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NBSIR 80-2107

Mathematical Modeling of Fires

R. S. Levine

Center for Fire Research

National Engineering Laboratory

National Bureau of Standards

U.S. Department of Commerce

Washington, DC 20234

September 1980

Final Report

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80-2107

1980

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U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

MATKMfAZ. BUKfiAt) or rTAKDttoa

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NBSIR 80-2107

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' MATHEMATICAL MODELING OF FIRES

NOV ? 4 1980

1^60

R. S. Levine

Center for Fire Research

National Engineering Laboratory

National Bureau of Standards

U S. Department of Commerce

Washington, DC 20234

September 1980

Final Report

U.S. DEPARTMENT OF COMMERCE, Philip M. Klutznick, Secretary

Luther H. Hodges, Jr., Deputy Secretary

Jordan J. Baruch, Assistant Secretary for Productivity, Technology, and Innovation

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

TABLE OF CONTENTS

Page

LIST OF FIGURES iv

Abstract 1

1. PART I 1

2. PART II 3

3. PART III 5

4. REFERENCES 7

APPENDIX A 18

APPENDIX B 24

APPENDIX C 33

iii
LIST OF FIGURES

Page

Figure 1. Schematic of the enclosure, showing mass fluxes in

and radiative fluxes to the target from layer and

flame 9

Figure 2. Computer fire code - main program 10

Figure 3. Subroutine vent 11

Figure 4. Path of flame spread 12

Figure 5. Diagram of a compartment fire 13

Figure 6. Typical wide-body transport aircraft cabin

arrangement 14

Figure 7 . Flame spread on seat group 1 at 100 seconds 15

Figure 8 . Steering committee organization 16

Figure 9. Benefits - mathematical models of fire 17
MATHEMATICAL MODELING OF FIRES

R. S. Levine

Abstract

This presentation has three technical parts, and ends with

audience participation and recommendations. First, a brief

discussion of fire growth in a compartment is presented, showing

why we need full scale tests, or a mathematical model adequately

simulating such growth. The second part of the talk describes

what several Federal agencies and their grantees are doing to

bring about the necessary engineering and mathematical capability

for this modeling. The third part illustrates some problems

that may be of interest to fire protection engineers that can

be solved relatively simply by using fragments of the modeling

capability now available.

Then a discussion was held with the audience to determine modeling

needs. Should we provide a series of simple models, each applicable

to a limited range of problems, or a major comprehensive model,

accessible from a computer terminal, that will solve a very wide

range of problems? The audience decided both were needed.

'' Key words: Fire; fire engineering; fire safety; mathematical

modeling; modeling application.

1. PART I.

Modeling and the Compartment Fire.

Figure 1 [1]^ is an illustration of the processes occuring in a fire in

a compartment with an opening in it. The fire over the burning object

generates a plume of hot gas that entrains air, M^^, from the lower

layer, and adds a flux of hot, partly unburned gas, Mp, to the hot

ceiling layer. Early in the fire, before the ceiling layer has grown

below the doorway height, H^, unburned air flows out the doorway to make

room for the hot, lower density gas in the ceiling layer. Later, for a short time, both hot ceiling layer gas and unburned air flow out the

doorway; then as the ceiling layer approaches the thickness hL, ceiling

layer gas flows out and outside air flows in. At the neutral axis, the

pressure outside the room and inside are equal. Buoyancy forces cause

the pressure above the neutral axis inside the room to be greater than

the outside pressure, and lower than the outside pressure below the

neutral axis.

The flow of the ceiling layer to the exterior is of key concern to the

safety of the rest of the structure, since this is the source of smoke

and toxic gases. The other rooms in the structure are generally made

untenable by smoke obscuration or toxicity before they are untenable due

to heat [ 2]

Numbers in brackets refer to literature references listed at the end

of this paper.

1
As figure 1 indicates, the processes within the room react on each

other. Thermal radiation from the fire and the hot ceiling layer, and

the upper walls and ceiling affect the burning rate (of the outside

surfaces) [3] of the burning object, and also heat up other objects in

the room, shown here as a "target", until they may eventually ignite.

If the flame is spreading, the rate of flame spread, as well as the rate

of burning of already ignited surfaces will be affected by the preheating

due to this radiation [4].

The plume above the fire and its entrainment of lower layer air is, of

course, affected by the burning rate of the fire, which in turn is

affected by the thermal radiation, the vitiation of the oxygen content

of the lower layer air caused by mixing between the two layers (not

shown in figure 1), and drafts due to M. . The upper layer gases are cooled by convective heat transfer to tfte ceiling and upper walls , and

this cooling can have a significant influence on the temperature of the

upper layer, hence its radiation, and hence the growth rate of the fire.

These interactive effects cannot all be scaled simultaneously in scale

models. Particularly thermal radiation, which depends on the optical

path length through the hot gases, and the plume entrainment, which

depends on the size of the plume, its height, and combustion in it, are difficult to scale.

So the Fire Protection Engineering Fraternity is rightly skeptical of

small scale tests, and has confidence only in realistic full scale

tests. These, however, are expensive and difficult to carry out.

Reliable, validated mathematical models would be valuable either to

extend the results of full scale tests to see the effect of desired

changes or to avoid the necessity of the test in the first place. Since

the mathematical model must reproduce the interactions described above,

where each process is affected by the other processes, it consists of a set of mathematical equations that must be solved simultaneously, and

usually iteratively, and is only practically done on a computer.

There are two kinds of fire compartment models being developed today.

The most useful currently are "control volume" models. In these the

room and its contents are divided into lumped thermodynamic control

volumes, with heat, mass, and momentum balance equations written for

each. In figure 1, control volumes are: the burning object, the plume

above it (up to the upper layer), the upper layer, the lower layer, the

heated walls and ceiling, and the heated surface of the target. Of

course, as these are further subdivided into control volumes, the

program becomes more versatile and more complicated.

As previously mentioned, in practice these calculations must be done by

computer. I shall illustrate the process with some slides from the

Harvard Computer Fire Code II [5]. Two of the subprograms that are used

with the overall major program are shown in figures 2 and 3. The main

2
program, figure 2, records the input data describing the room and the

objects in it, physical constants, etc., and then, for a particular

time, t, calculates the various flows, burning rates, radiation fluxes,

etc., based on values extrapolated from the previous time step. Then it

adjusts these values by an iterative (loop) process until they all

balance properly (converge) for the time step. Then it moves ahead one time step and repeats the process. Figure 3 shows one of these subprograms which calculates the flow through the opening, which in turn

calls whichever calculational method is needed for the state of the

ceiling layer at that time.

The newer computer model [6] bears only an evolutionary resemblance to

what I have just described. It is designed to make the convergence

process more efficient in respect to computer time, so it scales all

variables to within -1 and +1, does the mathematics, and rescales them

to real values. It is hoped that to the user the architecture of the

program will be of little concern. He should be able to use the program

by typing English words into a terminal.

For the control volume modeling to be accurate requires the wise selection

of control volumes. If the air and ceiling layer flows are complex,

involving mixing and recirculation in unpredictable ways, "Field Modeling"

may^ be used. The compartment is divided into a rectangular grid, and

the conservation equations are written for each grid cell. The resulting

set of equations together with boundary conditions is solved, as a function of time, on a computer and the mathematics predicts the flow

field as it varies with time. Combustion and radiation can be approximated, but the approximations required to obtain solutions in a reasonable

amount of computer time are of doubtful validity. Three-dimensional

effects can be calculated in only a few specialized cases with today's

computer capability.

Flow from room to room (figure 4) is only beginning to be attacked [7,8],

The problem is not simple since varying amounts of entrainment and

mixing between the ceiling layer and the lower layer occur, especially

where the flow has to change direction, such as at a doorway. Also, the

ceiling flow is cooled by heat transfer, both convective and radiative.

The ceiling layer in the second room may well have substantially greater mass flow, but be cooler and more dilute in smoke and toxic gases than

the flow leaving the room of origin.

2. PART II.

* The Agency Role.

Several agencies are concerned with developing mathematical modeling

capability for their responsibilities in fire safety. The Japanese

Building Research Institute took an early lead in this [9,10]. They

paid particular attention to the radiative ignition and spread of fire on walls and other surfaces, which reflects their concern with this

problem in Japanese housing. Figure 5, from reference [9], shows this

fire spread concept.

3
In this country, Professor Emmons and his co-workers at Harvard University

[1,11] have generated the most comprehensive computer program. This

work has been done in close collaboration with Factory Mutual Research

Corporation (see for instance reference [12]), and is continuing under a research grant from the National Bureau of Standards (NBS)

.

NBS is carrying out other work, both in-house and by grant. Dr. James

Quintiere [3,13] has developed a series of quasi-steady state models, one of which will be used in part III of this paper. Research on the

various processes important to these models is carried out both in-house

and at universities and other research institutions funded by grants

from the NBS Center for Fire Research. These processes include plume

combustion and entrainment, thermal radiation from soot, convective heat

transfer in the ceiling layer, flame spread and Ignition as affected by

thermal radiation, flow through openings and from room to room, and

smoke toxicity. As better information from this research becomes

available, it will be incorporated in new versions of the computer

programs

.

The Federal Aviation Administration (FAA) and the National Aeronautics

and Space Administration (NASA) are cooperating in a comprehensive

program to use modeling to achieve aircraft fire safety. Both the

effects of a fuel pool fire outside a crashed aircraft and fire within

the cabin are subjects of mathematical modeling efforts. The major

aircraft control volume modeling effort (figures 6 and 7) is being

carried out by the University of Dayton Research Institute [14], with

confirmatory fuselage fire testing done in-house by the FAA, by NASA,

and their grantees. Field equation modeling is being applied to the

pool fire problem and to the flow of gases down the long narrow fuselage

(a mixed ceiling layer cannot be assumed) . The Naval Research Laboratory

is similarly concerned with modeling compartment fires.

