REFERENCE

NBS

PUBLICATIONS

NAT'L INST. OF STAND & TECH

AlllOb D3M3EM

IMBSIR 85-3196

Slide- Rule Estimates of Fire Growth

4

J. R. Lawson

J. G. Quintiere

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

June 1985

Supported in part by: nr " ° r>avid Taylor Naval Ship

*ch and Development Center

100 igton, DC

• U56

85-3196

1985

NBSIR 85-3196

SLIDE-RULE ESTIMATES OF FIRE GROWTH

NATIONAL BUREAU

O? STANDARDS

library

,Vk3£

J. R. Lawson

J. G. Quintiere

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

June 1985

Supported in part by:

U.S. David Taylor Naval Ship

Research and Development Center

Washington, DC

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Table of Contents

Page

List of Tables iv

List of Figures v

Abstract 1

1. Introduction 1

2. Fire Size and Growth Rates 1

3. Radiant Heat Flux to a Target 8

4. Flame Height 9

5. Radial Flame Impingement and Heat Flux to a Ceiling 10

6. Smoke 12

7. Time to Carbon Monoxide Hazard With Smoldering Fires 14

8. Temperature Rise of Hot Gases in a Compartment 16

9. Ventilation Flow Rate 17

10. Does Flashover Occur? 19

11. Mass Burning Rate in Ventilation Limited Fires 19

12. Corridor Smoke Transfer and Filling 21

13. Smoke Concentration and Visibility 24

14. Estimation of Flame Spread Rates 28

15. Flame Spread Over Liquids 30

16. Fully Developed Fire Burn Time 31

17. Conclusion..... 31

18. References 32

19. Example

iii
List of Tables

Page

Table Bl. Results for PMMA pool fires of varying

scale 7

Table B2. Burning rates for liquid pool fires 8

Table B3 . Smoke properties for selected materials

burning in air 27

Table El. Fire growth predictions 42

Table E2 . Room smoke filling time predictions, steady

state fires 43

Table E3. Summary of critical event predictions 43

iv
List of Figures

Page

Figure Bl. Sketch of a wood crib 2

Figure B2. Reduced specific burning rate as a function

of the crib porosity for ponderosa pine

wood cribs 3

Figure B3. Rate of mass loss plot for easy chair 5

Figure B4 . Rate of mass loss plot for sofa with

"California foam" cushions 5

Figure B5 . Weight loss for cotton and mixed fiber core specimens 6

Figure B6 . Fire radiant heat transfer to a target 8

Figure B7. Flame height dependence on heat release

parameters 9

Figure B8a. For open flames 10

Figure B8b. Corner fire scenario 10

Figure B9. Flame length and geometric environment 11

Figure BIO. Room smoke filling model 13

Figure Bll. Ceiling layer height versus time and heat

input rate 13

Figure B12. Compartment temperature rise example 16

Figure B13. Sketch of compartment ventilation problem... 18

Figure B14. Corridor smoke transport 21

Figure B15. Smoke filling by a fire room to a closed

adjacent space 22

Figure B16. Dimensionless corridor smoke filling time 23

Figure B17. Visibility results derived from Rasbash [27],

Jin [28] and Lopez [29] 25

Figure B18. Smoke production for plywood as a function

of ventilation factor from Saito 27

Figure B19. Sketch of flame spread model 28

Figure B20. Schematic of the flame spreading rate as a function of the liquid temperature of the fuel 30

v
Figure El. Room fire example 35

Figure E2. Mass loss rate for fire growth example 44

Figure E3 . Heat flux predictions in room for fire

growth example 45

Figure E4 . Flame height and extension across ceiling

for fire growth example 46

Figure E5 . Room temperature rise for fire growth example 47

Figure E6 . Mass flow rate into the room for fire

growth example 48

Figure E7 . Visibility in corridor for fire growth

example 49

vx
SLIDE-RULE ESTIMATES OF FIRE GROWTH

by

J. R. Lawson and J.G. Quintiere

Abstract

A series of prediction methods have been assembled to provide an analytical

basis for estimating fire growth in compartmens. Solutions for each

prediction method can be made using programmable scientific calculators.

Prediction methods are presented for: fire size and growth rates, mass loss

rates, radiant heat flux, flame height, radial flame impingement, heat flux to

a ceiling, smoke filling of a room, carbon monoxide hazard with smoldering

fires, temperature rise in a compartment, ventilation flow rate, flashover

ocurrence, corridor smoke transfer and filling, smoke concentration,

visibility, flame spread rates, and fire burn time.

These predictive methods are useful for estimating many of the critical

elements related to fire behavior and help provide a better understanding of

this complex phenomenon.

This report appears as Appendix B in Fire Growth in Combat Ships by J.G.

Quintiere, H. R. Baum and J.R. Lawson, NBSIR 85-3159.

Key words: Calculators; computer programs; fire growth; fire models; room

fires.

I. Introduction

The purpose of this paper is to provide an analytical basis for estimating the

growth of fire in compartments and its consequences. All prediction methods

have been selected to allow for solutions to be made using programmable scientific calculators or pocket computers. The paper consists of a series of

equations or data each of which describes a particular process in a fire's

growth. Only minor discussions of theory are presented to provide some understanding of concepts related to the problem in question. For more information

on each process discussed, refer to the appropriate reference materials. The

equations presented will apply only to specific fuels or conditions and hence

will be approximate when used for more complex or different situations. Also,

any consideration of these equations as constituting a dynamic interacting

fire system will be filled with inconsistencies. Nevertheless, this series of

equations can provide a reasonable sense of the quantitative features of fire

growth. It will relate to material type - solids or liquids - not specific

materials. For specific materials other than those addressed in the text, one would have to acquire data that is unique to the materials being studied.

Moreover, the state-of-the-art does not fully allow for fire predictions of

specific materials.

2. Fire Size and Growth Rates

In order to make fire growth predictions, one must make a basic assumption

about what material is burning. This assumption is used to calculate an estimated burning rate for the model and is a key factor for calculating other

1
fire characteristics associated with fire growth. The four basic types of

fuels identified with fire are usually classed as:

A. Solids (non-metals)

B. Liquids

C. Electrical Equipment

D. Metals

In this paper we shall consider only some representative ways of estimating

Class A and Class B materials. For Class A we will consider first a wood crib

as representative of a complex structure; then a solid surface like a mattress, chair or slab of material. For Class B materials, a method for

estimating burning rates is suggested and input data will be provided for some common liquid fuels.

In 1976, Delichatosios reported work accomplished on the study of fire growth

in wood cribs [1]. In his work, it was shown that a simple model could be

used to predict fire growth rates for wood cribs. This model is put to use in

this report for the same purpose. The model pays particular attention to crib

geometry, surface area exposed for burning, and the wood's thermal properties.

The equation used for estimating burning rate, m^, for cribs ignited in the

center is,

BURNING RATES FOR WOOD CRIBS.

Figure Bl. Sketch of a Wood Crib.

m

-

mc = m A 7— for t < t f s 2 t - o

0

. ~l/2

specific burning rate found by: m" = cb f(P) where

( 1 )

io"3 / 3/2

c ~ 10 g/cm • s

b - wood stick thickness (cm)

f(P) - found in Figure B2

P = A. s

1 / 2 b

1 / 2 A^

2
- total exposed surface area of wood in the crib - 4£bnN where

l - stick length (cm)

s - stick spacing (cm) = 1 - nb

n - sticks per crib layer

N - layers of sticks in crib

A

v - total shaft cross-sectional area = s • (number = (n-1) ) of shafts)

t - time in seconds

t - time for flames to spread to the outer edge of crib = n/f/2 £)

l ~ 0.045 s" 1

m^ = A cb

_1//2 f(P) for t > t (2)

f s o

where f(P) is plotted in Figure B2 and when P > 0.07, f(P) = 1.

Figure B2. Reduced specific burning rate as a function of the crib porosity

for ponderosa pine wood cribs (taken from Heskestad) [2].

3
BURNING RATES FOR FURNISHINGS . With more complex solids like furnishings,

representative data is drawn from a report by Lawson, et al. [3]. Figure B3

exhibits the mass loss rate for a typical stuffed chair and Figure B4 provides

data on a typical three seat sofa. Mass loss rate data for burning mattresses

is obtained from a report published in 1977 by Babrauskas [4], Figure B5

presents data for cotton and mixed fiber core mattress specimens. Data from

these and other reports can be substituted in for calculations on burning

rates for furnishings. Furnishings are complex solids that do not currently

lend themselves to simple fire modeling, other common solid materials do.

