NBSIR 87-3682

Algorithm for the Mass-Loss Rate of

Burning Wall

Henri E. Mitler

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

December 1987

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 87-3682

ALGORITHM FOR THE MASS-LOSS RATE OF

A BURNING WALL

Henri E. Mitler

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

December 1987

U.S. DEPARTMENT OF COMMERCE, C. William Verity, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

TABLE OF CONTENTS

Page

Abstract 1

1. INTRODUCTION 1

2. THE PYROLYSIS RATE 2

3. THE RADIATION FLUX 4

4. THE CONVECTIVE FLUX 7

5. RERADIATION 8

6. CALCULATIONS FOR PMMA 9

7. COMPARISON WITH DATA 10

8. DISCUSSION 11

REFERENCES 13

NOMENCLATURE 16

LIST OF TABLES

TABLE 1. Parameter Values Chosen for PMMA and its Wall Flame 9

LIST OF FIGURES

Figure 1. Schematic of the appearance of a wall flame. The shaded

region is where pyrolysis is taking place 19

Figure 2 . Curve B is the experimentally measured radiation flux

from the flame, as measured by OMA. Curves A and C

are the results of calculation with a fixed ac and two

different assumed flame temperatures 20

Figure 3. Absorption coefficient of large PMMA wall flame, as a function of height above the base 21

Figure 4. Mass-loss rate of PMMA slab in Steckler's experiment

number 9 (with a vent width of 33 cm) 22

iii

ALGORITHM FOR THE MASS -LOSS RATE OF A BURNING WALL

Henri E. Mitler

Center for Fire Research,

National Bureau of Standards

ABSTRACT

A derivation is given for a simple algorithm which yields the quasi-steady

burning rate of a vertical panel of non-charring, non-melting material in an

enclosure with stratification of temperature and oxygen concentration. The

algorithm requires the solution of a transcendental equation; it is suggested

that this be done by successive approximations. Among the thermophysical data

which are needed, are the mean flame temperature and the height -dependent

absorption coefficient, /c(z) . It is found from experiment that /c(z) is well

described for PMMA by a two-parameter expression linear in 1/z. Comparison

with a transient experiment yields good agreement for the mass -loss rate, over

much of the range.

1. Introduction

There are a number of compartment fire models in existence now (see, for

example, [1-6]). Most of these lack an appropriate algorithm to describe a

wall fire. Of the above, only Smith's model [4] considers wall fires, and it

is tied directly to experimental output from a particular apparatus. A

general wall -fire model for burning in compartments must be able to predict

the ignition, and then the time -dependent burning and spread- rates (upward,

lateral, and downward) of a wall fire under conditions of temperature and

1
oxygen concentration stratification. It should include the effects of

external radiation, and of melting, charring, and burn- through . The present

work is a step in that direction. So far, there have been three published

models for the burning rate of turbulent wall fires [7-9]; several for upward

spread [ 10- 16 ]

.

The problem is to predict the mass -loss rate of a fire ignited on a vertical

surface, given the dimensions of the pyrolyzing zone, some material parameters

corresponding to the wall, any external heat fluxes, and some properties of

the flame and plume. Although much of the physics involved in burning is well

understood, the complexity of the processes is such, especially for turbulent

diffusion flames in an enclosure, that modeling all aspects of it from first

principles is as yet an impossible task. The k-c-g approximation (which does

not purport to describe the soot- formation process), has had some success in

describing the flame and its radiation [8,9], but is very complex. It is

demonstrated in this paper that by using some well-known relationships plus

one new result, the mass -burning rate can nevertheless be fairly accurately

predicted, with a quite simple integral model. Moreover, in distinction from

earlier work, this is extended to the case where there is strong stratification in the enclosure. The key is the finding that the mean radiation absorption coefficient varies with height, and that it does so in a simple way. The

present model is limited to yielding the steady-state mass-loss rate of noncharring solids.

2. The Pyrolysis Rate

The mass -loss rate can be calculated either point by point, or globally.

