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t&MM \nc:r.; MBS

PUBLICATIONS

NBSIR 81-2440

Modeling of NBS Mattress Tests

With the Harvard Mark V Fire

Simulation

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

Issued January 1982

1U0

,1156

61-2440

1982

c, 2

IONAL BUREAU OF STANDARDS

NBSIR 81-2440

MODELING OF NBS MATTRESS TESTS

WITH THE HARVARD MARK V FIRE

SIMULATION

Kiticnil Bureau ef Standards

Library, E-lt Admin, Bld|.

f€t l 4 1982

Rotate - - bre

auoo

(

J

r>°'

C - f

John A. Rockett

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

January 1 982

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

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Director

TABLE OF CONTENTS

Page

LIST OF TABLES iv

LIST OF FIGURES v

LIST OF SYMBOLS ix

Abstract 1

1. INTRODUCTION 1

2. GENERAL DISCUSSION OF THE HARVARD MODEL 2

3. SECONDARY OBJECT SIMULATIONS 4

4. INITIAL MATTRESS SIMULATIONS 7

5. PROGRAM AND INPUT DATA CHANGES STIMULATED BY THE INITIAL

SIMULATIONS 9

6 . SECOND SET OF MATTRESS SIMULATIONS 13

7. ADDITIONAL MATTRESS SIMULATIONS 16

8 . ROOM "B" SIMULATIONS 16

9. CONCLUSIONS 18

10. REFERENCES 20

APPENDIX I. The Effect of a Thin Char Layer on Pyrolysis Rate ... 23

APPENDIX II. Hot-Cold Gas Mixing at the Vents 25

APPENDIX III. Door Flows 30

TABLES 31

FIGURES 33

iii
LIST OF TABLES

Page

Table 1. The computed effect of adjacent, connected rooms 31

Table 2. The effect of a change of the smoke parameter, FS,

mattress M01 32
LIST OF FIGURES

Figure

Figure

Figure

Fibure

Figure

Figure

Figure

Page

1. Burning rate versus time for 5 standardized

wastebaskets. Also shown are the average

burning rate versus time and the burning rate

to be simulated 33

2a. Calculated temperature versus time for the

standardized wastebasket burned alone.

Temperature and time scales are the same as will be used for mattress data 34

2b. Mass loss rate versus time for wastebasket

simulation. Vertical scale 12 X that used for

mattress data 34

3. Room upper gas temperature versus time for

mattress M01 (data from [1, figure 17]).

Also shown is the calculated hot layer

temperature using Harvard default values

except as noted in the text 35

4. Room upper gas temperature versus time

for mattress M05 (data from [1, figure 21]).

Also shown is the calculated hot layer

temperature using Harvard default values

except as noted in the text 36

5. Room upper gas temperature versus time

for mattress M09 (data from [1, figure 25]).

Also shown is the calculated hot layer

temperature using Harvard default values

except as noted in the text. The small hump

at 450 seconds on the calculated temperature

curve is caused by ignition and burning of

the pillow. At this point the mattress

burned, has terminated 37

6. Room upper gas temperature versus time for

control mattress (data from [1, figure 16 J )

.

Also shown is the calculated hot layer

temperature default values except as noted

in the text. The small hump at 500 seconds

on the calculated temperature curve is caused

by the pillow burning. At this point the

bedding is burned out. This peak occurs slightly later than for the other mattresses

due to the slower rate of growth of this

relatively small fire 38 v
LIST OF FIGURES (Continued)

Page

Figure 7. Mass loss rate as a function of time for

mattress M05 (data from [1, figure 13]).

Also shown is the calculated mass loss rate

using the Harvard default values except as noted in the text. The off-set of the two curves is not considered important, the

difference in peak burning rate and rapid

drop of the calculated curve are 39

Figure 8. Semi-log plot of experimentally determined

fuel mass and mass burning rate for mattress

M05 (data from [1, figure 13] and numerical

integration). Mass scale to the left,

burning rate scale to the right 40

Figure 9. Remaining fuel mass plotted against mass burning rate for mattress M05. Straight line

corresponds to a "late burning constant" of

100 seconds (10 g/sec/kg fuel remaining)

Figure 10. Remaining fuel mass plotted against mass burning

rate for mattress M09. Straight line corresponds

to a "late burning constant" of 100 seconds

(10 g/sec/kg fuel remaining) 42

Figure 11. Remaining fuel mass plotted against mass burning

rate for mattress M02. Straight line corresponds

to a "late burning constant" of 100 seconds

(10 g/sec/kg fuel remaining) 43

Figure 12. Location of "Room A" within the NBS Fire Test

Building showing its relation to other,

connecting rooms and the fire gas exhaust

system 44

Figure 13. Upper gas temperature versus time for mattress

M01 (data from [1, figure 17];. Also shown is

the calculated hot layer temperature using

default values except as noted in the text.

Simulation includes door mixing 45

Figure 14. Height versus room temperature for mattress

M01 (data from [1, figure 23]). Also shown are

the calculated vertical distribution with and

without door mixing and for the door opening

narrowed to 71 percent of its actual width 46

vi
LIST OF FIGURES (Continued)

Page

Figure 15. Upper gas temperature versus time for mattress M05

(data from [1, figure 21]). Also shown is the

calculated hot layer temperature with door mixing

using Harvard default values except as noted in

the text 47

Figure 16. Upper gas temperature versus time for mattress M09

(data from [1, figure 25]). Also shown is the

calculated hot layer temperature with door mixing

using Harvard default values except as noted in

the text 48

Figure 17. Upper gas temperature versus time for control

mattress (data from [1, figure 16]). Also shown

is the calculated hot layer temperature door

mixing using Harvard default values except as noted in the text. The small hump at 430 seconds

on the calculated temperature curve is caused by

the pillow burning. At this point the bedding

is burned out 49

Figure 18. Height versus room temperature for mattress M05

(data from [1, figure 32]). Also shown are the

calculated vertical distribution with door

mixing and door narrowed to 71% of actual width ... 50

Figure 19. Mass loss rate as a function of time for mattress

M05 (data from [1, figure 13]). Also shown is

the calculated mass loss rate using the Harvard

default values except as noted in the text. The

offset of the two curves is not considered

important 51

Figure 20. Extinction coefficient computed from light

attenuation measurements taken in the doorway,

0.61 m below the ceiling, room A, mattress M05.

Also shown is the computed extinction coefficient for the upper gas layer with FS = 0.241 ... 52

Figure 21. Comparison of measured and calculated heat

flux at a target separate from the fire,

mattress M05. Experimental data from [1,

figure 43] 53

Figure 22. Effect of fire-target spacing on heat flux to

the target, computed for mattress M05 at time

of peak burning 54

vii
LIST OF FIGURES (Continued)

Page

Figure 23. Upper gas temperature versus time for mattress

M02 (data from [1, figure 18]). Also shown is

the calculated hot layer temperature with door

mixing using Harvard Code default values except

as noted in the text 55

Figure 24. Upper gas temperature versus time for mattress

M04 (data from [1, figure 20]). Also shown is

the calculated hot layer temperature with door

mixing using Harvard default values except as noted in the text 56

Figure 25. Upper gas temperature versus time for mattress

M06 (data from [1, figure 22]). Also shown is

the calculated hot layer temperature with door

mixing using Harvard default values except as noted in the text 57

Figure 26. Room B (ventilated) upper gas temperature for

mattress M05, data from [1, figure 21] and values

computed with the room door fully open and closed

to several widths 58

Figure 27. Room B (un-ventilated , augmented area) upper gas

temperature for mattress M05, data from [1,

figure 21] and values computed with the room door

closed to 0.2 m width 59

Figure 28. Calculated height of the lower surface of the hot

gas layer for several cases , room B and room B

(augmented) . Note that the layer descends much

more rapidly for the smaller area (actual) room B as compared to the augmented room 60

Figure A2 . 1 Room radiative heat flux calculation showing the

equations to be solved and the geometric relation

of the terms 61

Figure A3.1 Door mass outflow rate as a function of heat

release rate. Points from Steckler [A3.1], curve calculated 62

Figure A3. 2 Door mass outflow rate as a function of door

width. Points from Steckler [A3.1], curve calculated 63

viii
LIST OF SYMBOLS

A

c *H

A

v

C

D

d

e

FL1

FL2

FL3

FS

FSINIT

f

g

h

I

K

k

k

k

m

ra

cool layer surface area, m

hot layer surface area,

total area of that part of the vents above the hot-cool gas

Interface,

orifice flow coefficient = 0.68

height of the hot-cool interface in the room, m

char thickness, m

emissivity

subscripts: C cool gas layer

F floor and lower walls

H hot gas layer

W ceiling and upper walls

2 radiant flux exchanged between the hot layer and the ceiling, W/m

2 radiant flux exchanged between the hot and cool layers, W/m

2 radiant flux exchanged between the cool layer and the floor, W/m

mass of smoke produced per unit mass of fuel pyrolyzed

value of FS for fuel burned in ambient air

dimensionless factor in burning rate expression, defined in

section 5 of the main text

acceleration of gravity, m/s^

height above fuel surface of apparent flame radiation source, m

2 radiant flux, W/m

subscripts: 1 - upward flux in hot layer

2 - downward flux in hot layer

3 - upward flux in cool layer

4 - downward flux in cool layer

coefficient = 1/2 used in door mixing correlation [15]

dimensionless constant, section 5, main text

extinction coefficient, m

^

char thermal conductivity, appendix I, W/mK

fuel mass, kg mass flow rate in through the lower part of a vent, kg/s

xx
LIST OF SYMBOLS (Continued)

m

m

mass transfer rate from hot to cool layer by mixing, kg/s m mass burning rate, kg/s m

P

N

mass burning rate calculated from heat flux incident on fuel, kg/s

height of the neutral plain in the doorway, m

n exponent

R = 9/ (8C Ri), used in appendix II

Ri Richardson number

r dimensionless constant

r radius, m

subscripts: F radius of fire

L "radius" of hot-cool gas layer interface

S radius of fuel surface

STOIC1 value of XGAMMA for ambient air

STOIC2 value of XGAMAS for ambient air

T temperature, K

subscripts: A ambient air

C cool gas layer

F floor

TECPR

H hot gas layer

W ceiling

2 flame radiation incident on the cool layer, W/m

TECZR radiant energy gain by the cool layer

TEPZR total flame radiation

t o characteristic time, s u

.

