Quantifying the spread potentials of fires

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Quantifying the spread potentials of fires

Ser

THl

~ 2 1 d

National Research

Conseil national

no.

1184

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Council Canada

de recherches Canada

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BLDG

QUANTIFYING THE SPREAD POTENTIALS OF FIRES

by T.Z. Harmathy and J.R. Mehaffey

ANALYZED

Appeared in

Proceedings of the CSNl Specialist Meeting on Interaction of Fire and Explosion with Ventilation Systems in Nuclear Facilities

Los Alamos, New Mexico, April 25

-

28,1983 CSN l Report No. 83, Vol. 1 1, p. 479

-

493

Reprinted with permission

DBR Paper No. 1184

Division of Building Research

Les i n c e n d i e s confings peuvent s ' d t e n d r e s o i t p a r d e s t r u c t i o n , s o i t p a r convection. Les p o s s i b i l i t ' e s de p r o p a g a t i o n d'un i n c e n d i e p a r d e s t r u c t i o n ou p a r convection s o n t quantifi'ees p a r l a charge c a l o r i f i q u e normalis'ee e t l e f a c t e u r

IJ.

Ces possibilit'es peuvent donc S t r e calcul'ees b i e n que deux d e s donn'ees, l a charge cambustible e t l a v e n t i l a t i o n , s o i e n t d e s v a r i a b l e s a l h t o i r e s . On d k r i t dans c e t t e e t u d e l ' u t i l i s a t i o n d e l a charge c a l o r i f i q u e normalis'ee pour a s s u r e r l a s k u r i t ' e a u f e u d e s s t r u c t u r e s .

QUANTIFYING THE SPREAD POTENTIALS OF FIRES*

T.Z. Harmathy and J.R. Mehaffey

F i r e Research 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 Research Counci 1 Canada.

ABSTRACT

Compartment f i r e s can spread e i t h e r by d e s t r u c t i o n o r by

convection. The p o t e n t i a l s o f spread by d e s t r u c t i o n and convection a r e q u a n t i f i e d by t h e normalized heat l o a d and by t h e p - f a c t o r ,

r e s p e c t i v e l y . These spread p o t e n t i a l s a r e amenable t o c a l c u l a t i o n s , even though two o f t h e i n p u t v a r i a b l e s , f i r e l o a d and v e n t i l a t i o n , a r e random v a r i a b l e s . The use of t h e normalized heat l o a d i n s e c u r i n g s t r u c t u r a l f i r e s a f e t y i s d e s c r i bed.

I

I. INTRODUCTION

The concept o f f i r e - r e s i s t a n t compartmentation has been t h e core o f f i r e p r o t e c t i o n f o r s e v e r a l decades. I n t h i s concept a b u i l d i n g i s p i c t u r e d as

c o n s i s t i n g o f compartments a l l p e r f e c t l y i s o l a t e d f r o m each o t h e r ; and t h e spread of f i r e , as t a k i n g p l a c e by t h e successive f a i l u r e o f t h e compartment boundaries.

If t h e compartment boundaries a r e s u f f i c i e n t l y f i r e r e s i s t a n t , i t i s argued, f a i l u r e w i 11 n o t occur and f i r e s w i l l be c o n f i n e d t o t h e compartments i n which they s t a r t .

O f course, f i r e s

cannot

develop i n f u l l y i s o l a t e d compartments; they must have access

to

a i r . I n o t h e r words, t h e compartment on f i r e must communicate w i t h a t 1 east one o t h e r ( i n s i d e o r o u t s i d e ) space through an open door, a broken

window, o r any k i n d o f c e i 1 i n ' g o r w a l l opening. Consequently, t h e r e must be a t l e a s t one r o u t e a l o n g which t h e f i r e can spread by convection; t h a t i s , by t h e advance of flames and h o t gases. A f i r e i n a compartment, t h e r e f o r e , has two k i n d s of spread p o t e n t i a l : d e s t r u c t i v e and convective.

F i r e - r e s i s t a n t cornpartmentation addresses o n l y one aspect of t h e o v e r a l l problem of f i r e spread: spread by d e s t r u c t i o n ( o r perhaps heat conduction

.

A t present even t h i s aspect i s

based

on i n g b e r g ' s outdated f i r e l o a d c0ncept.l The o t h e r , more i m p o r t a n t aspect, spread by convection, has n o t been p r o p e r l y

I

*This paper was o r i g i n a l l y presented a t t h e Three Decades of S t r u c t u r a l F i r e Safety Seminar a t t h e F i r e Research S t a t i o n , Borehamwood, Herts (England). I

considered i n f i r e s a f e t y design, m a i n l y because t h e phenomena i n v o l v e d a r e n o t understood.

To p r o v i d e a b a s i s f o r r a t i o n a l f i r e s a f e t y design, t h i s paper d e s c r i b e s a technique f o r q u a n t i f y i n g t h e p o t e n t i a l s o f compartment f i r e s t o spread by d e s t r u c t i o n and convection.

11. THE ROLE OF A I R CURRENTS I N F I R E SPREAD

The mathematical models o f compartment f i r e s a r e i n a way f i t t e d t o t h e

concept o f f i r e - r e s i s t a n t compartmentation: t h e y t a c i t l y assume t h a t t h e b u i l d i n g spaces a r e i s o l a t e d from one another and t h e r e b y n e g l e c t t h e i m p o r t a n t r o l e o f a i r c u r r e n t s i n spreadi ng f i r e s by convection.