BURNING RATES FOR PLASTIC POOL FIRES. The burning rate for polyurethane foam

was estimated with the following pool fire model developed by Orloff [5j.

m

f = ae

<' at g/s (3)

where a = 0.033s ^

8 = 1.29 (corresponds to a time shift

of 30.35 which accounts for a particular ignition character in

this experiment)

t = time in seconds

for the period 80 < t < 170 s.

4
RATE

OF

MASS

LOSS

Cg/s)

PATE

0F

MAS<3

L0S3

(

y

/s;

53

TIME C sec

)

furniture CALORIMETER

Figure B3. Rate of mass loss plot for easy chair [3].

Figure B4. Rate of mass loss plot for sofa with "California foam" cushions [3].

5
TIME (•)

Figure B5. Weight loss for cotton and mixed fiber core specimens [4].

A review of data from furniture fires [3] indicates that for polyurethane foam

chairs, Eq. (3) may also produce useful estimates for t > 170 s.

Modak. and Croce [6] studied the burning of polyraethyl methacrylate (PMMA)

plastic pool fires and found that experimentally measured burning rates per

unit area, m"(t), at time t after ignition were correlated by the equation:

ra ” - m"(t ) , -2 = e 't/T

• •• • •• m - m

.

s l

(4)

Therefore m"(t) can be estimated by,

m”(t) = - [e

t//T (m"si- m") - m" ] (5)

s where ra’.' = 4 g/m s is the average burning rate per unit area; m" is the steady

burning rate, and t is the characteristic "gasification time” to reach steady

state.

Table BL contains data that can be used for calculating m"(t) for various size

pools of PMMA.

6
Table B1

Results for PMMA Pool Fires of Varying Scale [6]

Pool area

Measured

s teadv

burning rate

per unit area

ra"s (g/m2 s

)

Gasification

time

parameter*3

T(s)

Radiative

fraction of

total heat

release rate

X(-)

2.58 x 10"3 4.6 NA 0. 28 c

5.81 x 10 -3 5.6 NA 0. 32 c

0.0232 7.7 b 3448 0. 32 c

0. 0523 9.

0

b 1587 0.42

0.0929 17.

4

b 1136 0.42

0.3716 18.0 500 0.42

0. 5806 18.25 357 0.42

1.4865 20.0 118 0.42

^Best fit.

cVaried with time.

NA not available.

BURNING RATES FOR LIQUID POOL FIRES. In order to estimate burning rates for

liquid pool fires, data were taken from a report by Burgess, et al. [7],

Their study shows the burning rate for a number of liquid fuels is a function

of pool diameter. But for large diameter pools, flame radiation dominates and

a maximum burning rate is achieved. Empirically they suggest that this

maximum burning rate can be found by

• M m

max

6.5 x 10 3

mm p AH /AH

c v

( 6 )

where p is the liquid density

AH is the heat of combustion, and

c

AH is the heat of vaporization,

v

Some specific results are given below in Table B2 for pool diameters greater

than 1.5 m.

7
able B2

Burning Rates for Liquid Pool Fires.

m" x^, flame radiation fraction

max r Liquid (g/m2 s

)

(%

n-Hexane 76. 9 42

Benzene 87.9 35

UDMH 44. 3 24

Methanol 15.8 15

Gas oline 45. - Diesel fuel 43. -

3. Radiant Heat Flux to a Target

After the initial fire has been defined, it is important to know something

about the heat radiated from the source that could cause secondary ignitions.

A technique discussed by Modak [8] will be used to estimate radiant flux.

This method is depicted in the sketch below and is detailed in Eq. (7).

H R h

Figure B6. Fire radiant heat transfer to a target.

The incident heat flux at a target can be approximated as

2 q" = P/4 ttR (7)

o o where P is the total radiative power output of the flame. P can be

represented as y Q where x is the radiative fraction and Q is total energy

release rate. Usually y ranges from 20 to 45 percent for many fuels. For a typical pool fire Modak [8] finds that the above formula is > 90 percent

accurate when R

Q /R > 4. At R

Q /R = 2, the approximation is about 80 percent

correct.

8
4. Flame Height

Since burning rates and thermal radiation to targets have been defined, a third physical phenomenon relating to flame geometry must be considered.

Flame height is an important characteristic which provides information needed

for estimating heat transfer to a room's ceiling and other structures that may

be located above a fire. It has been shown by McCaffrey [9] that flame

height, Z £ , is related to the total energy release rate, and the diameter,

D, of the fire base. This is illustrated in Figure B7 which is taken from a report by Zukoski, et al. [10].

For flame heights where (Zf/D) > 2, Zukoski suggested the following equation

which provides a reasonable estimate:

Z

f = [0.23 m/kW 2/5

] 0

2/5

, (8)

q/D5/2 Kw-m-5/2

I 1 1—I I I I I l 1 l 0.2 0.4 0.8 1.0 2 4 8 10 20 40 80

Qd = Q/Poo /gD D

2

Figure B7. Flame height dependence on heat release parameters [10].

or use Figure B7 directly.

In addition, work reported by Hasemi and Tokunaga [11] for a 0. 5 m diameter

burner showed that the height of the continuous flame region could be estimated by

9
Z, . = fo. 11 ra/kw

2/5

l Q

2/3

(9)

f min 1

and the height to the flame tip could be estimated by

Z c = (0.21 m/kW 2/5

) $

2/5

(10)

f max ^ > For Open Flames

These results are consistent with Eq. (8) and Figure B7, but explicitly

address the variation of the flame structure from a continuous luminous region

to a region above which is intermittent flames terminating at the flame "tip”.

Their work also provides equations that are useful in estimating flame heights

in a corner fire scenario. See Figure B8b. Equations (11) and (12) provide

these estimates.

Figure B8a.

the continuous flame

the flame tip

(ID

( 12 )

5. Radial Flame Impingement and Heat Flux to a Ceiling

Now that flame height has been estimated, it is possible to estimate radial

flame impingement on a ceiling and heat flux at a ceiling using equations

offered in a report by You and Faeth [12]. When the height of a free burning

flame exceeds the height of the ceiling, flame impingement would occur for

that fire burning in a confined geometry. That effect is shown in Figure B8

where H

R gives the radial flame impingement length.

It has been found [12] that the height (Hf) of a free burning fire in the open

generally exceeds the sura of the ceiling height (H) and impingement length

(H

r

) under these conditions. Thus, for a given fire energy release rate once Hf exceeds the ceiling height, the radial flame extension can be estimated from the following formulae.

For a ceiling with no side walls,

^ . 0.5 [(Hf - H}/D] 0,96

; (13)

10
and tor a ceiling with side walls,

^

= 0.69 [

f

H

f - H]/Dl°*

89

( 14 )

where D is the fire base diameter and can be found from Eq. (8). (Here

and Hj; are the same; since we have not attempted to unify our notation but

have retained the notation of the original source. )

Figure B9. Flame length and geometric environment.

From the work of You and Faeth [12] an estimate of the incident (primarily

convective) heat flux to the ceiling just above the fire can be found. This

stagnation point heat flux q" is determined from the correlation:

q"H^/Q = 31.2 Pr

373

Ra (15a)

where H is the ceiling height and Q is the fire energy release rate. The

equation was established for a Prandtl number of, Pr = 0.7, H^/H < 1.5,

109 < Ra < 10l4 s and where flame radiative heat flux is small. The Rayleigh

number, Ra, is defined as (gB/pCpV^) = 7.9 x 10^ kW~^m~2.

q" = 0.28 $

5/6 H~

7/3 (15b)

where 0 is in kW and H is in m. Much of the data correspond to low Ra, or small scale so this formula may yield perhaps low estimates on extrapolation

to large scale. For Hf/H > 1.5, they found the stagnation point heat flux to

decrease significantly from the above formula. For large flames, flame radiation should be added, and also hot layer gas and surface radiation should be

included after the room becomes hot (> 300°C).

11
6. Smoke Filling of a Room

At this point in the calculation process, the basic fire has been characterized, and it is time to direct attention to changes in environmental conditions which result from the fire. In this section, estimates will be made on smoke filling time for a room. The "filling time", t^, can be estimated as follows, i.e., tf = time for the layer to reach a door soffit (see Figure BIO)

or a floor leak as in the case examined by Zukoski [13]. Figure Bll illustrates the dependence of ceiling layer height on time and heat input rate.