1 V

velocity of gas entering room, m/s

layer volume, m^ w width of room wall containing door, m

Wo width of door, m WL

2 area of interface between hot and cool gas layers, m

XGAMMA grams of air which must be entrained by a buoyant fire

plume to burn a gram of fuel

XGAMAS stoichimetric air/fuel ratio

x
LIST OF SYMBOLS (Continued)

x 4R/ (9 + 4R) dummy variable used in Appendix II

z =4 kV/A used in Table 2 ZUFI value of ZUFZZ for ambient air

ZUFZZ extinction coefficient for flame, m

^

ZYCO mass fraction of oxygen in the cool, lower gas layer

Greek letters

a Stephan-Boltzman constant

gas in the hot layer

ambient air

density of

density of

xi

MODELING OF NBS MATTRESS TESTS WITH THE HARVARD FIRE CODE

John A. Rockett

Abstract

NBS burned eleven mattresses made up with bedding in

two different rooms, typical of a residential bedroom and

a nursing home patient room, respectively. Seven of the

mattresses flamed and burned vigorously, the other four

were of a construction or so heavily flame inhibited that

they only smoldered. The burning behavior of the seven

that flamed was modeled with the Harvard mark V fire

simulation. The experimental burn behavior for tests

conducted in one room was well reproduced using only total

weight of combustible, surface area and heat of combustion.

Smoke production values were found to have little effect

on the predicted behavior except for the smoke production

itself. Fires in a second room, whose ventilation was intentionally restricted by the configuration of the

adjoining space, could not be as well reproduced by the

present, single room fire model.

During this study several changes were made to the

simulation. The most significant change was the inclusion

of mixing of the hot, exiting fire gases with the cold

incoming air. As a part of this, the inter-layer radiation

exchange was reformulated to include the effect of smoke

contamination of the lower layer. The reformulation of

the radiation model had a marked effect on the predicted

upper layer gas temperatures, generally improving the

quality of the simulation.

1. INTRODUCTION

Over a period of several years, beginning in mid 1976, NBS conducted

a number of tests involving mattresses. These included burning complete

beds in a room [1], and testing of samples cut from mattresses in "benchscale tests" [2]. During this same period. Harvard University had been

developing, under a series of grants from NBS, an analytic room fire

simulation [3-6]. A major input to the development of this simulation

was a series of full scale bedroom fires conducted by the Factory Mutual

Research Corporation between 1973 and 1975 [7-9]

.

The fires used by

Harvard for testing the operation of the simulation have been these or other, more idealized bed-like fires burned at Factory Mutual as a part

of the same program. This report compares the results from running the

Harvard simulation in various configurations with the corresponding NBS

full scale test results.

1
2. GENERAL DISCUSSION OF THE HARVARD SIMULATION

The Harvard Fire Simulations used for this study were interim versions

issued to NBS during 1980-1981 and designated as H04 and H05. A version,

designated H05.1, was an NBS modification of H05. The simulation

represents fire in a single room with vents opening directly to an infinite plenum. The program requires that initial values for a number

of variables be set. For all of these, values are provided internally by

the program. However, any of these can be altered by the user at his

discretion through the input routines. In default of the user making a change, the preset value is used. Following common computer terminology,

the unaltered, preset values are referred to in this paper as "default

values". The input routines allow for entering the following room data:

Geometric

:

Length m

Width m

Height

Number of Objects

Vents

:

Number of Vents

(for each vent)

m

Width m

Height m

Transom Depth m

Walls

:

Thickness m

Thermal Conductivity W/m °C

Specific Heat J/kg °C

Density kg/m^

Other

:

Ambient Temperature K

All these data were available for both rooms in reference [1] and the

values appropriate to the NBS rooms were used.

The full-scale NBS tests to be simulated were conducted in two

different rooms. Room A was 3.4 m wide, 3.5 m deep and 2.44 m high. It

was ventilated by a single opening, a door 0.91 m wide by 2.13 m high

(door transom 0.31 m deep). Room B was 4.22 m wide, 3.35 m deep and

2.44 m high with a single door 1.07 m wide by 2.03 m high (door transom

0.41 m deep). The walls and ceilings were cement-asbestos board [1,

p. 11].

2
The Harvard fire simulation allows up to five objects per room with

the possibility of one object igniting another. In the simulation as received, level 4’s, the only mechanism for secondary ignition was by

radiant heat. A simple change, now incorporated as a standard feature

of the simulation, allows ignition of contiguous objects by flame spread.

The fire simulation allows entering the following data for each

ob j ect

:

Geometric

:

(coordinates relative to the front, left, lower room corner)

x coordinate of object center m

y coordinate of object center m

z height of object top surface m

Thickness m

Initial burning radius m

Maximum burning radius m

Thermal

:

Initially ignited or not

Type of fire: gas burner

pool

growing

special

Effective air/fuel ratio default value

Stoichiometric mass ratio

Specific heat

Density

Surface emissivity

Fraction of heat of combustion actually released

Heat of combustion

Heat of vaporization

Initial fuel mass Temperature at ignition

Temperature at onset of pyrolysis

CO2 mass evolved/fuel mass burned

CO mass evolved/fuel mass burned

Smoke mass evolved/fuel mass burned

HO mass evolved/ fuel mass burned

Flame spread parameter

14.45

9.85

19.00 J/kg K

48 kg/m3

0.98

0.65

2. 87x10 ' J/kg

2 . 05x10° J/kg

6.852 kg

727 K

600 K

1.504

0.013

0.241

0.714

0.0109

For all of these, the default values built into the simulation are based on the polyurethane mattresses burned in the Home Fire Project room

burns [7-9]. Several of these data elements require explanation:

1. In the simulation, all objects burn as circular fires. A

growing fire starts at the center of the object with the given,

initial radius. The fire radius increases with a velocity that is

related to the heat flux incident on the fuel surface and is a linear

function of the flame spread parameter, until it reaches the specified

maximum radius [5], The maximum fire radius is chosen to yield a

3
burn area equal to the actual maximum burning area for the fully

involved object, regardless of its shape. The mass burning rate per

unit area depends on the heat flux incident on the fuel.

2. The stoichiometric mass ratio (default value 9.85) depends on

the fuel chemistry and is the mass of air needed to fully burn a unit mass of fuel under ideal conditions. The effective air/fuel

ratio (default value 14.45) is the amount of air which must be

entrained by a buoyant diffusion fire plume to burn (as fully as possible in such a flame) a unit mass of fuel. This exceeds the

stoichiometric mass ratio because, due to the poor mixing in the

turbulent plume, quite a bit of the air entrained never comes in

contact with fuel. Complete combustion is seldom approached in

diffusion flames. The degree of completeness is represented through

the fraction of heat of combustion actually released (default value

0.65).

The Harvard simulation, as received, provided algorithms for three

types of fire, all assume a smooth, horizontal fuel surface: (1) A gas

burner. For this the burning rate is set by the gas flow rate, specified

as input in addition to the above list. (Other, nominal input items not

applicable to a gas burner are ignored.) (2) A pool fire. This is a fire of fixed area, whose burning rate is set by the heat flux reaching

the fuel surface. (3) A growing fire. This is a fire whose area is a function of time and whose burning rate per unit area is set by the heat

flux reaching the fuel surface. For both growing and pool fires, the

fuel pyrolyses at a fixed temperature with a prescribed latent heat of

vaporization. Burning stops when all the fuel is exhausted. To prevent

numerical problems and better simulate actual burning behavior, burn-out

does not occur abruptly but is smoothed over a short time. The time

interval for burn-out is built into the algorithms.

In principal, if the burning behavior of the object to be simulated

will not be well represented by one of these three fire types, a special

algorithm for that object should be supplied. Another modification introduced to the NBS versions of the Harvard simulations was the provision of

a mechanism for calling for a fourth fire type, a Special Fire. With

this option the individual user is free to construct his own burn algorithm

as needed. This will be discussed later.

3. SECONDARY OBJECT SIMULATIONS

The simulations were to include several objects in the test rooms. For each test, the rooms were furnished with a bed and wastebasket. The

wastebasket was polyethylene, 282 g weight, 248 mm x 178 mm x 254 mm

high filled with a "standardized" fuel weighing 443 g for a total weight

of 725 g [1, table 6]. The bed was a steel frame with an open wire grid

on which the mattress and bedding to be tested were placed. The mattress

itself varied from test to test but each was "made up" with an identical

covering consisting of a cotton drawsheet, 2 50-50 cotton-polyester blend

4
sheets, and an 86 percent cotton, 14 percent polyester spread. These

covers weighed 2.67 kg. At the head of the bed was a single polyurethane

pillow with cotton cover, polyvinyl chloride protector and 50-50 cottonpolyester pillow case. The pillow and its covers weighed 1.04 kg [1,

table 5]

.

Figure 1 shows the result of burning five of the "standard wastebaskets", two burned by Babrauskas at University of California, Berkeley,

and three at NBS [10].* Also included on figure 1 are the average

burning rates at each of the nine times when data was recorded. The

numerical simulation of the wastebasket would have a more regular

behavior. This was selected by a further smoothing of the averaged

experimental data and is also shown on the figure. Note that the peak

burning rate of 1.64 g/s and integrated fuel consumption results in

only 350 g burned. Babrauskas indicated that the wastebaskets

were not fully consumed, but left a substantial residue of sticky char

[11]. The fuel weight used for the simulation, 350 g, rather than 725 g,

is consistent with the behavior illustrated in figure 1 and is believed

to represent the situation more correctly. Note that this average

behavior, which was arrived at from somewhat sketchy data prior to publication of [10], is slightly different from that found by analysis of

more complete data.

A wastebasket fire would not fall naturally into one of the three

fire types for which algorithms are supplied. However, it was possible

to find a set of input parameters for a growing fire which produced the

desired effect. Since modeling wastebasket fires was not a major

objective of this study, the somewhat artificial parameters needed to

accomplish this were not considered significant. The non-default values

used were:

Geometric

:

X 3.21 m

y 1.65 m

z 0.254 m

Thickness 0.25 m

Maximum Radius 0.1185 m

lal

:

Density 35

5

lcg/m

Heat of Vap. 4.0510 J/g

Initial Mass 0.35 kg

*The fire load in the Berkeley wastebaskets was not quite the same as in the mattress tests.

5
Figure 2 shows the calculated temperature history for the wastebasket

burned alone. The mass loss rate rises rapidly and, at 50 seconds,

stabilizes at a constant value. It remains at this value until 240 seconds

after which the mass loss rate drops rapidly. The available fuel is

exhausted at 270 seconds. This reproduces quite closely the smoothed,

average behavior illustrated on figure 1.

The wastebasket location was chosen to cause ignition of the bedding

30-40 seconds after the wastebasket ignited. The y and z values given

above were varied slightly to give consistent ignition times for the

various size and thickness mattresses.

It was reasonable to expect the pillow to be simulated fairly well by

the growing fire algorithm. Its location was at the "head of the bed".

The following non-default values were used for the initial simulations.