Other work is being done at the Illinois Institute of Technology "Research

Institute [15,16] with special reference to the burning of furnishings

in a compartment prior to flashover.

Obviously it is advantageous to all concerned to provide a vehicle for

these various contributors to cooperate and benefit from each other’s

efforts. The Ad Hoc Group on Mathematical Fire Modeling has therefore

been formed. Its composition is shown in figure 8. The Group is

divided into three subcommittees.

The Synthesis, Models and Scenarios Committee is chaired by Professor

Howard Emmons of Harvard University and is in turn divided into two subcommittees. The subcommittee on User's Needs is chaired by Mr. Irwin

Benjamin. Its duties are to impact the development of the final program

or programs so that they will be of maximum benefit to the users. This

can be accomplished by advising the modelers what to calculate, and

later to facilitate user adoption of the validated programs. The

4
subcoTnmittee on Programs is chaired by Dr. James Quintiere of NBS . Its

goal is to arrive at a program, or set of programs, that fit the most

important fire scenarios.

The Committee on subprograms, under Dr. John deRis of Factory Mutual

Research Corporation, is concerned with developing and validating

subprograms, such as models of ignition, flame spread, air and product

gas circulation, etc. These subprograms will be Improved by using the

results of research programs at various universities, government laboratories, and other organizations, when cast in mathematical form.

The Definition and Coding Committee, under Dr. John Rockett of NBS,

selects standard computer nomenclature and standard formats for both the

program and the subprograms, and for full scale testing. The latter

will make it possible for all of the investigators to use data from full

scale tests carried out at various institutions.

I am Chairman of the Steering Committee, which consists of representatives of the funding agencies and the three Chairmen. The funding

agencies will cooperate as best they can to facilitate the most important

portions of the work.

Benefits expected from the validated programs are listed below and in

figure 9 in the order of expected fulfillment.

The first benefit is to permit the results of full scale tests to be

extended to other conditions, resulting in an increased body of knowledge of the importance of various parameters, especially early in the

fire.

The second benefit is to allow us to direct our research resources to

the most important research areas. Sensitivity analyses of the programs

show which subprograms are really important, rather than merely technically interesting.

The third benefit will be to allow us to develop meaningful fire safety

property tests. Those now in use are generally based on the intuition

of practitioners, and their applicability is sometimes in doubt.

The fourth, and major benefit, is to provide a new quantitative tool for

the development of design criteria applicable to fire safety in rooms,

room-corridor combinations, and buildings, in both early and late stages

of fire.

3. PART III.

This portion of the paper is intended to illustrate how some of the

Information developed to date in the mathematical modeling effort can be

used, using nothing more complicated than algebra, to solve fire protection problems that would have been nearly impossible a few years ago.

Presented as appendices to this paper are samples of the application of

computer modeling to solve two problems.

5
Appendix A is an attempt to calculate the upper layer depth in a closed

room (leak under the doorway) as a function of the amount of material

burned. The actual complete calculation would have been quite complex,

since the upper layer is formed by both the combustion products and the

air they entrain in the plume. The entrainment, in turn, depends on the

height of the plume between the burning material and the bottom of the

upper layer. The correlations developed by Professor Edward Zukoski (on

a grant from NBS) were used, and the calculation using his work is

straightforward. Prof. Zukoski* s publication on this part of his work

is appended as Appendix B. In Appendix A, the gas temperature was calculated assuming there was no heat transfer to the walls of the room,

and that the leak was in the lowest part of the room. Other assumptions

are possible using Appendix B.

Appendix C is a rough estimation of the contribution of a "target"

material to the toxicity of the gases leaving a room. The target

material is heated by radiation from the hot gases in the ceiling layer.

Its pyrolysis gases are assumed to be substantially more toxic than the

combustion products of the room fire, but it doesn't decompose until it

reaches a relatively high temperature. By that time, the gas flow out

of the room from the primary fire is quite large, and only if the

exposed area of the target material were large enough to create, say,

lALOOO of this flow, would the target material be a factor in fire

safety. The pyrolysis rate of the target material as a function of its

temperature is not included in Appendix C, but provision is made for it.

This would, of course, require a separate laboratory experiment on the

material.

To solve this problem. Dr. Quintiere's relatively simple quasi-steady

state "RUNE" computer program at NBS was used to calculate the upper

layer height and flowrate and temperature. To the user this is no more difficult than typing the room dimensions, doorway size, and primary

fire heat release rate into a terminal. Without the computer program, a great deal of work would be required to obtain these data, which are the

basis of the rest of the calculation.

This paper was prepared for presentation to a Society of Fire Protection

Engineers' symposium on Systems Methodologies and Some Applications.

The audience was asked whether their goals were best met by relatively

simple models like those used in the appendices, or a comprehensive

model, requiring access to significant computer capability, that would

provide answers directly. The consensus was that these practitioners

needed both. A calculation that could be examined in detail, as found

using a simpler model, would provide their clients more confidence than

a number printed by a computer. On the other hand, the full computer

model will provide answers that are more accurate and comprehensive than

can be obtained practically by simpler models.

6
4 . REFERENCES

[1] Mitler, Henry E. , The Physical Basis for the Harvard Computer Fire

Code, Home Fire Project Technical Report #34, Harvard Univ. , Division

of Engineering and Applied Science, Oct. 1978.

[2] Friedman, R. , Quantification of Threat from a Rapidly Growing Fire

in Terms of Relative Material Properties, Fire and Materials, Vol. 2,

No. 1 (1978).

[3] Quintiere, J. and McCaffrey, B. , Assessing the Hazard of Cellular

Plastic Fires in a Room, June 1979.

[4] Benjamin, I. A. and Adams, C. H. , Proposed Criteria for Use of the

Critical Radiant Flux Test Method, Nat. Bur. Stand. (U.S.), NBSIR 75-950

(Dec. 1975).

[5] Emmons, H. W. , Computer Fire Code (II), Home Fire Project Technical

Report No. 20, Harvard Univ., Division of Engineering and Applied

Physics, Jan. 1977.

[6] Mitler, Henry E. , Users Guide to Computer Fire Code III, Home Fire

Project Technical Report No. 37, Harvard Univ., Division of Engineering

and Applied Physics, Apr. 1979.

[7] Emmons, H. D. , report to Ad Hoc Committee, Jan. 1979.

[8] Tanaka, T. , A Model on Fire Spread in Small Scale Buildings, in

Fire Research and Safety, Nat. Bur. Stand. (U.S.), Spec. Publ. 540,

p. 264 (Nov. 1979).

[9] Tanaka, T. , A Mathematical Model of a Compartment Fire, BRI Research

Paper #70, Feb. 1977.

[10] Hasemi, Yuji, Niimerical Simulation of Fire Phenomena and Its

Application, BRI Research Paper #66, June 1976.

[11] Emmons, H. D., The Prediction of Fires in Buildings, Seventeenth

Symposium on Combustion, p. 1101, The Combustion Institute,

Pittsburgh, PA (1979).

[12] Modak, A. T. , The Third Full Scale Bedroom Fire Test of the Home

Fire Project, Factory Mutual Research, Nov. 1976.

[13] Quintiere, J. , Growth of Fire in Building Compartments, ASTM

Special Publication 614, A. F. Robertson, editor, pp. 131-167 (1977).

7
[14] MacArthur, C. D. and Reeves, J. S., Dayton Aircraft Cabin Fire

Model, Report No. FAA-RD-76-120,1, June 1976.

[15] Pape, R. and Waterman, T. , Modifications to the RFIRES Preflashover

Room Fire Computer Model, Final Report IITRI Project J6400, March

1977.

[16] Report of the Ad Hoc Mathematical Fire Modeling Committee, Nov. 1979.

8
o iI 9

Figure

1.

Schematic

of

the

enclosure,

showing

mass

fluxes

in

and

radiative

fluxes

to

the

target

from

layer

and

flame
Input Data | —Geometric Constants —Properties of Objects —Vents —Layer —Physical Constants —Time Variables —Set Flags —Call Radiation —RADN —Call Heat Transfer —HTRN —Call Burn— BURN —Call Vent —VENT ^ —Call Plume —PLUM —Call Layer —LAYR —Call Room —ROOM —Has the time step converged? —^——

yes

no —Criteria for end of calculation —t = t+ st-H

yes —End

Figure 2. Computer fire code - main program

10
VENT

List

common

variables

needed

11

i

Figure

3.

Subroutine

vent
12

Figure

4.

Path

of

flame

spread
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-isnaiNOo

LJ

Q.O

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13

Figure

5.

Diagram

of

a

compartment

fire
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BBBS

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|B QB

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Figure

7.

Flame

spread

on

seat

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at

100

seconds
STEERING

COMMITTEE

16

Figure

8.

Steering

committee

organization
Extend Full Scale Test Results to Different Conditions

Delineate Important Research Areas

Define Meaningful Fire Tests

D Generate Design Data

Figure 9. Benefits'- mathematical models of fire

17
UNITED STATES DEPARTMENT OF COMMERCE

National Bureau of Standards

Washington, D.C. 20234

APPENDIX A

MEMORANDUM FOR Those Listed

From: R. S. Levine, Chief

Fire Science Division

Subject: Math Analysis of the "Closed Room" Toxicity Test

1.0 Problem Statement

The problem is to estimate whether the final toxic gas in a full scale

room test will correspond to the gases in a smaller scale apparatus with

the same "loading" (weight of original material per m^ of gas volume)

We will calculate only the likely results of the full scale room burn.

