Significant Parameters for

Predicting Flame Spread

V.

i

James G. Quintiere

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

February 1985

U.S. DEPARTMENT OF COMMERCE
A
NBSIR 85-3109

SIGNIFICANT PARAMETERS FOR

PREDICTING FLAME SPREAD

NATIONAL BUHEAU OF STANDARDS UBRARY

James G. Quintiere

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

February 1985

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldriga, Secretsry

NATIONAL BUREAU OF STANDARDS. EmMt Ambtor. Dinctor
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TABLE OF CONTENTS

Page

Summary 1

Introduction 1

Theory 1

References 7

Figure 1. Enclosure Wall Fire Spread 8

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SIGNIFICANT PARAMETERS FOR PREDICTING FLAME SPREAD

J.G. Qulntiere

Center for Fire Research, National Bureau of Standards,

Gaithersburg, MD 20894

Summary

Flame spread is considered on a vertical wall surface in a vented enclosure.

A theoretical formulation is developed to describe the burning and fire spread

behavior and its response to the changing environmental conditions of the room. These formulations have been kept simple in form, but consistent with

current levels of accuracy and completeness. The primary aim was to establish

the relevant and significant set of dimensionless parameters which govern the

fire spread process. These are given in terms of room geometric factors and

wall flammability properties. No solution of the equations has been

developed.

Introduction

The flammability of interior surface lining materials has received much

attention in the development of test methods used for hazard classification

and in the development of its basic understanding through research studies.

The former development produces relative hazard levels based on measurements

and judgement. The latter development offers the prospect of oredlction of

flame spread based on material property data and mathematical analysis. Yet

with the versatility of such a predictive methodology comes imprecision in

application techniques. Accordingly the introduction of many variables from

the predictive equations will present problems for decision-makers. Thus it

is necessary to simplify the analysis without ignoring the significant

processes of the problem, maintain a useful level of accuracy, and identify

measurable properties (data) to characterize the materials.

In this study, a set of governing equations is presented. The equations

describe the enclosure environmental conditions — room temperature, T; oxvgen

concentration, Yq^; and the flame spread behavior for a wall of the

enclosure. Some idealizations will be made, but they should not significantly

alter the characteristics of the problem. Indeed, no solution will be

developed; however, the resulting set of independent dimensionless variables

will be developed. These dimensionless groups could be useful in developing

experimental correlations, highlighting important properties, and perhaps

ultimately simplifying hazard assessment. But no conclusions will be made on these possible benefits at this time.

Theory

Several assumptions will be made at the outset to lay some concepts for the

model. As each of these assumptions are relaxed, of course the analysis would

change. Nevertheless, it is felt these changes would only be In detail, not

in substance. These assumptions are given below:

1
(1) The enclosure surface members are considered to be infinite in thickness

with respect to heat conduction phenomena, and of uniform thermal

properties;

(2) The enclosure interior surface temperature is considered to be uniform at

any t ime

(3) Fire originates on a wall which is the only combustible element in the

enclosure except for a line-source ignition fire.

(4) The wall fire burns by a simple vaporization process, and its pyrolysis

region is a rectangle (l.e., spread along the celling jet region is

considered by an equivalent but fictitious vertical spread region and

upward spread is more rapid than side or lateral spread)

The specific problem addressed is Illustrated in Figure 1. The enclosure has one vent — a window in this case — but several wall vents could be

considered. The rear wall is ignited by a line burner of energy release

rate Eq

this is assumed to be fixed over time in this example. Its

width, 2xp Q determines the initial wall pyrolysis width after ignition; the

height of the pyrolysis zone being given by yp, and its burn-out front given

l>y Yb* Because vertical spread is assumed much faster than lateral spread the

pyrolysis region is always approximately rectangular. Also as the pyrolysis

front reaches the ceiling [yp = h), the horizontal spread along the ceiling is

considered similar to upward spread since both depend on the same buoyancy

generated flow and any subsequent downward propagation from the ceiling is

considered the same as lateral spread to the side. Hence Ignore the

complexities of the flame front boundary on the wall, and need only be

concerned about the extent of the combustible rectangular region. This

concept is also consistent with the assumption of a uniform compartment

surface temperature.