Geometric

:

X 2.64 m

y 3.035 m

z 0.76 m

Thickness 0.15 m Maximum radius 0.488 m

Thermal:

Density 19.32 kg/m

Heqt of combustion 2.15x10 J/kg

Initial mass 1.04 kg

Fire spread parameter 0.2541x10"^

In addition to the wastebasket, the pillow and the mattress, one other object was placed in the room. The purpose of this was to force

the program to calculate and tabulate the heat flux at this object. Its

burning behavior was not considered; its ignition temperature was set

sufficiently high that it would never ignite. This object was positioned

to record the heat flux near the door. It was located at:

Geometric

:

x 2 . 16 m

y 0.01 m

z 0.75m

For a few cases, to be discussed separately this target object was moved to other locations.

It should be pointed out that inclusion of this target object

occasionally caused convergence problems late in the fire, after most or all the fuel had burned out. It has not yet been conclusively determined

why this happens. More often than not the problem didn't arise, making

its diagnosis more difficult. To complete the calculation to the desired

final time, when these troubles occurred, the target (fourth) object was

6
removed and the case re-run. This usually worked. Problems also arose early in the calculation from time to time. These did not seem to be

related to the fourth object. These problems could be eliminated by a seemingly trivial change, usually in location of one of the secondary

objects (wastebasket location changed a few millimeters —which changed

bedding ignition time a second or two, or the pillow—which changed its

ignition time slightly).

4. INITIAL MATTRESS SIMULATIONS

The mattresses tested are designated as M01 through M10 in reference

[1]. The same notation is used here. Three of the mattresses were

basically polyurethane foam construction, M01, M05, and M09 [1, table

8]. They differed in details of construction, type and amount of flame

retardants, and total weight of combustible material. Nevertheless,

they might be expected to burn in a manner similar to those tested by

Factory Mutual. Accordingly, initial runs were made to simulate the

burning of these three mattresses using the program default values for

all the mattress variables except location, size, weight and heat of

combustion. The weights used were those given in [1, table 10]. They

were increased, in each case, by 2.67 kg to account for the bedding. The

heat of combustion values used were weight averaged for the bedding and

mattress materials. The cotton-polyester value from reference [2, table

10], 21.2 MJ/kg was used for the bedding and the total heat value from

reference [2, table 11] for the mattress. The fraction of this heat

actually released, x> was taken from reference [2, table 11], again for

the mattress in question. One additional run was made in this series to

simulate the burning of the "Control" mattress, an inert fiberglass bun

(no combustible binder in the fiberglass) covered with the standard bedding

(designated as MOC).

The values used for all the mattresses were:

Geometric

:

X 2.64 m

y 2.28 m

z 0.61 m

Maximum Radius (see discussion below)

The maximum radius chosen for mattresses M01 and 5 corresponds to

twin size mattresses. M09 was cot size and a smaller radius was used.

Note, however, that M01 and 5 were not exactly the same size. The

maximum radius and thickness were varied in accordance with these small

differences in size. The result, except for M09, was probably not

significantly different than would have been found by using the same values for all the mattresses. The "Control" mattress had the same area as was used for M05; its thickness was taken to be that of the

bedding alone, 0.0033 m. The values used were:

7
Thermal:

Initial Mass Heat of Comb. X Effec. Heat of Comb.

M01 16.27 kg 28.2 MJ/kg 0.84 23.7

M0 5 8.57 kg 26.7 MJ/kg 0.79 21.1

M0 9 5.87 kg 25.8 MJ/kg 0.74 19.1

MOO 2.67 kg 21.2 MJ/kg 0.74 15.7

Note that the effective heats of combustion (heat of combustion

times x) vary only about 20 percent from the average for these three

mattresses while the total mass of combustible varies by almost a factor

of three from the lightest to the heaviest mattress. Thus, this first

set of simulations mainly demonstrate the effect of varying the amount

of combustible on the bed. It should also be born in mind that, although

these mattresses varied in type and amount of flame retardant, we do not,

currently, have any technically sound method for simulating the effect

of retardants. All these mattresses burn alike as far as the simulation

is concerned.

The first simulations used the standard growing fire algorithm and

did not include mixing of the upper and lower gas layers at the door.

The results of these simulations are compared with the test values in

figures 3-6. In all these figures, the temperature of the gas near the

room ceiling has been compared with the simulation's upper layer temperature,

a single average temperature for the gas in the entire upper part of the room. Note first, that the computed temperature (up to 200 seconds) is

controlled by the wastebasket, although the bedding ignites in each case

at about 35 seconds. Note also that in each case the simulation shows a rapid temperature rise at about 300 seconds as the bedding and mattress

become the dominant source of heat. The experimental and computed time

for rapid temperature rise are quite similar for M01 . But for M05 and

M09 the experimental temperature rise occurred quite a bit later than

for the simulation. The simulation of the control, M0C, figure 6,

appears qualitatively different than the test. Referring to the text

and figures in reference [1], from which the data used here were taken, we see that there was generally quite a lot of variation from test to

test with nominally similar mattresses, especially in the time when rapid

temperature rise occurred. Babrauskas [11] attributed this to variations

in the way in which the bedding became involved. He also said that the

bedding seemed to control the rate of development of the fire while the

mattress determined the severity of the fire. In our simulations there

is, of course, consistency in the way in which the fire develops.

Throughout this study differences in the time to reach maximum upper gas

temperature were found for the simulation as compared to the test data.

This difference was not considered significant in view of the scatter

in the experimental data in time to reach peak temperature. The value

of the peak temperature was, however, quite reproducible between tests

and was considered important to assessment of the quality of the simulation.

8
5. PROGRAM AND INPUT DATA CHANGES STIMULATED BY THE

INITIAL SIMULATIONS

These results were only moderately encouraging, and, on looking more

closely, definite problems appear. Figure 7 compares the experimental

and calculated rate of mass loss for mattress M05. It was typical of

all four of this first group of simulations. The peak mass loss rate was more than twice the experimental value and the burn-out, after the

peak mass loss rate occurs, is far too rapid. With this high maximum

burning rate, it is not surprising that the peak calculated temperatures

exceed the experimental values; for M01, the lower calculated maximum

temperature arises for a different reason which will be discussed later.

There are several reasons that the simulation might find too large a peak

burning rate. First, the heat of pyrolysis could be wrong, since burning

rate is directly proportional to heat of pyrolysis. For heat of pyrolysis

alone to account for the high burning rates, it would have to be off by a factor of about 2. Because no measured values were available for these

mattresses, the default values were used. It seems highly unlikely that

this could differ so much from the actual values. Second, burning area

could be wrong. The Harvard simulation assumes that the fire grows as a circle until limited by the (input) maximum burning area. Burning then

continues at that area until all the fuel is exhausted. But the mattresses

are relatively thin fuels. Before burning has stopped in one location,

complete burn-through may have occurred at another location where the

fire has been burning longer. This would be especially true for the

bedding. The idea was explored using a special fire algorithm built by

modifying the standard growing fire algorithm. The new routine provided

for both a circular, growing fire and also a central, circular non-burning

region which grew as the fuel became locally exhausted. This produced

some effect on peak burning rate, but not nearly enough to account for

the discrepancy. Furthermore, it had almost no effect on the too rapid

drop in burning rate after the peak occurred. The slow decay of the

fire could possibly also be simulated by accounting for the effect of a circular fire burning on a rectangular bed. After the centrally located

fire radius reached the smaller dimension of the bed, two circular arc fires would remain, the arc length decreasing with further growth. When

the radius reached the larger dimension, only four small fires would

remain. The arc lengths of these would also decrease with time. This was simulated though the algebra became somewhat complex. It helped

but not enough. As a part of this algorithm, provision was made for two

fuel layers, one, to be the bedding, lying on top of the other, the

mattress itself. The fire parameters of these two layers were entered

separately. Thus the same bedding data could be used for all mattresses.

In this way fire growth was controlled by the bedding parameters alone

but, since peak burning occurred after most or all of the bedding layer

had been burned off, peak burning rate was controlled by the mattress

parameters. Finally, the rate of pyrolysis would be wrong if the amount

of heat reaching the virgin fuel were wrong.

9
Because of the known presence of retardants in some of the mattresses,

and because it has been observed that flame retardants tend to increase

char at the expense of volatiles, it seemed worthwhile to explore the

possibility that the burning behavior, late in the fire, was modified

as a result of char formation. Accordingly, the laminated fuel algorithm

was further modified to include the effect of an inert char layer, formed

as the fuel was burned. The char layer impeded the flow of heat into

the fuel and its increased surface temperature increased radiation losses

from the fuel. Appendix I gives a numerical example of the effect of an idealized, inert char layer such as might be simulated by the empirical

changes detailed here. It shows that, to produce the observed effects,

i.e., a decrease in burning rate of mattress M05 from 118 to 46 g/sec,

a homogeneous char layer would be very thin (about 1/2 mm). So thin a layer is seldom homogeneous and more complex geometries are awkward to

model. Implicit in using char to explain the burning rate behavior is

the assumption that the char formation (or burning surface area) is

somehow related to the fuel mass remaining. This algorithm has a fairly

sound physical foundation, but had become quite complex and required

additional parameters as input for which there were no data. Thus in

practice, its use was quite empirical. It must be remembered, too, that

the growing fire algorithm, from which it derived, is essentially an empirical correlation of experimental data. A much simpler and just as logical approach would be to alter the original empirical correlation.

Figure 8 is a semi-log plot of experimental data for mattress M05.

