson. Building P r e s s u r e s C a u s e d by C h i m n e y Action and M e c h a n i c a l Ventilation, ASHRAE T r a n s a c t i o n s , Vol. 73, P a r t 11, 1967. (NRCC 9950)

8. T a m u r a , G. T. C o m p u t e r A n a l y s i s of S m o k e C o n t r o l with Building A i r Handling S y s t e m s , ASHRAE J o u r n a l , Vol. 14, No. 8, August 1972. (NRCC 12809)

9. T a m u r a , G. T. E x p e r i m e n t a l S t u d i e s on P r e s s u r i z e d E s c a p e Routes, Submitted f o r publication, November 1973.

APPENDIX

Simulation of P r e s s u r e L o s s e s i n V e r t i c a l Shafts

T h e p r e s s u r e l o s s e s i n a v e r t i c a l s h a f t c a n be s i m u l a t e d by dividing e a c h v e r t i c a l s h a f t i n t o s e p a r a t e c o m p a r t m e n t s of one f l o o r height with a n o r i f i c e in t h e h o r i z o n t a l s e p a r a t i o n a t e a c h f l o o r l e v e l . T h e p r e s s u r e d r o p a c r o s s t h e o r i f i c e would then r e p r e s e n t t h e p r e s s u r e l o s s i n t h e s h a f t f o r one f l o o r height. T h e s i z e of t h e o r i f i c e m u s t b e c a l c u l a t e d t o t a k e i n t o a c c o u n t t h e p r e s s u r e l o s s c h a r a c t e r i s t i c of t h e v e r t i c a l shaft.

where

b P L

=

preeeure lose for one floor height K

=

preeeure loas factor p e r floor (Ref.

9)

V H

=

velocity head

Q

=

flow r a t e through the ehaft

A

=

cross-sectional a r e a of the ehaft

P

=

a i r deneity

8

=

gravitational acceleration

This preegure loee can be aesuzqda t o s c c u r a c r o s s

the

arifiee of the horizontal

reprr&ttoa

ae followe:

where

Cd

=

coefficient of diechargs

a

=

a r e a pf orifice in the horizontal separation Combining equations (A- 1) and (A-2)

Ueing equation (A-3), the orifice opening in the horizontal separa4ion can be in- corporated in the mathematical rnQdal. Aleo a i r injection into the vertical ehaft at one or m o r e levels can be eimulataQ by epecifying a supply a i r r a t e into each fictitious compartment of the vertical ehaft.

The preeeuree in the vertical ahafte a t adjacent f l o o r s a r e now interrelated by the column weight of a i r and the preeqpre d r o p a c r o s s the orifice.

where

Pi

=

p r e r e u r e in the s t a i r ahaft at floor i h

=

floor height

It ehould be noted that with no p r e e e u r e loer in the vertical shaft a e aeeumed in the original mathematical model, the

last

t e r m in Equation (A-4) i a omitted. Ueing m a s s balance equations (3a) and (3b) arr bafare. p r e e e u r e differences and flow r a t e e through- out the building can be calculated.

F I G U R E

1

A I R F L O W S F O R A T Y P I C A L F L O O R A N D T Y P I C A L

S H A F T

F I G U R E

2