The a i r c u r r e n t s a r e caused by two f a c t o r s : t h e temperature d i f f e r e n c e between t h e b u i 1 d i n g i n t e r i o r and t h e o u t s i d e atmosphere, and t h e a i r-1 eakage c h a r a c t e r i s t i c s o f t h e b u i l d i n g envelope. The temperature d i f f e r e n c e c r e a t e s e s p e c i a l l y s t r o n g c u r r e n t s i n w i n t e r . The i n t e n s i t y and d i r e c t i o n o f t h e a i r c u r r e n t s i n a n i n e - s t o r e y b u i l d i n g on a calm w i n t e r day i s i l l u s t r a t e d i n Fig. 1. Wind may s u b s t a n t i a l l y change t h e d i s t r i b u t i o n o f a i r c u r r e n t s .

Fig. 1

I l l u s t r a t i o n o f a i r c u r r e n t s i n n i n e - s t o r e y o f f i c e b u i l d i n g

F i r e s tend t o f o l l o w t h e p a t h o f a i r c u r r e n t s . Thus, i f a f i r e breaks o u t i n a compartment below t h e mid-height o f t h e b u i l d i n g , i t w i l l f i r s t e n t e r t h e

c o r r i d o r ; then, i f doors a r e open, r i s e i n t h e s t a i r w e l l s o r e l e v a t o r shafts. I n t h e upper s t o r e y s , on t h e o t h e r hand, t h e f i r e w i l l spread towards t h e b u i l d i n g

envelope. On r e a c h i n g t h e envelope, flames emerging f r o m t h e windows may i g n i t e t h e e x t e r i o r c l a d d i n g , i f i t i s combustible, o r may break t h e windows above and

s e t t h e compartment on t h e next s t o r e y on f i r e .

111. POTENTIALS OF FIRE SPREAD BY DESTRUCTION AND CONVECTION

Since t h e b u l k o f t h e f u e l energy i s r e l e a s e d d u r i n g t h e ' f u l l y - d e v e l o p e d

'

p e r i o d of t h e f i re, i t i s g e n e r a l l y accepted t h a t o n l y t h i s p e r i o d needs t o be considered when d e s i g n i n g measures f o r s t r u c t u r a l s a f e t y . As an e x t r a p r e c a u t i o n , i t i s assumed t h a t t h e f i r e department w i l l n o t i n t e r v e n e ; t h e f i r e w i l l b u r n u n t i l t h e f u e l i s consumed.

The d e s t r u c t i v e p o t e n t i a l o f f u l ly-developed f i re s i s d e s c r i b e d by t h e t e r m ' f i r e s e v e r i t y ' , which a f t e r several decades s t i l l l a c k s a c l e a r d e f i n i t i o n . The temperature h i s t o r y o f f i r e gases i n a b u r n i n g compartment i s o f t e n regarded as t h e d e s c r i p t o r o f f i r e s e v e r i t y . The f o l l o w i n g c o n s i d e r a t i o n shows t h e inadequacy of t h i s concept. The heat t r a n s f e r f r o m t h e gases t o t h e compartment boundaries

(which o b v i o u s l y has something t o do w i t h t h e d e s t r u c t i v e p o t e n t i a l of f i r e ) i s mainly by r a d i a t i v e energy exchange. Since t h i s exchange i s r e l a t e d t o t h e f o u r t h power o f t h e temperature o f f i r e gases, a simple ( f i r s t power) temperature h i s t o r y

i s n o t a d i r e c t measure o f t h e f i r e ' s , d e s t r u c t i v e p o t e n t i a l .

It has been shown293 t h a t t h e s o - c a l l e d 'normalized heat l o a d ' i s a parameter t h a t c o r r e c t l y q u a n t i f i e s t h e d e s t r u c t i v e p o t e n t i a l o f f i res, r e a l - w o r l d and t e s t f i r e s a1 i ke. The normalized heat l o a d H i s d e f i n e d as

where

Jl<pc

i s t h e thermal i n e r t i a o f t h e compartment boundaries (k i s thermal c o n d u c t i v i t y , p i s d e n s i t y , and c i s s p e c i f i c h e a t ) , q i s t h e heat f l u x

p e n e t r a t i n g t h e compartment boundaries, t i s time, and T i s t h e d u r a t i o n of t h e

f i re.

The thermal p r o p e r t i e s o f some common b u i l d i n g m a t e r i a l s a r e l i s t e d i n Table I.

The 'theorem o f u n i f o r m i t y o f normalized heat l o a d ' (which i s of approximate v a l i d i ty ) appl i es t o compartments havi ng boundaries made from d i verse m a t e r i a l s . Accordi ng t o t h e theorem,

where

and

TABLE I

TYPICAL VALUES OF THE THERMAL PROPERTIES OF SOME COMMON BUILDING MATERIALS MATERIALS ( I N MOISTURELESS CONDITION) FOR THE APPROPRIATE TEMPERATURE INTERVALS

Thermal Speci f i c Thermal

c o n d u c t i v i t y D e n s i t y h e a t i n e r t i a k P c M a t e r i a1 Steel 42.00 7,800 530 13,177 Marble Normal weight c o n c r e t e B r i c k L i ghtwei g h t c o n c r e t e P l a s t e r board Vermi c u l i t e p l a s t e r Wood I n s u l a t i n g f i r e b r i ck Mineral wool 0.04 160 1,150 8 6 482

The i s u b s c r i p t s r e l a t e t o i n f o r m a t i o n p e r t i n e n t t o t h e i th boundary element o f t h e compartment, and A startds f o r boundary s u r f a c e area ( t o t a l , o r w i t h s u b s c r i p t i

,

component).