One curve gives the fuel mass (left scale) versus time and the other mass burning rate (right scale) versus time. In figure 9 this data is replotted

with fuel mass plotted against mass burning rate. Note that, after the

peak burning rate has occurred, burning rate becomes roughly proportional

to fuel mass remaining. In this example the constant of proportionality

is 10 g/sec/kg fuel remaining. (Straight line on fig. 9). Figures 10

and 11 show similar plots for two other mattresses, one, M09, has a urethane

core and the other, M02, is an inner spring construction whose principal

combustible is polyurethane padding. They do not show quite as "clean"

a trend as figure 9, but they are generally consistent with it. Now,

for quite another reason—to avoid numerical problems with a too abrupt

fuel burn-out—Harvard simulation has instructions which accomplish

precisely this burning rate behavior. The standard growing fire algorithm

(and pool fire too) include a relation which "adjusts" the pyrolysis rate

according to:

m = m (1 - exp (-m/ t m )) P op

where

m = the adjusted pyrolysis rate m = pyrolysis rate computed from (non charring) fuel properties

^ and energy flux to the fuel surface

m = remaining fuel mass

t Q = a time constant set equal to 2 sec. by Mitler

10
When m is large and m t small, m = m , but near burn-out, m becomes

p o p

small and this expression approaches

m = m/t . o Thus, the observed behavior of mattress M05 could be represented by

changing t from 2 seconds to 100 seconds. To test this idea a new

special fire algorithm was set up which differed from the standard growing

fire only by making t an input parameter. After a few preliminary

trials, a further change was made to decouple the time, t , at which

the shift (from energy flux determined pyrolysis to mass remaining determined pyrolysis) occurred and the proportionality constant applicable

after the shift. This was done by setting

f = m/t m

o p

k = 1 - (1 - r)tanh(l/f) m = m k(l - exp(-f))

P

Note that when f is large k = 1 and m = m , but when f is small k = r and m = m rf = mr/t . The next set of simulations presented here were

run with ? = 40 sec? and r = 1/2 (equivalent to a late fire burning

constant of 80 sec., somewhat less than the M05 indicated value of 100

sec.*)*

Experiments by Kashiwagi [12] provide an alternative explanation for

the Harvard code’s over estimation of pyrolysis rate. His data suggest

that a substantial fraction of the flame radiation directed toward the

fuel is absorbed by cool fuel vapor just above the surface. If 60

percent were absorbed, the calculated and observed pyrolysis rates for

mattress M05 would agree. Mitler had partially compensated for this

effect by his choice of flame temperature (somewhat lower than that

measured by Orloff [13]) in early versions of the Harvard code. The

more recent versions, including level five, use an average flame temperature of 1260 K which agrees with Orloff but the simulation does not

include radiation blockage. However, while radiation blockage is certainly

present and is probably of about the right order of magnitude, it would

not, alone, give the observed dependence of burning rate on mass remaining

late in the fire. In any event, we do not yet have available any data

on radiation absorption coefficient for raw fuel at pyrolysis temperatures,

nor a satisfactory model for the radiation blockage so, again, an empirical

approach is indicated for the present.

The empirical approach seems a simple way around a difficulty. It

does not, however, provide guidance in predicting burning behavior of

char-forming materials of a distinctly different class.

*80 seconds was chosen after a somewhat less careful study of the data

than that shown in figures 8-11 but, having started with 80 seconds, it was retained. As will be seen later, 100 seconds might have been better.

11
The above discussion deals with the too high burning rate. This was found for all the first set of simulations, but not all produced

too high an upper gas temperature. For M01, although the peak temperature

pyrolysis rate was high, the peak temperature was too low. Examination

of figures 27-36 of reference [1] showed that, for all the mattresses

which burned vigorously, the gas temperature in the lower part of the

room was well above ambient. This kind of behavior has often been found

and is attributed to mixing of the outflowing, hot combustion products

with inflowing cool air close around the vents [14-16]. From reference

[1, figures 27-36] it is apparent that considerable mixing may have

occurred (at the room door) between the hot combustion products leaving

and the cold incoming air. This is most obvious for the larger fires,

for example M01. The Harvard simulation, level five and earlier, does

not include this effect. Because mixing seemed important, changes were made to add mixing of the exiting and entering flows at the door.

Mixing results not only ip heating of the air in the lower part of the

room but also its contamination with combustion products. When mixing

is large, this can result in a significant radiant energy exchange

between the upper hot layer and the lower warm layer. This effect was

also included. A more detailed description of these changes is given in

appendix II. The door mixing modified simulation is referred to as H051

.

The room geometry shown in [1] is not strictly correct for room A.

The room itself is shown correctly, but its door did not open directly

to a large exhaust plenum as might possibly be inferred. Rather it

connected to another room which, in turn, exhausted into a 21 foot long

corridor connecting to the exhaust hood. The complete geometry is shown

in figure 12, taken from King-Mon Tu [17], Although he concluded that the

effect of the adjoining rooms was small, the state of knowledge at the

time he made his measurements would not necessarily have led to detection

of some effects.

To estimate the effect of the complete room-corridor system vis-a-vis

an isolated room, Tanaka’s multi-room fire simulation [18] was run for

two pairs of cases: room A by itself and room A plus its adjoining room

and corridor, each for two different fire sizes. Tanaka’s plume model,

which is valid for small area fires (his primary concern), under-estimates

the entrainment for large area fires. The plume algorithm was changed

slightly to correspond to that used in the Harvard simulation*. The

results of the two pairs of calculations are summarized in table 1.

Note that the flow for the complete room-corridor system was about 75

percent of the flow for the isolated room.

*This raised the question of which plume model was the better. A

partial answer is provided in appendix III.

12
To simulate the effect of the adjoining room and corridor on the

fire behavior as computed by the Harvard simulation, the room door was made narrower. The amount of narrowing to be used was based on the

following rather intuitive idea: Since the two doors between the fire

room and the vent (see fig. 12) were the same size, a uni-directional

flow would produce equal pressure drop across each door. Removing one

door, without changing the total pressure difference available, would

cause the flow to increase as the square root of the pressure drop across one door, now double its previous value. Thus, to reduce the flow to

its previous value, the door area should be reduced to 70.7 percent of

its original value. This area reduction was accomplished by narrowing

the door without changing its height. The result of this 70.7 percent

change and also a change to 50 percent of the actual door width are summarized at the bottom of table 1. Note that, for the 70.7 percent

door, the flow change is quite close to that predicted by Tanaka's model.

In all the remaining room A simulations to be discussed the door width

was 0.643 m, 70.7 percent of the actual width.

One further change was made at this point. Babrauskas pointed out

[11] that, in the Harvard simulation, the heat released in the plume is

the product of the fuel mass loss rate times the heat of combustion,

adjusted to ambient temperature, but based on fuel supplied in a gaseous

state. Some of the energy released in the plume is radiated away and a fraction of this is used to pyrolyze the fuel. The heats of combustion

given in [2, tables 10 and 11] assume the fuel is present as a solid.

Thus the heats of combustion taken from these tables should be increased

by the heat of pyrolysis for use with the Harvard model. This represents

about a 7 percent increase in the heat of combustion. Further, experience

with the laminated fuel model, discussed above, had shown that most of

the bedding had burned off prior to the time of peak burning. Accordingly,

the weight averaged heat of combustion was no longer used, rather the

mattress values from [2, table 11] were used. To make the values consistent

with the Harvard usage, these were increased by adding to them the Harvard

default value for the heat of pyrolysis.

6. SECOND SET OF MATTRESS SIMULATIONS

After making the program and input data changes discussed above, a second set of calculations were made. Figure 13 shows the temperaturetime comparison for the H051 simulation corresponding to the simulation

shown in figure 3. The peak temperature was still low, but, in this

case, the peak burning for mattress M01, which had been 146 g/sec., was now 97.32 g/sec. The drop in temperature after the peak, which had been

too abrupt, was now slower. Figure 14 shows a comparison of the vertical

temperature distribution as measured at three locations away from the bed

and calculated with and without mixing. Note that the lower gas temperature had risen much more than the upper. This is due to the rapid increase

with temperature of radiation loss from the hot layer. Without burning in

the upper layer, another effect that the present fire code does not include,

it may be difficult to match the upper gas temperature, although the method

13
of calculating radiative exchanges is also very important (see appendix II).

Figures 15-17 are temperature comparisons similar to figure 4-6. There

is a smaller effect of door mixing for these fires, see figure 18.

Figure 19 is similar to 7 and shows that the peak burning rate for M05

is now about correct. Except for M01, these results are quite encouraging.

The low peak temperature as simulated for M01 could be related to

the choice of the parameters which determine the hot layer emissivity.

Up to this point the Harvard values had been used. With these, the_^

extinction coefficient calculated for M01 at peak burning is 7.35 m

Babrauskas [1] found values of 3-5 m“l based on smoke measurements in

the room. Tewarson [19] reports various values for flexible urethanes

suggesting values for the Harvard input smoke parameter, FS, from as large as that used by Harvard (0.241 g smoke/g fuel pyrolyzed) to 1/3

that value. The extinction coefficient found by Babrauskas suggested

cutting the smoke parameter, FS, roughly in half; the new value would

still be consistent with Tewarson' s data. The calculated effect was

small. In view of the known importance of radiation in room fires this

was rather surprising.

Table 2 shows heat balances for M01 at peak burning for two values

of the smoke parameter. Note first that, because Mitler uses a variable beam length, [5, page 38], for heavy smoke, reducing the

extinction coefficient does not reduce the emissivity very much.

Halving the smoke produced changed the emissivity from 0.98 to 0.95.

Thus the layer is quite black for both rates of smoke production.

By far the biggest elements in the heat balance are the terms

expressing the energy convected through the hot layer. Almost exactly

half the energy released by the fire passes directly out the door. It

is the disposition of the remaining half that concerns us, but the large

energy "flushing" that accompanies this must always be kept in mind. The

difference between the energy added by convection from the fire plumes

and that removed out the door, and by convective mixing around the door,

is the net convective energy. While large, this does not completely

dominate the other terms. The net convective energy changes only slightly

with the change in smoke density—down 17 kW or 2 percent.

The largest change shown in table 2 is in the heat lost to the lower

layer —down from 770 to 689 kW, a reduction of 81 kW or 11 percent. The

next largest change is in the radiant heat from the flames absorbed

by the hot layer. This is reduced 31 kW or 6 percent. These two effects

are in the direction to be expected with the reduced layer emissivity.

Because the decrease in heat loss from the layer is more than the

decrease in the heat gain from the flames, the net effect is that, for

the less smoky case, the layer should be a bit hotter.

14
The third largest change is in the radiant heat lost to the ceiling,

which increased 23 kW or 7 percent. The decreased layer emissivity

results in a lower ceiling temperature. The radiation term in table 2 relating to the ceiling is the net radiative exchange. It is the

difference between two much larger numbers, the radiation from the layer

to the ceiling and the re-radiation returned by the ceiling to the layer.

Both are decreased, the layer to ceiling because of the lower gas emissivity

and the ceiling re-radiation because the ceiling temperature is lower (in

response to the decreased heat input from the layer). The net effect turns

out to be larger than the net gain just discussed (energy gained from flame

radiation minus radiative loss to the floor). Thus the layer actually

cools slightly. Note that, if the ceiling had been more thoroughly heat

saturated—lower thermal inertia or longer time—the layer temperature

would have risen with a decrease in smoke density.

Further numerical experiments showed that, for M05, changing the

smoke parameter, FS, from 0.24 to as low as 0.04 had virtually no effect on the upper layer temperature, but reducing the ceiling thermal conductivity (to decrease thermal inertia and reduce the ability of the ceiling

to remove heat) and reducing the smoke production raised the gas temperature

in agreement with the argument given above.

Although smoke produced had little effect on the thermal predictions,

it is obviously important to predicting the smoke measurements. Figure 20

shows the extinction coefficient for mattress M05 computed from doorway

smoke measurements [1, figure 54], and computed values for FS = 0.241.

Again setting aside the difference in the time to peak, the shape of the curves is quite similar. The comparison suggests that an FS = 0.16 would

have been a better choice than the default value, 0.241, for this mattress.