Since we are principally interested in the total mass-loss rate, any calculations which are made point by point - - i.e., as a function of height, will be

2
integrated. To begin, we assume that the ignited (and therefore pyrolyzing)

region is rectangular, with the width w and height z

p

. The pyrolysis rate,

m" , is proportional to the net heating flux at the surface of the wall: if we

have incoming radiation flux <f> in and incoming convective heat flux 4> c , then a

heat balance at any point of the surface yields

m "Lv = <*w 0in + <t> c

- <f> rr + k grad T (1)

where aw is the gray-body absorption coefficient of the wall material. Here

d!> is the reradiation flux from the surface,

Kr = ( 2 )

(the surface is at the temperature Ts

. The radiation from the environment

is to be included with any other incoming radiation flux) . The radiation

flux 4> in is the sum of the flame radiation <f> l f and that of any external heat

fluxes

d)

y in = d)uf~ + r<b ext. (v/3 )

The flux <^ ext explicitly includes the ambient radiation flux aTa

4 and the

"feedback" radiation flux from surrounding hot walls and/or hot gases,

k grad T is the heat conduction flux into the solid, and 1^ is the latent heat

of gasification (i.e. of evaporation or pyrolysis) of the wall material. In

experimental measurements of the heat of gasification, neither Ly nor k grad T

are measured separately. Instead, an approximately steady state is achieved;

then the energy required to vaporize a gram of material is that required to

raise its temperature from Ta , its uniform initial temperature, to Ts

, the

surface temperature during its vaporization, plus its latent heat of vaporization :

Hv - L, +

[

Ts c

p (T) dT

Ta

( 4 )

This is its effective heat of vaporization, and equation (1) becomes

3
m - + 4> c

- *„]/a. (5)

for the steady state, where

Note that radiation blocking [17-19] is ignored. In the sections to follow,

the various fluxes on the right hand side of Eq.(5) will be calculated.

3. The Radiation Flux.

The external flux will depend entirely on the particular circumstances,

configurations, etc. In a compartment within which there is a burning wall,

it would consist of the radiation fluxes from the igniting flame, from the hot

layer (s) , from the hot walls, floor, and ceiling, and from any other fires.

In a laboratory, it might be that produced by a radiant panel. Only the

radiation flux (f> rf from the wall flame will be considered in this section. In

order to calculate it, the flame temperature, thickness, and absorption

coefficient must be known. As shown in the work of Orloff, Modak, and Alpert

(ref [20], hereafter referred to as OMA) , the thickness of the flame at the

height z above the base of the flame, d(z), increases linearly with height up

to the top of the pyrolysis region (see Fig. 1):

d(z) = Az

,

0 < z < z

p (6)

where A is the (constant) slope of the flame envelope. OMA found that A~ 1/16

for their PMMA fire; we shall assume it to be the same for all materials.

Thus the flame profile is that of an inverted wedge, up to z

p

. Although the

flame width will explicitly be taken into account, it is here assumed that

there are no variations in the fluxes or in the mass -loss rate across the

pyrolyzing region, as if this were a two-dimensional calculation. A straightforward calculation gives the radiation flux as a function of height, for the

case where the temperature and the emission coefficient of the hot gases, k,

4
are uniform and constant. Simpler, however, is to use the approximation used

by OMA: they found the radiation flux from the hot flame gases at any point

on the contiguous wall surface by using an equivalent rectangular slab of the

same width and length, but of thickness equal to the local thickness of the

wedge. They then used the mean-beam- length approximation for that parallelepiped, for the local flux:

*rf ( 2 > = t 1 ' eXP(-01 (7)

where Tf is the (uniform) flame temperature, and £ is given by

£(z) 3 . 6/cV/A 1.8 K ( 8 )

where V is the volume of the emitting gas mass and A its surface area. For

the wall flame, w is the width of the flame, z f is the flame (and therefore

slab) length, and d(z) is the local thickness, given by Eq.(6). This

approximation underestimates the flux for 0 < z < z

p /2, and overestimates it

for z

p /2 < z < z

p

. OMA estimated that ac = 1.4 m' 1 and Tf = 1367 K, for the

PMMA flame; with these values, Eqs.(7) and (8) yield the flux shown by curve A

in Fig. 2. On the other hand, their measurements yield a radiation flux which

is very well fitted by

<f> x£ = 1.10 + 0.7483 z - 0.01 z

2 W/cm2

, 0.5 < z < 3.56 (9)

(with z in meters). This is plotted as curve B in the same figure; it is

distinctly different from curve A. The most important difference is that the

value extrapolated to the origin is a significant fraction of the maximum

measured value. Choosing a smaller value for Tf (1250 K) yields curve C, with

a smaller slope, but does not change the important differences.