So: Find the level of the ceiling layer in a room (door closed, leak

under the door) as a function of amount of fuel burned (assume wood)

at 10, 20, 30, 40 gm/m^ loading, and the gas composition and temperature

of that layer. Room = 10' x 10' x 8' high = 3 x 3 x 2.44 m = 22 m^

The source is localized, but the products form a ceiling layer that is

toxic.

18
Reference: Zukoski, E. F. , "Development of a Stratified Ceiling Layer

in the Early Stages of a Closed-Room Fire", Fire & Materials , Vol. 2, No. 2, 1978 (R7800406 in FRIS).

Zukoski gives the results of an analysis of the height of the hot gas

layer in a room, where the plume below the layer entrains fresh air.

The results of the analysis require only arithmetic to use. He shows

(part 7 of above) that the rate of heat addition has only a small

effect on the layer level when the same total heat addition has been

reached. Therefore, we arbitrarily set a burning rate of 0.1 gm/sec/m^.

The results will be applicable to any situation where a major part of

the thermal energy is not lost as heat transfer to the walls. This

latter problem will be calculated in a future memo.

Let us assxime the fuel is wood, (Ci^iH20)^ burned at 80% combustion

efficiency. Heat of combustion is about 5300 cal/gm. Fire size per

m^ is then 5300 cal/sec at a burning rate of 1 gm/sec/m^ or (5300 cal/sec)

(4.187 watts/cal/sec) (22m^) = 490 Rw. So burn at 0.1 gm/sec/m^ = 49 Kw = 2.2 gm/sec = 11,700 cal/sec. (Zukowski did most of his work

at about 100 Kw.) A loading of the products of combustion of 10 gms

of wood per m^, corresponds to burning 22 x 10 = 220 gms of wood (without

loss of product)

1/3 2.0 In Zukoski 's paper, figure 2, plots (Q*) t = vs y

where Q* = Q/p^

T = t (/gTil) (h2/S)

Height of ceiling layer = Y = yH

t is time, seconds, for layer to descend to y

H is room Height, meters

S is room area, m^

g is gravitational constant 9.8 m/sec^

19
Q is heat addition rate from fire, cal/sec

Cp = original (lower layer) room air specific heat

= 0.24 cal/gm®K

= density of original room air (1.3 x 10^ gm/m^ at 273°K)

T = temperature of original room air, °K

Let the room be 10’ x 10’ x 8’ high

= 3.05 X 3.05 X 2.44 m

Calculation Method - find where layer is in a time corresponding to

the burning time of the fuel at 2.2 gm/sec

_ 2.2 X 5300 cal m^ gm °K Sec sec 1300 gm 0.24 cal 275 °K 4.86 m 4.84m^

/gH = 9.8(2.44) = 4.88 m/sec

Q* = 2.6 X 10"^(2.2) = 0.0058

(Q*)^/^ = 0.18

gm fuel Tsec

T Y ceiling layer

height = YH

220 100 128 23 1/3

0 at Q* t=14 0 gas exits before

220 gm total fuel

440 200 256 40.5

660 300 385 61

These discharge some

or time = 60 sec. combustion products

880 400 505 80 (t=14/.18=77.8)

Layer hits floor at (220 gm) (60 sec/100 sec) = 132 gm of fuel burned.

T = t (g/M) 1/2(„2 /S2) = t (9.8/2. 44)^/^(2.442/3.052) = t (2.0)(0.64) = 1.28t

ceiling layer temperature

eq (25) p^/p^ = [(l-(Q*T)/(l-y)] = 1- (0 . 0058) (77 . 8) = 1-0.45 = 0.55

20
If the initial temperature is 20°C = 293K, final is 1/.55 (293) = 533°K = 260°C T final (after 124 gm fuel burned and ceiling layer has

reached the floor)

This part of the calculation shows that, if the fuel burns at 80% comb,

efficiency, the lightest dose (10 gm/m^ or 220 gm total fuel) will start

to spill combustion products out of the room in 60 seconds (or at 132 gm) . Higher doses will lose even more products, so we will not calculate them

further without making other provision.

Two solutions to the problem of retaining the products in the room:

(1) Transfer heat out of the room. It will make a major difference

whether this is done in the early plume or at the boundaries

of the room.

r

(2) Make the fire some distance above the floor (shorter plume

less entrainment)

Let’s try solution (2) and see what height the fire should be so that

the ceiling layer hits the floor at the end of burning.

3.0 Calculate the effect of putting the fire at various heights above

the floor—this will increase the room filling time. Assume the burning

rate remains at 2.2 gm/sec. Then the longer filling time allows more

fuel to be used.

Method: Assume various values of the fire height, AH, calculate total

filling time from t + At (Zukoski, section 6). Interpolate

for 20, 30, 40 gm/m^ (440, 660, 880 gm fuel) to find necessary

AH so as not to drive combustion products out of the floor vent.

21
Table 3.1

AH/H H AH Q Q*(H) T(y=0) AT (AH)

T

Total

sec

Fuel

Burned

gms

0.0 2.44 0 49 KW .0058 60 0 60 124

0.1 2.20 0.24 49 Kw .006 70.6 15.3 85.9 189

0.2 1.95 0.49 49 Kw .005 68.7 27.4 96.2 211

0.3 1.57 0.87 49 Kw .014 64.1 32.9 92.1 213

0.4 1.46 0.98 49 Kw .017 61.7 41.3 103 226

0.5 1.22 1.22 49 Kw .027 53.5 41.1 94.5 207

0.6 0.97 1.57 49 Kw .048 46.4 39.1 85 187

H + AH == 2.44 m >

AH = 2.44 - H

Q

= 49 Kw =C= 2. 2 gm/secO 11,700 cal/ sec

Q* = Q/p^ 1C Tc

P

H^

i' = 11,700 cal gm'’K sec 1300 gm 0.24 cal 273°K /9.8

= 4.4 X 10 = -.044

(3.13)

/h h2

Table 3.2: Calculations for Table 3.1

/if/H H /r /h" H^ 0* q1/3 t/T Tsec iTf T

Total

meters

at y=0 sec sec 0.1 2.2 1.48 7.16 0.006 .182 14 1.09 70.6 16.6 15.3 85.9

0.2 1.95 1.40 5.32 0.008 .200 12.5 0.91 68.7 25 27.4 96.2

0.3 1.57 1.26 3.11 0.014 .240 10 0.65 64.1 21.4 32.9 97.1

0.4 1.46 1.21 2.58 0.017 .256 9 0.57 61.7 23.5 41.3 103

0.5 1.22 1.105 1.64 0.027 .300 7.2 0.45 53.3 18.5 41.1 94.5

0.6 0.97 0.982 0.92 0.048 .364 5.4 0.32 46.4 12.5 39.1 85

t/T' = ^ —s h2 3.13 h2

0.335

h2

/n • (3.05)2 9.3

T — 1 1 v=0

y=o q*1/3 t/T

/T)

. AH

= IT • ^

(H)

22
4.0 Summary

From table 3.1, to burn 220 gm without losing products out the floor leak,

place the fire about 0.98 meters off the floor.

Table 3.1 shows that we cannot burn much more and not lose products

unless, of course, the combustion efficiency is lower than 80%, or heat

is lost to the walls, or both.

23
I^ I 0

( A. ^ - 1 Vwj.- 20234 APPENDIX B

Development of a Stratified Ceilin'^' Layer in

the Early Stages of a Closed-room Fire

E. IC /.ukoski

l'ri)tcs'>or of Jcl I’mpulMon, ( ';ilil'omia InsliUilc of rcchnoiogy. nasailcna. ( aliroi iiia 01 125. l.S \

A simple miulyticul nuidel hus iteeii developed to determine the time re<piired lor a room to till with produels of

eoml)Usti«>n from a small lire. The room is assumed to he closed except for small opeiiinus at either the Moor or eeilinu

le\el and the avsiimpliun is made that the leak is large enough to allow the iransient pressure term in the eiRig>

equation to be neglected. Products of comlnistion are assunu‘d to occupy a layer next to the ceiling and the model

prcHlicts the growth of the thickness and the mean density of this layer as a runction of time. I he anal.\sis shows

that times rcH|uired to till a typical rtHtni are small. For example, a typical bedroom (ills with produets from .i 20 k\\

lire in several minutes. 'I'he time requiri'd to till a riumi and the mean density of ceiling laser are delemiined in terms of lire si/.e, room geometry, leak position, lire elevation and geometry.

L IMKODCCHON

\^'hcn heal is atldcel to an ideal gas in a fixed volume,

the pressure must increase in response to ihe temperature

rise since the average density must remain fixed. In a huikhng lire situation, the rate of pressure rise is often kept very small by gas leaks through openings in the walls of the building such as cracks around windows and

doors.

Under circumstances for which leaks do keep ihc

rale of pressure rise to a negligible value, we are inleresieil

in Ihe lime required for the gas remaining in the volume

to be contaminated and healed by mixing with the products of combustion from a lire. In the following

|iaiagr.iplis, we will examine this problem for a very simple example. The lire will be treated as a point source of heal with a specified strength. We will restrict our examination to a volume composed of a single room

wiili .1 hori/tmlal ceiling layer of hot gas formal under

ihe ceiling. This layer may contain a nonuniform

icinperature (.lisiribulion but we will be concerned only

with Its average temperature or density. During the progress of the lire the thickness of this layer will grow

in tune and we will be interested in predicting when the lower boundary will reach the lloor level. We are also mteiesicd in the average density in this layer as a function

of lime.

1 his two layer model is appropriate for a lire of small gcoineincal area which is burning in u room of much

hirger lloor area prior to llashovcr of the room. Our purpose is to illustrate the general oaler of

magnitude of the lime involved and the manner in which

v.irious p.iramelers inlluence this time by looking at

V.. 1 NCS u Inch .lie inalheinalically very simple. 'I he complete

problem is a special case of a room lire and numerical

integration techniques are available if more accuracy and detail is required.