Figure 21 compares the radiation to the non-burning target, object 4,

for mattress M05 and a smoke factor FS = 0.24 with the experimental values

[1, figure 43], The trend is generally similar. If, however, the target

object is moved relative to the fire, or the fire center moves around

on the bed changing its position relative to the target, the contribution

of flame radiation will increase as the target and flame approach each

other. Figure 22 shows the effect of moving the target to vary target- tofire spacing. Also indicated on the figure is the bed "diameter". This

is the approximate amount the target- to-f ire spacing might change as the

apparent center of the fire is moved to the extremes of the bed. Note

that the dominant contribution to the target heat flux comes from the

hot gas layer. This is virtually constant except when the target is very

close to the wall. The drop as the wall is approached is due to the

changing view factor (the relative amount of the hot layer and cold

wall seen by the target). At peak burning the hot gas layer under the

ceiling is relatively thick. Its bottom is only about 40 cm above the

target. The decrease in heat flux received from the ceiling (as distinct

from that received from above due to the hot gas) as the target is moved

is also a view factor effect. Because the hot layer is so thick, the

target "sees" relatively little of the flame (only that below the layer)

.

15
The flame radiation at the target increases as the two approach each

other, but is never as large as the hot layer contribution. In these

calculations the target was assumed to be a flat, horizontal surface.

The Harvard code, level 5, allows the orientation of target surfaces to

be varied. Were the target vertical, the heat flux received from the hot

gas layer would be somewhat reduced and that coming from the flame would

be increased.

7. ADDITIONAL MATTRESS SIMULATIONS

The above simulations were for those mattresses where the dominant

fuel was flexible urethane foam. As a matter of interest, similar

calculations were made for the remaining mattresses in the NBS test

series which flamed significantly, M02, 4 and 6. The results are shown

in figures 23-25. As in the previous simulations, only input data

specific to the particular mattress size, weight of combustible and

heat of combustion were used, all other values were the Harvard parameters.

The H051 simulation was used with the door narrowed to account for the

adjoining structure as already discussed. The results generally compare

about as well with experiments as the results obtained with the urethane

mattresses. Again, the upper gas temperature is a bit low where the

free burn maximum flame height, as computed by, for example, McCaffrey

[20], would place the flame tip well above the room ceiling height (M01

and M04). As stated above, this discrepancy is believed to arise either

from the failure of current room fire models to account for burning in

the hot, upper layer or from inadequacies in the layer radiation computation.

8. ROOM "B" SIMULATIONS

As described in [1], two sets of room tests were conducted; one set

in the facility shown in figure 12, the second set in a different structure.

The burn room for the second set is designated as room "B". The room "B"

tests consisted of two series with different ventilation arrangements.

Room B was located midway along a corridor which connected at one end to

a cross corridor and at the other to a large lobby. In both room "B"

test series the room door to the corridor was fully open and the room

window closed. In the first series the corridor was force ventilated

from the cross corridor end with the ventilation air exiting into the

lobby and, from there, to the outside of the building. This series is

referred to as the ’ventilated room "B" tests'. The measured flow in

the corridor prior to ignition was about 1.6 nr/sec (compared to a computed flow for the isolated room of 1.17 m^/s with mattress M05) . In

the other set no forced ventilation of the corridor and lobby was provided.

Doors connecting the fire room, corridor and lobby were open, but all

vents to the outside were nominally closed off. The total volume of the

room-corridor-lobby complex was 259 m3 with a ceiling height of 2.44 m. These are referred to as the ' non-ventilated room "B" tests'. Simulations

based on the room "B" geometry were made using the M05 mattress parameters.

16
In the first set of simulations, the burn room was considered isolated,

vented by its door to the atmosphere. As with the room "A" simulations,

it was to be expected that the adjoining space would alter the room

conditions. The first simulation used the actual door width. The result,

for temperature, was quite similar to that shown for room "A" in figure

15. In the room "B" case maximum upper gas temperature was 439 C at

380 sec. The experimental temperatures were much lower, suggestive of a fairly strongly ventilation-limited fire. However, unlike the room "A"

simulations, Tanaka's model could not readily be used to estimate the

"correct" amount of door closure to use to simulate the remaining structure.

The version of his model which was available at the time these simulations

were made did not include forced ventilation. Instead, several runs were

made with successively smaller door openings. With a 0.2 m door width

the peak temperature had increased to 649 C. The fire was oxygen limited

from 297 to 455 seconds but the induced flow was large enough to allow a substantial fire. Further closing the door to 0.1 m sufficiently reduced

the oxygen available that the peak temperature dropped to 350 C s or nearly

to that observed for this mattress in the ventilated room "B" test. The

result of the simulations and test are shown in figure 26.

Walter Jones of the Center for Fire Research, in work still in

progress, has compared the predictions of single and multi-room models

for essentially closed, multi-room configurations quite similar to the

non-ventilated series of room "B" mattress burns. Here "single room"

means that the volumes of the burn room, corridor and lobby have been

combined to define a single, large room with the same ceiling height as the actual room. Jones has found that, for certain purposes, the single

room results are better than might, at first, be expected. The single

room models do best where doors interior to the multi-room complex are distinctly larger and have shallower transoms than the vents to the outside.

Room "B", in the non-ventilated tests would meet these criteria. Accordingly

simulations for the non-ventilated series were made for such a single

room. Because the predicted temperatures were to be compared to measurements made inside the burn room where the hot gases had had little

opportunity to be cooled by contact with the ceiling, the ceiling thermal

conductivity was reduced to the assumed conductivity times the artificial

(augmented) room area. This would make the convective heat loss to the

total ceiling about the same as that lost within the burn room at the

same upper gas temperature. The first simulation used a small vent, near the floor. As long as the top of this vent was below the mattress

surface its area made little difference. The fire quickly became oxygen

limited; the maximum temperature reached was quite low. Next a series

of simulations were made with a 2 m high door of increasing widths.

(There is no reason to suppose that such leakage as existed came predominantly from floor level.) With a 0.2 m wide x 2 m high door the

peak temperature reached 156 C, nearly as high as the test value.

Results of these simulations are compared with the test data for a non- ventilated test in figure 27. Although this application clearly stretched

the single room model, the simulation suggests that there was substantial

leakage in the unventilated case.

17
Figure 28 shows the calculated height of the lower surface of the

hot s upper gas layer for various door openings. Note the slower descent

of the layer in the larger (augmented) room than in the actual size

(isolated) room. In the actual fire the layer would descend initially as simulated by the isolated room. At around 40 seconds from ignition, when

the layer had dropped below the door soffitt (indicated on the right of

figure 28), its descent would be retarded as fire gases spilled into the

corridor and spread to the lobby. When the layer’s descent resumed it

would follow more closely the augmented room simulation. Note also that

the isolated room with a 0.1 m width door forced the layer down about as far as the 0.2 m door for the augmented room.

The use of a single room for the room "B" tests does not seem

justified by the results. They do suggest that the flow situation in

the corridor is quite complex with, probably, a great deal of mixing

occurring just outside the fire room door. This is consistent with

Zukoski’s mixing experiments [16] although he has no data on the forced

flow "T" configuration encountered here. Note that the flow situation

is complicated by the up-wind propagation of the fire gases along the

corridor ceiling. The extremely small door openings required to get

close to the experimental observations results in a great deal of interlayer mixing. Because the present model does not include vitiated air

burning, the depletion of oxygen in the lower part of the room has no effect on the predicted burning rate. If vitiated burning were included,

much less severe flow restriction would almost certainly have been

necessary. The basic data and ideas on which to build vitiated air

burning models are only just now being developed by CFR supported research.

We should be able to address this important, missing, piece of the fire

models soon.

9. SUMMARY, DISCUSSION AND CONCLUSIONS

Simulations for the seven mattresses considered reproduced the

general burn behavior for room A quite well using only three properties

specific to the separate mattresses: total weight of combustible, total

burn surface area and heat of combustion. The total weight of combustible had a more than six fold variation over the set considered and the

simulations showed qualitative differences in behavior from the lightest

to the heaviest. Thus combustible weight is clearly an important

parameter in assessing mattress burn behavior. Total burn area, for

a given weight of combustible, influences both fire intensity and duration.

Excluding the control, the lightest and smallest mattress burned to produce the least challenging fire but, had a similar construction been used

to make a double bed size mattress, it would have had more combustible and

a larger burn area than either of the two mattresses which caused flashover

conditions to develop, M01 and M04. It would have been the worst performer

rather than the best of the group. That burn area is important is also

no surprise. Heats of combustion varied about + 17 percent for this

sample of seven material assemblies. For this range, the gas temperature

could be expected to vary about + 12 percent, or about + 100 C. This is

18
a large enough variation that, were it present, one’s assessment of the

quality of the simulation would suffer. Thus, while not large enough to

produce gross changes in behavior, heat of combustion is important to the

overall fire assessment.

Smoke production, expressed as grams of particulate per gram of fuel

pyrolyzed, did not seem important to thermal behavior for a six fold

variation spanning values representative of most materials. Polystyrene

would be higher and poly-oxy-methelene lower than the range covered.

Smoke production was important for prediction of extinction coefficient

and, given suitable input data, the observed behavior could be well

represented

.

Although some time was spent in studying the rate of heat release

data [2, table 5], this test offered little information useful to these

simulations; x in [2, table 11] comes from the rate of heat release tests.

Note, however, that some test is needed to determine if a mattress will

flame. The six mattresses which flamed, and the control, were well

modeled by the present fire code. But four mattresses failed to sustain

flaming. These would not be well modeled by any of the burn algorithms

of the present fire code since they burn in a qualitatively different

way from the behavior described by the available simulation algorithms.

It must be remembered that the actual burn behavior of several of

the mattresses for which the Harvard model gave reasonable simulations

did not burn in the way the model supposes. The model assumes a circular,

growing fire on a flat surface. Some of the mattresses melted off substantial amounts of fuel which dripped to the floor and burned under the

bed, not on its surface. At the same time, fire was observed on the

upper bed surface with the flames of the two merging. M04 was an extreme

case of this. This detailed behavior was not simulated, yet the predictions

were in fairly good agreement with observations.

It should be kept in mind that some parameters, which were not varied

for these simulations, may be very important. For example, heat of

pyrolysis and pyrolysis rate are directly related. Heat of pyrolysis

was not varied for two reasons: first, because no data was available for

the mattresses in question, and, second, because adequate agreement with

the experimental burn behavior was obtained by changing the burn

algorithm without changing heat of pyrolysis from the nominal value.

In some cases, although a parameter is important to burn behavior, its

value may actually not vary much in practice. In other cases, most

obviously geometry, the parameters are important but we may not know

how to assess them. Beds display the fuel in an especially simple

geometry. The same material used to build a sofa-bed might burn quite

differently in its sofa configuration than in its bed configuration.