F i r e u s u a l l y spreads n o t by d e s t r u c t i o n , b u t by convection: t h e s p i l l i n g o f uncombusted v o l a t i l e products o f p y r o l y s i s i n t o t h e surrounding spaces.

I r r e s p e c t i v e o f t h e m a t e r i a l s 1 i n i ng t h e s e spaces, f u e l s and c o n d i t i o n s conducive t o t h e massive combustion o f t h e v o l a t i l e s o u t s i d e t h e f i r e compartment boundaries p r e s e n t a very r e a l danger as t o f i r e spread. A f a c t o r has been i n t r o d u c e d t o c h a r a c t e r i z e t h e c o n v e c t i v e spread p o t e n t i a l o f f i r e s . 2 It i s denoted by p and

d e f i n e d as t h e r a t i o

U = r a t e of heat e v o l u t i o n o u t s i d e f i r e compartment

t o t a l r a t e o f heat e v o l u t i o n from f u e l

I V . CHAR-FORMING AND NONCHARRING FUELS

What goes on i n a compartment on f i r e i s u s u a l l y r e f e r r e d t o as ' b u r n i n g ' . Some c o n f u s i o n has e x i s t e d about t h e i n t e r p r e t a t i o n o f t h i s word. Burning

c o n s i s t s of two o r t h r e e completely d i f f e r e n t k i n d s of r e a c t i o n s : ( i ) p y r o l y s i s o f t h e combustible m a t e r i a l ( f u e l , f o r s h o r t ) i n t o v o l a t i l e products and p o s s i b l y char, ( i i ) combustion o f v o l a t i l e s and p o s s i b l y ( i i i ) o x i d a t i o n o f char.

Researchers i n t e r p r e t t h e ' r a t e o f b u r n i n g ' as t h e r a t e of l o s s of f u e l mass due t o p y r o l y s i s and p o s s i b l y t h e o x i d a t i o n of char.

With c h a r - f o r m i n g f u e l s ( c e l l u l o s i c s i n g e n e r a l ) , t h e o x i d a t i o n o f t h e

s u r f a c e char l a y e r p r o v i d e s much o f t h e heat f o r p y r o l y s i s r e a c t i o n s . Since t h i s o x i d a t i o n depends s t r o n g l y on t h e a i r supply t o t h e f u e l surface, t h e r a t e o f p y r o l y s i s i s s e n s i t i v e t o t h e a i r f l o w r a t e p a s t t h e f u e l bed b u t i s r e l a t i v e l y i n s e n s i t i v e t o thermal feedback f r o m t h e flames t o t h e f u e l . I n c o n t r a s t , t h e r a t e o f p y r o l y s i s o f noncharring f u e l s , which do n o t have a ' b u i l t - i n ' heat supply, depends p r i m a r i l y on thermal feedback from t h e flames and t h e h o t surroundi ngs.4

Because o f t h e s e b a s i c d i f f e r e n c e s i n t h e b u r n i n g c h a r a c t e r i s t i c s of f u e l s , some models of compartment f i r e s a r e i n a s t r i c t sense a p p l i c a b l e o n l y t o c h a r r i n g f u e l s , o t h e r s o n l y t o n o n - c h a r r i n g f u e l s . According t o a v a i l a b l e s t a t i s t i c a l data, t h e combustible m a t e r i a l s used i n b u i l d i n g s s t i l l c o n s i s t predominantly o f c h a r r i n g f u e l s , namely c e l l u l o s i c s . For t h i s reason, f i r e s o f c h a r r i n g f u e l s w i l l r e c e i v e i n t h i s paper primary a t t e n t i o n .

V. INDEPENDENT (INPUT) VARIABLES

There a r e f i v e independent ( i n p u t ) v a r i a b l e s on which t h e n a t u r e o f f u l l y - developed compartment f i r e s p r i m a r i l y depends:

A, t o t a l area of t h e compartment boundaries,

G, t o t a l f i r e l o a d ( t o t a l mass o f combustibles i n t h e compartment), hC, h e i g h t o f t h e compartment,

6,

thermal i n e r t i a o f t h e compartment boundaries (as d e f i n e d i n Eq. ( 3 ) ) , and

O f these, A, hC, and

6

can be determined from t h e b u i l d i n g plans. G and

r

a r e random v a r i a b l e s .

V I . FIRE LOAD

T r a d i t i o n a l l y , t h e t o t a l f i r e l o a d i s expressed w i t h t h e a i d o f t h e ' s p e c i f i c f i r e l o a d ' L as f o l l a w s :

where AF i s t h e f l o o r area and L i s t h e s p e c i f i c f i r e load; t h a t i s , t h e mass o f conventional ( c e l l u l o s i c ) combustibles p e r u n i t f l o o r area. ( I f nonce1 l u l o s i cs a r e present, t h e i r mass i s converted i n t o a c a l o r i f i c a l l y e q u i v a l e n t mass o f wood. ) Surveys have i n d i c a t e d t h a t t h e t y p e o f occupancy i s t h e most important f a c t o r i n t h e s p e c i f i c f i r e load. Yet, even f o r s i m i l a r occupancies, L i s s u b j e c t t o s u b s t a n t i a l and u n p r e d i c t a b l e v a r i a t i o n .

