Reference

NBS

Publi - rations

NBSIR 78-1511

AlllOM Eb03T3

EXPERIMENTAL AND THEORETICAL

ANALYSIS OF QUASI-STEADY

SMALL-SCALE ENCLOSURE FIRES

J. G. Quintiere, B. J. McCaffrey and K. DenBraven

Center for Fire Research

National Engineering Laboratory

National Bureau of Standards

Washington, D.C. 20234

October 1 978

U.S. DEPARTMENT OF COMMERCE. Juanita M. Kreps. Secretary

Dr. Sidney Harman, Under Secretary

I" QQ —' Jordan J. Baruch, Assistant Secretary for Science and Technology

2QQ NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

,U56

78-1511

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NBSIR 78-151 1 ^

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. f EXPERIMENTAL AND THEORETICAL

ANALYSIS OF QUASI-STEADY

SMALL-SCALE ENCLOSURE FIRES

J. G. Quintiere, B. J. McCaffrey and K. DenBraven

Center for Fire Research

National Engineering Laboratory

National Bureau of Standards

Washington, D.C. 20234

October 1 978

U.S. DEPARTMENT OF COMMERCE, Juanita M. Kreps, Secretary

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

CONTENTS

Page

LIST OF FIGURES iv

LIST OF TABLES iv

TABLE OF NOMENCLATURE V

Abstract 1

1. INTRODUCTION 2

2. DESCRIPTION OF THE EXPERIMENT 3

3. EXPERIMENTAL RESULTS 4

4. THEORETICAL MODEL 6 4.1. Flow Model 6 4.2. Energy Conservation for the Fuel (CVj) 7 4.3. Energy Conservation for the Fire Plume (CVjj) 8 4.4. Energy Conservation of the Hot Upper Layer (CVju) .... 9 4.5. Conservation of Energy for Upper Walls and Ceiling .... 10

4.6. Conservation of Energy for the Floor 10

4.7. Solution of the Conservation Equations 11

5. DISCUSSION OF RESULTS 11

6. REFERENCES 14

APPENDIX A - TYPICAL EXPERIMENTAL RESULTS A-1

APPENDIX B - ESTIMATE OF THE OXYGEN CONCENTRATION OF THE FIRE PLUME

ENTRAINED FLOW B-1

APPENDIX C - CONSISTENCY OF TEMPERATURE AND HEAT FLUX DATA C-1

APPENDIX D - SOLUTION OF THE EQUATIONS D-1

APPENDIX E - COMPUTER CODE E-1

iii
LIST OF FIGURES

Page

Figure 1. Experimental arrangement .... 16

Figure 2. Control volumes (CV) used in the mathematical model ... 17

Figure 3a. Experimental results for rate of mass loss 18

Figure 3b. Theoretical results for rate of mass loss 18

Figure 4a. Experimental results for gas temperature 19

Figure 4b. Theoretical results for gas temperature 19

Figure 5a. Experimental results for incident heat flux to the floor . 20

Figure 5b. Theoretical results for incident heat flux to the floor . 20

Figure 6a. Experimental results for rate of induced airflow 21

Figure 6b. Theoretical results for rate of induced airflow 21

Figure 7. Fuel mass loss rate as a function of ventilation

and fuel area 22

Figure 8. Fuel mass loss per unit area as a function of

incident heat flux 23

Figure A-1. Experimental results for W = 0.077 m and

A = 0.0056 m ° A-2

V

Figure A-2. Experimental results for W = 0.077 m and

A = 0.010 m ° A-3

V

Figure A-3. Experimental results for W = 0.077 m and

A = 0.0225 m A-4

V

Figure B-1. Estimated oxygen concentration for the flow

induced into the flame B-4

Figure C-1. Measured incident heat flux to a water cooled sensor

as a function of the upper gas temperature C-2

Figure C-2. Measured incident heat flux to a water cooled sensor

as a function of the upper ceiling temperature C-3

LIST OF TABLES

Page

Table I. Summary of experimental results 24

Table II. Specified parameters for the theoretical model 25

Table B-1. Estimated entrainment rate B-3

Table B-2. Calculated oxygen mass concentrations B-5

iv
A

c

g

h

H

AH

AH

V

k

k

e k , k . g soot

K

L

m

P

q

r

T

W

X

n

e

Y

6

e

P

OJ

TABLE OF NOMENCLATURE

Surface area

Orifice coefficient

Specific heat of solid, fluid

Geometric configuration factor between the thermal discontinuity

plane and the floor

Geometric configuration factor between the lower walls and fuel

surface

Gravitational acceleration

Convective or total heat transfer coefficient

Height

Heat of combustion

Heat of volatilization

Thermal conductivity

Entrainment constant

Absorption coefficients for gases, and soot

Thermal conductance

Length of room

Rate of mass flow

Pressure

Rate of heat flow

Mass air to fuel ratio

Temperature

Width of room

Height of neutral plane

Height of thermal discontinuity

Parameter defined by eg. 6 Area ratio, A„/A

Wall thickness

Emissivity

Density

Parameter defined by eq. 7 V
Subscripts

a Air

b Burning

d Thermal discontinuity

e Entrainment

f Flame

fuel Fuel

F Floor

g Hot gaseous combustion products

n Neutral plane

o Doorway

p Plume

py Pyrolysis

r Radiation

s Fuel surface

V Volatilization

w Hot walls and ceiling

Superscript

0" Per unit area

VI
EXPERIMENTAL AND THEORETICAL ANALYSIS OF

QUASI-STEADY SMALL-SCALE ENCLOSURE FIRES

J. G. Quintiere, B. J. McCaffrey and K. DenBraven

Abstract

Forty-six small-scale experiments were conducted

to measure the characteristics of horizontal plastic

(PMMA) pool fires in an enclosure as a function of

doorway width and fuel area. A 0.30 m high enclosure

was instrumented to measure sample mass loss, the upper

gas layer and ceiling temperatures, heat flux to the

floor, and the pressure drop across the doorway. Results

are reported for the maximum steady burning period; however, a few cases do not seem to have reached a steady

state. For small sample sizes, a distinct fire plume

could be perceived in the enclosure, while for larger

sample sizes flames tended to fill the enclosure (sometimes to within 2 or 3 cm of the floor) , and extended

out the door opening.

The rate of mass loss is a strong function of the

radiative feedback from the enclosure. However, reduced

oxygen concentration in the flow entrained by the fire

plume seems also to affect the mass loss rate. For the

smaller doorway widths, the rate of mass loss increases

almost directly with ventilation. As the width is

increased, the mass loss rate instead becomes a function of sample area and radiative heat transfer. For

some sample sizes, as the doorway width is increased a maximum rate of mass loss is achieved, followed by a decrease in burning rate at higher ventilation levels.

The temperatures and floor heat flux also tend to follow

this trend.

The data were then compared to the results of a theoretical model. Agreement between theory and data is

qualitatively good. But overall, good quantitative agreement is not achieved. This lack of agreement appears

consistent with inaccuracies of the flame radiation

model and an incomplete description of the flame chemistry.

Key words: Burning rate; enclosure fires; experiment;

mathematical models; radiation; small scale; ventilation.