However, one need not assume that ac is constant; indeed, by working backward

5
from the data, it is possible to infer an effective value for the absorption

coefficient and the gas temperature at each height. When this was done, the

values shown in Fig. 3 were obtained, and it was found that Tf is remarkably

constant, at 1285 K. Note, incidentally, that Markstein found a similar

variation of k with height for pool fires [21] . Since d(z) is proportional to

z, it is clear from Eqs.(7) and (8) that as z approaches zero, <f> It approaches

a value proportional to zk . In order to obtain a non-zero value of <f> rf at the

origin, therefore, the expression for k( z) must approach const. /z. It is

remarkable that the absorption coefficient shown in Fig. 3 is in fact very well

fitted by a simple binomial, linear in 1/z

/c(z) = kq + k^/z, (10)

with

kq — 0.651 m" 1 and k1 = 0.562 (11)

This expression is the key which permits one to properly obtain the

radiation as a function of height. Note that this is a new application of the

experimental results of OMA.

In the simplest approximation, we may take the mean flux to be that received

at the midpoint of the slab:

?rf “ aTf

A

( 1 ' exP-?) ( 12 >

with £ obtained by using Eq.(8) with d given by

d = Az

p /2 = z

p /32 (13)

and k = Ac(z

p /2) (14)

In fact, according to Eq.(10), the volume -weighted average absorption coefficient in the pyrolysis region is also given by the midpoint value; that is,

«av = K = *0 + 2 «i/z

P (15)

Note that k is not a constant, so that different-sized slabs will

6
experience different radiation levels. It also follows that xR will not be

constant; it also will vary with slab height.

4. The Convective Flux

The mass -loss rate of a burning object whose flame is small and non- luminous

is given by the well-known expression [22]

m" - — in (1 + B) (16)

c

p where B is the Spalding mass - transfer number, h is the heat- transfer coefficient, and c

p is the specific heat of the gas. B can be written as

B - [vyQ Hc + c

p (T

g

- Ts ) ] /Hy. (17)

where v is the stoichiometric fuel/oxygen mass ratio, yQ is the mass fraction

of oxygen in the air, and T

g is the local gas temperature; the other symbols

have already been defined. When combustion is incomplete, and there is energy

loss from the combustion zone via radiation as well, then the appropriate

value for the heat of combustion that should be used in Eq.(17) is

V = (*A - *r )Hc (18)

where is the combustion efficiency and xR the fraction of energy lost to

radiation. With that change, B becomes B' , and is the value to be used in

Eq.(16). When there is radiation impinging on the pyrolyzing surface, leading

to additional heat deposition, there will evidently be an increased rate of

pyrolysis. It has been shown [23,24] that for the case where the pyrolyzing

gases do not themselves absorb any of the radiation, the radiation can be

incorporated as a boundary condition; this permits one to continue to use

Eq.(16), but with B' modified by using the "convective B-number"

Bc = — (19)

1 - q"/m"Hv

7
in place of B' , where q" is the net radiative heat transfer flux (including

reradiation) . From the energy balance equation (5)

,

the denominator in

Eq.(19) can be expressed in terms of the convective heat flux; inserting that

into Eq.(16), the latter can be rewritten as

m" B'HV

<f> c =

7

( 20 ) exp(m"c

p /h) - 1

This is the expression used by De Ris [25] and others [26,27]. In order to

use it, h/c

p must be known; from the experiments of Orloff et al [28], the

value

h/c = 7.943 g/m2 sec (21)

can be inferred.

5. Reradiation

If the material is a pure substance (such as water) , then there will be a

well-defined evaporation temperature Tev , and the reradiation flux is given

by Eq.(2), with Ts

-*• Tev . For a substance such as PMMA, on the other hand,

the (local or global) mass -loss rate depends on the surface temperature; for

PMMA it can be expressed as an Arrhenius function:

m" = A exp(-EA /RT) (22)

Therefore (see OMA)

4 r Ts ° R

m" 1 *r. -

[

X - — -^-J

-4

(23)

where R is the universal gas constant (R=8.314 J/mole °C), EA is the activation energy, aw the grey absorption coefficient, m" the actual mass -loss rate,

and m0

" the mass-loss rate at the reference temperature Tso . (For PMMA, OMA

8
yields aw = 0.927, Tso = 636 K, and EA = 83.7 kJ/mole; at T = Tso , the massloss rate is mQ

" = 8.316 g/m2 sec, and <f> rr0 = aw

£7 Tso

4 = 8.6 kW/m2

) .