Table I 1 c o n t a i n s data on t h e s t a t i s t i c a l median L and standard d e v i a t i o n aL f o r s p e c i f i c f i r e loads based on Swedish data.5 There pave been suggestions t h a t t h e design v a l e o f t h e s e s c i f i c f i r e l o a d be regarded as t h e v a l u e p e r t a i n i n g t o e i t h e r t h e 8 0 t ' o r t h e 95 p e r c e n t i l e i n t h e c u w l a t i v e p l o t f o r t h e a p p r o p r i a t e occupancy. I f t h e l a t t e r , s t r i c t e r , c o n d i t i o n i s accepted, t h e design value o f t h e s p e c i f i c f i r e l o a d L can be o b t a i n e d as

V I I . COMPARTMENT VENTILATION

The r a t e of e n t r y o f a i r i n t o t h e b u r n i n g compartment i s c h a r a c t e r i z e d by t h e v e n t i l a t i o n f a c t o r 8. It i s a l s o a random v a r i a b l e . I t s value i s m i n i m m when t h e b u i l d i n g i s f r e e o f a i r c u r r e n t s . This minimum i s r e l a t e d t o t h e s i z e o f t h e v e n t i l a t i o n opening as f o l l o w s :

where p a i s t h e d e n s i t y o f atmospheric a i r , A,, i s t h e t o t a l area o f t h e

v e n t i l a t i o n openings, h V i s t h e h e i g h t o f t h e v e n t i l a t i o n openings, and g i s t h e g r a v i t a t i o n a l constant.

Under r e a l - w o r l d c o n d i t i o n s , 4 4 and i s determined l a r g e l y by t h e a i r c u r r e n t s i n t h e b u i l d i n g b e f o r e a f i r e reaks out. Since these c u r r e n t s depend s t r o n g l y on c l im a t i c c o n d i t i o n s , they a r e d i f f i c u l t t o assess.

TABLE I I

INFORMATION ON SPECIFIC FIRE LOAD3 ( I N TERMS OF CALORIFICALLY EQUIVALENT MASS OF WOOD)

m aL Occupancy k g m-2

-

kg m-2 Dwell i ng 30.1 4.4 O f f i c e 24.8 8.6 School 17.5 5.1 H o s p i t a l 25.1 7.8 H o t e l 14.6 4.2 F o r t u n a t e l y , a s s i g n i n g a d e s i g n v a l u e f o r o usual l y does n o t r e q u i r e s t o c h a s t i c c o n s i d e r a t i o n s . As w i 11 be v e r i f i e d l a t e r , t h e p o t e n t i a l of f u l l y - developed f i r e s f o r d e s t r u c t i v e spread i s maximum when o = o i

,.

T h e o r e t i c a l s t u d i e s have shown t h a t s e l e c t i n g o m i n as a d e s i g n v a l u e w i l y n o t o v e r t a x t h e f i r e s a f e t y design.

V I I I. PROCESS (OUTPUT) VARIABLES

Once t h e i n p u t v a r i a b l e s a r e s a t i s f a c t o r i l y d e f i n e d f o r t h e d e s i g n

c o n d i t i o n s , one can t h e n c a l c u l a t e t h e e x p e c t e d c h a r a c t e r i s t i c s of t h e compartment

f i re.

I n general, t h r e e energy balances can be w r i t t e n f o r t h e f i r e process: one over t h e v e n t i l a t i o n opening, t h e second o v e r t h e f u e l surface, and t h e t h i r d o v e r t h e s u r f a c e of t h e compartment. To d e s c r i b e f u l l y t h e f i r e process, t h r e e more e q u a t i o n s a r e needed: one f o r t h e r a t e o f e v o l u t i o n o f energy w i t h i n t h e

compartment from t h e f u e l , t h e second f o r t h e d u r a t i o n o f t h e f i r e , and t h e t h i r d f o r t h e f l o w r a t e of a i r i n t o t h e compartment.

A l l t h e s e e q u a t i o n s , e x c e p t t h e one f o r t h e d u r a t i o n of t h e f i r e , can be f o r m u l a t e d i n two ways: t h e y may d e s c r i b e e i t h e r momentary c o n d i t i o n s , o r average c o n d i t i o n s c h a r a c t e r i s t i c of t h e e n t i r e d u r a t i o n of t h e ( f u l ly - d e v e l o p e d ) f i re. Since t h e a u t h o r s be1 i e v e t h a t t h e n a t u r e of t h e problem does n o t w a r r a n t more r e a l i s m t h a n t h a t p r o v i d e d by d e s c r i b i n g average c o n d i t i o n s , t h e y have chosen t h e second procedure.