< llcvilcii iV .Soil l.lU. 19 /S

2. FRF.S.SUUi; RISE IN A ( I.OSI I) \01 t M l

In order to juslifv ihe coiisUiiU j•>^e^^ule a^Milll;nlon used in examining a leakv i ouni-lire coiisnk-i the p:e--ine

increase producctl b> a fire in a cKwe.l \oiume I oi many mteresiing situations ihe pressuic v'.ill i. e to ,i quasi-steady stale value in a lime w Inch is short coinp.ned

with the time scale of other mieiesimg event' lo

illustrate this conclusion consider the iniein.i'i eiiergv

balance for :i perfectly closed volume I' eoniainii.L’ an

ideal gtis which is healed al a r.ne <J

.

O': "

I he mass balance is

If we iissume that s|vecilic lieals are ..oi'si.iiu, liie m'. i' ideal, that hvdrostalic pressuie di'leieiKC' .ne ne;'li'nl'',r and that he.il arldilioii one. (J. is ^larianl. liici. 1 qii'

(I and 2) can he combined and inieei.iie.i to give

- it)

Here, the subscript a design. iics the amoieiit comi nou'

before the heal addiliini suris. .A lUiineiica! example o

of interest. Consider ,i room wnh a voiume ol 2.s I 2 nv' which contains a lire ol Ibb fW heal mpul r.iie 1 hen

{() l .,) 0.007 s ' and conseqiienif, ihe pie -uie

rises by tiboiil 0.07 aim m 10 A pie"ure dillerenii.il

ol this amouni across a wnuh'vv ol on m will po'vliiv.e

a total load of about .1.5(10 Newloio wi.iui (a) imgl i le encHigh to destroy ifie wmiK'w .iikI ioi wdl pi oo rc a velocilv of about 1.20 m s ‘ m loom tempei.iim .in through a leak. Both ellecis aie l.nce .ii.d p:e'i..'i..iniv would lead lo sulficienl le.ik> lo keep i..i'.Iki g...''Un.

rise iVuin occurimg. asm 7K/nO(P iXlsJ s(U s()
i:>r:Vi:LOPMi::NT or a STRAn ii-iED ceiling la .'er in the early stages oi a closi.o-room i iri

Tills example sui>}:esis llial c|uasi-slcaily pressure

uilliin a biirniiii: room is a reasonable assumplion. A

i|uaiuilaiive measure ol leak areas needed lor a given room and lire is given in Section 10.

3. lIlvAT ADDITION TO A MXi:i) VOLtMl£ WITH

l.KAKS

Consider a lixed volume in space coniaining an ideal gas to which heal is added. Nr)le, that here the lire is considered to be a source of heal alone and the mass of

fuel is neglected. Mass is alloweil to have the volume

such that the work done by the rale of change of pressure within the volume absorbs a negligible rraclit)n of the

heat input. VVe will show here that under these circumstances

the enthalpy Ilux produced by this mass Ilux is ct|ual

to the heal addition rate and thiit the enthalpy of the gas remaining in the volume is constant regardless of

the distribution of temperature within the volume.

The energy equation for the mass within the volume

I' can be written tis

/'xcdrj I

I

(/)!•. d.SV/) (j I (),. (4)

where e is the internal energy. V is a volume lixed in space. .V is the surface of the volume, />r.d5 is local mass

Ilux ihiaiugh an clement of surface area due to vector

velocity r. h is enthalpy of gas crossing ,V, Q is rate of

heal addition by the Tnc,‘ and the last term Q^ is the

rale of heal conduction across the boundary into the room.

If \\c now combine Lqn (4) with IZqn (2) for continuity

and the ilefmitions of internal energy tind enthalpy for :m

ideal gas:

li 1 (5)

h — C p( 7 — 7 r) (6) Wc can rewrite Lqn (4) as C y \ 1 *

l< (j/ ) + (7)

Here / , is a reference temperature, and Cp and Cv are

suitably chosen values of s|wcilic heats of the gas at amslanl pressure and constant volume. We have also made use of the approximtilion thtil the specific heats of

the gas are constant and that the gas follows the state equation for the ideal gas.P = f>RT ( 8 ) When the transient pressure term in (7) is small compared

with the heat term, we can neglect the cITect of pressure

transient, l urther discussion of the conditions under

which this pressure term must he included in the equation

is given in Section 10 of this paper. When the first term of (7) can be neglected, wc gel

I j,»i-.d.V)(rpT)=C>T (?.

If wc restrict the out How to a single point where coriOit mu .

tire uniform in sjiace. then

) ^ (/)!’. d.Sj niX\J v

where /»/,. is mass How at the exit (e) ;ind ' he

local gas enthalpy. Thus (9) iviay be written as

or, if there arc a number of leaks ^ liiiC (j (), i '

will hoM. When eonduciion is igiuned. G, will !'> /u<i

and we gel the particularly simple result that the enin.i.py

Ilux from the volume equals the heat additmn reiMone's

ol' temperature ilistribution within the volume:

y,- O ii:i

4. ROOM rROm.KM

We are inlcresle».l in determining the lime leqmied to

fill a room with pi\)duels i4' combustion Irom ,i lire We want to make a simple caleulaln>ii ami to eslmi.iie the elVecls of leaks mi this process. The lire is treated as a iiomi source >4 he. it aOviiiam.

the fuel How rale is neglected ainl the plume alnwe the

lire is treated in the usual Ikuissmesq manner. I he ceiling

layer is taken as an tidiabalic region. Hee.uise ae are

interested in predicting the le\el ol' the eeilmg la er

( Y in Fig. I), wc need not make assumpiii'ns coiieernme

the degree of mixing in this region. Symbols aie deiineJ

in F'ig. 1. The lower boundary of the eeilmg layei is assumed to be hori/ont;il. We want to preoiei me

downw'ard motion of this boundary.

In the following analysis, the \olume of ilie plume and

fuel mass How rale are ignored,

leak case

In this first example let the leak be at the Horn ie'. . i s,i that only uncontammaled gas escapes. .A nuss h.ii.u.ce for the cold region is given by

(;>,• )'.V) I I /U|, 0 i 1 .M

Flere 6' is the area of lloor of the room : /i, }'.S is the mass

of uncontaminaleil gas: is the i.iie ai which m iss Hows out of the cold region due to eniiamment into me

25
E. 1. ZUKOSKI

Illume; aiul ih,. is ihc mass losl ihrough leaks IVom ihc

cold rceioii. If we choose i s (13) becomes

(pdfS)

I +»/,. + »/p = 0 (14)

The mass flow rale ai ihe leak, which is ihe only leak, is aiven by (12) as

/;/(. = |( /"c = ^jC" ^^T(r or nh'^(QllhC H-) iPi Vf(/l //-)

If we live a noiulimensional lire heat inpiil parameter,

Q*^Qlp,.C„r,\ v// //-

then

i)U.=^Q*P,\ kII (15)

I’revious analysis has yiven a reasonable eslimalc of

plume mass Ilu\ as

>»i|. = ((^*)' •* ip, \ nil (16)

where » is a collection of constants (n(\Cr) whose

proiliicl IS about (I '5.4)'. This result is also discussed

brielU in the Ap(ieiuli\. C’ollectini! these items, (15) aiul

( 1(>). we can rewrite ( 14) as

dr + = 0 (17)

where r is a nondimensional time delined as

T = /(v'je///)(//-/i) US)

I lere .V is area of the floor of the room and // is the height

«>r the rtxmi. The second term in (17) is the contribution

ol'llie leak aiul the third, is ilue to plume entrainment.

Ihe inleeration of (IS) is easily accomplished by

numerical technii|ues when (7* is a constant. Thus r- l

' (di/(C>*+ (i‘7)

, V Values i>r T versus y are given in Table I and also in

I ig. 2 for the three Tires*. The parameter (t( (/•)•"») is used in presenting these results because of its convenience

in the nest examine. Note that times here are sluirt. Tor

example, if our rtu>m is 2.44 m (S ft) wide by 2.44 m

high by 0.75 m long and if () 05 kW. then (>*- ().t)l; ilr 2 s; t; i =o;'= 5I and llie corresponding time i is 102 s. Thus the ceiling layer would reach the floor level

in less than 2 min. lX'|vndcncc on (>* is strong W'hen

{)* is larger than 0.01.

Tuhlc I. lk‘|K-iidi'iicc of limes required to iiil upper half ofu

room on Hre si/.c and tuom area fur //i-s 2.44 m

Ftocr Ceiting

H S

s d U 0 O' /:v=i/2; r.v=i/2i

R 0 m 0.75s lOOkW 0 010 11s 16.5s

30 3 100 0.010 45 66

143 12 100 0.010 178 264

36 3 20 0.002 97 117

36 3 100 0.01 45 66

3o 3 500 0 05 16.5 40

I I I 1 — j . i-L. i.e. 0 5 0 7 10 2 3 4!) iC

0epe'’rter.r.e . i'' ;

Figure 2. Dependence of ceiling luy'.r height on imio .'inri he,it input rate.