A brief sketch of the equations will be given. The gas temperature T in the

upoer region of a compartment due to a fire energy release rate E can be given

as^

1 2/3

T = T 1 + C„

h A

w w

i-1/3

p T c /g A /H

o o p o c pc /g A /Ho p o o

( 1 )

where C-j* = 1.63, Tq = 295 K, A^ is the Interior enclosure surface area

and Aq Is the vent area with Pq and Cp the ambient gas properties. A thermal

conductance h^, is given for an infinitely thick wall as /kpc/t with kpc the

enclosure properties, and t is time. The energy release rate is considered

composed of the Ignitor and the pyrolyzing wall. The wall pyrolysis rate per

unit area is approximated as^

m" = — ln(l+B) « — B (2)

c c

P P

where the "Spalding" B-number Includes surface and flame radiative effects in

terms of a radiation fraction of total energy release.

2
Xj-; compartment radiation flux, » oT^^; and surface radiative

loss, cjTjfg with the vaporization temperature. The B-number is defined as follows

B ox

(3)

where AH is heat of reaction, L is heat of vaporization,

= Yqx/0.233 the normalized oxygen mass fraction in the enclosure, (f) = T/T^g the normalized enclosure gas temperature, and h is the

convective transfer coefficient given by

hH

k

C, (GrPr)^^^ (A)

which applies to turbulent natural convection conditions — the Grashof

number Gr = g[l-<()Q

h^/v^ and Prandtl number Pr = pvcp/k with ((>0 = H the enclosure height. It should be noted that h is approximately constant

for these conditions, and it will be thus regarded as such. Also, a nominal

convective B number is

B = 0.233 AH (1 - X )/L = 0.233

o ox ^ r (5)

with the heat of reaction per unit mass of oxygen, AHq^ = AH/y,

and Y is the stoichiometric oxygen to fuel mass ratio.

Hence the energy release rate is given as

t < t,ig

E + m"A , t > t. o p

- ig

( 6 )

where Ap is the pyrolysis area and tj^g is the time to ignite the wall by Eq.

The Ignition time can be given by

[(T^^ -To)/q;f (7)

where qQ is the incident exposure flux by Eq roughly 2 to 3 W/cm due to a moderate size flame 1 m).*^ But if q^ is less than crT^g the material will

not ignite since the loss at pyrolysis is greater than the heat supplied.

The pyrolysis area Ap following ignition is given by 2xp(yp

values at t = t^g determined by the width and height of the

i.e. Xp^Q and Yp^o* dimensionless terms,

a= Ap/2xp oyp^o'is given by

a = (q - n, )

^ p b^

- y^j) with Initial

Eq flame:

( 8 )

where Pp^b ~ yp,b/yp,o respective pyrolysis and burnout fronts,

respectively, and 5p is the lateral pyrolysis position,

Xp/^p,o*

3
The upward pyrolysis front can be found from^

dn

d^

"f ~ % ( 9 )

where x * t/ tf and Xf » tf/tf { / [^‘(^“‘1* 0 ) ] }^ ^f ® normalizing

time variable associated with upward spread time, and is given as [pp(Tlg - To)/(hB„L)] 2 .

The dimensionless flame height is given by^

hf = + 1 +

ox C-B Tf, f o 4

2/3

( 10 )

where Cf is a constant and p = B/Bq. The initial condition is

X = Xig' n = 1, n, = 0.

p b

The burnout front can be estimated from the following equation^.

<^0, n hv b _ p b

dx X,D

*

( 11 )

where x^, = t|j/tf and the burn time t^j = m"/m", m" being the consumable mass

per unit area available. The initial condition is

X = Xj^g + X]j Q (where X]^, q

is ev2iluated at x^g) and Pb “ !•

The lateral spread rate is given by**

( 12 )

r $ 1

o (O - *0)1

dx

X (hT,

L p,o'' ig^ -J

|\ L / Vi -

where $q is a flame heating parameter measured under normal air conditions as given in ref. 3.

The enclosure surface temperature was estimated by considering the net

radiative and convective enclosure heat transfer from T to Tg (the surface

temperature) as equal to the heat transfer rate from the gas into the

enclosure to a sink at Tq. As a consequence it can be shown that

<j) - <t> s ^o

(j) - (j) 1 +

w

h + h

(13)

where h^ is a radiative gas-surface exchange coefficient vdilch depends

primarily on those corresponding temperatures. As an approximation let h^ be

represented as oT^ where emisslvltles , geometry and surface temperatures have

been ignored. Thus hj./h can be represented as (j)^(oT| /h).