For these results, heat loss from the smoke layer is neglected, and the room filling times are somewhat shorter than would be expected in a real fire. The

governing equation and notation from Zukoski's analysis [13] are described

below.

Smoke Filling Time

+ Q* + a (Q*

)

1 /3

y

5/3 = 0 (16)

where

y = Z/H nondimensional height of smoke layer interface (17)

2

r = t /g/H (H /S) nondimensional time (18)

t = time

g

= acceleration of gravity 9.8 m/s^

H = room height

S = floor area of the room

Q* = Q /(p^T^Cp • /gH • H^) which is a nondimensional fire heat (19)

input parameter.

0

= energy release rate of the fire

p = density of the air in room

ao

Cp = specific heat at constant pressure for air

a = 1/5.4, the mass entrainment coefficient

12
Figure BIO. Room smoke filling model.

Figure Bll. Ceiling layer height versus time and heat input rate [13]

In Eq. (16), if Q* is small, < 0.01

y > [1 + (^£)(Q*)

1/3

t1

_3/2 ( 20 )

13
and if Q* is large, > 0.4,

y

» 1 - Q*t ( 21 )

To solve for when Q* < 0.01, Eq. (20) is solved for x,

T

1 2/3

S3 2_

2a

3

( 22 )

The time tf to fill to a specific position y is then found by inverting Eq.

(18) as follows:

t = - ^ (23a)

I7h (H /s)

Smoke layer height from the floor, Z, can be calculated by Eq. (23b)

Z = H 1 + ^

? t /g/H — (23b)

pTC /gHH 00 00 p

To solve for t^ when Q* > 0.4, Eq. (21) is solved for t,

T

S3 i Z—L

Q* (24)

and then solved for t^ again using Eq. (23).

In cases where 0.01 < Q* < 0.4 one must integrate the ordinary differential

Eq. (16) or use Figure B10.

7. Time to Carbon Monoxide Hazard With Smoldering Fires

The previous section presented a method for estimating smoke filling in a room when an opening is present in a wall or a leak is near the floor. This section

uses smoke filling time and other data to estimate hazard time related to

carbon monoxide exposure which results from a smoldering chair. Equations

used in this estimate are taken from a report by Quintiere et al. [14]. In

that analysis the smoke filling time is calculated using Eqs. (16) through

(23) where the value of 0 is estimated by

0

= m A H (25)

where m is the rate of mass loss due to smoldering and AH is the heat of

reaction for the smoldering process. Here we adopt a simpler procedure based

on that study to allow ease in making first order estimates.

It is shown that m could be approximated for a smoldering fire in polyurethane

or cotton using

14
01 ct (26)

— 9 “9

where c = 0.206 gm min ~ for polyurethane and c = 0.33 gm min ^ for cotton,

and t represents time in minutes. The heat of reaction for polyurethane is

AH = 15 ± 8 kJg~l and cotton is aH = 1 1 ± 1 kJg -1

. These results were only

for slabs of particular samples of cotton and polyurethane. Moreover the

smoldering rate of an upholstered chair composed of cotton and polyurethane

initially grew quadratically with time, then remained constant for the next

hour. Thus, Eq. (26) with the constants given can only be taken as a rough

estimate for m. It was, however, found that the mass generation rate of CO

could be taken as proportional to the mass loss rate in smoldering, and that

constant y was estimated as about 0. 1 g CO/g fuel lost for both the polyurethane and cotton samples discussed above. Thus for those cases the CO

generation rate was estimated as

m = yet. (27) co

As a first estimate we will use Eq. (27) and consider a well-mixed closed

volume (V) in which the smoldering takes place. The more general stratified

case with "filling" was discussed in ref. [ 1 4 j , but in actuality the dispersal

of smoldering products is not so well defined. Consequently a uniformly mixed

volume is reasonable alternative. For this case the mass fraction of CO in

the volume defined to be Y is given by

dY_ =

yjh

dt pV (28)

where p is the gas density. Finally adopting a critical dose of 4.5% CO-min

for human incapacitation as suggested by t£e work of Stuart et al [14], and

since the dose D can be expressed as D = ^ Ydt it follows from Eqs. (26-28)

that

D (29)

where D = 0.045 min for the critical dose, the hazard time can be estimated.

Rewriting this equation to solve for t

t =

r 6 D p v a/3

( c y

' (30)

where V = volume of the room

p = density of the gas

c = values shown above for polyurethane and cotton

y = the mass fraction of CO produced per smoldering mass loss of fuel

For example, with a cotton sample t = 25.3 where t is in minutes and V is

m3. The time to critical dose is finally calculated using Eq. (30).

It should be emphasized that the above analysis is very approximate and not

generally applicable to all smoldering conditions. It is only offered as a first-order of magnitude estimate.

15
8. Temperature Rise of Hot Gases in a Compartment

A second environmental condition that requires consideration in a room fire is

the resulting temperature rise. This has been studied and correlated by- several different investigations. The method for estimating temperature

rise, AT, here comes from reports by Quintiere [15] and McCaffrey, et al.

[16]. This model considers temperature rise in compartments containing single

or multiple wall vents, and the venting action is created only by natural

convection. Figure B12 describes a compartment example and defines some parameters.

H

H0

Wo h

Figure B12. Compartment example.

The equation used for making this estimate of compartment gas temperature rise

is

at

T

o 1.6

/g C p T A /H

p O 0 0 o

2/3 h

k

A

g C p A /H

p o o o

-1/3

where T

Q = initial or ambient air temperature

0

= rate of energy release

g = acceleration of gravity 9.8 m/s z

Cp = specific heat of air at constant pressure

o = density of ambient air

A

q = W 0 H0 , vent area

W Q = horizontal vent dimension

H

q = vertical vent dimension

(31)

16
/kpc/t, t < t effective enclosure

P

h, k/6, t > t P conductance

k = thermal conductivity of the enclosure structure

P density of the enclosure structure

c specific heat of the enclosure structure

6 = enclosure material thickness

t = f f ~ > thermal penetration time

p

v k

' ' 2'

A = total surface area

Both h^A and AQ /H0 should be summed for multiple structural materials and

openings, respectively. The procedure for addressing multiple features is

elaborated on in refrence [15].

Now that methods have been presented for estimating burning rates and AT in a fire compartment, it is time to consider ventilation flow rates in the fire.

It was pointed out by Steckler, et al. [17] that the flow of air and gases in room fires has a significant influence on the development of a fire. As a fire develops, the air and gas flow rates control compartment temperature and

heat transfer which then affects the rate of fire growth. When a compartment

fire reaches a fully involved state, the air flow rate usually controls the

fire, and the fire is then considered to be ventilation controlled. The mass

flow rate of air and gases will be estimated first in this section, and ventilation limit conditions will be examined later.

In order to further understand the terminology of vent flow refer to Figure

B13. Under natural convection conditions and after the hot gases fill the

compartment and spill out of the vent, the flow will be countercurrent at the

vent. Air will enter at a rate m. and combustion products will flow out at a rate m . These flows result from pressure differences (Ap) set up at the vent

due to the differences in compartment and ambient gas temperatures. At the

flow reversal point in the vent, the Ap is zero and this position is termed

the neutral plane. The flow rates depend on the fuel mass release rate mf,

the height of the neutral plane X

2

» the height of the hot gas layer Xp its

temperature T, and the vent dimensions H

Q and WQ

. In general the vent equations are coupled nonlinear algebraic equations which we will avoid solving,

but suggest the approximate procedure below.

9. Ventilation Flow Rate

17
Figure B13. Sketch of compartment ventilation problem.

To make this ventilation flow rate estimate, it is necessary to assume a free

burning condition. The first step in making this estimate is to calculate a fuel mass burning rate, mf, with one of the methods found in section 2, and

then calculate the compartment gas temperature by the formula presented in

section 8. At this point the dimensionless mass flow rate MQ can be calculated [18] using,

M

q = U

1/2

/(l + *)] (1 - y

2

) V2 (32)

T - T

where

and y2 = X 2 /HQ can be estimated as 0.5 to 0.6 for ij> < 1 and for wellventilated fires where mf/mi is small as found in reference [18]. For the case of larger \p and mf/mi not small, the neutral plane can be estimated from

the work of Kawagoe and Sekine [19] or from reference [18] in which x^ = 0:

y-> =

1 + fa

1/3

2/3 *

1 +

(33)

This will yield the lower limit for y 2 when the hot layer tends to the floor

and the enclosure tends toward a uniform gas temperature. Then mass flow rate

out, m , can be calculated using,

o

ra = — M Cp

o 3 o a 2g W

o o (34)

18
where C = opening flow coefficient which is ~ 0.