Ceiling exit case

If the exit is in the ceiling l.i>ei. the pixhieiii is e-.eii simpler, for tins case, no mass Ic.iks iiDin ilie I 'ld region, and the ci|uation lor mass b.ii.mec *'l iiic s>ild fluid, licin (17), lexUiees to

i.U)

(.1 r which can be mimciiiaidy iiuc^raiccl u> ci\c

.r I I •' T " t:2)

Values of t rct|uircd for the ceiling laser to reach a specified 0 arc given in Tabic 2 and Kie. 2. Nuie that

|( (?*)'=» r] is clearly the appropriate sctilinj paiameicr

for this ease. Consider the room diseiissai above with ()" t)i)l and //t~2 s. At r~U/2. t - 22 and i 44 s. ;ind when

.» =0.l, t=I.36 ami r -- 272 s. Note that i approaches

zero usymplotically and that lor all r. s.ilues ol r are larger for the ceiling leak than for the floor leak. However. as approaches zero. Eqns (17 and 21) hegm to converge as long as r>0. for a very weak lire, s.iy Q* -().()(1()5. e.g. ((.) 5 kVV. // 2.44 m). the ilillereiiscs are reduced to a few |X*ieenl .it r I 4 and c.in be ignoi cil. The result given in lain (22i is identical to ilial ohiaiih'd by Uaines and l urner- lor a similar problem nisoUiue an incompressible flow in which the eflecis oi‘ leaks could he ignored. Ihe results tire similai bec.iiisc in both calculations the densil> of the cold laser below

llie iiueiraee is tissumed to be eonsuml and sonsequeiitls

only the plume entrainment enters the prtrbicm. lApenmcnls of Uains timl Tiirnei'* seiilieil the tteeuraes of the equation for values of heat addition Ibuos.mee lliis m

their ease) corresponding to 2 - 10

'

- 3 / 10

l-'or llte exiimples discussed here, r ; r; depeiuls on O-'' which is fixed by the heal in|-uil rale and // finis r :s a function of lire heat input rate tind room hei jhi bill is independent of roinii tirea. f\|uatiun (IM shows ilui the lime / svill scale linctirly wiih floor area V. .Sesertil examples are shown for both eeilmg tmd floor leak eases

in Table I

.

Sealing with room height is more eon. pies If we compare rooms with lixenl floor .uea and iietii inpui.

- 26
i:>r\ 1.1 oi>mi:nt oi- a si kaih ii-d ci.iunc; i.a'iMK in ihl l:AKl,^ siac.is oi \ i iosid-koom i iki

r;iltU‘ 2. l)cj)i.'n(loiK'C' ul ceiling layer lieii'lil and mean densily on dinu'n.sionicss time lor lloor and eeiliiiK leaks

Floor leak

Q

• = 0 . 002 Q' = 0.01 0- -0 05 Cc- iii'.n Alt O'

Y

T T>\J pi- T 'p\J Pi- 7 T'u/' Pi tO-i ‘ -

1 .0 0 0 — 0 — (1 0.75 12.2 0.99 6.0 0.76 2.4 0 53 1 .71 0.50 32.2 0.87 14.9 0.70 5.5 0 45 4 76 0.25 71.5 0.81 29.1 0,61 9.4 0,37 12 31 0.00 164 0.67 51 0 49 14 2 0 29

aiul chaniic ia>om liciylu. then bolh (J* aiul llic \ ,i,’/7/ (Si/l-) parainclcr will cltaii”c. 'I'ltc clVocl of cliaMiiini;

// on t ; 1

j lor a lixcd (j is slii>wn in labic 3 lor ihc lloor leak ease aiul Tor r= 1/2 aiul 0. Note lhal incretisini: //, tieereases Q*. increases t. has a mi.xeil clVecl on / |l^2;

aiul increases / ;0|. Thus, a room with ti hiuh ceilinu

Tills up cmly sliehily sKrwer lhan a room with a lower

ceilini: hut ihe same lloor area.

5. ( i;il.lN(; I.AM:K IKMPKUArUUK KSIIMAIKS;

I 1 OOU I.KAk

C^Misklcr the case lor which ihe lc;ik is al ihc lloor le\cl.

An cnci i’v bal.incc lor an ailiabalic ceiliny layer eiscs

j ()<// j '/> ( V//) ilf (/; -//,.) (23)

M . f/ where /; is ihe enlh;il|>y oT Ihe i>as. Thus, if (J is eonslanl we liiul

C)/- r /<(.v//)(cii)(r„y -c,.T,.)

.

II we use aeain // Irom ihe irleiil jztis eijualion oT slate, we Tim.1 that

(jt -- ,uC ^:i\[Sll)(\ - y)- )' pdf (24;

when we eleline ihe nn-an ceilinit layer densily as

pii SH ( I - f) = p(.V//) d f we can rearranjic Eijn (24) lo give

iinJl>r) (2.S)

Values ol pi, f},. are listed in Table 2 Tor the three examples

discussed there. NtUe. lhal even Tor ihe smallest lire. densiiN dilVerences are tipprcciable: certainly for the

larger two lires the Uoussinesq approximation is not

salisTaclvuv. Tven lor the weak lire described above. ((_) — .*» kW. — -44 m. and (y* =0.0005) the average density in the ceiling layer when i =0 is about 10"„ below lhal oT

the eool gas.

lahlc Dependence of time rc<|uired to till u room on room

height for (>-100 k\V

H Q- S T;y=1/2| t;i/2i T'.y'=0; riO:

1 . 28 m 0.050 143 m- 5.5 174s 14.2 448s

2.44 0.010 143 14.9 179 51 609

4.63 0 002 143 32.2 148 164 750

27

In the cases Tor winch an iinpunl> Icsci. s.r. monoxide, can be relaletl to ihe he.ii in|n:i rale iv. a rehtlionship such .is

///,,, - C i (j C|, / , ).

the mass fraction of impiiril\ in liic coiimg la\er wiii ix-

(mass iV.iction) -- C O' r i 1 m i2n)

tqualion (2.^) lu'Uls for the lloor le.ik .Mil. Nin.i^ir results can be (.leveloped fiu ilie ceiling leal, s.oe ImiI retiuire numerical mlegi.iluMi and. ino,e nniir n i.nii. some assumption ahiuil the temper. iinie ,noi;le ;n the

ceiling layer.

6. MUK u:\ l.l. AiU)\ i: I I OOK

The level of the lire ;ibo\e the lloor ll.l^ irter. o nn.'

ell'ecls. 1 or the ceiling leak c.oe. the ime:l.a.e Ic-el .'ill asymptotically approach the lire le\el .ind c.o nene.iih the lire will remain uncont.iniiiuled. snxe m our nnutel cold gas is only removed from the rc>om b\ enir.nm eni into the plume. Ilowever. l\>r the llo.u ie.ui le.d, ihe interlace will still retich the lloor. alihou.:i, 1 vpi li'i is not valid ttl'ler the interlace reaches tiie fne level \ :ei that lime, plume entrainment iiii longer enters liie problem. Thus. lit|n (17) is reduced to

We use the same notation to rlescnhe the ueomeii;. ;1 m the room above the lire as above, .ind tuki a rhstanre A// tiv the room below the lire isee fig ,'i e .issume

that the ceiling laver interlace re.iciies the level "i the

lire f = 0 at a time r,. .md in.it .m aovhiion,:! ii.-o. d
t. r. ZUK.OSKI

4. lin’ccl <tf lire elcviiiiun on lime required lo lilt a room for //+ A//=2.44 m

\H

H H 5 Q Q'\H\ ! y - 0 ; AtI i,

-

t 0 2.44 m 3f3 m- 100 kW 0.01 51 0 3 s 0 25 1 .83 36 100 0.02 29 16 7 4,62 21

1

Ati is required lo lill llie lieigiil below ilic lire level. Iniegralion of ihc above equation leads lo A// 1

// 0*1 //I where O* is based on //. the dislaneo from ihc lire lo ihe ceiling.

To illuslralc ihe solulion eomixire ihe iwo e.samples

deseribed in Table 4. In ihe second, ihe lire is elevated

0-6I m (2 I'l) above ihe lloor and in ihis case ihe clTcclive

v.ilue of ceiling height // is 1.63 ni (6 I'l) rather than

2.44 m (S Cl). Hence, for the same heal inpul rales. Q*

is larger for ihe second example and t I r = Ol is smaller. Howeser. lo delermine ihe value of t al which the

inlerlace reaches ihe lloor level we nuisl add the \t(

term so lhal lor the second example Ihe value of t reiiuired lor ihe ceiling layer interface lo reach Ihe lloor

IS 2‘M 17 -46. This is converted lo the dimensional

liihe as usual hul again // is used, not ihe room height

which IS ( // 4 A// ). The lime for the elevated lire is about

4l)"„ greater than for Ihe lloor level case.

l inally. a leak al an inlermediale level can be sludied

as a combin.iiion of our two extreme cases. The motion

of the interface will be described by tqn (17) until ihe

interface reaches the level of ihe leak and by Eqn (21)

ihere.ifler.

7. NON-CONSTANT HEAT INPUT RA'ITS; CEILINC. I.KAK

If the heal inisui is not conslanl. Ia|ii (21) for the ceiling leak can still be integrated directly to give

r - I - i

(' O*

j H

In order to examine Ihc impact of nonuniform heating

rale let = </t, lhal is, consider a linear increase in

2 <1 8 12 16 32 64 128 256

T Figure 4. Dependence of ceiling layer height on time for lime depemtent he.it input.

28

(ire heat input, fhen the above equ.ilion can be c\.ilu..i as

r - ('/) ri! ,1 4

i27- Consider three luimerical exampies. I usi .nui second,

lires with consumt heal iniiul'< given by C" u.Oi .it t=I 60. figure 4 gives values of r for liicse evainpi.s

up to T= 160. Note that t= 16t), total heal atideil in case' two aiul three is c(.|ual, and lhal ihe v.iIiks of i le.iciieil al this lime arc almost equal, 'finis, ihe loial heal .iddit ion rather than details of the rales inv olved is ihe c: iiical lacior.