19
To some, the input requirements of the Harvard simulation may seem unreasonably complex. To the fire scientist they all clearly relate to some known, important aspect of fire behavior. It may be that the inputs

can be re-cast in a form more readily understood by practicing engineers,

but it is doubtful if any can be eliminated. It may be, however, that for

broad classes of furnishings, some of the inputs can be left at suitably

chosen values and only a much more limited set of variables used to

describe the specific behavior of objects from these classes.

During the course of this study a number of changes in the Harvard

simulation were studied and several adopted. The simulations were

distinctly improved as a result of these changes. There are further

improvements, some of them associated with the lower gas layer, which, if

made, would further improve the quality of the simulations. Perhaps

the most important area for work is related to burning in vitiated air.

Improvements are needed both where flames can be expected in the upper

layer and where the lower layer is contaminated with combustion products.

Studies are underway to provide a sound basis for these changes, but their

introduction is probably still a year off. Nearly as important is work

related to the pyrolysis rate prediction. The questions of cold fuel

radiation absorption and char-formation need to be sufficiently studied

and documented so that these clearly important effects can be included

in the model.

This study also showed the importance of being able to represent

adjacent structure (multi-room model). Although a single room or augmented

single room may be able to be adjusted to give good agreement with

experiment, the way to adjust it may not be obvious. In this study an appropriate door adjustment for room "A" was deduced from the geometry

and confirmed using Tanaka's multi-room simulation. For the room "B"

this was not possible and empirical adjustment failed to produce a satisfactory representation of the data. For this case a multi-room

simulation was needed.

Finally, much more information is needed on door and window mixing

so that the crude correlations used in the new subroutine MIX can be

replaced with more general and more accurate forms.

10. REFERENCES

[1] Babrauskas, V. , "Combustion of Mattresses Exposed to Flaming

Ignition Sources, Part I. Full-Scale Tests and Hazard Analysis",

Nat. Bur. of Stand. (U.S.) NBSIR 77-1290 (1977).

[2] Babrauskas, V. , "Combustion of Mattresses Exposed to Flaming

Ignition Sources, Part II. Bench-Scale Tests and Recommended

Standard Test", Nat. Bur. of Stand. (U.S.), NBSIR 80-2186 (1980).

[3] Emmons, H.W., "Computer Fire Code II", Home Fire Project Technical

Report No. 20, Harvard University, Cambridge, MA, 1977.

20
[4] Emmons, H.W. , Mitler, H.E., Treffethen, L.N., "Computer Fire Code

III", Home Fire Project Technical Report No. 25, Harvard University,

Cambridge, MA, 1978.

[5] Mitler, H.E., "The Physical Basis for the Harvard Computer Fire

Code", Home Fire Project Technical Report No. 34, Harvard University,

Cambridge, MA, 1978.

[6] Mitler, H.E., Emmons, H.W. , "Computer Fire Code V" , Home Fire

Project Technical Report No. 45, Harvard University, Cambridge, MA,

1981.

[7] Croce, P.A. , Emmons, H.W., "The Large-Scale Bedroom Fire Test, July

11, 1973", FMRC Serial No. 21011.4, Technical Report R.C. 74-T-31,

Factory Mutual Research Corp., Norwood, MA, July 1974.

[8] Croce, P.A., "A Study of Room Fire Development: The Second FullScale Bedroom Test of the Home Fire Project (July 24, 1974),

Volumes I and II", FMRC Serial No. 21011.4, Technical Report,

RC75-T-31, Factory Mutual Research Corp., Norwood, MA, June 1975.

[9] Alpert, R.L., Modak, A.T., Newman, J.S., "The Third Full-Scale

Bedroom Fire Test of the Home Fire Project (July 30, 1975)",

FMRC Serial No. 21011.6, Factory Mutual Research Corp., Norwood,

MA, Oct. 1975.

[10] Babrauskas, V., "Will the Second Item Ignite?", Nat. Bur. of Stand.

(U.S.) NBSIR 81-2271 (1981).

[11] Babrauskas, V., private communication.

[12] Kashiwagi, T., "Radiative Ignition Mechanism of Solid Fuels",

Fire Safety Journal, Vol. 3, 185-200 (1981).

[13] Orloff, L. , "Simplified Radiation Modeling of Pool Fires", Factory

Mutual Research Corp., Norwood, MA 02062, Jan. 1980 (Paper for

presentation at the 18th Symposium (Inti.) on Combustion, University

of Waterloo, Ontario, Canada, Aug. 1980).

[14] McCaffrey, B.J. and Rockett, J.A., "Static Pressure Measurements

of Enclosure Fires", Journal of Research, Nat. Bur. of Stand.,

Vol. 82, No. 2, Sept. -Oct. 1977.

[15] Ouintiere, J.G. and McCaffrey, B.J., "The Burning of Wood and

Plastic Cribs in an Enclosure", Vol. 1, Nat. Bur. of Stand. (U.S.)

NBSIR 80-2054 (1980).

[16] Zukoski, E.E., "Progress Report for Nov. 20, 1980, Experimental

Study of Environment and Heat Transfer in a Room Fire", Cal. Inst,

of Tech., Pasadena, CA, Nov. 20, 1980.

21
[17] Tu, King-Mon, "The Calibration of a Burn Room for Fire Tests on Furnishings", NBS Technical Note 981, U.S. Department of Commerce,

Washington, DC, Dec. 1978.

[18] Tanaka, Takeyoshi, "A Model on Fire Spread in Small Scale Buildings,

2nd Report", Building Research Institute, Ministry of Construction,

Tokyo, Japan, March 1980.

[19] Tewarson, A., "Physico-Chemical and Combustion/Pyrolysis Properties

of Polymeric Materials", Nat. Bur. of Stand. (U.S.) NBS-GCR-80-295

(1980).

[20] McCaffrey, B.J., "Purely Buoyant Diffusion Flames: Some Experimental

Results", Nat. Bur. of Stand. (U.S.) NBSIR 79-1910 (1979).

22
APPENDIX I. THE EFFECT OF A THIN CHAR LAYER ON PYROLYSIS RATE

The argument is as follows: We start with the heat flux reaching

the fuel surface as calculated for a flame with the final, desired

pyrolysis rate. We also determine the heat needed to pyrolyze fuel at

the desired rate, 46 g/sec. The difference between these two must be

lost by the surface. This can happen by three mechanisms — surface

radiation, convection and conduction into the fuel body. We ignore

convection and neglect the conduction loss here; all the heat is to be

carried away by radiation. Now, using the thermal properties of charcoal given in [Al.l], the heat conducted through a char layer can be

found as a function of the layer's thickness and the temperature difference across the layer. We know the temperature at the fuel-char

interface must be the pyrolysis temperature and that the heat which must

be transmitted is the amount needed to pyrolize the fuel. As stated

above, we also know the amount that must be radiated from the char surface. These conditions are used to find the char surface temperature

and thickness.

Radiation reaches the fuel from three sources: the flames over the

surface itself, the hot gas layer trapped under the ceiling and the

ceiling (attenuated by absorption in the hot layer). These are reported

outputs of the Harvard simulation. Their sum, for a mattress fire

burning at 46 g/sec., is 96.8 kW/m .

2 The fire a^ea at this point was 2.446 m , giving a pyrolysis rate

of 18.8 g/sec-m . Taking the Harvard default heat of pyrolysis, 2.05^

MJ/kg, the heat needed at the fuel surface is 18.8 x 2.05 = 38.5 kW/m .

Therefore the heat that must be lost from the surface by

radiation is

96.8 - 38.5 = 58.3 kW/m

Assuming a black surface with unit emissivity, the surface temperature

must be

oT

4 = 5.67 x 1011 x T

4 = 58.3 kW/m2 or

T = 1007 °K

Taking the Harvard default pyrolysjs temperature, 600°K, the char

thickness which will transmit 38.5 kW/m with a temperature difference of

1007 - 600 = 407°K

is

38.5 = (k/d) x 407

23
(k/d) = 0.0947 kW/m - °K

[17, p. 1784] gives k = 0.37 BTU/hr-f t-F/in for char, or

k = 5.33 x 10 kW/m - °K

Therefore

d = 0.56 mm

References

[Al.l] Hodgman, C.D. , "Handbook of Chemistry and Physics", Twenty-Seventh

Edition, Chemical Rubber Publishing Co., Cleveland, Ohio, 1943.

24
APPENDIX II. HOT-COLD GAS MIXING AT VENTS

Inclusion of mixing at the vents entails a number of changes

throughout the program as the implications of the changed properties of

the lower gas layer in the room are accommodated. To date only a fraction

of all the "consistent" changes have been made and only those made will

be discussed. The changes described here were made in a way to least

disrupt the H05 code. It is intended that they should be fully integrated

in the code structure, but only after their general operation has been

debugged.

Because the mixing information is needed in a number of subroutines,

a new COMMON, CVENT3 was added. It provides communication throughout

the program.

One effect of mixing is to vitiate the air in the lower gas layer.

This results in a change in the stoichiometric coefficients, XGAMMA and

XGAMAS, which are defined in terms of amount of air rather than amount

of oxygen needed to fully burn the pyrolysis products of each object.

This is done by storing initial values in CVENT3 and adjusting XGAMMA

and XGAMAS by the ratio of ambient to actual lower layer oxygen mass fraction as vitiation occurs. Initial values for the stoichiometric

coefficients are obtained in INPUT3 and initialized in CVENT3 in LAYR.

The initial values are called ST0IC1 and ST0IC2. During each iteration

XGAMMA and XGAMAS are adjusted using

XGAMMA = ST0IC1 x 0.2318/ZYCO

XGAMAS = ST0IC2 x 0.2318/ZYCO

where ZYCO is the oxygen mass fraction in the lower gas layer.

Another effect of the vitiation of the lower layer is to reduce the

smoke production. Data on this effect is still scarce [A2.1] so the

correlations used only express the trend. The input smoke production

constant is FS. It is set for each object in INIT, carried in CVENT3 as FSINIT and corrected in LAYR according to

FS = FSINIT x ZYCO/ (0.2318 4- 2 x FSINIT x (ZYCO - 0.2318)

ZUFZZ is the extinction coefficient for the flame brush. It is

adjusted using a similar functional relation; the initial value, stored

in CVENT3 is ZUFI.

H05 makes no provision for entering emissivities for the floor,

walls or ceiling of the room. In H051 default values of 0.82 are set in

LAYR and carried in CVENT3 as ECEIL and EFLOOR. The upper walls are assumed to have the same characteristics as the ceiling and the lower

walls those of the floor. No provision has yet been made to input

alternative values.

25
Within the subroutine MIX two operations are performed: first,

following the definition of Zukoski [16], a Richardson number is found.