6 . Calculations for PMMA

Measurements made by OMA show that for the 3.56 m slab, the average massloss rate is m" = 12.38 g/m2 sec. The radiation loss fraction has been

measured by Tewarson and others [27] to be Xr = 0.33 ± .03 for large PMMA

pool fires; also, xA = 0-94. Although Xr was not measured by OMA for their

wall fire, it has been observed [29] that the radiation fraction is generally

smaller for wall fires; we have assumed that Xr = 0.30. All the parameter

values chosen for PMMA are displayed in Table 1. Most of these values are

taken from the literature, or inferred from the OMA data. Using these

Table 1. Parameter values chosen for PMMA and its wall flame [8,20,26].

XA = 0.94

kq = 0 . 651 m” 1 K = 1 - 611 kJ /s

C

p = 1.0 J/g ° C

a = 0.927

XR - 0.30

k 1 = 0.562

Hc = 25.2 kJ/g

Tso = 636 K

Tf - 1310 K

7S = 8.268

h/c

p = 7 . 943 g/m2 sec

Ea = 83.7 kJ/mole

values, a calculation can be made for the mass-loss rate for any other vertical PMMA sample. The calculation proceeds as follows: Eq.(5), with

Eqs.(12) for <f> r f , (20) for <f> c , and (23) for 0 rr , is a transcendental equation

for m" . A simple method for solving it is to choose an initial value for the

mass -loss rate, m1 " , and calculate <f> c , and <f> rr with "

; then Eq.(5)

yields a resulting m" . A second choice is then made for the mass -loss rate

on the basis of this first result, and the process repeated. Generally, half

9
a dozen iterations suffice to yield an answer to four or five significant

figures. m" is involved in the calculation of <j> rf through the flame height

z

f in Eq.(8). This height is calculated according to

z

£ - 0.06 (Q’) 2/3

m (24)

(see [16]) where Q' is the total power output of the fire per unit width, in

kW/m. On the other hand, the calculated value of m" is insensitive to the

exact choice for z

f

; for simplicity one may take z f - 1.8 z

p in order to

speed the calculation, if desired. Some experiments [5] made earlier than

that of QMA used slabs with a width of 41 cm and height 1.57 m. Proceed- ing

as described above, the value m" = 8.65 g/m2 sec was calculated. This is

only 2% smaller than the measured value, 8.84 g/m2 sec.

The values chosen in Table 1 are all approximate ; undoubtedly a set could be

chosen (still within the experimental bounds) which would precisely yield the

measured value of m" for the 1.57 -meter slab as accurately as for the 3.56-

meter slab. Such precision would be spurious, however.

7. Comparison With Data

A more challenging test of the algorithm is to see whether it will yield

reasonable results for cases where there is an external flux, and where the

local temperatures and oxygen concentrations vary. This is the situation for

a wall burning in a compartment. There, indeed, the fluxes, temperatures,

and Y(02

) all vary with position. Since the algorithm has been developed for

the case of uniform conditions, it must be generalized. The simplest

approximation is to use area-weighted values of Y(02 ) and T

g in Eq.(17), and

assume that xA

- Xr remains unchanged in Eq.(18). (This is nearly identical

10
tc summing the contributions from each zone). In a two-zone model, this is

particularly easy to do, and that is the procedure used in the following.

Steckler [30] has carried out a series of wall- fire burns on a reduced

scale; the floor of the compartment was 1 m x 1 m, and it was 75 cm high; a

doorway 55 cm high provided the only ventilation. A 1" -thick slab of PMMA,

28.25" high and 7.31" = 18.57 cm wide was attached to the rear wall. A line

burner ignited the PMMA; when the latter was fully involved, the burner was

turned off, and the fire allowed to develop. This development was sufficiently slow that the quasi- steady approximation is probably valid throughout most

of the experiment. Sensors measured the various temperatures, fluxes, and

oxygen concentrations. A load cell measured the mass of the slab, and

therefore the mass-loss rate can be calculated. That is shown, for his run #9

(with the doorway width at 33 cm), by the solid curve in Fig. 4. The algorithm

described above was used to calculate m" (and therefore m) at several times;

those results are shown by the open circles, which have been joined by a

smooth dashed curve. It is seen that the agreement is quite good from t = 468

sec (when the igniting flame, which gives an extra, unmeasured, flux, was

extinguished) to t - 1300 sec. It is increasingly poor from there to t - 1500

sec; after that time, comparisons cease to be meaningful, as the slab buckled

and collapsed starting then.