8. IIEAI’ l.OSSKS TO l lll. W Al.l S: I I.OOR I 1 \ k

'fransfer of heal lo ihe w.dls from ilic ceiiine l.ivei region will modify ihe le.ik r.ile iec|Uiied i.i keep ll;e loud room cnlhalpv consuiiu. fc|ualion il7i for ihe

lloor leak example can be rewriiten as

'*' d ( I - A) -i M tCf ’

r'> I) <.::s) dr

where A is the fraction of heal avhliiion bv ilie liie vslueli

is losl by conduction lo the walls. Note ih.ii if .1 - 1, the second term in the above eiiualion virops out and die

e(.|ualion becomes iilenlical to dial usevl lor the ceiiing

level leak. Hence, the ell'eci of heal loss will be 10 m.ike

the i' versus t curve for a floor leak case uiih heal loss

lie between the avliabalic lloor level leak c.ise .md die

ceiling level leak case shown 111 I ig. 2. ( lead , die elhAis

of heal loss will be larger for the larger values of {)*

To illustrate these ell'ecls, values of r .ire showi'i below

in Table 5 as a funclion of r vv uh (J* and .\ as p.irameiei s. Comparison of the lirsi two eolimiiis and Iasi two coIumm'

for T shows that when 1/2 values of r are incic.ised by about a factor of l..‘' .ii r 0 and by sm.iller f.ici>>r for g>0. 'finis, if 30'‘„ of die heal inpul is losi lu die

walls, a -W’,, or less increase w ill occur in r. The Q* Old.

A 0.5 case aiiel (A'*" — t).U05. A d c.ise have die s.nne

net heal inputs. However, die l\irnier c.ise li.is a sironger

plume entrainment and consequendy smaller r values. Similar results are fouinl bv comp.irmg (A" o.iji. A = O.K with CA* = ().0()2. A = d. For the ceiling leak example, conduclion losses do not enter the problem ai all since die onlv m.tss loss mechanism for die unconi.imm.iled g.is is plume

entrainment.

9. LINE FIRE EXAMPt.E

A similar development c.in be carried out for a iu(i- dimcnsional or line plume.' for this conligurai .. m.

the entrainment in the plume at an elev.uuiii i i i//i
ni \ t I.Ol’Mf.NT or A SI'RATII IF.O ('ElUNG LAV| R IN THE EARLY STAGES OE A ( LOS ED- ROOM I IRI

1 able 5. I.ll’ccl of lical loss. lire si/.e and ceiling layer level on dimensionless time Q- - 0.01 0.005 0 002 0 05

/\ = 0 0 5 0.8 0 0 0 0 C y=i 0 0 0 0 0 0 0 0.75 6 6.8 7.5 7.5 12 2 2 4 3.2

0.50 15 18 20 24 32.2 5.5 7.5

0.25 29 38 47 54 72 9 4 14 0.0 Cl cc 127 126 164 14 23

lahle (.. Dependence of tiiinensionless lime on ceiling level liei)’.lii. lire si/e and liaik posiiioii lor a line liie

Ceiling leak Floor level leak

o,* = All or 0.01 0.002 0.01 0 05

/ T (0, •)!:-, 7 (Q:’)' '7 7 (F.'r-) (O'

1 .00 0 0 0 0 0 0 0.92 0 0 0.75 0.57 2.7 0.555 4.4 0.514 2.4 0 91 0 438 1 -9 0.50 1 .37 6.4 1 .33 10.6 1 .21 5.6 0 . 90 1 i; a 2 /

0.25 2.74 12.7 2.60 21 2.29 11 0 88 1 78 4 33

0.10 4 55 21 4.12 33 3.46 16 0 85 2 4f, n 1 0.05 5.99 28 5.07 40 4.07 19 0 83 2 .7!) 7 0 0 •/ 1 f) 6.97 55 4 . 93 23 0 81 h'f ;! A y 0 1

iibovc .1 plume ol' Iciiglh '/ aiul lolal heat input Q is eiven hy

>ii „ ( \ ' -c\ -jC I (H /'

t r)

)

can be a very miiioilanl parameler. I he il.!! .iciicc between tlie ceilmg and lloor leai\ posumnN aie Mimlar

for the line plume and axisymnielnc plumes.

\\ he I e

(V''rrCv-Cu)sa. = (0.5l)

Nuie that here y. The mass balance for the cold air layer can be written

as

-f + ' =0

llT w here (r mS)

Here, y- 1 l\>r lli^or leak and y — 0 for ceiling leak. Integration oT this ec|uation leads to

(Q.* !//:)' •*r

I ( ^Ey \ X |ar + y(C;..*)^->)

or appro.ximately

://;)''-‘r-2 In

(1 + 2 ytCT. *)- ='!

l.r I 2 y

.'\ number ol" examples are given in Table 6. Note

that if the room involved is 2.44 m high by 2.44 ni wide

by 9.7s long and if ^’ = 2.44 m. (i!t) = 2 s. Ihe ilensiiy ralii> can Ix' calculateil easily lor the

lloor level leak ease and the result is the same as Eqn (26)

which was obtained for the axisymmelric plume. The

ratio I'or t

() and r - 1.0 is the value obtained at the

start of the gas How. / = ()-!-. when the plume first reaches

the ceiling. The line and axisymmetrie fires are compared

in l ig. 5 lor lloor leak cases with (9* =0.01.

The lime required for the interfaee to reach a given

level IS much shorter for the line lire. Thus, lire geometry

29

10. NONCONSr.AM' I’RE.SSl KK

We want to return now to examine m more deia.: :lic relationship between room si/e, heat moai. .n.ii 'iii assumption that the rale ol' change of |srcNsmc is negligible.

Equation (S) can be wriuen .is /r J'v ,IJ'

V R I ih

//;, C / •• ij - 'h

Figure 5. Dependence of niean dens.ty ntio -inci reilr n- ’i.er height on dinronsionless time lor .iMi.ymn'.' u .i-' ; m. a i'-. ter 0‘=0.01.
E. F. ,'UKOSKI

I'oi' ;i room uilh a siiiiilc cxil. a lime depcndenl prcssarc. and no conduclion; I'nrlhcr Icl Q be conslanl. For

•simplilicaiion. lei ilie leak be al ihc lloor level and

ignore any adiabatic beating of the nnconiaminated gas by compression. Then density and temperature at the

leak are conslanl and have the ambient values, p,.,

7',.. If the heal addition starts at 1 — 0. the pressure within

the room uill rise until a steady state is reached. Steady

state condition implies the pressure is conslanl so that

(29) becomes

//jr-sC ^ (30)

where the subscript s designates the steady stale. If the llow through the hole resembles that ihrough an orilicc, the velocity /»• is related to the pressure dilVerence across the leak {P by

Table 7. IClTcel ot leak and fire si/e on pressure transient, amt

gas velocity in the leak

Q’ AelHO r;v-o:

, r;X=0.86:

' t;/=0; * t.S 0.002 0.003 164 0.0006 6 . 6 V 1 0 n ft s 0.01 0.003 51 0 on 1 6 • 10 5.1 0.05 0.003 14.2 0.20 4 1- 10 - 267

0.01 0.003 51 0 Oil 1 6 10 ' 0.01 0.002 51 0 025 3 7x10 ^ .5.', 0.01 0.001 51 0 10 1 5 10 '

1 50

li>r the coi I espoiuliiig llooi leak ease II ihr. small, the t|uasi-sleady state solution discussed m pievious paragraphs will be uscl'ul. 1 he ratio is

-/>,' - A/')

or

r.. = \/2A/Vp,

and

/Vs-\'2A/\/p.. (31)

Here is the ambient pressure and />,. is taken to be

the cold air rlensily p,.. 'I'he corresponding mass flu.xcs a rc

\^ 2p,.A/M,.=--.^,

2pc A f,/f e ~ t' (32)

where .1,. is the clVectivc leak area. For the steady case we can use (.30), (31) and (32) to express A/*s as

or A/\- ip,.(A'//. )(//,.-//l..)M(7*)‘

‘ (33)

We can use this result, Fqn (30) and the delinilions,

.\ A/VA/'s

H =(y/2) (\'KUHIa.r) C>*(//^//f..) (A///-i) (34)

aiul yU

to rewrite (29) as d.V

Oil + A

' >'•-*==

1 (35)

1 he soluliv.)!! I'or (35) is 0-21ln(l/l - A'‘'-) - A'O^J (3(>t The dimensionless time required for the pressure to reach its equilibrium value X = 11*1 1/\— 1 is, of course,

inlinite. However, if we pick a value close to I, say

A' 0 X(). wc can obtain a good iilea of the time required

to appioach the equilibrium value. From (36),

/(; A’ 0.X6;

/|0.H6i

/(• = 3.46

Thus, in a tune (3.46 / ,.) the pressure will rise to S6"„

ol' Its equilibrium value. We are interested in ci)m|Virmg this time with that required lor the ceiling layer to reach the lloor r; f-01

/: A' -O.S6:

/l.r-o;

/(;.\ = 0.S6;

r; l-.-t)|

t '

I

Note, that in lumc of the terms on ilic right docs i .S II I appear cither explicitly or implicitly. Hence. iiie lioor area S docs not enter the ratio of the times. Also note

that (7* increases. t;io t)| decreases, and thus the r.itto increases strongly with (J*. Several examples .ne gi.cii

below in Table 7 lor llmir leak case I'or winch //, 2 M

m. and a,, 360 in s '.

l-'or an 2.44 m high room a x.ilue (il I, II- "oo,'

gives a leak area ol' IhS cm- t2N m d. I In-- is niU .m unreasonable value for a 10 m long liali wiiii ilnec doors. If each door is 1 m wide aiui has a I 2 ^m si.a k the leak area would be l.sO cm-. Note, in Table 7. that as O' increases ihe i.iiio .ii limes increases rtipidly. T'or (>''o-().lH)2 and o.ul. the

ratio is snnill enough that the (.[uasi-steailv assumpiion

is a good one. For (O'"' -0.05 it is in>l ;is satisi'acioi v

Hence. Tor a large (ire. pressure changes uill be n.oie important. In all cases the [nessuie iise is sp mu. ill that gas density and pressure are virtu. iil\ un.ilVecievl. The results presented above allow a qu.miit.inve

determination to be made of the le.ik area required t : a given room-lire coiihguralion to insiirc tli.ii ihe smislant pressure assumption be valid Ihe leak aie.i required incretises rapKlly with the omieii'ionless heat addition parameter and scales as ihe loom heigin

sc|uared.