The simultaneous s o l u t i o n o f t h e s i x a f o r e m e n t i o n e d e q u a t i o n s , t o be o b t a i n e d by successi ve i t e r a t i o n s , wi 11 y i e l d s i x process v a r i a b l e s . They a r e :

Ua, r a t e of e n t r y o f a i r i n t o t h e compartment (temporal average),

R , r a t e of ' b u r n i n g ' of t h e f u e l ( r a t e o f mass l o s s m a i n l y by p y r o l y s i s , temporal average),

Q, r a t e of h e a t e v o l u t i o n f r o m t h e f u e l (temporal average),

-

T o , t e m p e r a t u r e of t h e f i r e gases (temporal and s p a t i a l average),

3

4 ,

f l u x o f h e a t a b s o r p t i o n by t h e compartment b o u n d a r i e s ( t e m p o r a l and s u r f a c e average), and T, d u r a t i o n o f ( f u l l y - d e v e l o p e d ) f i r e . For c h a r - f o r m i n g f u e l s t h e s o l u t i o n of t h e s i x e q u a t i o n s i s g r e a t l y simp1 i f i e d . As d i s c u s s e d e a r l i e r , t h e i r r a t e o f p y r o l y s i s , R, depends p r e d o m i n a n t l y on t h e r a t e o f a i r s u p p l y t o t h e f u e l s u r f a c e . This, i n t u r n , i s a

f u n c t i o n o f t h e r a t e of e n t r y o f a i r i n t o t h e compartment Ua; R can t h e r e f o r e be c o r r e l a t e d w i t h Ua (as w e l l as w i t h some o t h e r f a c t o r s o f l e s s e r i m p o r t a n c e ) , w i t h o u t making use of t h e e q u a t i o n e x p r e s s i n g t h e energy b a l a n c e o v e r t h e f u e l s u r f a c e .

The r a t e of e n t r y of a i r i n t o t h e compartment Ua can be d e s c r i b e d

( a p p r o x i m a t e l y ) i n terms o f t h e v e n t i l a t i o n parameter @ as f o l l o w s :

Since, i n g e n e r a l , @ >> R, t h e v e n t i 1 a t i on parameter can be regarded as a d i r e c t

measure o f t h e compartment v e n t i l a t i o n .

The i t e r a t i v e t e c h n i q u e s f o r c a l c u l a t i n g t h e s i x p r o c e s s v a r i a b l e s have been

d e s c r i b e d i n d e t a i 1 i n an e a r l i e r pub1 i c a t i on.2 Once t h e process v a r i a b l e s a r e

known, t h e two parameters of spread p o t e n t i a l , namely t h e n o r m a l i z e d h e a t l o a d H

(spread p o t e n t i a1 by d e s t r u c t i o n ) and t h e - f a c t o r (spread p o t e n t i a1 by

c o n v e c t i o n ) can a l s o be q u a n t i f i e d . F o r example, by v i r t u e o f Eq. (1) t h e

normal i z e d h e a t l o a d can be expressed w i t h t h e a i d of ti and T as

Using two s e r i e s o f c a l c u l a t , i o n s , two k i n d s o f f i r e s were e ~ a m i n e d : ~ f i re s

o f c e l l u l o s i c m a t e r i a l s and p o o l f i r e s o f n o n c h a r r i n g p l a s t i c s . The f o l l o w i n g c o n c l u s i o n s were drawn: 1. W i t h r e s p e c t t o d e s t r u c t i v e spread p o t e n t i a l , f i r e s o f c e l l u l o s i c s a r e u s u a l l y more dangerous t h a n f i r e s o f n o n c h a r r i n g p l a s t i c s . As r e g a r d s c o n v e c t i v e spread p o t e n t i a l , t h e o p p o s i t e i s t r u e . 2. F o r b o t h k i n d s o f f u e l , t h e d e s t r u c t i v e spread p o t e n t i a l decreases w i t h i n c r e a s i n g v e n t i 1 a t i o n (as c h a r a c t e r i z e d by

a ) .

3. The c o n v e c t i v e spread p o t e n t i a l decreases w i t h i n c r e a s i n g v e n t i l a t i o n i f t h e

fi r e 1 oad c o n s i s t s of n o n c h a r r i ng p l a s t i c s , and i n c r e a s e s w i t h i n c r e a s i n g

I X . APPROXIMATE EXPRESSIONS FOR SPREAD POTENTIALS

For those (by no means uncommon) compartment f i r e s i n which t h e f u e l c o n s i s t s predominantly of c e l l u l o s i c s , one can bypass t h e i t e r a t i v e t e c h n i q u e d e s c r i b e d i n Ref. 4 and c a l c u l a t e t h e two spread p o t e n t i a l s from e x p l i c i t formulas o f

approximate v a l i d i t y as f o l l ows :6

Normalized heat l o a d ( p o t e n t i a l f o r spread by d e s t r u c t i o n ) :

- f a c t o r ( p o t e n t i a1 f o r spread by c o n v e c t i on) :

I n these equations 6 i s t h e f r a c t i o n o f t h e energy o f t h e v o l a t i l e p y r o l y s i s products r e l e a s e d i n s i d e t h e compartment. It appears from an a n a l y s i s of a comprehensi ve experimental study conducted i n

B r i t a i t - 1 ~ 9 ~ t h a t t h i s f r a c t i o n i s p r i m a r i l y a f u n c t i o n o f t h e h e i g h t o f t h e compartment hC and t h e v e n t i l a t i o n parameter 4. The f o l l o w i n g empi r i c a l expression has been recommended:

0.79

d

m

,

whichever i s l e s s

.