7

p = density of ambient gas surrounding area

g

= acceleration of gravity (9.8 ra/s^)

W Q = opening width

H

o

= opening height

The mass inflow rate of air, V, can be calculated by,

fn. = fh - fti c (35)

l o f for which steady flow conditions have been assumed. Of course if mf/m^ is

found to be large, then iteration is required in the above computations.

Moreover the ratio mf/m^ should be compared with the mass stoichiometric fuel

to air ratio to examine whether the fire is ventilation limited. We will

return to this point shortly.

10. Does Flashover Occur?

The methods presented have provided a basis for predicting the fire environment up to the point of rapid transition in fire behavior. This critical

point is called "flashover”, and it has been defined in many different ways.

A paper by Thomas, et al. [20] describes five different processes or combinations of processes that could lead to flashover. It is pointed out that

flashover usually results in a sharp increase in room temperature and rate of

energy release. Thomas shows that flashover is typically associated with

compartment gas temperatures which range between 300-650°C. For the flashover

estimates calculated in this paper it is suggested that a critical gas temperature rise of 500°C be selected. Thus for a given Q(t) the formulae for AT,

given by Eq. (31), can be solved to find the time, t, at which AT = 500°C or

the "flashover" time.

Alternatively, the condition for flashover with a constant energy release

rate $ follows from Eq. (31) in which AT is set equal to 500°C. That result

is given as

$

= 610 (t^A A

q

/TT) 1/2 (36)

for which 0 is in kW , h^ is in k.W/(m2 K), H

q

in m, and A and AQ are in m“.

This result says that the energy release rate to cause "flashover" depends on the compartment thermal properties, its surface area, and the vent size.

11. Mass Burning Rate in Ventilation Limited Fires

After "flashover" or in fires where small openings restrict ventilation, the

fire will probably become "ventilation limited." That is the supply of air to

the room is less than that amount needed for stoichiometric burning of the

available gasified fuel. It can also be defined as the point when the oxygen

level in the compartment reaches a low value (ideally zero) such that the

reaction between fuel and oxygen ceases to produce products or proceeds very

slowly.

19
In general, the energy release rate of the fuel burning in the compartment, is

given as

m. AH for rn/ra < y

f f a -

Q = (37)

(0.233) m AH for m./m > y

a ox f a -

where Y is the mass stoichiometric fuel to air ratio

AH is the fuel heat of reaction

m

a is the air flow rate through the vent

and AH ox

is the heat of combustion per unit mass of oxygen and is taken

as 13 kJ/g.

The fire is termed "f uel-controlled” for fcf/fh a < y, and the energy release

rate depends on the fuel pyrolysis rate. Since the air flow rate is primarily

controlled by vent size, the available air supply will reach the limit for

combustion as mf increases. Thus as the fire grows, the rate of energy

release within the compartment will be governed solely by the air supply

rate. The excess fuel will exit the compartment with combustion continuing in

the vent flame. This limit condition in which the maximum possible energy

release rate is achieved in the compartment roughly occurs when mf/ma = y and

the fire is termed "ventilation-controlled” as long as mf/ma > y. Fires are generally fuel-controlled before the occurrence of flashover, and ventilationcontrolled afterwards [20].

In order to estimate the point of transition to ventilation control, both the

fuel mass loss rate and the air supply rate must be known. The mass loss

rate m^ depends on the enclosure conditions as illustrated qualitatively

below

m. m

f o 0.233 (38)

where

and L

is the free burning value

is the local oxygen concentration around the combustion region

within the enclosure

is the net heat transfer rate from the enclosure to the fuel

is the fuel "heat of vaporization"

There is some evidence from full-scale experiments [14] that up to flashover

or shortly before, the mass loss rate in an enclosure is nearly equal to its

free burn value. After flashover, the mass loss rate will differ distinctly

from its free-burn value. As a first estimate to assess whether the ventilation limit has been reached, the free burn mass loss rate should be compared

with the maximum vent air flow rate. The latter can be estimated by using

20
Eqns. (32 and 33) for mf/ra^ = 0 (i.e. , small). Thus, the maximum possible

vent air flow rate is for T/T > 2:

ci

ro = 0. 5 W H

3//2 (kg/s) (39)

a, max a o with W

Q and H 0 in m. Hence the ratio of the free burn mass loss rate and

maximum air supply rate can be compared with the stoichiometric ratio (y).

After ventilation-limited conditions prevail, the mass loss rate of the fuel

can not be directly computed. Nevertheless, results for wood crib fires have

been empirically correlated [19,21] to yield:

fc_ = 0.09 W H 3/2 (kg/s) (40)

t o o with W

Q and H 0 in m. An estimate of the corresponding compartment gas temperature rise might also be made by computing the energy release rate from the

maximum possible air flow rate Eq. (39). The result follows [15]:

AT = 896 [A /iT/fh A]l 1/3 (0c) (41) L o o ^ k

; J

2 where A

Q is the vent area (m ), H 0 is the vent height (m), h^ is the enclosure

structure conductance (kW/m^k) and A is the structure surface area (m^).

12. Corridor Smoke Transfer and Filling

Much work is currently being done to develop meaningful correlations and

models for smoke transfer and filling in corridors. The interest in this

subject springs from the need to predict changes in environmental conditions

which occur throughout a building as a fire develops. This is of great importance to life safety. An estimate made for the smoke front velocity, will

be taken from work in progress by Zukoski and Kubota [22]. Figure B14

displays the phenomenon of a smoke layer progressing along a corridor.

V f £5 V c

Figure B14. Corridor smoke transport.

From their preliminary analysis, we have extracted a result that represents an upper limit to the front velocity. This corresponds to the limiting case of

the smoke layer filling half the corridor height and does not consider viscous

effects which would retard the front speed. Thus a simple order of magnitude

estimate is given below.

21
where

v

f - V2 [g(

P

-a ' —

° C

) H]

1/2

(42)

a

g

= acceleration of gravity,

o = density of ambient air,

a

p = densitv of the corridor fluid,

H = corridor height.

Density can be related to the fire room temperature provided no heat loss occurs. Thus from the ideal gas law:

where T

a

= ambient temperature,

and T = gas temperature in fire room.

Subsequently the time (tjr) for velocity front movement through a corridor is

estimated by

where L = corridor length

Smoke filling time for a closed corridor or adjacent space to a room can be

estimated using the appropriate formulas selected from section 6. But that

approach would ignore the geometrical aspects of the room and corridor and

their connecting doorway. It necessitates treating the corridor and room space as a single volume. Alternatively, work by Jones and Quintiere [23]

suggest another approach. Figure B15 illustrates this smoke filling from a room fire to a closed adjacent space.

Transit time

HU

"

~ > —T 1 T

H of Hc ^T7 I

Tr~"“ 1 1 Layer falls for closed

T n

Height of Z/ adjacent space

^ neutral plane i v

B = width /

of room door -J _ 1L “ — ^

Figure B15. Smoke filling by a fire room to a closed adjacent space.

22
* Ln this method a scaling parameter, P, for the room door is considered, where

* 3/2 5/ 9 P = B (H r

/Z /(H ) D/ “ (44)

u c where B = width of the connecting door,

H

u = height of connecting door,

H

c = height of corridor.

A correlation based on dimensionless variables was developed using both experimental and computational results. The conditions examined were a room and

closed corridor of equal height (Hc = 2.32 m), a fixed room door height

(H n

= 2.0 m), variable door widths (0.13 <_ B <_ 1.07 m), and varying heat

release rates (25 <_ 0 <_ 225 kW). These conditions are representative of many

building and developing fire conditions. The correlation is presented in

Figure B16 which gives the dimensionless filling time i as a function of the

fire and door parameters, $ and P, respectively. The time for filling was

selected as the time for the smoke layer to descend to 1 m above the corridor

floor. The dimensionless parameters are defined as follows:

Figure B16. Dimensionless corridor smoke filling time [23]

23
Q represents dimensionless heat release rate and is defined by the equation

Q = 0 / fC T m

where

and

0 -

C

P =

T

a

=

*m

=

P a

net heat release rate

specific heat of air

ambient temperature

a dimensionless characteristic mass flow which is defined as

(45)

* / u a/2u 2

ra =

p (gH ) H (46)

where p = ambient density

a

y

g

= acceleration of gravity

H

c = height of corridor.