II. SlI.MMAin

The rmnn Till up limes have been examinevl im lomiis

which have large enough leaks to make the quasi-sie.idv pressure assumption reasonable, .md Tor a nimiTier ..I other special coiKlilivms which siinphhevi tlie an. d. tic work and which were inieresting hirnimg cases Smr,e

interesting results are as Tolluws:

1. The lime depends on location oTlhe leak and c.m be considerably dacior oT two) shorter Toi a Ih^or leak than a ceiling leak.

2. For a constant rate of heat input, nil up lime vanes

linearly with room lloor .ireti and loughly tis the 0.4 power oT room height.

3. For the ceiling leak, the time is mveiselv pi opo; -

lional to the 1 1 .3) power oT the he.il input parameter

(7'" which is rhrecllv propoitu.nal to the tue heat

j input rate
1 )i \ I I \ I Ul A SI KA I II 11 n ( I II.INCi LAM K IN 'I Hh l.AKLV S'l ACll S ()l A ( 1

i )SI D-KOuV I iKl

4 I «'i iciilly siniil.ii' loi'ins aiul lircs uilli llic sjino O'" \;ilucs. ilic time scales as the square root

li'iC loom heielu.

5. Meat loss to walls has an ell'ecl on the lime for lloor leak example, but none for the ceiling leak

case.

b. A scheme is given lo alU)w estimation of leak area

rei-imreil lo make the ijiiasi-steady pressure assumption a usel'ul one.

7. 'I'he cll'ecls itf positioning the lire above the lloor can

be treateti lor either leak position. Raising the (ire will increase the Till up time for the lloor letik aiul

uill also produce an imconlaminaled l;i\er below

the lire level li>i the ceiling leak ease.

N. I he time requireel l\ir the mlerface te) reach the

llot'i IS not sirongle dcpeiulcnl '>n the time «..e,". donee of heat addition, hut does tlcpeiiel on ii.e total cnerg\ added.

9. Geometry (d' the lire has a strong mlluen^e on :i density in the ceiling la\er and on the liii'ic resiiine : lo lill the room with products.

These results indictile ih;it reasonable estinutes o! .

lill up lime can be made uilhout roqtiiring pix delinilions ol'heal input rates or hetit losses ti> bouuua'

Acknowledgement

t he work reporksl in ilns p,i,'er l'k ^ .'..i ,i Ui'i'iiv-h':.

I he an I lull ,11 nt I >i . .1 . < inn il iru- .i i ul I Ki s i.i ll > il ; In- I in. h' i. .

( eiuer. NaiKin.il Hmeau ol .Siaiul.iiiK .nul w.is eaiiied on: aiuiei gram rmni ihc I ire Kescaieh ( enicr.

UKI KRKNC KS

1. F E. Zukoski, Cnnvoctiva Flows Associ,ile<l with Room Fires. Received 15 July 1977

Calilorni.i Insliiulc of Technology (June 1975).

2. W D. B, lines and J. S. Turner, J. Fluid. Mech. 37, 51 (1969). c Heyden £r Son Ltd, 1978

Al'l'KNDIX 1: NOiMKNCLA IT'Ki:

List ot s\ niliuls

(\, Specilic heat at constant pressure. (\ Specilic heal at constant volume.

« Internal energy.

.g (jias iiatiomil constant. h I nlhalpy

// Room lieiglil y 1 cngih of line lire

III M ass llu\

n'),. Mass Ilux at exit.

.\/' I’lessure r,lillerence across leak.

(j llciil addition rale from lire

(J^ t'.iC'ii /a \ ,g////-

(Jr lle.it conducted out of ceiling layer gas

</ stv l:t|n (27)

R Cias constant

.S Area ol' lloor of room.

.S',. Are.i of opening.

/ lei 1per.it lire.

/ lime.

/, Critical time, r Volume ol' room.

/ Velocity.

/'.d.V Volume (lux at opening.

,V M‘M\. see I7.qn (.^4).'

)' Height of lower edge ol'ceilmg l.iver

r )'///.

\ Dimensionless constant, see .Appcnrlis. y y— I lor lloor leak. ;iikI y

-O lor ceding le.ii-.. in Eqn (34) y is specilic he;il ratio equal o> ! 4o

for air.

(I III,-, see l;.c|n (34). A lletit loss factor, l ire hetit input lost ly. coiuiuclion to walls. P Density.

/Ill Mass tiveraged density ofceiling la\er. see I i.|n i2.s) T Dimensionless time ' q \ g //)(//-’ S). Ati Dimensionless lime rce|Uired to lill \olume hene.it

lire level.

Sub.seripls

a Ambient condition ouisu.le room,

c Cool gas pro|ieri_\ in room,

e I'.xil.

/ /Th exit, m Maximum salue. p Plume property,

r Reference value,

s Steady stale value.

2 Line lire jsarameier.

APPKNDIX 2: PLUME PKOPERIILS AND .MAS.S HAI ANCL

'I he turbulent lire plume can be chariiclcri/ed by the following equ.iiions when density dilTerences arc small

and when the elevation above the lire. /, is laree com-

/v/

C, ,s (A3,

pared with the lire diameter: /'I' .r ^ IIS tA4

. Ct^9.1

/ I /M and

c\.i3,.s

\ e/

(A2)

A / ... esp : ll /. 1-;.

-* • III 31
E. H. /UKOSKI

-exp : ~(i-'7v)-;.

Here. A r..,, and u are ccnlcrlinc icmperalure diflcrencc and vclotily. and

(A5)

is a dimensionless huoyaney parameter baseil on (J, \vhieh IS the heat adililion: \p = (p\ — p) is positive,

and /\ and /| arc veloeity and temperature scale leneths,

Given these approximations, we can show that the mass avcraj:cd temperature and density in the plume arc

c.

II rrC^Cr /hC|, /|

( Atij

arid mass llou m the plume at a Iteiglit Z is

/U|, - /Jin'N.Tr/^- ( A7)

or

p\ 1 {-(\Cry' - (Zf‘

(AV "

/>!

In (AS). (A/</'/'i) 'vas used to rejilace (uhiUi e: through ir„, via Hc|ii (7h) b\ use oT F.qn (Ad) .mo A, evaluated at /.

»

32
UNITED STATES DEPARTMENT OF COMMERCE

National Bureau of Standards

Washington, D.C. 20234

July 15, 1980 APPENDIX C

MEMORANDUM FOR Those Listed

From: Robert S. Levine, Chief

Fire Science Division

Subject: A Preliminary Attempt to Assess a Material’s

Toxic Hazard from Toxicity Data

Any assessment of toxic hazard must be relative to some reasonable fire

scenario. In this memo I have chosen as a scenario a fire in a small

room the size of a bedroom with an open door. A fuel corresponding to

wood is assumed to be burning at a steady, or very slowly increasing,

rate. The target material, on a table 3 ft. above the floor, is heated

by ,radiation from the hot gas layer in the upper part of the room, loses

heat only by radiation, and so reaches an equilibrium temperature. It's

decomposition products are mixed with the other gases (air and fuel

products) leaving the room. For a given amount of the target material,

the following "toxic hazard" statement is suggested.

W^(TF.)

Toxic Hazard =

where: W,^, is the target material decomposition rate, gm/sec, at the

temperature indicated

Wj is the fuel bum rate to create the given gas flow and

gas temperature condition

(T.F.) is the toxicity factor, relative to wood, as measured

by an agreed-upon protocol.

The following pages show the calculation. Briefly:

1st Assuming the room geometry, the mathematical fire Model RUNF

is run at several Fire Sizes on the 7/32 computer. This calculates

upper layer gas temperatures, flow rates, and layer depth.

I 33
2nd Assuming wood as a fuel, burning rates and gas compositions

are estimated.

3rd The equilibrium temperature of the target material is

estimated.

4th Given knowledge of the target material decomposition rate

and toxicity relative to wood at the equilibrium temperature, toxic

hazard is calculated. This will, of course, be a strong function

of the assumed fire size. Alternately, a fire size can be calculated

that will cause the material to reach a given temperature at which

the toxicity data were obtained, and these data used to rate "Toxic

Hazard".

Jim Quintiere's Program on 7/32 Computer - Steady State Fire in a Room

"RUNF"

W L H

Room 10' X 12' X 8' high = 3.05 x 3.66 x 2.44m high

H

Doorway =2' x6' =0.61x 1.83m

Upper Gas Layer Doorway Flow

Fire Size Temp. Height cfm

100 KW. 112° C-233F 0 . 4m (1.3 ft) 846 cfm - 0.48 Kg/sec

300 246 474 0.95 1.5 1215 0.69

500 386 111 0.46 1.5 1269 0.72

600 473 845 0.46 1.5 1293 0.73

700 523 974 0.45 1.5 1292 0.73

800 595 1102 0.45 1.5 1285 0.73

900 666 1231 0.45 1.5 1276 0.72

34
Calculate Fire Gases

Assume - Combustion of cellulose - wood

°2 . »2° . O.ICO

31.2 33.6 *'44 18 2.8

Assume CO is 10% of CO

2

Nike Site Mattress burns ^ CO = 0.1 to 0.2 CO^

Bldg. 205 upholstered chair burns, CO = 0.05 to 0.1 CO

2

heat of combustion = 12,000 Btu/lb = 6600 cal/gm.

assume 80% combustion efficiency =0^5300 cal/gm.

