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NATL INST OF STANDARDS & TECH R.I.C. 86-3459

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Mitler, Henri E/How accurate is mathemat QC100 .U56 NO. 86-3459 1986huw Accurate is Mathematical Fire

Modeling?

Henri E. Mitler John A. Rockett

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

December 1986

^•cau o* S

" ° DEPARTMENT OF COMMERCE

-QC

ONAL BUREAU OF STANDARDS

100

. U 5 6

86-3459

1986

c.2

MBS

RESEARCH

INFORMATION CENTER

Qctoo

NBSIR 86-3459

HOW ACCURATE IS MATHEMATICAL FIRE

MODELING?

C.-9'

Henri E. Mitler John A. Rockett

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

December 1986

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Director

TABLE OF CONTENTS

Page

List of Figures iv

Abstract . 1

1. INTRODUCTION 2

2. SCOPE OF THE MODEL 4

3. MODELS OF THE PHYSICAL PROCESSES 6

3.1 The Burning Object b

3.2 The Flame 8

3.3 The Fire Plume 9 3.4 The Hot Layer 11

3.5 The Vents 14

3.6 Radiation 15

3.7 Convective Heat Transfer 15

3.8 Conductive Heat Transfer 17

4. THE TESTS 17

5. RESULTS 18

6. PREDICTION VS EXPERIMENT 20

7. DISCUSSION 23

8. CONCLUSIONS 2b

9. REFERENCES 2b

-iii-
LIST OF FIGURES

Page

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

of the room, and radiative fluxes to the target from layer

and flame 28

Figure 2. Fuel layout ... 29

Figure 3. Mass-loss rate of fuel (tests no. 0, 1, and 2 correspond

to curves A, B, and C, respectively) 30

Figure 4. Depth of the hot layer in the room, tests 0, 1, and 2 (A, B, C, respectively) 31

Figure 5. The "measured" hot layer temperature, T^ 32

Figure 6. Mass-loss rate for the standard run. The dashed curve is

the experimental result 33

Figure 7. Mean layer temperature in the room, T^, for standard run .... 34

Figure 8. "Experimental" vs predicted values of layer depth,

standard run 35

Figure 9. "Measured" vs predicted values of hot gas outflow rate,

standard run 36

Figure 10. Experimental vs calculated values of oxygen concentration

in the layer, standard run 37

Figure 11. Experimental vs predicted species concentrations,

standard run 38

Figure 12. Test #1, July 6. Radiative flux at center of floor 39

Figure 13. Mass-loss rate of primary fuel, test //6 (window) 40

Figure 14. Hot layer temperature for test //6 41

Figure 15. Predicted vs experimental layer depth for test // 6 42

Figure 16. Hot gas outflow rate, test #6 (window only) 4 3

Figure 17. Predicted vs measured wall/ceiling temperature,

test #6 4 4

Figure 18. Measured oxygen concentration at various depths,

test #6, vs prediction 4 5

-iv-
HOW ACCURATE IS MATHEMATICAL FIRE MODELING?

Henri E. Mitler and John A. Rockett

Abstract

It is important to be able to predict the development of a fire in an

enclosure of arbitrary complexity. A mathematical model valid for a single

room, with multiple vents and objects in it has been developed. The fifth

version of the model has just been completed ; it is the Harvard Computer Fire

Code V, or Mark 5 for short. In 1977, Factory Mutual Research Corporation

carried out a series of eight well-instrumented full scale room fires, against

which the single room model can be tested. The test fire room was 2.4 m x

9.6 m x 2.4 m high, with an open doorway; a slab of polyurethane foam in one

corner, and a polyurethane foam target in a facing corner. The primary slab

was ignited at its center, and the fire followed. The other tests were

variants of this one. We compare the results of the calculations with the

results of two of the experiments: the standard configuration and the case

with a window replacing the doorway. The model "predictions" are in good to

excellent agreement for most of the variables. The disagreements are

discussed, and it is found that the most probable causes are: failure to take

heating of the bottom gas layer into account, inadequacy of the burnout

algorithm, and the lack of understanding of the CO-production mechanism.

ifc This article is based on a paper presented at the US-USSR Scientific Exchange

Meeting, Tbilisi, USSR, July 1981, which has appeared in Russian. The long

delay in publication is partly due to an agreement with the USSR to wait for

preliminary Russian publication. There has since then been substantial

development of Mark 5 (see ref. [21]).

- 1 -
Keywords: CFC V; compartment fires; computer modeling; Mark 5; Mark V;

room fires.

1 . INTRODUCTION

The growth of a fire in a building is an extremely complex phenomenon.

Nevertheless, with modern scientific tools, it should be amenable to analytic

prediction. Perhaps the first research in predicting fire behavior was that

of Ingberg [1] at the National Bureau of Standards. He considered the effect

of amount of fuel (fuel loading) on fully-involved room fires; Kawagoe [2]

improved the analysis by taking ventilation into account. The last decade has

seen a rapid development in the understanding of fire physics and in synthesizing and quantifying this understanding in analytic models. These advances

will not be reviewed here. Good bibliographies can be found in Mitler [3] and

Babrauskas and Williamson [4], Much has also been learned about physically

modeling fire (Heskestad [5]). However, this discussion will be confined to

mathematical modeling.