1
1 . INTRODUCTION

One basic objective of fire safety research is the evaluation of the

risk of fire growth within a room. Such an evaluation must consider all

possible fuel sources and their arrangement, as well as the geometry and

description of the enclosure. The present study is directed at improving

the methodology for making this evaluation.

Specifically, a global mathematical model has been formulated [1]^ for an idealized mode of fire growth. It considers the fire as a steady burning

horizontal slab of fuel on the floor of the compartment. The resulting fuel

vaporization and corresponding thermal and flow characteristics are then

calculated. In general, the model can be used to predict thermal conditions

which may be judged as conducive to rapid fire growth and spread. In order

to validate the model, experiments have been conducted on a small scale to

match this idealized mode of burning. This paper reports on the comparison

of that data with the theoretical results.

Traditionally, compartment fire research has been aimed at the fullydeveloped fire with application primarily to the prediction of the fire

resistance of structural members. This work has been done essentially with

wood cribs, and has elucidated two burning regimes: "fuel controlled" in

which the pyrolysis rate is dependent on the exposed fuel surface area, and

"ventilation controlled" in which the pyrolysis rate is dependent on the

size of the compartment opening (or more precisely the factor A^/h^ ) . The

latter regime has not yet been quantitatively explained, although it is

generally accepted that a reduction in airflow seems to reduce the extent

and rate of heat transfer to the fuel surface, thereby reducing and controlling the pyrolysis rate. The work of Gross and Robertson [2] illustrates

these two regimes of compartment burning, while more recently the work of

Thomas and Nilsson [3] illustrates a third burning regime related to the

porosity of the cribs.

To study developing fires in rooms, many have considered flat horizontal

or vertical slabs of fuel. These surfaces exhibit a greater sensitivity to

radiation from the enclosure, resulting in a greater pyrolysis rate than for

crib fires in rooms. For example, Friedman [4] cites an increase in the

rate of mass loss for a wood crib fire in a room of up to 1.6 times its

corresponding free burn value, yet a threefold increase was associated with

^Numbers in brackets refer to references listed at the end of this paper.

2
the burning of a horizontal slab of polymethyl methacrylate (PMMA)

.

Experiments with liquid fuel pool fires in compartments [5,6] indicate

a similar relationship between mass loss rate and A^/h^ as seen in wood

crib fires, but with less enhancement of burning as that found for PMMA.

In recent years the mathematical modeling of developing fires has

received increasing attention. This has occurred because of the need to

evaluate furnishings items and materials in a room fire scenario, and ultimately to predict the spread of the fire through a building. Representative of the current state of modeling are an analysis by Tanaka [7] of fire

spread over the interior surfaces of a room, and a generalized computer code

developed by Emmons et al. [8]. This code has favorably predicted transient

measurements from full-scale experimental room fires. In contrast, the

model to be presented here does not consider time as a parameter. Instead,

it can be used to indicate the "critical" values of fuel area and room

opening at which thermal conditions in the room would exceed a tolerable

level or would promote further fire growth.

2. DESCRIPTION OF THE EXPERIMENT

Square slabs of polymethyl methacrylate (PMMA) were burned in a small

compartment constructed of low density alumina silica block. A sketch of

the experimental arrangement is shown in figure 1. The internal dimensions

of the enclosure were 0.30 m x 0.30 m x 0.56 m deep with a doorway height of

0.225 m and widths ranging from 0.015 m to 0.285 m. Five PMMA sample sizes

were burned, ranging in face area from 0.0025 m^ to 0.0225 m^ with a constant

thickness of 0.013 m. The PMMA was burned on a platform 0.03 m above the

floor and centered 0.40 m from the doorway. The weight was continuously

recorded by a (linear variable differential transformer type) load cell

which supported the platform, and was sufficiently below the floor to remain

cool. Two bare chromel-alumel thermocouples of 0.025 mm diameter wire were

used to measure the upper gas and ceiling temperatures at the locations

shown in figure 1. The ceiling thermocouple was pressed flush into the

surface. A water-cooled thermopile heat flux sensor of absorptivity 0.97

was used to record the incident heat flux to the floor. The pressure

difference across the compartment wall was measured with a sensitive

electronic manometer.

Except in the flame region, the thermocouples yielded representative

temperatures of the upper hot gas layer and upper walls and ceiling. The

heat flux sensor indicated the incident radiative flux from the enclosure to

3
the PMMA surface, since the PMMA flame has a small emissivity. The pressure

drop measurement was used to estimate the induced flow rate through the

doorway.

Forty-six experiments were conducted with the fuel size and doorway

width varied. Runs were repeated if instruments malfunctioned or to check

reproducibility; in general, reproducibility of the results was very good.

The procedure for each experiment consisted of first inspecting and cleaning

the probes. A mixture of PMMA chips and paraffin oil was used as an accelerant to insure uniform ignition of the PMMA sheet. The PMMA sample was

lined along the sides and bottom with aluminum foil to prevent uneven burning

at the edges. Just prior to ignition, a small amount of pentane was added

to the PMMA surface. The sample was ignited and allowed to burn completely,

during which time the data were recorded continuously.

For the most part, two modes of burning could be discerned in these

experiments. The first mode was exhibited by the smaller PMMA samples.

This was characterized by a distinct pulsating laminar-like flame plume

within the enclosure. These samples burned slowly, with complete consumption

generally taking 25 to 30 minutes. A steady burning period persisted for a minimum of five minutes. The second mode of burning was exhibited by the

larger size samples. The consumption period for this mode averaged about 15

minutes. These samples initially burned slowly and steadily, then the

burning increased rapidly as turbulent flames stretched across the ceiling

and extended out of the doorway. For the small door widths the flames

filled the enclosure to within 2 to 3 cm of the floor. In general, a steady

burning period could be discerned over the last several minutes of the burn,

but in a few cases no steady-maximum burning was achieved before consumption

(see appendix A)

3 . EXPERIMENTAL RESULTS

The data were analyzed to determine the period of maximum steady burning

and the corresponding average values of the variables measured. This was

done by identifying a significant period over which the rate of mass loss

was at its steady peak. The corresponding periods of maximum-steady temperature were nearly coincidental. These maximum-steady values are listed in

table 1 along with their deviation during this "period of steady burning."

Also listed in table 1 are calculated values of induced airflow rate.

This was determined using the following assumptions:

4
1 . the fluid in the room is stratified into two horizontal regions

of uniform temperature,

2. the pressure in the enclosure follows a hydrostatic distribution,

and

3. an orifice flow model applies at the doorway.

The first assumption is generally acceptable, the second is valid based

on the work of McCaffrey and Rockett [9], and Prahl and Emmons [10] have

demonstrated the applicability of the third assumption. Based on these

studies the procedure for calculating the induced airflow rate, iti is as

ci follows

:

(neutral plane height i.e., the position of zero pressure drop and velocity

in the doorway)

X

n

( 1 )

where Ap is the pressure difference at the ceiling height, H.