4
Finally, the enclosure oxygen concentration can be estimated by a specie mass balance

Y = 0.233 - E/(m AH 1 rvv ^ r\ r\-v ' OX ' O OX

in which the vent mass flow rate was taken as

(14)

m = -=- C A /H p o 3 o o o o (15)

with N/H^ taken as 1/2.

Combining eqns. (14) and (15) and making variables dimensionless leads to

C = 1 - ox .(%)(s) V(r)('4)

(16)

The dimensionless equation for temperature corresponding to eq. (1) can be

given as

4, - (j)^ 1-1/3

(17)

with ij) the dimensionless energy release rate E/E given as

o

=

1 + poC^B TT, , T > T

f O 4

(18)

ig

Also the initial pyrolysis height, taken to correspond to the flame height

caused by E^ can be found from eq. (10).

From these equations the following Independent dimensionless groups can be

identified and interpreted. These are listed below:

TT 1

E

o

cpoo T p /g /H

o

Ignition energy/ vent enthalpy

5
hA

w enclosure heat lo8s

* vent enthalpy flow pc /g A

o p o

^ mass of oxygen required

’ ' mass of fuel pyrolyzed

c T X \l/3

P o P.o \ oxygen required In combustion

induced air supply

c T

p ig ignition energy

L ' vaporization energy

ig radiative heat loss

h ' convective heat loss

buoyant force

viscous force

Pr

viscous effect

thermal conduction effect

radiative heat loss

applied ignitor heat

m”

(kpc/hc ) P

burnable mass heated mass

$o X

p,o (hXig)'

flame heat transfer in opposed flow

energy required for spread

flame energy radiated

^r’ total flame energy
, Ignition temperature

^13 TMlg Initial temperature

_ combustion energy

14 L ’ vaporization energy

_ ^ convective heat

15 k ’ conductive heat

w Interior surface area = — - —

16 2

' Initial pyrolysis area *p,0

The above dimensionless groups govern the problem and must be accounted for by

measured data. The next step Is to evaluate their significance In terms of

their variability and sensitivity vrlth respect to a solution of the equations.

References

1. B.J. McCaffrey, J.G. Oulntlere and M.F. Harkleroad, Fire Technol., 1, 98

(1981)

2. D.B. Spalding, 4th Symp. (Int.) on Combustion, 180 (1983)

3. J.G. Qulntlere and M. Harkleroad, "New Concepts for Measuring Flame Spread

Properties", ASTM/SFPE Symposium on Application of Fire Science to Fire

Engineering (to be published as ASIM STP), Denver (1984).

4. J. Oulntlere, M. Harkleroad and Y. Haseml, "Wall Flames and Implications

for Upward Flame Spread", Paper No. 85-0456, AIAA 23rd Aerospace Sciences

Meeting, Reno, Nevada, January 14-17, 1985.

5. M. Slbulkln and J. Kim, Comb. Scl. Technol., 17, 39 (1977)

7
O)

c

8

Figure

1.

Enclosure

Wall

Fire

Spread
NBS-114A (REV. 2.80) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publication Date

SHEET (See instructions) NBSIR 85-3109 February 1985

4. TITLE AND SUBTITLE

SIGNIFICANT PARAMETERS FOR PREDICTING FLAME SPREAD

5. AUTHOR(S)

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 8. Type of Report & Period Covered

Gaithersburg, MD 20899

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

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 information. If document includes a significant

bi bliography or literature survey, mention it here) Flame spread is considered on a vertical wall surface in a vented enclosure. A

theoretical formulation is developed to describe the burning and fire spread behavior

and its response to the changing environmental conditions of the room. These

formulations have been kept simple in form, but consistent with current levels of

accuracy and completeness. The primary aim was to establish the relevant and

significant set of dimensionless parameters which govern the fire spread process.

These are given in terms of room geometric factors and wall flammability properties.

No solution of the equations has been developed.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons

flame spread; room fires; vents; walls

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PRIN T t o PAi.l s Unlimited

1 1 For Official Distribution. Do Not Release to NTIS IZ

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20402. 15. Pr.c.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $7 .O'l

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