1

I n f i r e s a f e t y design, t h e value o f G _{t o be used i n Eq. (11) i s t h a t o b t a i n e d}

from Eqs. ( 6 ) and ( 7 ) , and t h e value o f @ t o be used i n Eqs. (11) and (13) i s t h a t d e f i n e d f o r @,i by Eq. (8).

If a l l h e a t were r e l e a s e d by t h e f u e l i n s i d e t h e compartment and absorbed by t h e compartment boundaries, t h e normalized heat l o a d c o u l d be expressed by t h e f o l l o w i n g equation:

where t h e s u b s c r i p t m has been a f f i x e d t o H t o i n d i c a t e t h a t i t represents t h e conceivable maximum, and AH i s t h e t o t a l heat o f combustion o f t h e f u e l .

The normalized h e a t l o a d on t h e compartment boundaries i s o n l y 10 t o 40 p e r cent o f H

.

Some o f t h e f u e l energy i s released o u t s i d e t h e compartment; of t h e enerqy reyeased i n s i d e , some l e a v e s t h e compartment w i t h t h e f i r e gases as

s e n s i b l e heat and some i s l o s t by r a d i a t i o n through t h e v e n t i l a t i o n opening. By d i v i d i n g Eq. (11) by Eq. (14) and u s i n g A H = 18.8 x

lo6

J kg'l ( f o r

c e l l u l o s i c s ) , t h e f o l l owing equation i s obtained:

H = 0.5856 + 0.085

- ₍₁

₅₎

Hm ₁

₊

_{935 &/(A}

_{6 )}

An i n t e r e s t i n g f e a t u r e o f t h i s e q u a t i o n i s t h a t t h e group &/(A

6)

appears t o be t h e dominant v a r i a b l e . H/H i s p l o t t e d a g a i n s t t h i s group w i t h 6 _{as a}

parameter i n Fig. 2. T h i s p l o T p r o v i d e s a v a l u a b l e i n s i g h t i n t o t h e 'i n e f f i c i ency ' o f f i r e s due t o spread by d e s t r u c t i o n .

F i g u r e 2 c l e a r l y confirms t h a t t h e d e s t r u c t i v e spread p o t e n t i a l o f f i r e s i s maximum when @ = omi n.

I -

-

- - I a. 0 0 1 0 002 0 003 0 004 0.005 r n I ( ~ ~ V k p c ) k g K , - I Fig. 2

Normal i zed heat 1 oad imposed on compartment boundaries, as f r a c t i o n o f h y p o t h e t i c a l maxi mum v a l u e

X. STANDARD FIRE RESISTANCE TEST

Standard f i r e r e s i s t a n c e t e s t s a r e i n a sense a l s o f u l l y - d e v e l o p e d

compartment f i r e s . A convenient f e a t u r e o f standard t e s t f i r e s i s t h a t , u n l i k e r e a l -world f i res, they have a unique temperature h i s t o r y . D e t a i l e d studies9 have r e v e a l e d t h a t t h e normalized h e a t l o a d f o r s t a n d a r d t e s t f i r e s i s more o r l e s s a f u n c t i o n o f t h e d u r a t i o n o f t h e t e s t o n l y , p r o v i d e d t h a t t h e t e s t i s performed i n an ' i d e a l ' h i g h e f f i c i e n c y furnace, i.e., . i n a f u r n a c e heated by ' b l a c k '

combustion gases. I f t h e t e s t s a r e c a r r i e d o u t i n r e a l furnaces, t h e normalized h e a t l o a d w i l l a l s o depend on such secondary f a c t o r s as t h e s i z e o f t h e furnace, i t s 1 i n i n g m a t e r i a l s , t h e n a t u r e o f t h e combustion products of t h e f u e l , and t h e t e s t specimen.

Curve 1 i n Fig. 3 shows t h e approximate r e l a t i o n between t h e normalized h e a t l o a d H and t h e d u r a t i o n o f t h e t e s t T f o r an i d e a l t e s t furnace. Curve 2 shows

t h i s r e l a t i o n f o r a r e a l furnace, namely f o r t h e f l o o r t e s t f u r n a c e a t t h e

National Research Council o f Canada. This curve can be d e s c r i b e d by t h e f o l l o w i n g approximate formula:

where

l I N ( ~ 1 1 1 01 t X P O 5 L I K E 10 5 T A N D A R D l E S T I I K t , r h

Fig. 3

U n i f i e d c o r r e l a t i o n s between H and T f o r standard f i r e t e s t s

Curve 1 - f o r h i g h - e f f i c i e n c y furnaces

X I . D E S I G N TO COUNTER DESTRUCTIVE SPREAD

C l e a r l y , i f a specimen o f a compartment boundary element can, w i t h o u t f a i l u r e , w i t h s t a n d i n a t e s t f i r e t h e n o r m a l i z e d h e a t l o a d (which, a c c o r d i n g t o Eq.