As of this writing, the method has been tested against only one of

Steckler' s trials; further testing remains to be done.

8. Discussion

The agreement with the Steckler experiment in the region 468 < t < 1309 is

surprisingly good, in view of the crudity of the approximations. On the other

11
hand, one may ask why then there is a significant disagreement in the region

t > 1309. There are five possible explanations for this disagreement:

a. Radiation blocking, which has been ignored, will reduce the flux absorbed

by the PMMA, and the effect will be strongest at high mass -loss rates.

b. The calculation assumes that a steady state existed, whereas the

experimental conditions were transient.

c. The PMMA melts, as well as pyrolyzing, and this will

i) uncover lower- temperature material in the upper regions, and

ii) cover (and thereby inhibit the pyrolysis of) material in the lower

regions

.

d. The radiation from a flame burning with vitiated air is weaker than that

from the usual flame

.

e. The oxygen concentration in the upper layer may be too low to support

combustion there, in the late stages ("oxygen starvation").

These phenomena are subjects for future investigations. Note, however, that

the contribution to the disagreement from items d and e must be small in this

case, since the data shows that [according to Eq.(5)], the external flux

alone, without any contributions from the flame, should still yield a massloss rate in excess of the measured value, for t > 1350.

The method described in this paper is easy to use, and is quite accurate for

PMMA. However, it requires extensive knowledge of material and flame properties. For the flame emission coefficient, indeed, it requires information

(k.

q ,k 1 ) which is not generally available. This may be viewed as an experimental challenge; in order to obtain results immediately, however, the obvious

procedure is to ignore k 1. Alternatively, one can speculate that since k =

1.5 m" 1 when it is measured for a pool fire [31], then

12
and

k q - 0.651 /c/1.5 = 0.434 k

k 1 — 0.562 /c/1.5 = 0.375 /c.

Another calculational alternative which has been examined is to use an

integral (global) approach, without using averages. However, that presents an

analogous difficulty: it requires that one know what fraction of the total

energy released falls on the pyrolyzing portion of the slab; indeed, it

requires knowing it accurately, as the calculation is very sensitive to that

fraction. For the 3.56 m case, this fraction is 8.22%; this is just as

unknown a number, generally, as are kq and k 1

. Moreover, it is not constant:

for the 1.57 -meter slab, the figure is 7.45%.

An interesting question is the sensitivity of the results to the parameter

values which are chosen. For example, suppose that Xr had been taken to be

XR = 0.26 rather than 0.30, above. In order to get the same value of 4> c for

the large slab, h/c

p would then have to be chosen to be 7.949 g/m2 sec (rather

than 7.943), and the mass-loss rate calculated for the smaller slab would then

be 8.649 g/m2 sec (rather than 8.645). Thus, the results are insensitive to

the precise value chosen for Xr

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No. 1-2, p .

13
[4] Smith, E.E., and Satija, S., "Release Rate Model for Developing Fires",

J. Heat Transfer, 105 (1983) 281.

[5] Jones, W.W.

,

"A Multicompartment Model for the Spread of Fire, Smoke,

and Toxic Gases", Fire Safety Journal 9 (1985) No. 1-2, p.55.

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Fire Modeling", Underwriters Laboratories report, file NC 554 (1983).

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,

"A Simple Algebraic Model for Turbulent Wall Fires"

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.

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

PA. (1979) 1149.

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Surface Heat Transfer, II. Upward Burning", Comb. Sci. and Technology

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of Externally Applied Thermal Radiation", Comb. Sci. and Technology

17(1977)81.

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Fire Safety J. 3(1981)201.

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,

"Flame Spread on a Vertical Wall With a Constant

External Heat Flux" , presented at the Eastern Section of the Combustion

Institute, Nov. 1981.

[14] Saito, K. , Quintiere, J.G., and Williams, F.A.

,

"Upward Turbulent Flame

Spread" , Fire Safety Science - Proceedings of the First International

Symposium (Eds., C.E. Grant and P.J. Pagni) ; Hemisphere Publishing

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.

[15] Quintiere, J.G., Harkleroad, M. , and Hasemi, Y. , "Wall Flames and

Implications for Upward Flame Spread", Comb. Sci. and Tech. 48(1986) 191

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Thermal Radiation", Ph.D. Thesis, U. of London, 1959.

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[18] Kashiwagi, T. , "Experimental Observation of Radiative Ignition Mechanisms," Comb, and Flame 34(1979)231.