(exit mass flow rate)

% = I - («o-Xn)

(inlet air mass flow rate)

m = m - m

a g V

(3)

(Since numerous symbols will be used in the text, most will be defined in

the table of nomenclature only.) The measured values of Ap, T , and m

. . g

\' were used to determine X , m , and m . The flow coefficient, c, v^’as taken

n g a as 0.7, but could be higher for this scale experiment [10]. In cases where

the measured value of the pressure difference, Ap, was low due to soot

clogging the pressure tap, values of airflow were not calculated. The

application of this procedure could overestimate X^ by about 30% [^^].

Since the flow coefficient for the exit can exceed 0.7 (but is not likely

to be greater than 1) , the net effect of variations in c and X could

yield an estimated 20% error or less in m^

.

5
4 . THEORETICAL MODEL

The basis of the theoretical model has been previously derived [1]

.

Consequently, no detailed derivation will be presented; however, the equations

will be listed along with a description of their significance. Basically the

equations have been derived by applying the conservation laws to distinct

spatial regions (or control volumes, CV) that possess an approximately

uniform character. These regions are identified in figure 2. The fuel

(CVj) is considered to be a steadily vaporizing solid. The fire plume

(CVjj) is considered to be the region in which all of the combustion occurs,

and is assumed to be a cylinder for radiation calculations. The upper

region (CV^^j) , roughly considered as the smoke layer, is considered to be

at a uniform temperature, T . Energy balances are also applied to the upper

walls and ceiling, and to the floor, to determine these surface temperatures.

These surfaces are considered to be black for radiation calculations. The

philosophy of this development has been to include all of the processes that

have been identified and that are amenable to mathematical description.

Chemical processes have not been completely modeled, and some processes have

been modeled approximately since a more elaborate description may not be

justified at this time.

4.1. Flow Model

The calculation to determine the rate of induced flow is based on Rockett's derivation [11]. The flow exiting the doorway has already been

given by eq. (2). The airflow entering the compartment is given by:

m

2T c W p , 3 o ^ a

(4)

This same flow is assumed to be entrained in the fire plume and eq. (4) is

based on the result from Steward [12] for a turbulent diffusion flame.

6
and to 1

(7)

rC T

g a

The applicability of this turbulent plume model may be questioned for this

scale experiment since the flame did not always appear to be fully turbulent.

Moreover, such models may not be very accurate near the base of the plume.

In this regard, McCaffrey and Rockett [9] have found that the measured

doorway airflow has a much stronger dependence on the fuel supply, m^,

than eq. (5) indicates; and that the entrainment coefficient, , appears to

vary accordingly. Consequently an expression for k^ has been developed from

the experimental results of m for large doorway openings. This was estimated

3L as

k = 0. 1 + 0. 5 m (8) e V

where m is in g/s.

Equations (3), (4), and (5) may be considered as having three unknowns:

airflow rate, m , neutral plane height, X , and the height of the hot layer,

a n • X,. In fact, these were solved in that fashion with m specified and T

d V g

determined through an iterative process from a solution of the energy

equations to follow.

4.2. Energy Conservation for the Fuel (CV^)

The solid is assumed to vaporize at a constant surface temperature, T^,

and steady burning is assumed. The vaporization rate, m^, for a solid of

surface area, A^, exposed to a net surface heat flux, q^" is

m

V

V

C. , (T -T ) + AH fuel s a V

(9)

The surface heat flux cannot easily be determined without a complete understanding of the flame chemistry and radiation properties. An approximate

expression is used which at least includes the major contributing factors.

+ (l-£j) FpgOTj,- - OT^-

( 10 )

7
This sum represents the convective heat flux from the flame; the incident

radiative flux from the flame, upper hot layer and surfaces, and the lower

heated surfaces; minus the surface reradiation. The unsatisfactory aspects

of this formulation may be obvious:

1. The flame temperature is constant and uniform over a prescribed

volume

.

2. The convective contribution ignores the effect of fuel vaporization

and the convective coefficient has been treated as a constant,

independent of the fuel dimensions.

3. Flame emissivity is based only on flame height, and is represented

as

where

1 - exp (- H^)

= 16.2

(r+(jop /p ) 2 a V CO P^2g (l-oo) ^ Vs. V

m.

( 11 )

(12a)

or Hf = X^, (12b)

whichever is smaller [12]. A representation that includes flame

diameter, or flame shape in the compartment (if this were available)

,

could improve this formulation.

4.

The contributions of compartment radiation are based on approximate

expressions for the interchange factors between these sources of

radiation and the fuel surface. The geometric shape factor

is calculated for parallel surfaces at the layer depth and the

floor, and the shape factor between the lower walls and fuel

surface is heuristically represented as

FFS 1

W

Vw^ + 4X,2d

(13)

4.3. Energy Conservation for the Fire Plume (CV^^)

The assumptions for the energy balance on the fire plume are that all

combustion occurs within that region, the fluid crosses into the hot layer

region with temperature T^, and the flame plume radiates as a cylinder at

temperature T^ . Essentially, this energy balance equates the sum of the

combustion energy and the radiant energy absorbed by the flame minus the

energy radiated from the flame to the convected energy transported through

the control volume (CV )

.

8
( 14 )

m, ah + e. F,^a (e T + (1- e )T ""V “ e oT ^ • 2H. * b fdF\gg g'wyv ff f\v

= m C (T -T ) + m

g g p a py

AH + T (T -T ) - C (T -T ) V fuel s a g s a

Where there is insufficient air for complete combustion, m /m < r: 3. V

m, = m /r

,

b a (15a)

m = m - m, ; py V b (15b)

and, for excess air, ra /m > r

a V

m. m , V

(16a)

and

m =0

PY

(16b)

4.4. Energy Conservation of the Hot Upper Layer (CV^^^)

This energy balance considers only convective and radiative phenomena.

It considers a uniform fluid temperature, , and a uniform surface temperature, T^, for the bounding walls and ceiling. These assumptions are aood

since this region is well mixed unless extensive combustion occurs within

it. No mixing with the layer below is considered except for the plume

penetration. This is not valid near openings where the entering air jet

will entrain some hot fluid into it. This point will be addressed later.

m C (T -T ) g g p g

hwwgw A (T -T ) + q" A + q" , A„ + a T A ^r,ww ^r,dF w o

(!"'>

The net radiation from the gas to the walls is

‘r , w

c oT '" + Y (1-c ) aT„"* - g g g F

1- (l-^)d-eq)

where

( 19 )

9
the ratio of floor to the wall and ceiling area bounding CVjjj

radiative flux from the lower plane of the hot layer is

The net

‘r,d 9 9

(1-e )0T ^ g' w

- a T ( 20 )

The radiation emitted through the doorway is relatively small. Hence, it

has been approximated in eq. (17) . The emissivity of the hot upper layer is

represented as a function of the soot concentration and the H2 O and CO2 composition of the layer.

eg = 1 - exp (k + k (H-X,)

' g soot d

( 21 )

where k and k . are the absorption coefficients for the gases and soot

g soot

respectively.

4.5. Conservation of Energy for Upper Walls and Ceiling

Since the characteristic time for thermal penetration of the compartment

walls was approximately 10 minutes, and most experiments exceeded this time,

steady conduction was assumed for the enclosure structure. The resulting

energy equation is

^r ,w w

(T -T ) gw . = K (T -T ) w w a

( 22 )

where K

w

1

(23)

which accounts for conduction through the wall and a convection loss on the

outside

.