( Z ) ,

i s t h e same f o r a l l boundary elements) l i k e l y t o a r i s e i n a r e a l - w o r l d f i r e under t h e d e s i g n c o n d i t i o n s , t h a t boundary element i s a c c e p t a b l e f o r t h a t p a r t i c u l a r a p p l i c a t i o n . Thus, t h e d e s i g n t o c o u n t e r t h e p o t e n t i a l o f a f i r e t o spread by d e s t r u c t i o n c o n s i s t s o f t h e f o l l o w i n g steps:

C a l c u l a t e

a ) t h e design f i r e l o a d G, u s i n g Eqs. ( 6 ) and ( 7 ) and t h e i n f o r m a t i o n i n Table 11,

b ) the v e n t i l a t i o n f a c t o r o, u s i n g Eq. ( 8 ) ,

c) t h e thermal i n e r t i a o f t h e compartment boundaries

6,

u s i n g Eq. ( 3 ) and t h e

i n f o r m a t i o n i n Table I,

d ) t h e n o r m a l i z e d h e a t l o a d H f o r t h e compartment, u s i n g Eqs. (11) and (13) (by v i r t u e o f t h e theorem o f u n i f o r m i t y o f n o r m a l i z e d h e a t l o a d , Eq. ( 2 ) , t h i s same v a l u e i s a p p l i c a b l e t o a l l i n d i v i d u a l boundary elements of t h e

compartment), and f i n a l l y

e) t h e r e q u i r e d l e n g t h o f f i r e exposure T ( i n h o u r s ) ; i n o t h e r words, t h e f i r e

r e s i s t a n c e r e q u i rement, u s i n g Eq. (16).

Since t w o o f t h e most i m p o r t a n t i n p u t v a r i a b l e s t o t h e f i r e problem, G and @, a r e random v a r i a b l e s , t h e q u e s t i o n may a r i s e : What i s t h e f a i l u r e p r o b a b i l i t y i n r e a l - w o r l d f i r e s o f c o n s t r u c t i o n s designed a c c o r d i n g t o t h e o u t l i n e d procedure? T h i s problem has been i n v e s t i g a t e d i n a r e c e n t paper.10 F i g u r e 4 s h w s t h e r e s u l t s o f a numerical study performed f o r a s p e c i f i c case. I n i t , t h e f a i l u r e p r o b a b i l i t y Pf i s p l o t t e d a g a i n s t v e n t i l a t i o n expressed i n terms o f w i t h

I L

t h e s p e c i f i c f i r e l o a d t a k e n as t h a t c o r r e s p o n d i n g t o t h e 95Ln p e r c e n t i l e i n t h e c u m u l a t i v e p l o t . As expected, i f

o

= omi

,,

t h e f a i l u r e p r o b a b i l i t y i s about 5 p e r cent ( i n f a c t s l i g h t l y h i g h e r ) b u t decreases r a p i d l y w i t h an i n c r e a s e i n

v e n t i l a t i o n . As d i s c u s s e d e a r l i e r , one can expect t h a t i n r e a l - w o r l d s i t u a t i o n s @/amin > 1 because o f t h e presence o f a i r c u r r e n t s .

X I I . DESIGN TO COUNTER CONVECTIVE SPREAD

A1 though t h e p o t e n t i a l o f c o n v e c t i v e f i r e spread can be c h a r a c t e r i z e d q u a n t i t a t i v e l y by t h e p - f a c t o r , t h e r e i s as y e t no e s t a b l i s h e d method on how t o use t h i s v a l u e i n f i r e s a f e t y design. An a c c e p t a b l e a p p r o a r l ~ would be t o r e q u i r e some e x t r a measures o f c o u n t e r i n g t h e c o n v e c t i v e spread f l r e s whenever t h e value o f p exceeds some s p e c i f i e d 1 im i t, say 0.4.

Although no p h i l o s o p h y seems t o e x i s t on how t o d e a l w i t h t h e problem of c o n v e c t i v e f i r e spread, i n most s i t u a t i o n s common-sense c o n s i d e r a t i o n s may s u f f i c e . The danger o f f i r e spread i s more severe i f uncombusted v o l a t i l e s can p e n e t r a t e t h e i n t e r i o r o f a b u i l d i n g , f o r example by a c o r r i d o r , than i f t h e y l e a v e through w i n d o w s t o t h e o u t s i d e . I n h i g h - r i s e b u i l d i n g s , t h e r e i s an

i n c r e a s e d danger t h a t t h e v o l a t i l e s w i l l e n t e r t h e c o r r i d o r s , because t h e p r e s s u r e drop i n t h e l o w e r s t o r e y s d u r i n g t h e h e a t i n g season i s d i r e c t e d away f r o m t h e o u t s i d e s h e l l o f t h e b u i l d i n g towards t h e major s h a f t s . Consequently, e q u i p p i n g t h e 1 ower s t o r e y s o f h i g h - r i s e b u i l d i n g s w i t h s e l f - c l o s i n g doors, p r e f e r a b l y

O F F I C E O C C U P A N C Y : L m = 2 4 . 8 k g m"

-

a 0 . 0 2 5 - 1. on 1 . 0 5 1 . 1 0 1. 15 1 . 2 0 _{1. 25} @"@ml n Fig. 4 F a i l u r e p r o b a b i l i t y as f u n c t i o n o f v e n t i l a t i o n (design value o f s p e c i f i c f i r e l o a d according t o Eq. ( 7 ) )

s l i d i ng doors t h a t open and c l ose w i t h ease i r r e s p e c t i ve of pressure condi t i ons

,

may be t h e b e s t p o s s i b l e investment i n f i r e s a f e t y .