Next, this is used in an empirical data correlation to find the amount

of mixing flow leaving the hot layer. Several data correlations for the

amount of mixing were tried. A slight modification of the one used by

Quintiere [15] was adopted. He calculates the mixing flow using

where

m =

• m

m. = w

1 = W = K

C =

P T =

D = N = n =

mass flow transfered from the hot layer to the cool layer mass flow entering the door

width of the wall containing the door

width of door

constant set equal to 1/2, c.f. [15]

density of the hot layer

density of the entering gas

height of the hot-cool interface in the room

height of the neutral plain in the doorway

1/4

Note that, in this form, the door width correction (W/W ) increases

indefinitely as this ratio increases. Actually one suspects (there is

little good data) that, beyond a certain point, increasing the space around

a door will no longer increase the amount of mixing. To retain the

dependence expressed by Quintiere' s expression for values of the ratio

near unity, yet have it approach a constant for large values, the

expression

[1 + 3 (W/W ) ] / [2 (1 + W/W )] c c was used. The asymtotic value, 3/2, was chosen somewhat arbitrarily.

To use Quintiere' s mixing correlation a value for (1 - D/N) is needed.

This is obtained, again following Quintiere, from the basic door flow

equation (slightly simplified)

m. „ / (p - P ) ~ = 4 C P \ 2 § — — ['/N - D (N +D/2)] W 3 o i p c o

where

C = orifice flow coefficient = 0.68

26
This relation cannot be readily used with the present VENT subroutine

of the Harvard code as the neutral plain height, N, is not directly

available. It can be expressed in terms of Zukoski’s Richardson number

2 Ri = g(p - p ) D/u

but, since °

u . = m . /p W D

x IOC

Ri = gp (p - p ) D

3 (W /m.)

2 o L o c x This leads to a cubic equation for (1 - N/D) = x whose solution it is

desirable to side-step.

Ri = or

8C (f)

s/

[(1 - D/N) (1 + D/2N)]

x (3 - x)

2 = 4R (1 - x)

3

R = 9/ (8C Ri)

This is done by noting that a very good approximation to the solution

is

x = 4R/[(9 + 12R) - x

± (6 + 12R) + x

2 (l + 4R)

]

x

1 = 4R/(9 + 4R)

It must be stressed that this correlation is based on data for

doors. Windows are known to produce much more vigorous mixing, especially when the hot-cool interface in the room is below the window sill

[ 16 ].

The hot, and now also the cool layer characteristics are calculated

in subroutine LAYR. The procedure used for the hot layer is augmented

with parallel calculations for the cool layer. For each vent the mixing

flow and rate of transport from the hot layer of energy, oxygen, CO^

,

CO, H^O and particulate/aerosol are summed. These rates are combined

with corresponding ambient quantities entering through the lower part of

the vents. Loss rates from the lower, cool layer for the same quantities

are determined from the gas entrained by all the fire plumes. The

accretion less loss, for each of these quantities, is integrated to give

the current amount of each in the cool layer. Mass fractions are also

computed

.

The mass fraction of oxygen in the cool layer is then used to

correct XGAMMA, XGAMAS , FS and ZUFZZ as discussed above.

Because the cool, lower layer is contaminated by smoke and combustion

products, it can absorb radiation and re-radiate to its surroundings.

The cool layer emissivity/absorptivity is calculated by a method similar

27
to that used in RDNL for the hot, upper layer. The calling statements

for ABSRB2 and ABSRB3 have been changed to facilitate this. The cool

layer energy balance currently includes radiant energy incident from the

ceiling and hot layer above it and from the cool walls and floor which

surround its remaining sides*. Lower vent areas are treated as radiating

at the same temperature as the walls. Radiant energy from flames is

also included. The cool layer radiates to all its surroundings.

The radiation balance used is similar to but slightly more inclusive

than that used by H05 and RDNL for the hot, upper layer. The correct

calculation of radiative equilibrium between two non-planar surfaces at

different temperatures separated by two absorbing and radiating gas

layers with different emissivities and temperatures is a rather complicated problem [A2.2]. Adding a conical flame volume would still further

complicate the already difficult situation. The equations currently

programmed in H051 are outlined in figure A2.1. They approximate the

actual room by a pair of parallel planes separated by two emitting/absorbing gas layers with differing characteristics. Gas emissivities are based on a mean beam length = 4kV/A. Two pairs of radiant flux equations

are written for the upward and downward streaming fluxes in each layer.

Four matching conditions are set up at the upper and lower boundaries of

the layers. The flux equations are solved in a new subroutine, FLUX,

called from RDNL. The quantities returned are the net radiant energy

lost by the upper, hot gas layer to the ceiling, FL1 = e (I T ),

the net radiant energy lost by the upper layer to the lower, cool gas

layer, FL2 = (I

? - I ) , and the net Radiant energy lost by the lower

layer to the floor, FL3 = e (I. - T ).

The flame radiation contribution to the lower layer is computed in

RDNL. There the flame radiation to the upper layer is found assuming

the radiation comes from a point source one flame radius above the fuel

surface. The radiation incident on the lower layer, TEPCR, is the total

flame radiation less that incident on the hot layer and less that which

intercepts the fuel surface.

TECPR = e E TEPZR x 1/2 [(1 + cos(0)) - (1 - cos(0 ))]

plumes

where

TEPZR = total flame radiation

cos(0) = h/v/fT + x'lL

f~2 2 cos (0-. ) = r //r + r

1 s s s r = WL/ = "radius" of the upper layer

JLj r = radius of the fire

r r = radius of the fuel surface

s e^ = lower layer emissivity

*Note that the present Harvard code does not allow the lower walls to be

heated, they remain at the "outdoor" ambient.

28
The upper layer radiant energy gain is

- o(A^ - WL - Avt) FL1 - oWL FL2 - oAvt (T* - T^)

+ flame contribution as calculated in H05.

The lower layer radiant energy gain is

TECZR = oWL FL2 - a (A - WL) FL3 + TEPCR

c TECZR is passed to LAYR via CVENT3.

The calculations reported in this paper were done with an intermediate version of the mixing calculation which did not include flame

radiation absorbed by the cool layer. It also used the upper layer

radiation absorption as given in the Harvard simulation, level V - i.e.,

the upper layer saw the lower layer and floor at the now elevated room

ambient temperature.

For M01, using the upper layer radiation balance as detailed in

this appendix, raised the peak temperature about 55°C. Including flame

radiation in the lower layer radiative balance raised the peak temperature, for M01, an additional 65°C. Adjusting the stoichiometric coefficients had no appreciable effect. With all these changes, as described

here, for M01 , the peak temperature was 886°C at 420 sec compared to

768°C calculated at 420 sec as shown in figures 13 and 14. Lower layer

temperature was 265°C compared to 378°C as shown in figure 14. The hotcool interface had moved down 0.1 m to 1.0 m. With this improved treatment of radiation, overall, the simulation was significantly closer to

the test data for M01 and M04, and slightly closer for M02, 5, 6 and 9.

The room B simulations were about the same but, as noted in the main

text, the single room model really couldn’t deal adequately with this

complex geometry.

References

[A2.1] Santo, G. , "Influence of Oxygen Depletion on the Radiative Properties

of PMMA Flames", Factory Mutual Research Corp., FMRC J.I. 0A0E6.BU-3,

RC79-BT-6, Norwood, Mass., August, 1979.

[A2.2] Siegel, R. and Howell, J.R., "Thermal Radiation Heat Transfer",

NASA SP-164, National Aeronautics and Space Administration,

Washington, D.C., 1971.

29
APPENDIX III. DOOR FLOWS

Dr. Tanaka's model, unmodified, yielded a single room flow at the

time of peak burning of 0.49 Kg/sec; the Harvard code 1.10 Kg/sec. To

choose between the two, the data of Steckler [A3.1] was referred to.

The Harvard code prediction of the flow in Steckler 's room, which discharged into a not too large plenum but one equipped with an exhaust

vent directly over the door, is compared with the measured values in

figures A1 and A2 . The prediction is about 10 percent low. The Harvard

code makes no provision for interaction of the fire plume and door jet as discussed in [A3.2], so it is not surprising that the prediction is low.

The amount of plume-door jet interaction to include is obviously a function

of the room and object geometry. Furnishings may not be placed as favorably

for a strong interaction as in Steckler' s fire and objects between the door

and principal fire may break up the door jet. On the whole, the Harvard

code predictions seem quite satisfactory, and, by inference, Tanaka's seem

too low for the type of burner used by Steckler. After modification, the

Tanaka code gave a flow of 1.2 kg/sec., slightly higher than H051 and very

close to the Steckler data.

References

[A3.1] Steckler, K.D.

,

"Fire Induced Flows Through Room Openings - Flow

Coefficients", Nat. Bur. of Stand. (U.S.), to be published.

[A3. 2] Quintiere, J.G., Rinkinen, W.J., and Jones, W.W., "The Effect of

Room Openings on Fire Plume Entrainment", Combustion Science and

Technology (to be published)

.

30
Table 1. The computed effect of adjacent, connected rooms on the fire induced flow from room "A"

Item Room 1 of 1 Room

Q 1.0 MW 1.0

time 366 sec 366

T layer 702 K 742

vent out-flow 1.20 kg/s 0.90

vent in-flow 1.20 kg/s 0.90

layer depth 1.60 m 1. 66

Q 0.125 MW 0.125

time 372 sec 372

T layer 387 K 399

vent out-flow 0.86 kg/s 0 . 66

vent in-flow 0.86 kg/s 0.65

layer depth 1.51 m 1.59

Ratios

Flow (1 of 3) /flow (1 or 1) = 0.899/1.200 = 0.749

0.660/0.862 = 0.766

0.653/0.859 = 0.760

H051 (70.7% door)/ (100% door) = 0.854/1.105 = 0.773

(50.0% door) / (100% door) = 0.653/1.105 = 0.591

of 3

MW

sec K

kg/s

kg/s

m

MW

sec K

kg/s

kg/s

m

31
Table 2. The effect of a change of the smoke parameter, FS

Mattress M01

Item Run 191 Run 192

FS 0.241 0.120

time 420 sec 420 sec

Q 1.84 MW 1.84 MW

T upper 1041 K 1021 K

T ceiling 984 K 953 K

T lower 651 K 614 K

T ambient 293 K 293 K

Smoke fraction 0.0274 0.0141

Extinction Coefficient 7.25/m 3.74/m

Emissivity * 0.978 0.946

Layer Energy Balance

Stored -2 kW -6 kW

Plume convection 1797 kW 1764 kW

Door convection -902 kW -898 kW

Net convection 895 kW 866 kW

Inter-layer mixing -162 kW -150 kW

Ceiling convective heating -83 kW -100 kW

Radiation, hot layer to:

Ceiling (net) -328 kW -351 kW

Out vents -41 kW -37 kW

Lower layer -770 kW -689 kW

Flames 487 kW 456 kW

Net gain -652 kW -621 kW

* e = 1 - EXP(-z/(l + 0 . 18z)

)

z = 4 kV/A

V = layer volume

A = layer surface area

32
00 o a +j

a) a) 4J 4J

CO

csi

( 08S/3) 3iva SS01 ssww

33
Figure 2a. Calculated temperature versus

time for the standardized wastebasket

burned alone. Temperature and time scales

are the same as will be used for mattress

data.