4.6. Conservation of Energy for the Floor

A balance of radiation, convection, and conduction for the floor yields

''dF = hp(Tp-T^) + K„(Tp-T^). (24)

10
4.7. Solution of the Conservation Equations

The algebraic equations were solved numerically employing a NewtonRaphson technique for first the flow equations (2) - (5), then the energy

equations. Basically the procedure is to specify m^, and guess to solve

the flow equations for , X^, and m^ . The energy equations are then solved

for T , T , T_ , and A . This process is reiterated using a new value of T w g F V

^ g

until satisfactory convergence is achieved (appendices D and E)

.

The values selected for the parameters that best matched the experimental

conditions are listed in table 2. Some remarks explaining or justifying

their selection are listed there also.

5. DISCUSSION OF RESULTS

The experimental results display a strong coupling effect between the

rate of burning and the energy feedback to the fuel from the compartment.

The theoretical results are in good qualitative agreement with the data, and

in some cases, good quantitative agreement also. These features are evident

in figures 3-5 where the rate of mass loss, gas temperature, and radiative

heat flux to the floor have been plotted against fuel surface area for each

of the experimental doorway widths (W^) selected. The ceiling temperature

results have not been plotted since they are similar in character to the

gas temperature results for theory and experiment.

Figure 3a shows that as the fuel area is increased, the rate of mass

loss increases, almost linearly with at first, then more rapidly as the

compartment is heated and significant radiation is received by the fuel.

Eventually so much fuel is vaporized that it cannot be burned within the

compartment due to insufficient air. This excess fuel serves to dilute the

products of combustion and hence to reduce the temperature and rate of heat

flux received by the fuel surface from the compartment. This results in a decrease in the dependence of m^ on A^. Since airflow rate sets an upper

limit to the burning rate in the compartment, a larger fuel sample can burn

in a compartment with a wider doorway before the effect of excess fuel is

noted

.

The corresponding theory shown in figure 3b displays multivalued results

indicated by dashed curves that are physically impossible. This mathematical

phenomenon was displayed in this case since the solution procedure used m^, as the independent variable. Initially, as m^ was incremented, the solution

11
yielded increasing values for A^. But as heat transfer from the enclosure

to the fuel became significant, an increase in m^ resulted in a decrease in

That is, at this higher surface heat flux a smaller area was required

to support this fuel supply rate. Moreover, the upper inflection point on the dashed curves marks the stoichiometric point above which excess fuel is

released. One interpretation of this result is that a critical fuel area

exists above which a rapid increase in the burning rate, temperature, and

heat flux would occur. The state of the fire would move from a relatively

small fire with sufficient air for combustion to a fire which produces

excess fuel and is "ventilation controlled." Thus the steady-state model

suggests one mechanism for a rapid transition in fire growth (flashover)

The validity of this interpretation must be more fully explored with a transient model; however, the data in figure 3a tend to support this idea —

particularly since the "unsteady" data points are on the steepest portion of

the curves.

The results for gas temperature in figure 4 demonstrate that the temperature is highest for the smallest doorway and smaller fuel areas. However,

for large fuel samples, the inverse is true with regard to doorway width.

Thus it is clear that the assessment of the severity of thermal conditions

due to a fire is a complex function of fuel and ventilation conditions.

Moreover, the agreement between theory and experiments tends to follow that

of the mass loss results. This suggests that a more accurate determination

of mass loss would improve temperature prediction.

Figure 5 displays the results for incident heat flux to the floor. The

theoretical value was calculated as

q

II F aFdF e T + g g

(1-e )T

g w (25)

where the first term represents the incident flux from the upper hot layer

and the second term represents the heat flux from the flame (insignificant

for this scale analysis) . The disparity in agreement here is due to the

inaccuracy of the temperature prediction.

Figure 6 shows good agreement between theory and the data for airflow.

However, that is based on empirical selection of the entrainment relationship

(eq. (8)). More study must be made of this aspect of the flow model.

12
Figure 7 is presented in a form common to results for the burning of

wood cribs, i.e., as a function of compartment ventilation. For wood cribs,

the data initially follow a linear plot (e.g., m^ ~ followed by

horizontal lines of constant burning rate for corresponding crib sizes. The

PtlMA data suggest this same initial trend, but with some preferred ordering

with fuel area. The compartment radiation has a pronounced effect on the

PMMA burning rate at high ventilation which is markedly different from crib

fires. A locus of theoretical fires with an incident floor heat flux of

2 W/cm^ is also shown on figure 7. This corresponds approximately with the

data. The utility of this plot can be appreciated if the heat flux locus is

recognized as a condition for other potential ignitions within the enclosure.

Finally, the effect of radiation on the mass loss rate of PMMA is

plotted in figure 8. It appears that a reduction in the oxygen concentration of the flow entrained by the fire plume reduced the mass loss rate.

This is qualitatively consistent with the results obtained by Tewarson [13]

with a calorimetric apparatus. In fact, despite the differences in experimental conditions, his data [14] taken under normal air conditions are in

some agreement with the enclosure results, especially at high flux. The

results in figure 8 can be explained by considering the mass loss rate per

unit area to be directly dependent on the sum of the incident floor heat

flux and the heat flux from the flame. A reduction in the oxygen would

reduce the flame heat flux. This effect is not accounted for in the current

model (eqs. (9) and (10)). However, the values of oxygen concentre tion

calculated for figure 8 were based on the rate of mixing between the hot

upper layer and the jet of induced airflow at the doorway. The mixing rate

was determined from measurements taken in a similar experimental configuration

(appendix B) [15].

In conclusion, the theory presented yields good qualitative results

when compared \,’ith the data. Weak features of the model appear consistent

with the accuracy of the results. Improvements in the models for radiative

transport, particularly from the flame, should improve the results. Also in

the flow model, plume entrainment needs to be better understood along with

mixing within the compartment. Finally, the effect of oxygen depletion on

burning should be included. In general, it appears that a conceptual basis

for predicting features of fires in compartments has been established and

with refinement should lead to more accurate results.

13
6 . REFERENCES

[1] Quintiere, J. G., Growth of fire in building compartments. Fire

Standards and Safety, ASTM STP 614, 131-167 (1977).

[2] Gross, D. and Robertson, A. F., Tenth Symposium (International) on

Combustion, 931-942, The Combustion Institute (1965).

[3] Thomas, P. H. and Nilsson, L., Fully developed compartment fires:

new correlations of burning rates, F.R. Note No. 979, Fire Research

Station, Borehamwood, England (Aug. 1973).

[4] Friedman, R. , Behavior of fires in compartments. International

Symposium Fire Safety of Combustible Materials, 100-113, Edinburgh,

Scotland (oct. 15-17, 1975).

[5] Tewarson, A., Combustion and Flame, Vol. 19, 363-371 (1972).

[6] Takeda, H. and Nakaya, I., Small-scale model fire in enclosure

using liquid fuel - effect of ventilation factor. Paper presented at

the Second Joint Meeting of the U.S. - Japan Panel on Fire Research

and Safety, UJNR, Tokyo (Oct. 19-22, 1976).