The dimensionless time t in Figure B16 is given as

t = t(m/p AH ) (47)

a c where t = time (s)

and A = floor area for the corridor or adjoining space

. * To make an estimate^f or filling time t, a Q is selected from which Q is calculated. Using this Q, t can be determined from Figure B16. Rearranging Eq.

(47) to solve for t yields

t - -j—£ (48)

(n,/oaA H

c

)

13. Smoke Concentration and Visibility

The production of smoke in fires is an important feature in evaluating life

safety. Technically smoke might be considered to include particles, hot

combustion products, and toxic gases. Here we will only address the particulate nature of smoke and its effect on visibility. Smoke obscures vision by

the reduction of light transmission. Smoke may also reduce vision by

irritating the eyes. In this section estimates for smoke concentration and

visibility will be calculted for a closed system which consists of a room and

adjacent space.

The production rate of smoke particles (m ) in a fire can be expressed as

m

s m r (49)

24
where x

s = fraction of particulate mass to fuel mass loss

fuel mass loss rate

The objective is to compute this production rate and relate it to visibility.

Some background on needed data and applications can be found in reports by

Quintiere [24], Babrauskas [25] and Tewarson [2b]. An approximate relationship to predict visibility, defined to be L v the length one can see through

smoke when no eye irritation is present, is given as

L

v = k v /(D/L) (50)

where D/L is the optical density per unit path length

k v

is a constant selected from Figure B17.

This relationship is derived from the results shown in Figure B17 [24] and is

merely an approximate fit to those data. Of course the selected value for k v should be consistent with those results but could also represent a conservative design value. To apply Eq. (50) to a particular situation we must

compute (D/L) for that fuel and the configuration it burned in.

>

m

<75 >

10

5

2

1.0

0.5

0.2

0.1

0.02 0.05 0.1 0.2 0.5 1 2 5 10

D/L,

OPTICAL DENSITY PER PATH LENGTH OF SMOKE (itT 1

)

O Illuminated sign

Diffusa light

VM Focused lamp In yellow amoks

A Backlighted sign

Illuminated placard

Illuminated sign

Figure B17. Visibility results derived from Rasbash [27], Jin [28] and Lopez [29].

25
To compute (D/L) for a closed system, for example a room and adjacent space,

the following relationship must be integrated over time:

d(D/L) ax

s . dt V “f (51)

where t is time

a is the particle optical density

and V is the volume of the enclosed space.

The mass loss rate m should be initially estimated from free burn analysis as before. This will be valid in the early stages of the fire. Data on a and

X s , properties of the burning fuel, are needed for each fuel. Seader and Ou

[30] suggest a a 3300 m2/kg for fuels burning in air, and these results for a wide range of fuels are given by Tewarson [26]. (However Tewarson defines x

g and Yg and reports a, which is related to a, as a = a/(2.303 Ys ).) Also axs can be estimated from the Smoke Density Chamber Test Method described in ASTM

E-662. It can be shown that

axs

D

s , max

m” (52)

where D

g max is the maximum specific optical density measured in ASTM E-662

and m" is the mass of sample consumed per unit of exposed surface area.

Of course the values of a and Xs f° r a given material will depend on the

exposure conditions during the burning of those samples. For first order

estimates these effects are ignored, but judgment must be used in the application of such data.

The estimate based on Eq. (51) assumes that the volume of interest is well

mixed and here the filling time has been ignored. Table B3 gives some representative values for a and x

•

An important point that should be noted in the discussion above is that in

ventilation limited conditions, mf depends cm air flow and Xs ^as been shown

to increase. The ventilation parameter A0 /H 0 is reduced. This is shown in

Figure B18 from the work of Saito [31] for plywood burning in an enclosure of

floor area A.

26
Table B3

Smoke properties for selected materials burning in air [26]

Material

Particle Optical

Density

a

( 10^m^./kg)

Fraction of Particulate

Mass to Fuel Mass Loss

x

s (-)

Oak 3. 17 0.013

PMMA 4.65 0.021

Polyurethane foam

flexible (GM-25) 0.426 0.32

Granular Polystyrene 2.11 0. 15

0.0

1

0.1

Ventilation factor, A 0 *J{H0

) /A (m 72)

Figure B18. Smoke production for plywood as a function of

ventilation factor from Saito [31]

27
14. Estimation of Flame Spread Rates

After an unwanted fire has started flames spread away from the point of

origin. The rate of flame spread, Vf, is affected by several environmental

factors and the thermophysical/thermochemical properties of the materials.

For solids of thickness > 1 mm Eq. (53) Quintiere and Harkleroad [32]

illustrate some of these variables.

Solids

(t, - t. r

V « —1

f 2 kpc(T. - T ) ig s'

where Tf - is the flame temperature which depends on available oxygen

(53)

T^g - is the ignition temperature

T

s - is the upstream surface temperature resulting from an external heat flux.

Figure B19 schematically depicts the plume spread phenomena.

Figure B19. Sketch of flame spread model.

28
The relationship shown above can be converted into an estimate of downward

flame spread rate using,

Flame Spread Opposed to Flow (downward)

V a $

kpc(T. - T ) 2 ig s where

4

> = V (kpc) (T, - T. ) 2 a

M 'g f ig'

and

( 54 )

(55)

V

a

M g

- T

1/3

opposed flow characteristic gas velocity

( 55 ) under natural convection conditions

where thermal conductivity of gas phase

specific heat of gas

specific heat of gas

gravitational acceleration (9.8 m/s z

)

adiabatic flame temperature

ambient and initial temperature

It has been found for a wide range of materials that $ generally

ranges between 1 and 15 (kW)^/m-^; ranges between 250 and 600°C;

and kpc ranges between 0.01 and 1.0 (kW/m^K)^ [32]. These are to be

considered pseudo-properties valid for Eq. (54) under opposed flow natural

convection flame spread in vertical orientation.

For upward flame travel, flame spread rate can be described by:

Upward Flame Spread

(q"

f

) 5

f f 2 kpc (T - T ) ig s

(57)

where = heat transfer per unit time and per unit area

and 5 ^ = flame extension length

Practical applications of Eq. (57) have not been developed, and general

methods for predicting q£ and 6

^ do not exist.

29
15. Flame Spread Over Liquids

Glassman [33] reports on recent research efforts and theories for flame spread

over liquids. As is shown in Figure B20, there are basically two different

regimes for fires on liquids. One regime relates to flame spread which is

controlled by gas phase phenomena when the bulk liquid temperature (T^)

reaches its flash point or, for sustained burning, its fire point temperature Tf. The other regime occurs when the bulk liquid temperature is below

its fire point temperature. This slower flame spread phenomena depends on the

evaporation of the liquid to sustain and control the process. As the liquid

temperature rises above the fire point temperature to T^st* a stoichiometric

fuel-air mixture is formed near the surface, and consequently flame spread occurs in the gas phase. This rate of flame spread is related to the bulk

liquid temperature and its surface tension.

LIQUID FUEL TEMPERATURE (TL )

Figure B20. Schematic of the flame spreading rate as a function

of the liquid temperature of the fuel [33].

A report by Williams [34] gives a qualitative formula for the flame spread

rate, V^, on liquid fuels.

(58)

where a' = gradiant in surface tension

d j

dT

- T )/i

o

’ (59)

30
T • j. = liquid ignition temperature

*• O = initial liquid temperature

l = length characteristic forward flame heat transfer to the liquid

U

l liquid viscosity

= liquid density

The application of this equation to practical problem solving is not straightforward since 1 depends on the heat transfer characteristics of the particular

problem. Referral to references [33,34] will give some further background and

insight on potential applications.

16. Fully Developed Fire Burn Time

Once a fire has started and has become fully developed, it is of interest to

be able to estimate the duration of burning. This can be easily estimated by

or

(60)

(61)

where me is the mass of fuel available to burn (vaporize) and mf is the

burning (vaporization) rate of the fuel under the specified environmental

conditions. The value for can be estimated using the equations located in

section 2.

17. Conclusion

To conclude this paper, it would be appropriate to use the techniques

presented to make estimates for the development of a hypothetical fire. An

exercise of this type is presented in the "Example" which follows section 18.

This report has brought together a number of techniques developed by various

researchers for evaluating the fire environment. These predictive methods can

be useful in estimating many of the critical elements related to fire behavior

and help provide a better understanding of this complex phenomenon. It should

be remembered when using this report while making predictions that the results

are only estimates. These estimates, which spring from the state-of-the-art,

are meant to provide a reasonable approximation and in some cases just an order of magnitude for the particular elements under study. More accurate

predictions typically involve more complex calculations using more powerful

methods than a simple calculation. In many cases, additional research is

needed to formulate new solutions, derive more data, and to develop more sophisticated fire models than currently exist. Nevertheless the approach

presented here provides, in addition to its estimates, a conceptual framework

for what we can do and what we must learn to do.