I n t h e upper s t o r e y s o f h i g h - r i s e b u i l d i n g s , t h e pressure d i s t r i b u t i o n

favours movement o f uncombusted f i r e gases towards t h e o u t s i d e , so t h a t t h e use of s e l f - c l o s i n g doors may n o t be j u s t i f i e d . Even i f t h e uncombusted gases a r e

d i scharged towards t h e o u t s i d e atmosphere, f o r example through w i n d w s , t h e r e s t i l l remains a p o t e n t i a l danger o f c o n v e c t i v e f i r e spread. The heat from t h e i s s u i n g flames can break t h e windows o f t h e compartment above and s e t i t s c o n t e n t s on f i r e . This danger o f v e r t i c a l f i r e spread along t h e b u i l d i n g facade may be lessened by means o f flame d e f l e c t o r s , which a r e l i g h t metal panels mounted v e r t i c a l l y above t h e windows. When a c t i v a t e d by flames, t h e y lower i n t o a h o r i z o n t a l p o s i t i o n , t h u s s h i e l d i n g t h e compartment above f r o m t h e flames and r a d i a t e d heat.

X I I I . CONCLUSION

The design o f b u i l d i n g s f o r f i r e s a f e t y c o n s i s t s o f two components:

c o u n t e r i n g t h e spread o f f i r e by t h e d e s t r u c t i o n o f compartment boundaries and c o u n t e r i n g f i r e spread by convection (advance o f flames and h o t gases). The l a t t e r aspect o f t h e design must r e c e i v e more a t t e n t i o n w i t h t h e expanding use of s y n t h e t i c m a t e r i a l s .

The p o t e n t i a l o f f i r e spread by d e s t r u c t i o n can be q u a n t i f i e d by t h e

normalized heat load, and i t s p o t e n t i a l t o spread by convection, by t h e p - f a c t o r . A f t e r a d o p t i n g design values f o r two i m p o r t a n t i n p u t v a r i a b l e s , s p e c i f i c f i r e l o a d and v e n t i 1 a t i on, t h e design o f b u i 1 d i n g elements t o w i t h s t a n d t h e d e s t r u c t i v e p o t e n t i a1 o f f i r e becomes a determi n i s t i c procedure. U n f o r t u n a t e l y , no agreed-

upon d e s i g n p r o c e d u r e e x i s t s as y e t f o r t h e use o f t h e p - f a c t o r i n c o u n t e r i n g t h e p o t e n t i a l o f f i r e s t o spread by c o n v e c t i o n . NOMENCLATURE s u r f a c e area, w i t h o u t s u b s c r i p t : t o t a l s u r f a c e a r e a of compartment, m2 s p e c i f i c heat, J kg-' K-1 g r a v i t a t i o n a l c o n s t a n t , -9.8 m s-2 t o t a l mass o f f u e l ( t o t a l f i r e l o a d ) , k g h e i g h t , m n o r m a l i z e d h e a t load, s i K t o t a l h e a t o f combustion, J kg'l thermal c o n d u c t i v i t y , W m'l K-1 s p e c i f i c f i r e l o a d , w i t h o u t s u b s c r i p t : d e s i g n value, k g m-2 f a i l u r e p r o b a b i l i t y p e n e t r a t i o n h e a t f l u x , w i t h o u t s u b s c r i p t : o v e r a l l v a l u e f o r compartment, W m-2 q averaged o v e r

+,

W m-2 r a t e of h e a t e v o l u t i o n f r o m f u e l , W r a t e o f l o s s o f f u e l mass, ( r a t e o f ' b u r n i n g ' ) , k g s-1 time, s average temperature, K mass f l o w r a t e , k g s-1 Greek 1 e t t e r s 6 _{f r a c t i o n a l h e a t e v o l u t i o n f r o m v o l a t i l e s i n t h e compartment} f a c t o r of c o n v e c t i v e spread p o t e n t i a l aL Standard d e v i a t i o n f o r s p e c i f i c f i r e l o a d , kg rnm2 p d e n s i t y , k g ~n-3 T f i r e d u r a t i o n ; l e n g t h o f s t a n d a r d f i r e t e s t , s ( o r h )

o

v e n t i l a t i o n f a c t o r , k g s'l S u b s c r i p t s a o f a t m o s p h e r i c a i r C o f compartment F o f f l o o r g o f f i r e gases i o f o r f o r t h e ith c o q a r t m e n t boundary m mean ( w i t h L ) m maximum ( w i t h H ) min minimum V o f v e n t i l a t i o n opening. REFERENCES

1. S.H. Ingberg, "Tests o f s e v e r i t y o f b u i l d i n g f i r e s " , Q u a r t e r l y , NFPA, 22, 43 (1928).

2. T.Z. Harmathy, "Fi r e s e v e r i t y : Basis o f f i r e s a f e t y design", Paper p r e s e n t e d a t t h e I n t e r n a t i o n a l Symposium o f F i r e S a f e t y o f Concrete S t r u c t u r e s , F a l l Convention o f A C I , San Juan, P u e r t o Rico, September 21-26, 1980.

3. T.Z. Harmathy & J.R. Mehaffey, "Normalized heat l o a d : A key parameter i n f i r e s a f e t y design", F i r e and M a t e r i a l s , 6, 27 (1982).

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