[7] Tanaka, T. , A mathematical model of a compartment fire, BRI Research

Paper No. 70, Ministry of Construction, Japanese Government

(Feb. 1977) .

[8] Emmons, H. W. , Mitler, H. E., and Trefethen, L. N. , Computer fire code

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

Cambridge, Mass. (Jan. 1978) .

[9] McCaffrey, B. J. and Rockett, J. A. , J. Research, National Bureau

Standards (U.S.), Vol. 82, No. 2, 107-117 (1977).

[10]

Prahl , J. and Emmons, H. W. , Combustion and Flame, Vol. 25, No. 3,

369-385 (Dec. 1975).

[11] Rockett, J. A. , Combustion Science and Technology, Vol. 12, 165 (1976)

[12] Steward, F. R. , Combustion Science and Technology, Vol. 2, 203 (1970)

.

14
[13] Tewarson, A. and Pion, R. F., Combustion and Flame, Vol. 26, 85-103

(1976) .

[14] Tewarson, A., Fire and Materials, Vol. 1, 90 (1976).

[15] McCaffrey, B. J. and Quintiere, J. G., Heat Transfer and Turbulent

Buoyant Convection, Vol. II, 457-472, Hemisphere (1977).

[16] Modak, A. T. and Croce, P. A.: Plastic Pool Fires.

FMRC Serial No. 22361-3, Factory Mutual Research, Norwood, Mass.,

June 1976.

[17] Markstein, G. H., Radiative properties of plastic fires. Seventeenth

Symposium (International) on Combustion, The Combustion Institute

(to be presented)

.

[18] Zukoski, E. E. and Kubota, T., An experimental investigation of the

heat transfer from a buoyant gas plume to a horizontal ceiling - part 2. Effects of ceiling layer, Progress Report. Grant No. 5-9004,

National Bureau of Standards (U.S.) (June - Sept. 1975).

k

15
16 i

Figure

1.

Experimental

arrangement
17

Fiqure

2.

Control

volumes

(CV)

used

in

the

mathematical

model
X

1.115

(t/lj ‘SS01 SSVN iO 31VH

18

Figure

3a.

Experimental

results

for

rate

Figure

3b.

Theoretical

results

for

rate

of

mass

loss

of

mass

loss
CO

19

Figure

4a.

Experimental

results

for

gas

Figure

4b.

Theoretical

results

for

gas

temperature

temperature
Wa=l.2l5

«= 2

(;UI3/Ml .^b ‘H001J 01 XnU 1V3H 1N10I3NI

20

Figure

5a.

Experimental

results

for

incident

Figure

5b.

Theoretical

results

for

incident

heat

flux

to

the

floor

heat

flux

to

the

floor
kg=0.1+0.5

ihy

(riiy

in

g/s)

21

Fi'iurp

FxFx.-r

im^rnt

a1

ro^ult-s

for

r.itf.

I'iquro

r,b.

Theoretical

results

for

rate

of

inhucod

airflow

of

induced

airflow
RATE

OF

MASS

LOSS,

|g/s)

Figure 7. Fuel mass loss rate as a function of ventilation

and fuel area. Theory: Data: A - 0.0025 , O - 0.0056 m2, > - 0.0100 m2

,

Q ~ 0.0156 m2,

- 0.0225 m2. Open symbols represent data less

than 2.0 W/cm2 . Shaded symbols represent data

greater than 2.0 W/cm2

.

22
l/> rvi

C/> GO

oo

GO

I-’iquro 8. Fuel moss loss per unit as a function of

incident heat flux. (The oxyqen concentration

in the flov/ entrained by the fire plume v\?as

er. t i :no ted . )

28
TABLE I Summary of experimental results

"v

'fP ip "*3 w Duration Steady T Maximum

^0 Duration of Mass W Incident Room Calculated

Exp Doorway Fuel of Steady Loss Gas Ceiling Floor Heat Pressure Air

No. Width Area Burn Burning Rate Temperature Temperature Flux Rise Flow Rate

m m* min min g/s •c -c W/cm* N/m® g/s

IS 0.015 0.0025 26 - (0.040) 270 + 5 202 + 10 0.39 ^ .07 1.16 1 .04 0.712

14 0.0025 26 - (0.040) 280 + 10 212 + 10 0.39 .07 1.16 1 .08 0.680

SA 0.0025 26 6.5 0.040 315 + 12 245 + 12 0.54 + -07 [0.68 , .08]

6A 0.0056 25 5 0.100 522 * 12 450 + 12 2.01 i 'll

4A 0.0100 22 4 0.207 725 + 25 660 + 25 5.40 1 i;”

7A 0.0225 23 6 0.383 645 + 35 590 + 50 4.03 .58 1.48 + .32 0.157

1 0.030 0.0025 >20* (0.032) 300 + 10 235 + 20 0-52 i 1.16 1 .04 1.30

2 0.0025 >19* (0.032) 275 + 10 205 + 5 0. 40 + .01 l.l4 1 .04 1.34

lA 0.0025 27 9 0.032 285 ^ 5 212 + 10 0.84 1 .08 0. 54

8A 0.0056 24 4 0.098 463 + 5 393 + 12 1.31 1 .04 1.01

2A 0.0100 20 3 0.300 717 + 50 645 1 60 4.37 + 1.4 -

6 0.0100 19.5 (0.30) 778 jL 50 730 ^ 50 5.98 + . 23 2.16 1 .08 2.01 9A 0.0100 18 3 0.292 732 ^ 50 683 + 50 4.60 ^ 1.2 [1.44 , O]

3A 0.0225 19 2 (0.490) 730 + 35 680 + 50 4.83 +-1.4 2.00 1 0 1.54

lOA 0.0225 19 s 0. 490 740 + 25 700 + 25 6.21 + 1.2 [1.64 , .08]

3 0.0225 21 (0. 490) 635 + 75 610 + 75 5.75 + 2.3 2.00 1 .08 1 . 78

llA 0.077 0.0025 24 6 0.037 210 + 5 160 7 0-21 1 -.11 0.68 1 .08 1.14

12A 0.0056 24 4 0.097 37B ^ 10 288 + 10 0.74, 1.00 1 .08 1.S7

13A 0.0100 16 if 0.500 960 + 35 778 + 35 6 44 + .69 [0.92 , .12] 31A 0.0156 11.5 2 0.790 910 + SO 865 + 50 9.88 + .65 [0.72 + .20] 15A 0.0225 10 2 0.870 902 + 25 854 + 35 10.0 ^ 9 [1.28 , .08] 14A 0.0225 10 3 0.875 902 + SO 865 + 50 8.05 + 1.2** 1.80 jL -12 2.53

4 0.115 0.0025 23 (0.038) 188 + 5 141 + 5 0.17 + .01 0,72 + ,04 2,38

17A 0.0025 26 6 0.038 195 + 5 149 + 3 0.16 jL -01 0.76 + .08 2 ,85 18A 0.0056 27 5 0.078 317 + 7 239 ^ 5 0.39 + .03 1.12 + 0 4 . 26