Now calculate burning rate for "Fire Size - KW" values on pg. 1.

conversion: 11 gm-cal/sec = 4.187 watts

1 KW = 1000

4.187

= 240 cal/sec- .045 sec

Then: Gases Products

Fire Size

KW

Burn Rate

gm/ sec Mol/Sec O2 reqdimol/ sec

CO

mol/ sec

CO 2

mol/ sec H2O

mol/ se

100 4.5 0.144 0.151 0.0144 .144 .144

300 13.5 0.43 0.45 0.043 0.43 0.43

500 22.5 0.72 0.76 0.072 0.72 0.72

600 27.0 0.86 0.90 0.086 0.86 0.86

700 31.5 1.01 1.06 0.101 1.01 1.01

800 36.0 1.16 1.22 0.116 1.16 1.16

900 40.5 1.30 1.36 0.130 1.30 1.36

RUNF gives doorway flow in Kg /sec.

1 gm mole air = 29 gms, 1 Kg/sec = “ 34.5 gm moles/sec.

©2 concentration is 21%. Molar Flow Rate = (Kg/sec) (.21) (34.5) = (7.2 moles/sec) (Kg/sec)

From Page 1 (RUNF) 0 flow = ^ moles/sec

2 0.73 X 7.2 = 5.3

35
So we are not 0^ limited in this series, since a max of 1.36 mol/sec

is required.

Mol wt fuel 1.1 X 12 = 13.2

31. 2 gm +16

+ 2

31.2

36
Calculate

Upper

Layer

Gases,

Contd

00

m <1- St

<t on 00 iH St vo

CM o

CM o

(U

CO CM CO O QJ tHoso

0)

CO CM CO Z 0)os

CJd)

CO

CO ^ tu O rH H Os

•H< 0

01

CO00

CU (U

!-i

N 5

•H -H

Pq in o

CM 00

I—

v£l vO IT)

PM o 00 CNJ Cti St as

CM oo 00 CM 00 CO OV • rH CM CO CO St

CM 00 CM <Ti as

4-1 o 00 rs 00 CM 00 CO OV c CJ

(U iH CM CO CO o

Pi

CU PM r-- 00 CM Cti <J- ov o oo 00 CM 00 CO Cti CJ o rH CM CO cn

iH CO in in in rH VD CM 1^

cC (U rH iH in rH CM iH

4J rH • o o vO in VO vO vO VO H S rH CM CM CM CM CM CM o CO CM vO 1 1 vO O CM rH 00 O CO w

rH rH

a

(U

CO

CO CM CO CM vO rH vO o (U o rH ts 00 o rH CO

iH CJ o rH rH rH X

'vT St CO CM vO rH VO o iH 1^ 00 o tH CO o O o O O rH rH rH

CJ • • • • • • • o o o o o o o

P! •H in in 00

CM ccJ CO St CM o 00 o e • • • • • • • CU pd CO St •<1" St CO

X) rH

CU in in vO o vO CM vO

CM pi rH CJ\

O CM CO

O Pi • • • • • • • 3 o o o o rH rH

U-) 00 o CM 00 00 CO • • • • uo in m IT)

CM

in

in* CM

00 vO • • 00 o^

0\

Cti

Cti

CT\

CTi VO

OV

iH

00 CJV OV

in

00St

CO

CM

cjv vO

St

CM

CMts

in

CM

CO

n

CM

CO

rs

m

CM

00 o o o o o o o o o o o o rH CO in vD rs 00

ov

St

CM

CMoo

Ct\ co

•H ts

4-1 •iM + mo vO &e + ou in

X) +

PJ

ct) St

cn +

<u

4-t iH

CO Od CO

P3

13

a

O 3

rH rHO

(J

CO

CO II CJ1 00 1 3

CM

a3

(U iH

iH

O

XI

O

CO H

37
Calculate equilibrium temperature of object at 3 ft level in the center of

the room. - Ceiling gas of temperature and

composition previously calculated, object is

insulated - loses heat by radiation only -

[

egF1-2 Tg + (1 eg)F^_2T^

]

e F

T 2-3 (T^)

The view factor F for the target receiving radiation from the hot gas

^ ^

( 1 ) can be evaluated from Hot tel Fig. 4.

Assume the target is the area, dA, and sees four rectangles as shown here:

(1/4 the room area)

= 5 ft

L

2 = 6 ft

F = 0.19 for each of the four rectangles

then F^_2 = 4F = . 76

^

2 - 2

* view factor for radiation from the target is assumed to be 1.0.

eg can be calculated from the gas composition already calculated, plus a soot correction. The higher eg, the larger the 1st term and the smaller

the 2nd term in the equation above. If we take a worst case and assume the

wall temperature, Tw, reaches the gas temperature Tg, this is equivalent

to gas radiation alone with eg = 1.0. Making this assumption:

F^_

2Tg^ = T^^, or T^ = Tg ^ ^

^1.2 7^ = ^g (0.76)^^^

T^ = 0.92 Tg (both temperatures in °K)

38
(1) McAdams, heat transmission - 3rd Ed (1954) pg. 68- Chapter written

by H. C. Hottel.

If we want to evaluate the toxic hazard at a particular temperature as used

in the protocol, then plot vs. fire size in KW—and evaluate the flow

rates, material and gas composition at this protocol temperature.

Fire Size, KW.

This Scenario - Plotted from Table 3

Summary

With this calculation, the contribution of the target material to the

toxic hazard can be judged from the next table (where Wg is the decomposition rate, gm/sec, of the target material at temp T^) . Obviously,

Wg and the "Toxic Factor" must be obtained by some means outside the scope

of this calculation.

39
Summary

of

Calculated

Data

2’X

8'

Room

with

2'x

6’

Doorway

X)

>-< nJ X) N o

rt o

32 :s a dJ •H pd XoH U u o

•H

W

X

O o rt H ft,

<u w

ca P2 o

ca (U

•iH

H cu

m

U •:2 e

0) o a

4J o bo

ca (U s o

•u

(U >3- vO CN CJN CO M bd O 00 CO CTi \£)

f-i • 0 CO <r vO 1^ 00

ca Ci H a

(U H

u rH CO -cr o> vO o o CX) O CO tH cn CM (T, CN CO m m

f-l o

4Ju

ca

ft,u

•HXoH

M-i •!2

H • r2

II XI

taN

ca 32a

•HXoH

XO

CM CO o • • u VO CT^ fH 00 tH

OJ tH CO CO CT)

m +j

ca o

pci 0)

CO CM & ^ o o a

tH bo

ft4 tH uo <r CM O MT 00 CM v£> o • • • • • • « o o rH CM CM CM CO CO

>-i (U>, CM 00 CM ov 'd" CTv

ca o 00 00 CM 00 CO ov

hJ o • • • • • • • o tH CM CO CO -d- m

ca 4-1 o c in 'd' 'd0) 00 tH 'd- vO

f-l

O CM • • • • • • • 01 V4 o o 00 vO vO m 'd- a (U CM rH iH tH tH tH t—

a pL, 33 00 CM CJ^ mJ- Ov

00 00 CM 00 CO ov o O fH CM CO CO 'd' <1- CJ • • • • • • • o O o o O o O

(U CO Ov C3^ vO vO 00 ov

V4 bd 00

m <Ti vO CO 3 O CO LiO vO 00 C3V

4-1 ca

>-i 04CL CM vO VO CO CO uo v£) B U I—

00 CM <Ti vO

0) 0 1—

CN CO cn liO VO

H

(U

H 4J

<u ca o 3 pd OJ

mm lO o m o LO

CO 3 ^ <r CO CM fH vO o 4-4 L4 a fH CM CM CO CO 3 3 60

PQ

(U 01

IL

N o o o o o o o

•H •H o o o o o o o c/3 tH CO lO VO 00 ov

CO

<u rH

rO

ca H

40
NBS-114A (REV. 9-78)

»>.S. DEPT. OF COMM. i<G6v*t AC60»$ion No, BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 80-2107

4. TITLE AND SUBTITLE

Mathematical Modeling of Fires

5. Public ition Dale September 1980

6. Performing Organization Code

7, AUTHOR(S)

Robert S . Levine

8. Performing Organ. Report U

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

lt» |>ro|ect/Tasl</Work Unit No.

11. Contract/Grant No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS fSrreer. City, State, ZIP) 13. Type of Report & Period Covered Final

Agency Code

15. SUPPLEMENTARY NOTES

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

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or

literature survey, mention it here.) This presentation has three technical parts, and ends with audience

participation and recommendations. First, a brief discussion of fire

growth in a compartment is presented, showing why we need full scale

tests, or a mathematical model adequately simulating such growth. The

second part of the talk describes what several Federal agencies and

their grantees are doing to bring about the necessary engineering and

mathematical capability for this modeling. The third part illustrates

some problems that may be of interest to fire protection engineers that can be solved relatively simply by using fragments of the modeling

capability now available.

Then a discussion was held with the audience to determine modeling

needs. Should we provide a series of simple models, each applicable to a limited range of problems, or a major comprehensive model, accessible

from a computer terminal, that will solve a very wide range of problems?

The audience decided both were needed.

17. KEY WORDS r® /X to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name;

separated by semicolons)

Fire; fire engineering; fire safety; mathematical modeling; modeling application,

18. AVAILABILITY [3 Unlimited

I I For Official Distribution. Do Hot Release to NTIS

[7j Order From Sup. of Doc,, U.S. Government Printing Office, Washington, DC

20402, SD Stock No. SN003-003-

Order From National Technical Information Service (NTIS), Springfield,

VA. 22161

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

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21. NO. OF

PRINTED PAGES

44

22. Price

$6 .00

USCOMM-DC
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