OoUJ

Q£

Q_

WASTEBASKET ALONE

LU

1“

C3g£ ocCO o

CO <u o to _J be

CO —

CO

0 200 400 600

TIME (secj

Figure 2b. Mass loss rate versus time for

wastebasket simulation. Vertical scale

12 X that used for mattress data.

34
1100

1000

900

800

700

600

500

400

300

200

100

0

T T

200 400 600 800 1000 1200

TIME fsecl

Figure 3. Room upper gas temperature versus

time for mattress M01 (data from [1,

figure 17]). Also shown is the calculated

hot layer temperature using Harvard default

values except as noted in the text.

35
Figure 4. Room upper gas temperature versus

time for mattress M05 (data from [1,

figure 21]). Also shown is the calculated

hot layer temperature using Harvard default

values except as noted in the text.

36
Figure 5. Room upper gas temperature versus

time for mattress M09 (data from [1,

figure 25]). Also shown is the calculated

hot layer temperature using Harvard default

values except as noted in the text. The

small hump at 450 seconds on the calculated

temperature curve is caused by ignition and

burning of the pillow. At this point the

mattress burned, has terminated.

37
Figure 6. Room upper gas temperature versus

time for control mattress (data from [1,

figure 16]). Also shown is the calculated

hot layer temperature default values except

as noted in the text . The small hump at

500 seconds on the calculated temperature

curve is caused by the pillow burning. At

this point the bedding is burned out. This

peak occurs slightly later than for the

other mattresses due to the slower rate of

growth of this relatively small fire.

38
120

110

100

90

80

70

60

50

40

30

20

10

0

Figure 7. Mass loss rate as a function of

time for mattress M05 (data from [1,

figure 13]). Also shown is the calculated

mass loss rate using the Harvard default

values except as noted in the text.

TIME (sec)

39
FUEL

MASS

(kg)

Figure 8. Semi-log plot of experimentally

determined fuel mass and mass burning rate

for mattress M05 (data from [1, figure 13])

and numerical integration) . Mass scale to

40

MASS

BURNING

RATE

(g/sec)
11

10

9

8

7

6

5

4

3

2

1

0

10 20 30 40 50

MASS BURNING RATE (g/sec)

60

Figure 9. Remaining fuel mass plotted against

mass burning rate for mattress M05. Straight

line corresponds to a "late burning constant"

of 100 seconds (10 g/sec/kg fuel remaining)

.

41
11

10

9

e

i

6

5

4

3

2

1

0

igure 10. Remaining fuel mass plotted

against mass burning rate for mattress M09.

Straight line corresponds to a "late

burning constant" of 100 seconds (10 g/sec/kg

fuel remaining)

.

MASS BURNING RATE (g/sec)

42
Figure 11. Remaining fuel mass plotted against

mass burning rate for mattress M02. Straight

line corresponds to a "late burning constant"

of 100 seconds (10 g/sec/kg fuel remaining).

GO

GO

43
EXHAUST

HOOD

44

Figure

12.

Location

of

"Room

A"

within

the

NBS

Fire

Test

Building

showing

its

relation

to

other,

connecting

rooms

and

the

fire

gas

exhaust

system.
Figure 13. Upper gas temperature versus time

for mattress M01 (data from [1, figure 17]).

Also shown is the calculated hot layer

temperature using default values except as noted in the text. Simulation includes

door mixing.

45
HEIGHT

(m)

Figure 14. Height versus room temperature

for mattress M01 (data from [1, fig. 23]).

Also shown are the calculated vertical

distribution with and without door mixing

and for the door opening narrowed to 71

percent of its actual width.

46
Figure 15. Upper gas temperature versus

time for mattress M05 (data from [1,

fig. 21]). Also shown is the calculated

hot layer temperature with door mixing

using Harvard default values except as noted in the text.

47
Figure 16. Upper gas temperature versus time

for mattress M09 (data from [1, figure 25]).

Also shown is the calculated hot layer

temperature with door mixing using Harvard

default values except as noted in the text.

48
Figure 17. Upper gas temperature versus time

for control mattress (data from [1, fig. 16]).

Also shown is the calculated hot layer

temperature door mixing using Harvard

default values except as noted in the text.

49
HEIGHT

(m

2.5

2.0

1.5

1.0

0.5

1 I - CEILING ^1 T

- 1 T T

5-

1

o

\ o o

/

/

11 O GO

/

f

-

/

/

OQO / /

/

/

/

/

/

/

M05

TEST

CALCULATED

-

1®

*

1

1

\

\ AoJ 1 if FLOOR

J J 1

0 200 400 BOO BOO 1000

TEMPERATURE (°C)

1200 1400

Figure 18. Height versus room temperature

for mattress M05 (data from [1, fig. 32]).

Also shown are the calculated vertical

distribution with door mixing and door

narrowed to 71 percent of actual width.

50
120

110

100

90

80

70

60

50

40

30

20

10

0

Figure 19. Mass loss rate as a function of

time for mattress M05 (data from [1,

figure 13]). Also shown is the calculated

mass loss rate using the Harvard default

values except as noted in the text.

M05

Test

Calculated

400 600 800

TIME (sec)

1000 1200

51
TIME (sec)

Figure 20. Extinction coefficient computed

from light attenuation measurements taken

in the doorway, 0.61 m below the ceiling, room A, mattress M05. Also shown is the

computed extinction coefficient for the

upper gas layer with FS = 0.241.

52
HEAT

FLUX

(kW/m

2)

Figure 21. Comparison of measured and

calculated heat flux at a target separate

0 200 400 600 800 1000 1200

TIME (sec)

53
HEAT

FLUX

(kW/m

2)

Figure 22. Effect of fire-target spacing on heat flux to the target, computed for

mattress M05 at time of peak burning.

54
Figure 23. Upper gas temperature versus time

for mattress M02 (data from [1, fig. 18]).

Also shown is the calculated hot layer

temperature with door mixing using Harvard

Code default values except as noted in the

text

.

55
1100

1000

900

BOO

700

600

500

400

300

200

100

0

56

|\ /V1 M04

>i\ >

i f V I —Test

f fl —Calculated"

i '

i

200 400 SOO 800 1000 1200

TIME (sec|

Figure 24. Upper gas temperature versus time

for mattress M04 (data from [1, fig. 20]).

Also shown is the calculated hot layer

temperature with door mixing using Harvard

default values except as noted in the text.
Figure 25. Upper gas temperature versus time

for mattress M02 (data from [1, figure 22]).

Also shown is the calculated hot layer

temperature with door mixing using Harvard

default values except as noted in the text.

57
(3d 3HniVMldW31

bo 4-1 •H

|j-f

0) <4-1 J-4 >-( Cu 0) B »> oj >

Cl)H ,C (U >—' 4J W

58
(Go) 3dfUVd3dW31

59

Figure

27.

Room

B

(un-ventilated,

augmented

area)

upper

gas

temperature

for

mattress

M05

data

from

[1,

figure

21]

and

values

computed

with

the

room

door

closed

to

0.2

m

width.
(ui ) 1H9I3H

60

Figure

28

.

Calculated

height

of

the

lower

TIME

fS6Cl

surface

of

the

hot

gas

layer

for

several

cases,

room

B

and

room

B

(augmented).
ho -

13

CEILING:

TEMPERATURE Tw

EMISSIVITY ew

ewh ewTw4

////// ////////////

I20 - ewTw4+

( 1 -ew) h

I30 = 6fTf4 + ( 1 -eF) 1 4

40 = I2

li =

(1-6 h) ho + eH TH

4

h = ( 1 -eH) I20 + chTh4

I3 = (1-ec) 1 30 + ecTc4

U = (1-ec) ho + ecTc 4

1 Th

it 120

en

1

110

j L 1 Tc

13 , 1 40

ec

1 30 I' 4

///// //////// ' f /////

6 FTf4 eFh

FLOOR:

TEMPERATURE TF

EMISSIVITY e F

Figure A2.1 Room radiative heat flux

calculation showing the equations to be

solved and the geometric relation of the

terms

.

61
MASS

FLOW

RATE

(kg/seoj

Figure A3.1 Door mass outflow rate as a function of heat release rate. Points

from Steckler [A3.1], curve calculated.

62
MASS

FLOW

RATE

(kg/sec)

Figure A3. 2 Door mass outflow rate as a function of door width. Points from

Steckler [A3.1], curve calculated.

63
NBS-114A (REV. 2-80

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 81-2440

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

January 1982

4.

TITLE AND SUBTITLE

Modeling of NBS Mattress Tests with the Harvard Mark V Fire Simulation 5.

AUTHOR(S)

John A. Rockett

6.

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

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

8

.

Type of Report & Period Covered

9.

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

10.

SUPPLEMENTARY NOTES

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

11.

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

bi bl iography or literature survey, mention it here)

NBS burned eleven mattresses made up with bedding in two different rooms, typical

of a residential bedroom and a nursing home patient room, respectively. Seven of

the mattresses flamed and burned vigorously, the other four were of a construction

or so heavily flame inhibited that they only smoldered. The burning behavior of

the seven that flamed was modeled with the Harvard Mark V fire simulation. The

experimental burn behavior for tests conducted in one room was well reproduced using

only total weight of combustible, surface area and heat of combustion. Smoke production values were found to have little effect on the predicted behavior except for

the smoke production itself. Fires in a second room, whose ventilation was intentionally restricted by the configuration of the adjoining space, could not be as well

reproduced by the present, single room fire model.

During this study several changes were made to the simulation. The most significant

change was the inclusion of mixing of the hot, exiting fire gases with the cold

incoming air. As a part of this, the inter-layer radiation exchange was reformulated

to include the effect of smoke contamination of the lower layer. The reformation of

the radiation model had a marked effect on the predicted upper layer gas temperatures,

generally improving the quality of the simulation.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) Fabric flammability; fire models; fire tests; home fires; hospitals; mattresses;

nursing homes; room fires; smoldering

13. AVAILABILITY 14. NO. OF

Unlimited

[_| For Official Distribution. Do Not Release to NTIS

[2T1 Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

PRINTED PAGES

74

15. Price

jxxj Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $9.00

U S COMM* D C S043-P80

7