5 0.0100 14 (0.367) 876 + 12 766 + 25 7.59 ^ .46 1.96 + .04 6.04

16A 0.0100 17 1.5t 0.367 741 + 10 644 + 5 4.03 + .30 1.68 + .08 4,74

30A 0.0156 11 i.st 1.000 993 + 25 937 + 25 11.0 + .8 [1.00 , .20] -

7 0.0225 8 tl.225) 927 + SO 902 ^ 50 10.8 ^ .23 2.24 ^ .12 7.09

2 3A 0.0225 8 2 1.225 902 * 50 854 ^ SO 9.62 + .78 2.24 + .08 7.26

8 0.185 0.0025 21 (0.030) 158 + 5 112 + 5 0.23 + .2 [0.80 , .20] 19A 0.0025 28 6 0.030 154 + 5 112 + 3 0.09 + .01 0.56 + .04 2.60

20A 0.0056 27 4.5 0.075 263 + 10 205 + 5 0. 30 .13 0.88 ^ .08 4.42

21A 0.0100 25 5 0.163 385 IS 344 + 10 0-91 1 :°ct 1.24 ^ .04 7.11

9 0.0100 22 (0.163) 415 ^ 10 337 + IS 0.99 + .12 1.32 ^ .12 7. 75 29A 0.0156 16 It 0.908 973 + 25 863 ^ 25 [1.16 , .08] -

10 0.0225 6.5 (1.50) 975 + 50 927 + 50 9.2 12.3 2.04 + .04 8.87

22A 0.0225 9.5 2 1.50 950 + 75 902 + SO 10.8 1 .78 1.88 ^ .08 7.29

11 0.285 0.0025 22 (0.033) 139 + 3 100 + 3 0.18 1 .02 0.52 + .04 3.81 24A 0.0025 28 6 0.033 146 + 7 110 1 3 0.08 1 .01 0.48 + .08 2.37

25A 0.0056 33 5 0.068 220 + 3 170 + 3 0.21 1 .01 0.80 ^ .08 6.76

12 0.0100 25 (0.148) 341 * 10 268 + 10 0.62 1 1.12 jL •0'^ 9.77

26A 0.0100 27 4 0.148 330 + 12 268 + 12 0.52 1 .01 1.04 + .08 8.17

28A 0.0156 20 IT 0.527 693 + 25 595 + 25 3.1 1

.26 1.43 + .08 8.18

13 0.0225 7 (1.56) 1034 + 25 902 + 25 10.4 1 .69 1.84 + .08 10.4 27A 0.0225 8.5 2 1.56 1022 + 25 925 + 25 10.4 +1.3 1.92 + .12 11.9

Sample was extinguished before complete consumption

^ May not have reached steady-state

’•^Pressure tap clogged

Estimated to calculate m

ft A a Water coolant hose melted

Note: Variation in the measured quantity refers to the span of values about a mean over the duration of steady burning

24
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25

APPENDIX A TYPICAL EXPERIMENTAL RESULTS

Three experimental conditions have been selected to illustrate the

general characteristics of the data recorded over the duration of an experimental run. For illustration, the doorway condition = 0.077 m was selected

for three fuel areas: 0.0056, 0.010, and 0.0225 m^ . The smallest area exhibited the first mode of burning, while the largest area sample exhibited the

second mode of burning. The intermediate sample size appeared transitional,

and did not necessarily reach a steady state.

The results are shown in figures A-1, A-2, and A-3. These plots have

been traced from the continuous data records and converted into the units of

the physical variable measured. It could be anticipated that the radiant

heat flux would be very sensitive to temperature since q" ~ T^^ and that

the room pressure difference would be relatively insensitive to temperature

since Ap ~ 1 - T /T by eq. (1) . These trends are confirmed by the results.

a g

Also the good reproducibility of the results is indicated in figure A-3.

A-1
Figure A-1. Experimental results for W = 0.077 m and A = 0.0056

o V

A2

INCIDENT

HEAT

FLUX

TO

FLOOR

|W/cm2|
MASS

|g)

GAS

AND

WALL

TEMPERATURES

|°C|

TIME (minj

Figure A-2. Experimental results for W

o 0.077 m and A = 0.010 mV

A3

INCIDENT

HEAT

FLUX

TO

FLOOR

|W/cm2)
Figure A-3. Experimental results for = 0.077 m and = 0.0225 m^

A4
APPENDIX B. ESTIMATE OF THE OXYGEN CONCENTRATION

OF THE FIRE PLUME ENTRAINED FLOW

As air enters the doorway of the enclosure it mixes with some hot fluid

resulting in a vitiated air layer along the floor. This flow is then en- trained into the fire plume. This vitiated air would reduce the energy

release and thus affect the fuel mass loss rate. A simple model for this

(based on eq . (9) ) suggests that the rate of mass loss per unit area is

proportional to the heat flux from the flame (q^) and the enclosure

(q" ) enclosure '

m ~

V enclosure

.

(B-1)

For a fixed heat flux from the surroundings, a reduction in the oxygen

concentration would reduce q^. This is consistent with the results of

Tewarson and Pion [13].

It is believed that the data shown in figure 8 follow the model given

by eq . (B-1) . To establish this relationship, the oxygen concentration of

the entrained vitiated air must be determined. The following analysis

attempts to estimate this concentration

.

P.'ODEL

Assumptions: (1) Upper layer is well stirred at a uniform concentral ion

.

(2) Air enters at the doorway and is contaminated by uases

entrained from the upper layer.

(3) The entrained fluid is well mixed with the incoming air

but only a mass flow rate equal to m^ is entrained into

the fire plume and mass flow rate m is recirculated

.

B-1
Oxygen specie conservation for CVIV

[Oxygen In] = [Oxygen Out]

0.23 m+<t>m = 4> (m+m) (B-2)

a g e a a e

where

and

[>g is the oxygen mass concentration in the upper layer (CV^^^)

3^ is the oxygen mass concentration leaving and entrained into

the fire plume.

Oxygen specie concentration for

0

^ supplied 0

^ consumed

+ 0„ recirculated |0_ out"]

to fire (CVjj) in fire (CV^^) L ^ j L 2 J

) m - 0.23 rm + (<|3 a a V a

3 ) m

g e

3 m

g g

(B-3)

Solving these equations results in:

For excess air, m S o-r

~

' V 0 . 23r

and

0.23 (m - rm ) __a

^

m + m

a V

= 0.23

m

m + m

a e>

(m - rm ) a V m

(m + m ) (m + m ) a V a e

(B-4)

(B-5)

. <f> m

3. cL For insufficient air, m > - V 0.23r

= 0 (B-6)

and

m

= 0.23

m + m

a Gj

(B-7)

B-2
Finally, the entrained flow was estimated from the measurements made

in a similar scale experiment and doorway configuration [15]. These results

are presented in table B-1 as fractions of the doorway airflow rate. The

fractional factor is given as a function of the width ratio W /W. ^ o

m = f • m (B-8)

e a

Table B-1. Estimated entrainment rate

w

o

(m)

w /w

o

f = m /m

e a

0 . 015 0 .05 1 .