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,

and Alpert, R.L., "Burning of Large-Scale

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,

"Scanning-Radiometer Measurements of the Radiance

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on Combustion; the Combustion Institute, Pittsburgh, PA. (1981)537.

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,

(1953) 847.

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,

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Pittsburgh, PA (1978)1053.

15
NOMENCLATURE

A

B

c

p

d, d(z)

ea h

Hc

»v

t Hc

k

K

m"

q"

Q'

R

t

T

V

w

y0 = y (°2

)

z

Surface area of flame; proportionality constant [Eq.(22)]

Spalding mass- transfer number

Specific heat of air

Thickness of flame, at height z

Activation energy for pyrolysis reaction

Heat- transfer coefficient

(Lower) heat of combustion

Effective heat of vaporization

Heat of combustion, modified for combustion efficiency

and radiation

Thermal conductivity

Latent heat of vaporization

Pyrolysis (mass-loss) rate

Net radiative heat transfer flux

Power output per unit width

Universal gas constant

Time

(Absolute) temperature

Volume of the flame

Width of the flame

Mass fraction of oxygen

Height above base of slab (and of flame)

Greek symbols

a Absorption coefficient

7 Stoichiometric air/fuel mass ratio; = 1/VY(02

)

16
K Emission coefficient of flame gases

K 0

’ K 1 Terms in the expansion of k( z) [see Eq.(10)]

A Slope of flame envelope

V Stoichiometric fuel/oxygen mass ratio

<t> Heat flux

a Stefan-Bolzmann constant

z Dimensionless optical depth

Xa Burning efficiency

A'r Fraction of energy produced going into radiation

Subscripts

a Ambient

c Combustion; convection

ev Evaporation

ext External

f Flame

g (Hot) gas

in Inward

o Reference value

P Pyrolysis

r Radiation

rf Radiation from flame

rr Reradiation (from surface)

s Surface; stoichiometric

V Vaporization

w Wall

17
Other Symbols

a Mean value of a

a Time derivative of a: da/dt

' Per unit length; modified quantity

" Per unit area

18
19

Figure

1.

Schematic

of

the

appearance

of

a

wall

flame.

The

shaded

region

is

where

pyrolysis

is

taking

place.
RADIATION

FLUX

FROM

FLAME,

<|>

rf

On

W/cnra

20

Figure

2.

Curve B

is

the

experimentally

measured

radiation

flux

from

the

flame

as

measured

by

OMA.

Curves A

and C

are

the

results

of

calculation

with a

fixed k

and

two

different

assumed

flame

temperatures.
4_w) (Z)» ‘ 1N3I0U33O0 NOIldHOSSV

•H r

4-J a • u

o r CO <

cn

a)

jma

&o

Pm

21

HEIGHT

ABOVE

BASE

OF

SLAB,

Z

(m)
(S/6) 31VU sscn ssvw

CT\

22

Figure

4.

Mass-loss

rate

of

PMMA

slab

in

Steckler’s

experiment

number

(with

a

vent

width

of

33

cm)

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

BIBLIOGRAPHIC DATA

SHEET (See instructions)

4. TITLE AND SUBTITLE

1. PUBLICATION OR

REPORT NO.

NBSIR-87/3682

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

December 1987

Algorithm for the Mass-Loss Rate of a Burning Wall

5. AUTHOR(S)

Henri E. Mitler

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

NATIONAL BUREAU OF STANDARDS -

U.S. DEPARTMENT OF COMMERCE

GAITHERSBURG, MD 20899

9.

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

. Type of Report & Period Covered

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

bibliography or literature survey , mention it here)

A derivation is given for a simple algorithm which yields the quasi-steady burning

rate of a vertical panel of non-charring, non-melting material in an enclosure with

stratification of temperature and oxygen concentration. The algorithm requires the

solution of a transcendental equation; it is suggested that this be done by

successive approximations. Among the thermophysical data which are needed, are the

mean flame temperature and the height-dependent absorption coefficient K(Z). It is

found from experiment that K(Z) is well described for PMMA by a two-parameter

expression linear in 1/Z. Comparison with a transient experiment yields good

agreement over much of the ranges.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) algorithms; burning rate; computer models; fire models; pyrolysis rate; wall fires

13. AVAILABILITY 14. NO. OF

PRINTED PAGES

j^J Unlimited

| | For Official Distribution. Do Not Release to NTIS 26

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