31
18. References

1. Delichatsios, M.A. , Fire Growth Rates in Wood Cribs, Combustion and

Flame, 27, 267-278 (1976).

2. Heskestad, G. , Modeling of Enclosure Fires, 14th Symposium

(International) on Combustion, The Combustion Institute, Pittsburgh,

p. 1021, (1973).

3. Lawson, J.R. , Walton, W. D. , Twilley, W.H. , Fire Performance of

Furnishings as Measured in the NBS Furniture Calorimeter. Part I,

National Bureau of Standards (U.S.) NBSIR 83-2787 (1983).

4. Babrauskas, V. , Combustion of Mattresses Exposed to Flaming Ignition

Sources - Part I. Full Scale Tests and Hazard Analysis, National Bureau

of Standards, (U.S. ), NBSIR 77-1290, (1977).

5. Orloff, L. , Fire Growth on Polyurethane Foam, Modak, A. T. , ed. , Influence

of Enclosures on Fire Growth, Volume II - Analysis, Tech. Report, FMRC

J. I. OAOR3.BU, RC78-BT-24, Factory Mutual Research Corp. , Norwood, MA

(July 1978).

6. Modak, A.T. , Croce, P.A. , Plastic Pool Fires, Combustion and Flame, 30,

251-265, (1977).

7. Burgess, D.S., Grumer, J. , Wolfhard, H.G. , Burning Rates of Liquid Fuels

in Large and Small Open Trays, International Symposium on the Use of

Models in Fire Research, Publication 786 National Academy of Sciences,

(November 1959).

8. Modak, A.T., Thermal Radiation from Pool Fires, Combustion and Flame, 29,

177-192 (1977).

9. McCaffrey, B.J. , Purely Buoyant Diffusion Flames: Some Experimental

Results, National Bureau of Standards, (U.S.) NBSIR 79-1910 (1979).

10. Zukoski, E. E. , Kubota, T. , Cetegen, B. , Entrainment in Fire Plumes, Fire

Safety Journal, 3, 107-121 (1980/81).

11. Hasemi, Y. , Tokunaga, T. , Modeling of Turbulent Diffusion Flames and Fire

Plumes for the Analysis of Fire Growth, Fire Dynamics and Heat Transfer,

The American Society of Mechanical Engineers, 21st National Heat Transfer

Conference, HTD-Vol. 25, (1983).

12. You, H.Z., Faeth, G.M. , Ceiling Heat Transfer During Fire Plume and Flame

Impingement, Fire and Materials, Vol 3, (1979).

13. Zukoski, E.E., Development of a Stratified Ceiling Layer in the Early

Stages of a Closed-Room Fire, Fire and Materials, Vol. 2, No. 2, (1978).

14. Quintiere, J. G. , Birky, M. , McDonald, F. , Smith, G. , An Analysis of

Smoldering Fires in Closed Compartments and Their Hazard Due to Carbon

Monoxide, Fire and Materials, Vol. 6, Nos. 3 and 4, (1982).

32
15. Quintiere, J.G. , A Simple Correlation for Predicting Temperature in a Room Fire, National Bureau of Standards (U.S.), NBSIR 83-2712, (1983).

16. McCaffrey, B.J., Quintiere, J.G. , Harkelroad, M.F., Estimating Room

Temperatures and the Likelihood of Flashover Using Fire Test Data

Correlations, Fire Technology, 17, 2, p. 98, (May 1981).

17. Steckler, K. D. , Quintiere, J.G. , Rinkinen, W.J. , Flow Induced by Fire in

a Compartment, Nineteenth Symposium (International) on Combustion, The

Combustion Institute, pp. 913-920, (1982).

18. Quintiere, J.G. , Steckler, K. , Corley, D. , An Assessment of Fire Induced

Flows in Compartments, Fire Science and Technology, Vol. 4, No. 1, p. 1-14, (June 1984).

19. Kawagoe, K. , Sekine, T. , Estimation of Fire Temperature - Time Curve for

Rooms, Ministry of Construction, Japanese Government, (June 1963).

20. Thomas, P.H. , Bullen, M.L. , Quintiere, J.G. and McCaffrey, B. J.

,

Flashover and Instabilities in Fire Behavior, Combustion and Flame, 38,

159-171, (1980).

21. Thomas, P.H. , Heselden, A. J.M. , Law, M. , Fully-Developed Compartment

Fires — Two Kinds of Behavior, Ministry of Technology and Fire Offices

Committee, Fire Research Station, Borehanwood, England Technical Paper

No. 18, (1967).

22. Zukoski, E.E., Kubota, T. , Experimental Study of Environment and Heat

Transfer In a Room Fire, Final Report, Grant NB82NADA3033 , National

Bureau of Standards, (U.S. ), (July 1984).

23. Jones, W.W. , Quintiere, J.G. , Prediction of Corridor Smoke Filling by

Zone Models, Combustion Science and Technology, Vol. 35, pp. 239-253,

(1984).

24. Quintiere, J.G. , Smoke Measurements: An Assessment of Correlations

Between Laboratory and Full-Scale Experiments, Fire and Materials,

Vol. 6, Nos. 3 and 4, (1982).

25. Babrauskas, V., Applications of Predictive Smoke Measurements, Journal of

Fire and Flammability, Vol. 12, p. 51, (January 1981).

26. Tewarson, A. , Physico-Chemical and Combustion/Pyrolysis Properties of

Polymeric Materials, National Bureau of Standards (U.S.), NBS-GCR-80-295,

(1980).

27. Rasbash, D. J. , Smoke and Toxic Products Produced at Fires, Plastics

Institute Transaction and Journal, pp. 55-61, (January 1967).

28. Jin, T. , Visibility through Fire Smoke (Part 2), Report of the Fire

Research Institute of Japan, Nos. 33, 31, (1971).

29. Lopez, E.L. , Smoke Emission from Burning Cabin Materials and the Effect

on Visibility in Wide-Bodied Jet Transports, Journal of Fire and Flammability, Vol. 6, (October 1975).

33
30. Seader, J.D. , Ou, S.S., Correlation of the Smoking Tendency of Materials,

Fire Research, 1, 3-9, (1977).

31. Saito, F. , Smoke Generation from Building Materials, 15th Symposium

(International) on Combustion, The Combustion Institute, 269 (1974).

32. Quintiere, J.G. , Harkelroad, M. , New Concepts for Measuring Flame Spread

Properties, presented at Symposium on Application of Fire Science to Fire

Engineering, ASTM, SFPE, (June 1984).

33. Glassman, I., Dryer, F.L. , Flame Spreading Across Liquid Fuels, Fire

Safety Journal, Vol. 3, Nos. 2-4, (January -March 1981).

34. Williams, F.A. , Mechanisms of Fire Spread, Sixteenth Symposium (International) on Combustion, The Combustion Institute, 1281-1294, (1976).

34
19. EXAMPLE

This exercise is designed to provide an example of the use of the predictive

methods presented in this report. It is intended as a hypothetical illustration and should not be construed as representative of the hazard associated

with the particular items, materials and occupancy configuration selected.

The first step in analyzing a fire scenario is to define the problem in terms

of information required by the relevant predictive formulae.

Problem:

The fire takes place in a hotel room. A fire starts from a cigarette lighter

in the center of a bed with a polyurethane foam mattress. The room door is

Left 1/4 open as the occupant flees the room. Figure B21 shows the plan for

the hotel section being studied.

1

1— h

Fire

1 room Hr—4-4—

1 t i|

4 —1

4.5 rrs Room 'S'l' Room Utility Room Room

Bed fire-^

room * "3.6 m

—es

4—1 4— i < > i 4—1— —

Exit

door

ClOMd

Room door

1 / 4 open Corridor 2 m

Exit

door

cloeed

20 m

Note: Ceiling height in rooms and corridors 2.4 m.

All doors are closed except the fire door.

Figure El. Room Fire Example

Analysis of Fire Growth and Consequences

In this section, the prediction methods presented earlier are used to

calculate mass loss rate, heat release rate, flame height, ceiling heat flux,

temperature rise, ventilation flow rate, visibility, smoke filling, and smoke

transport for the sample problem. The data required to make these calculations are provided as well as the assumptions used to simplify the calculation

process. Tables of predicted values are presented and selected results are shown graphically.