6

0 . 030 0.10 1.2

0 . 077 0 .257 0.5

0 . 115 0. 383 0.4

0.185 0 .617 0. 3

0 .285 0.95 0 .

2

The values of

^ and

$ ^ were then determined from the experimental airflow rate and equations given above. The results of those calculations are

given in table B-2. From those results as shown plotted in figure B-1, it is

clear that for large fires and small doorway widths, the entrained flow into

fire has a low oxygen concentration. The effect of this vitiated air on fuel

mass loss was shown in figure 8 by discriminating between a high and low set

of oxygen concentration values in the data. A closer examination of the re- sults may indicate a more continuous effect of reduced oxygen on mass loss

but there are some exceptions in the data. In general, the effect of oxycfcn

appears to have been demonstrated.

B-3
C>l

^0 ‘uiv asanoNi 3iiiJ 3hi jo

NOliOVyj SSVW N39AX0 a31VNIlS3

B-4

Figure

B-1.

Estimated

oxygen

concentration

for

the

flow

induced

into

the

flame
Table B-2

,

Calculated oxygen mass concentrations

Exp

.

No

.

W

o Doorway

Width

(m)

A

V

Fuel

Area

(m2

)

"g

Calculated

0

^ Mass

Cone

.

^ a Calculated

0

^ Mass

Cone .

15 0 . 015 0 .0025 0 . 12 0.16

14 0 .0025 0.11 0.16

5A 0 .0025 -- -- 6A 0 .0056 -- 4A 0 . 0100 -- -- 7A 0.0225 0.0 0.09

1 0 .030 0 .0025 0 . 18 0.20

2 0 .0025 0. 18 0 . 20

lA 0.0025 0 . 11 0 . 17

8A 0.0056 0 . 04 0.13

2 A 0 .0100 -- --

6 0 .0100 0 . 0 0. 10

9A 0 . 0100 -- -- 3A 0 . 0225 0 .

0

0 .10

lOA 0.0225 -- --

3 0.0225 0.0 0. 10

llA 0.077 0 .0025 0. 16 0.21

12A 0. 0056 0. 11 0.19

13A 0 . 0100 -- -- 31A 0. 0156 -- -- 15A 0.0225 -- -- 14A 0 .0225 0.0 0. 15

4 0 .115 0 . 0025 0 . 20 0.22

17A 0.0025 0 .20 0 . 22

1 8A 0 .0056 -- --

5 0. 0100 0. 11 0 .20

16A 0 .0100 0 . 08 0.19

30A 0 .0156 -- --

7 0 .0225 0 .

0

0 . 16

23A 0 .0225 0.0 0.16

8 0 . 185 0.0025 -- -- 19A 0 .0025 0 . 21 0 . 22

2 0A 0.0056 0 . 19 0 . 22

21A 0.0100 0.18 0.22

9 0.0100 0.19 0.22

29A 0.0156 -- --

10 0.0225 0.0 0. IS

2 2A 0 .0225 0 .

0

0 . 1 s 11 0 .285 0 .0025 0. 21 0.23

24A 0 . 0025 0 . 20 0.2 3 2 5A 0. 0056 0.21 0.2"

12 0 .0100 0 . 20 0 . 22

26A 0. 0100 0 . 19 0.22

2 8A 0.0156 0 . 10 0 . 22

13 0.0225 0.0 0. 1^

27A 0.0225 0.0 0.

R-5
>:• ..

hi::'

-,0 '

fmn Si.ft

,ji W-—1J4 ..A.-

,m^H \.n

cji^ . .qM#^.»r>,^

.. -MJ

'',! *^''''.lT.a«-

,i

, y ••^" i-'V ^ 5 V /'/ ? /'

^1

| *^^y li

i>»

<'

>i

’fyfr, ftvis,g^

h'^'V

"'^'r ^

/ WA‘-C ,4:f

j; f '

' >'. >: '.'iMM.

tsf^0iA

*r ,v

. ^WF^V'sj,; • ';;

; ... -'i

,. . .;i.

•- ‘ .?

iiJEv,,,; -^,.

ii

f'

' ':i;r:,^ ' -.I*';’ ,,

*., ;i ^ \ "C‘ WM:-

' i!;-i:. ':*• %*H'*""«s ‘ ;»> '•m i’ * •'" '' •’Allfj’

P Jf .i:/. d'.,
APPENDIX C. CONSISTENCY OF TEMPERATURE AND HEAT FLUX DATA

Equation (25) gives an approximate expression that could be used to

relate the measured gas and ceiling temperatures (T^ and T^) with the

measured floor heat flux, q" . It can be shown that the contribution from

r the flame is insignificant for this small scale experiment, and the shape

factor is between 0.7 and 1. Therefore dF

q

MF

"F dF (1 (C-1)

Also for small values of X^ ("large" fires)

^ F.^ -0.5 (0.96) -0.5

g dF

while for large values of X^ ("small" fires)

e F,^ - 0.25 (0.68) ~ 0.15

g dF

Based on these estimates, and equating "large" and "small" fires to hiqh

and low temperature levels it follows that

q

MF

0 .

5

oT + 0.5

g

nTw

for high temperature levels;

and

(C-2)

q^ - 0.15 oTg'^ + 0.53 nT^^

for low temperature levels.

(C-3>

Since T

g

is greater than T by up to 100°C, it follows that

w

aT

g ^ ^F ^ ^’^w

is true for high temperature, and almost true at the lower temperature I eve Is

in these experiments. Figures C-1 and C-2 seem to follow that trend. Moreover, since T and T are of similar magnitude, q" plotted auainst

w g

either T or T tends to follow a fourth power relationship,

w g

C-1
INCIDENT

HEAT

FLUX

TO

FLOOR

Qp

(W/ctn’j

GAS TEMPERATURE, Tg |K|

Figure C-1. Measured incident heat flux to

as a function of the upper gas

C-2

a water cooled sensor

temperature
INCIDENT

HEAT

FLUX

TO

FLOOR,

qj'

(W/cm^)

Figure C-2. Measured incident heat flux to a water cooled sensor

as a function of the upper ceiling temperature

C-3

APPENDIX D. SOLUTION OF THE EQUATIONS

This section outlines the method of solution

Flow Equations: eqs . (2) - (7)

Introduce dimensionless variables as

m

m

miax

M

V

m

V

m

max

;vherc

Also

mmax

/— V

^ c ‘ 2g P W H

^ : 3 ^ a o o

z =

and d =

The resulting three equations follow:

V2

M + M

a V

M

/d(l-d) (1-y)

V:

v'l-d (y-z;

M

ft) — I (3z + l)

VSquaring eqs. (8) and (9) and combining yields

f(y,z) = (y-z) y+^

(^)

~\ 2 wM ( ,< z+1

)

(1-d)

= 0

(D-1)

(D-2)

(D-3)

(D-4)

(D-5)

(n-6)

(D-7)

(D-S*'

1

D- I'

D-1
And combining eqs . (7) and (9) gives

V3 r M

y = 1 - V

d(l-d) ^^3

Pal /2

1 +

1 y

w • ( gz+1)

/3

(D-11)

Equation (D-10) is solved by a Newton-Raphson method for z, then y is

determined from eq. (D-11).