Mass Loss Rate

The first step in these predictions of fire growth and hazardous conditions is

the determination of an expression for energy generation rate of the fire.

Using Eq. (3) with 8 = 0 yields the following expression for fuel mass loss

rate.

35
m = ae where a = 0.03

The solution to this expression is shown in Table El and Figure E2 for times

up to 250 s. Mass loss rates for times from 250 s to 300 s are calculated

using the steady state burning formula for wood cribs:

3/2

ro c = 0.09 W H

' f oo

where W

Q = 0.23

- 2

This represents the ventilation-limited fire case. It is employed at the time

when the ratio of fuel mass loss rate to air flow rate to the room exceeds its

stoichiometric ratio (8).

Heat Release Rate

Heat release rate was calculated using the equation:

Q

= mAH

where AH = 15.7 (kJ/g) for the polyurethane foam mattress in the example.

Radiant Flux

From the heat release rate the radiant heat transfer to a nearby surface can

be calculated using Eq. (7). In this prediction, it is assumed that R

Q , the

distance from the heat source to the wall is 1.8 m. The y r value for polyurethane foam in this example is 0.35. Both values for Q and qQ (RQ

) are presented in Table El The radiant flux q" (RQ

) as a function of time is shown

in Figure E3.

Flame Height

The values for flame height, H^, and ceiling flame impingement length, H^, in

Table El and Figure E4 were calculated using Eqs. (8) and (14),

respectively. In Eq . (14), the value for H = 1.8 m since the bed height is

subtracted from the overall ceiling height, and D was selected as a constant

of 0.5 m. (Although the fire is growing, it is not strongly dependent on D.

)

Ceiling Heat Flux

Table El and Figure E3 also contain predictions for heat flux to the room's

ceiling. These results were developed using Eq. (15b). The values for

radiant flux derived from Eq. (7) were added to values from Eq . (15b) to

predict the total heat flux to the ceiling. In this example radiation from

the hot gas layer has not been included in the total heat flux to the ceiling.

However, an upper limit for radiation to the ceiling from the hot gas layer can be estimated as aT 1^ whe re a is 5.6697 x 10 8 W/m^ - K^.

36
Temperature Rise

Predictions for gas temperature rise, AT, in the room are presented in column

8 of Table El. Also see Figure E5. These values were generated using Eq.

(31), but before the various temperatures were calculated thermal penetration

times, tp, for the gypsum walls and plywood floors were determined. The

following parameters were used in these calculations:

Gypsum wallboard (walls/ceiling)

t p = 393 s

p = 960 kg/m^

c = 1.1 kJ / (kg-K)

k = 1.7 x 10~4 kJ/(m-K)

5 = 0.0159 m

Plywood (floor)

t p = 711 s

p = 540 kg/m^

c = 2.5 kJ/ (kg-K)

k = 1.2 x 10"4 kJ/(m-K)

5 = 0.0159 m

As a result of these calculations, it was found that values for h^ in Eq. (31)

would be determined using /kpc/t where t < tp. At this point, it is important

to note that new values for hk are calculated with each new time in the

prediction of aT. For t _< t p

, hk was calculated by

\

* A l\,l + VHc.Z

A

where

9 A^ = 55.08 m area for walls and ceilings

2 ~ 16.2 m area for floor

A = 71.28 m^ total

and h

k ^ and h^

^ correspond to the gypsum board and plywood respectively.

When extended calculations are made for t > t for either the walls and

ceiling or floor, k/6 should be substituted into the above equation. For

37
AT calculations at times greater than the point of flashover, Eq.(41) was

used. Values for the parameter in Eq. (31 and 41) are as follows:

g

= 9.8 m/s 2

c

p = 1.046 kJ/(kg-K)

P o = 1.25 kg/m3

T

q = 293 K

AQ = 0.46 m

2

H

q = 2 m

Ventilation Flow Rate

Since both Q and AT are now available, ventilation flow rate is calculated.

In this procedure, Eqs. (32, 33, 34 and 35) are used to make the predictions. For times down to 220 s where ip < 1, y 2 = 0. 5 was used in the calculation. For i|; > 1, Eq. (33) was used to calculate an estimated value of y 2

» This was done by substituting the preceeding result of m^ into the equation.

The values of M0 and m^ were determined using Eqs. (32 and 34), and m-[ results were found with Eq. (35). The values used in this calculation were as follows

= 1.25 kg/m3 a

g = 9.8 m/s 2

WQ = 0.23 m

H

q = 2 m

It can be seen in Table El and Figure E6 that the ventilation starts to drop

off at about 220 s and then starts to rise again. The 220 s point is where

the estimated value for y 2 was started, and it is continued until the ventilation limit condition is reached at a time between 250 and 255 s. At this

point and beyond, the fhf value is based on steady state enclosure ventilation

limited formula, and the calculation for m^ was stopped.

Corridor Visibility

The last column in Table El consists of predictions of visibility, Lv , in the

corridor. Also see Figure E7. The equation used in this prediction was as follows

k V t L = —— f m dt

v ct x Jo

38
where

k

v " 2

V = (Width)(length)(height) of corridor

( 2ra) (20m) (2.4m)

at it

e -1 for mattress 1 o

a = 3300 m“ /kg

x = 0. 3 g smoke particulates/g fuel

These predictions show that visibility would be about 0.1 m when flashover

(based on AT = 500°C) occurs. (It should be noted that this calculation

assumes a well-mixed gas state in the corridor. But this does not occur until

181s approximately. So use of the formulae before this time will over estimate the visibility by the ratio of corridor volume to actual smoke layer

volume.

and

t t

f . , r

ac t y J mdt=jae dt=

o o

Smoke Filling

Two other tables are presented in this example. Table E2 is a listing of

various room smoke filling times based on different steady state heat release

rates. Equation (23b) was usd to calculate these values. The following

values were used in these calculations:

a = 1/5.4

p = 1.25 kg/m3

00

T = 293 K

oo

Cp = 1.046 kJ/kg-k

g

= 9.8 m/s 2

H = 2.4 m

s = 16.2 m

2

These results suggest that combustion products begin to leave the room i. e. , the layer is just below the door soffit (H = 1.99 m) at about 10 to 35 s.

Table E3 contains additional predictions which provides an order of events for

the fire growth example. Smoke filling time for the room was taken from Table

E2, and visibility in the corridor was taken from Table El. The value for

smoke filling time in the corridor was generated using Eqs. (45, 46, and

48). Parameter values used in this calculation were as follows:

39
P a = 1.24 kg/m^

g

= 9.8 m/s“

H = 2.32 m

c

Q

= 100 kW

L

c = 1.046 kJ/kg-K

T

a

= 293 K

T = 47

A = 40 r

The time for the occurrence of flashover and the ventilation limit time was taken from Table El. The time for flashover is based on a 500°C temperature

rise, and the ventilation limit is based on the effective fuel-air mass ratio

where

Y

AHair

AHfuel

3.03 kJ/g air

15.7 kJ/g fuel

= 0.193 g fuel/g air

This mass ratio was compared with fuel and air values contained in Table El.

Smoke Transport

The predictions at the bottom of Table E3 were developed using Eq. (42)

where

p c was selected to correspond to the room temperature (T) so that

Parameters used in this calculation were as follows:

g = 9.8 m/s^

T = 293 K a

T = 303 K

H = 2. 4 m

Smoke transport times to the corridor ends were calculated using Eq. (43).

Center line distances from the hotel room door were 4.2 m and 15.8 ra respectively for the near and far ends of the corridor.

40
Thus a chronology of significant events and the magnitude of physical fi

effects have been estimated for this scenario. It’s accuracy is at leas

to an order of magnitude and more exact assessments of accuracy must be

on the assumptions and support literature for each of the formulas used.

re

t good

based

41
c (s)

0

1020

304045

50

556065

70

758085

90

95 100

105

1 10 115 120

125 130

135 140

145 150

155 160

165 170

175 180

185 190

195 200

205

210

215

220

225

230

235

240

245

250

255

260

265

270

275

280

285

290

295

300

Table El • Fire Gr ovth Predictions

<5

q 0 <R 0

^ Corridor

if Hf hr q“ (0) AT “i Lv

( E / S ) (kW) (kW / in 7 ) (m) (n) (kW/m2

) rc) (ke/s) (is)

0.00 0.0 _ . 0.04 0.6 - - - - - - - 0.05 0.3 - - - - - - _ 0.07 1.1 - - - - - - - 0.10 1 .6 - 0.28 - 0.11 i 0.034 83.6

0.12 1.9 - 0.29 - 0.12 7 0.090 67.9

0.13 2.0 - 0.30 - 0.13 8 0.095 55.7

0.16 2.5 - 0.33 - 0.15 9 0.101 46.1 0.18 2.8 - 0.35 - 0.17 10 0.106 38.4

0.21 3.3 - 0.37 - 0.19 11 0.111 32.1 0.24 3.8 - 0.39 - 0.22 12 0.115 27.1 0.28 4.4 - 0.42 - 0.24 14 0.124 22.8

0.33 5.2 - 0.44 - 0.28 15 0.128 19.3

0.38 6.0 - 0.47 - 0.22 17 0.135 16.4 0.45 7.1 - 0.50 - 0.36 19 0.142 14.0

0.52 8.2 - 0.53 - 0.41 21 0.149 11.9 0.60 9.4 - 0.56 - 0.46 24 0.157 10.2

0.70 11.0 0.09 0.60 - 0.52 27 0.164 8.7

0.81 12.7 0.11 0.64 - 0.59 29 0.169 7.4

0.94 14.8 0.13 0.68 - 0.67 33 0.178 6.4

1.10 17.3 0.15 0.72 - 0.76 37 0.186 5.4

1.28 20.1 0.17 0.76 - 0.87 41 0.194 4.7

1 .48 23.2 0.20 0.81 - 0.98 45 0.200 4.0

1.72 27.0 0.23 0.86 - 1.11 50 0.208 3.4 2.00 31 .4 0.27 0.91 - 1 .26 56 0.216 3.0

2.32 36.4 0.31 0.97 - 1 .42 62 0.223 2.5

2.70 42.4 0.36 1 .03 - 1 .61 69 0.231 2.2

3.14 49.3 0.42 1.09 - 1.83 77 0.238 1 .9 3.65 57.3 0.49 1.16 - 2.07 86 0.245 1 .6 4.24 66.6 0.57 1 .23 - 2.35 95 0.251 1 .4

4 .92 77.2 0.66 1 .31 - 2.66 106 0.257 1 .2 5.72 89.8 0.77 1.39 - 3.01 117 0.263 1.0 6.64 104.2 0.90 1 .48 - 3.41 130 0.267 0.9

7.72 121 .2 1.04 1.57 - 3.87 145 0.272 0.8

8.97 140.8 1 .21 1 .66 - 4.39 161 0.275 0.7

10.42 163.6 1.41 1.77 - 4.97 178 0.278 0.6

12.10 190.0 1 .63 1 .88 0.07 5.63 198 0.279 0.5

14.06 220.7 1.90 1.99 0.10 6.38 219 0.280 0.41

16.34 256.5 2.20 2.12 0.25 7.23 243 0.279 0.36

18.98 298.0 2.56 2.25 0.34 8.19 270 0.278 0.31 22.05 346.2 2.98 2.38 0.42 9.28 300 0.288 0.26

25.62 402.2 3.46 2.53 0.52 10.52 332 0.293 0.23

29.77 467.4 4.02 2.69 0.62 11.92 369 0.297 0.20

34.59 543.1 4.67 2.86 0.73 13.51 409 0.300 0.17

40.18 630.8 5.42 3.03 0.83 15.30 453 0.301 0.14

46.69 733 .0 6.31 3.22 0.94 17.34 503 0.301 0.12

54.24 851 .6 7.32 3.42 1.06 19.65 558 0.300 0.11 58.55 Steady state wood crib burning 630

58.55 632

58.55 634 58.55 636

58.55 638

58.55 640

58.55 642

58.55 644

58.55 646

58.55 648

42
Time

(s)

0

24

6

810

12

1416

1820

2224

26

2830

32

3436

3840

**2

Table E2 . Room Smoke Filling Tine

Predictions, Steady State Fires

Heat Release Heat Release

Rate 0.5 kW Rate 1 .0 kW

Smoke layer Smoke layer

height height

(m) (m)

0.00 0.09

2.38 2.37

2.35 2.34

2.33 2.32

2.31 2.29

2.29 2.26

2.27 2 .24 2.25 2.21 2.23 2.19

2.21 2.16

2.19 2.14

2.17 2.11 2.15 2.09

2.13 2.07

2.11 2.04

2.09 O O') 2.07 2.00

2.06 1.98

2.04

2.02 Note : 1 .990)

2.00 Reached

1 .99 0 3 3 ( s )

Heat Release Heat Release

Rate 10 kW Rate 100 kW

Smoke layer Smoke layer

height height

(a) (m)

0.00 0.00

2.34 2.27

2.28 2.15

2.22 2.04

2.17 1 .95 2.12

2.07 Note : 1 .99 (m

)

2.02 Reached

1.97 0 7(s)

Note: 1 .99(m)

Reached

0 15(s)

Table E3. Summary of Critical Event Predictions

Event Time Velocity

(s) (m/s

)

Smoke filling of room -10-35

Visibility of l(m) in corridor -175

Smoke filling of corridor -181

Occurence of flashover -245

Ventilation limit in room -250

Smoke front velocity with AT of 10*C 0.44

Smoke transport time to near end

corridor

of

- 9.5

Smoke transport time to far end

corridor

of

-35.9

43
MASS

LOSS

RATE

(s/6) 31VU sscn ssvw

Figure E2 . Mass Loss Rate for Fire Growth Example.

44

TIME

(s)
HEAT

FLUX

PREDICTIONS

IN

ROOM

O

O

CO

o in

CO CM

o in o in

CM T- T-

( 3

tu/M>i) Xflld 1V3H

O

O

in

CM

O

o

CM

o

o

o

in

o

in

Figure E3 . Heat Flux Predictions in Room for Fire

Growth Example.

45

TIME

(s)
FLAME

HEIGHT

AND

EXTENSION

ACROSS

CEILING

in

CN

F igure

(w) 1HOI3H 3WVU

E4 . Flame Height and Extension Across Ceiling

for Fire Growth Example.

46

TIME

(s)
ROOM

TEMPERATURE

RISE

(Do) 3Hn±VH3dW3±

Figure E5. Room Temperature Rise for Fire Growth

Example.

47

TIME

(s)
MASS

FLOW

RATE

INTO

THE

ROOM

o

o in o in o in o o

CO CO CM CM T— T- in

o d o o o o o o

(s/6>0 31VU MOId SSVW

Figure E6 . Mass Flow Rate into the Room for Fire

Growth Example.

48

TIME

(s)
VISIBILITY

IN

CORRIDOR

O

O

CO

in o m o 10 o

04 CM t- t-

(w) 30Nv±sia anaisiA

Figure E7 . Visibility in Corridor for Fire

Growth Example.

o

o

o

in

i

49

TIME

(s)
NBS-114A (REV. 2-8C) U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report No. 3. Publication Date BIBLIOGRAPHIC DATA

SHEET (See instructions)

REPORT NO. NBSIR-85/3196 June 1985

4. TITLE AND SUBTITLE

Slide-Rule Estimates of Fire Growth

5. AUTHOR(S)

J.R. Lawson and J. G. Quintiere

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE ». Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City. Stote, ZIP)

U.S. David Taylor Naval Ship

Research and Development Center

Washington, D.C.

10. SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant in formation. If document includes a significant

bi bl iography or literature survey, mention it here) A series of prediction methods have been assembled to provide an analytical

basis for estimating fire growth in compartments. Solutions for each prediction

method can be made using programmable scientific calculators. Prediction

methods are presented for: fire size and growth rates, mass loss rates,

radiant heat flux, flame height, radial flame impingement, heat flux to a ceiling, smoke filling of a room, carbon monoxide hazard with smoldering fires,

temperature rise in a compartment, ventilation flow rate, flashover occurrence,

corridor smoke transfer and filling, smoke concentration, visibility, flame

spread rates, and fire burn time.

These predictive methods are useful for estimating many of the critical

elements related to fire behavior and help provide a better understanding

of this complex phenomenon.

This report appears in Appendix B in Fire Growth in Combat Ships by

J.G. Quintiere, H.R. Baum and J.R. Lawson, NBSIR 85-3159.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) Calculators; computer programs; fire growth; fire models; room fires.

13. AVAILABILITY 14. NO. OF

PRINTED PAGES

Qx) Unlimited

| | For Official Distribution. Do Not Release to NTIS

l_

] Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

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56

15. Price

Lxl Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $ 10.00

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