Energy Equations

The following dimensionless variables are introduced

0 =

T_

T

M = -

$ =

a -

a =

b =

max

d.

V

Aw

w

oT 3 a

c =

d =

e =

f =

g =

AH m

max

A aT ^ w a

C m

g max

A aT 3 w a

^fuel ^max

A aT 3 w a

D =

s =

aT 3 a

w

aT 3 f

k =

a dF

/S~

w

K,

AH m

V max

A aT 4 w a w

aT 3 a

The dimensionless equations to be solved result as follows:

From eqs. (14) and (17), along with subsidiary relationships:

CD II $ r ,d

- 'f PdF * j r ,d

+ b (0 - w

1) + M d

g

(0

g

- 1)

+ e 0

^ f f

2/lT s f /a cM,b

+ M

py

g + (e-d) (0g - 1) + P w

= 0

(D-12)

(D-13)

D-2
From eqs . (18) and (22):

G 0

w

(1 - 1 (1 - Y) (1

4 0W

- b (0,^ - 1) + a (0^ - 0 ) = 0 w gw (D-14)

From eq . (24):

H (0 ,0 ,0^) g' w' F^ 0„-l-k$ , = 0 F r ,d (D-15)

where from eqs. (9) and (10) :

M

V

[e (0 ^

- 1) + g]

U

(l-£f)FdF L 0

^

L g g + j (0,-0^)

(D-16)

and from eq. (20) :

^ =

r ,d

c g

4 0 +

g

<1 - ^g> - ®f“ (D-17)

Equations (D- 13) (D-14) and (D-15) are solved by a Newton-Raphson method

for 0,0,

g w

and 0p. a is then determined from these results.

D-3

APPENDIX E. COMPUTER CODE

Please note the following about the computer code:

1) A small change was made in eq . (D-13). The term

replaced by p(e O ^ + (1 - e ) G '+). Hence, results are not

yg g w precisely those calculated for the graphs. Resulting changes

were minor

2) For the smallest doorway, temperature and flow equation solutions

for the highest mass flows did not converge (numbers 17-20 on output)

i

E-1
FLOW CHART

START

E-2
Nomenclature for Program

Main Program:

Program Theory Program Theory

A a KE

AF A

F KFLR

ALPHA a KG

AMASS m

a KW

AV A

V L

AW A

w MA

B b

."lAX BETA 6 MB

BMASS m,b MG

C c MPY

CFUEL ^fuel MV

CG C

g

OMEGA

CO c (flow coefficient) P

CS C

s PI

D d PYMASS

DELH AH QFIRE

DELHV QFLR

DR ^a/Tg QR

E e QWALL

EF

^f R

EG ^g RATIO

F24 ^dF

RD

FF f RF

FFLR F

SF

RFDOT

FUEL m

V

RHO

RHOV

GA^'iMA Y RW

GG g

SIG^IA

GRAY g

TA

H H

TFLAM

HF «f TFLR

HFLR ^f TG

HO H

o THFLAM

HS h

s THFLR

HW h

w THG

THS

THW

TS

w

K

V L

-M m

max

M,

M

M

g

I py

M

m

P

TT

‘py

radiant flux from flame

q" (includes flame radiation)

• r q" (excludes flame radiation)

r .“Wr M /M

a V

r ,d

r,f

rate of radiant energy from flame

"a

‘V

1-

, w

OV T

a

g

'g

' s

' w

E-3
Program Theory Program Theory

TW T

9 $ , r ,d VMASS

w

rti RDX

V 9X

W W

9$ , r ,d WO W

RDY

o 9y

XD

XJ j

O z

X

n

X 0 XN g

Y y Y 0 W

Z z

Z

Subroutine TEMP:

Subroutine FLOWS

:

ALX 9 a 9X F f (Y/ z)

ALY 9 a FY 9f

9Y 9y

ALZ 9 a FZ 9f

9Z 9 z F F Y Y

FAL 9F YZ dy

9 a dz

FX 9F Z z 9X

FY

9Y

FZ 9F

9Z

G G

GX

9X

GY iG

9Y

GZ iG

9Z

H H

HX

9X

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BEGIN

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FOR

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MASS

FLOU

RATE,

KG/S.

NOTE

THAT

C

THE

FUEL

INCREMENT

INCREASES

WITH

DOORUAY

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IF

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NBS-1 14A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 78-1511

2. Gov’t Accession

No.

3. Recipient’s Accession No.

4. TITLE AND SUBTITLE

Experimental and Theoretical Analysis of

Quasi-Steady Small-Scale Enclosure Fires

5. Publication Date October 1978

6. Performing Organization Code

7. AUTHOR(S)

J. G. Quintiere, B. J. McCaffrey and K. DenBraven

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 7515676

11. Contract/Grant No.

12. Sponsoring Organization Name and Complete Address fStreef, City, State, ZIP)

Same as No. 9

13. Type of Report & Period CoveredF inal

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most si^ificant information. -If document, includes a sj^ificant,

... „ . , . . , , Fortv-six small-scale experiments we« tonaucted to

bibliography or literature survey, mention it here.) Tutcy ssxa oiiiaj-x ^ measure the characteristics of horizontal plastic (PMMA) pool fires in an enclosure as a function of doorway width and fuel area. A 0.30 m high enclosure was instrumented to measure sample mass loss, the upper gas layer and ceiling temperatures, heat flux to the

floor, and the pressure drop across the doorway. Results are reported for the maximum

steady burning period; however, a few cases do not seem to have reached a steady state.

For small sample sizes, a distinct fire plume could be perceived in the enclosure, while

for larger sample sizes flames tended to fill the enclosure (sometimes to within 2 or 3 cm of the floor), and extended out the door opening.

The rate of mass loss is a strong function of the radiative feedback from the

enclosure. However, reduced oxygen concentration in the flow entrained by the fire

nlume seems also to affect the mass loss rate. For the smaller doorway widths, the

rate of mass loss Increases almost directly with ventilation. As the width is increased,

the mass loss rate instead becomes a function of sample area and radiative heat trans er For some sample sizes, as the doorway width is increased a maximum rate of mass loss is

achieved, fallowed by a decrease in burning rate at higher ventilation levels. The

temperatures and floor heat flux also tend to follow this trend. I The data were then compared to the results of a theoretical model. Agreement be- j tween theory and data is qualitatively good. But overall, good quantitative agreement

j is not achieved. This lack of agreement appears consistent with inaccuracies of the I flame radiation model and an incomplete description of the flame chemistry. ;

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a otoper name; separated by semicolons) Burning rate; enclosure fires; experiment; mathematical

models; radiation; small scale; ventilation.

18. AVAILABILITY I I Unlimited E For Official Distribution. Do Not Release to NTIS

I I Order F rom Sup. of Doc., U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. CH

I

^ Order From National Technical Information Service (NTIS1

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCI. ASSIEIED

20. SECURITY CLASS

(THIS P.AGE)

UNCLASSIFIED

21. NO. OF PAGES

22. Price

* itie main text of this report will be available in a non-NBS publ icati\.mcoMK»-oc

This expanded version is for limited distribution to specialists.


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