A significant feature of recent fire models is their attention to the

initial growth of fire from a small ignition source to full room involvement

(flashover), and beyond. This is in response to the belief of many fire

protection engineers that fire can be controlled before flashover. Emphasis

on the early fire has been possible because the physics of fire is now much

better understood than it was only ten or fifteen years ago.

The pre-f lashover fire is inherently more complicated than the postflashover fire, but the development of modern computers permits the solution

of the equations, at least in some restricted form.

-2 -
There are basically two kinds of mathematical models. First, "field" (or

continuum) models, where the Navier-Stokes equations are used for the fluid

flows, together with equations describing the combustion and radiation.

Second, "zone" models, which employ much-simplified equations to describe each

of the several phenomena which can be conceptually isolated in a zone. The

latter seem (for the moment) more practical, since the solutions of their

equations, even in the time-dependent case, are literally orders of magnitude

faster than the solution of the more nearly exact field equations. Zone

models are able to represent a much more varied physical content than field

models but at the cost of much less spatial resolution. There is a degree of

artistry (or arbitrariness) involved in zone "modeling", since the models

representing each phenomenon must be simultaneously reasonably accurate yet

simple enough to be described by equations which are readily solved.

Numerous studies have been carried out with zone models; of particular

note is the work of Quintiere [6], MacArthur [7], Pape [8], and Emmons,

Mitler, and Trefethen [9]. A survey of recent developments in modeling is

j||f given by Friedman [10].

Ultimately, it should be possible to predict the development of a fire in

an enclosure of arbitrary complexity. What has been achieved so far is a fair

simulation of what happens in a single room with maltiple vents and one or

more objects. Several multi-room models are also available of which the most

elaborate is probably that of Tanaka [11]. His model, however, while allowing

for multiple rooms at multiple levels, assumes a fire with a prescribed energy

release rate as a function of time. There are strong similarities among the

Also see refs. [22] and [23]

.

- 3 -
single room zone models currently in use although they differ in detail. In

this paper attention is focused on the simulation developed at Harvard over

the past seven years. The latest major revision of this computer program is

called the Harvard Fire Code V, or Mark 5 for short. It simulates fire in a

single room vented directly to ambient air. It allows for up to five vents

and five combustible objects. Each object can heat up and possibly ignite.

The simulation allows for one of three possible initial fires: a burner

fire—i.e., one of constant radius and heat release rate, a pool fire—i.e.,

one of constant radius, and a growing fire—one ignited over a small area,

which then spreads.

This paper will describe the principal features of the Harvard Mark 5

simulation and then compare its predictions for two fires with the

experimentally observed behavior.

2. SCOPE OF THE MODEL

We will describe some of the pheonomena which take place when a fire is

ignited in a room, below. This has been done in more detail elsewhere (see,

for example, ref. [3]). Most of the important physical effects involved in a

room fire have been explicitly taken into account in Mark 5, to one or another

degree of approximation [3,9-13] . The phenomena not included are mainly

associated with post-f lashover behavior or events immediately preceding

flashover. Although classed as a zone model, the zones of Mark 5 are not

necessarily clearly delineated subdivisions of the room volume . They are:

(1) the objects, (2) the fire plumes over any objects which are burning,

-4 -
(3) the layer of heated gas trapped under the ceiling (assumed to have a

sharply delineated lower surface although, in practice, this may not be the

case), (4) the ceiling and that portion of the walls in contact with hot gas

layer, (5) the floor and lower walls, (6) the vents. Note that the vents are

a phenomenological zone but physically a boundary between the inside and

outside of the room. Some of the phenomena associated with the zones are:

(a) entrainment of air into the hot, buoyant plume produced by the fire,

(b) the production of soot and gaseous combustion products and depletion of

oxygen in the plumes, (c) the (transient) formation of the hot layer under the

ceiling, (d) radiative energy exchange between the fire plume, hot layer,

upper and lower walls, ceiling and floor and with the space outside the vents,

(e) the heating of the ceiling and upper walls and the objects in the room,

(f) ignition of objects not initially burning, either through auto-ignition or

by flame contact, (g) mass flow through the vents. Some situations not

currently included are: (1) vents located in the ceiling, (2) external winds,

(3) mixing at the vents between the hot exiting fire gases and entering

ambient air, together with effects associated with this mixing on the lower,

cool gas layer, (4) the effect of pre-ignition pyrolysis, burning in vitiated

air and upper layer flashover, (3) the effect of sprinklers or other extinguishers. Although CO production is calculated, the present method for doing

this reflects our very imperfect understanding of the production mechanism and

is based on very limited data correlations. Finally, the effects of initial

stable gas stratification, gas compression and finite transit times have been

assumed to be of minor importance. This last could become a problem were Mark

5 used for estimating the performance of fire detectors in high ceilinged

rooms

.

- 5 -
In the following paragraphs, a brief outline of the equations defining

the model will be given. This has already been done in some detail by Emmons

[12], and in more detail in reference [9] . The model has, of course, evolved

since these reports were written, and the more comprehensive set of equations

is found in references [3] and [13]

.

Figure 1 shows the situation to be simulated a few mintues into the fire,

and some of the room dimensions (h) and selected variables, such as the mass

flows (m) and radiative fluxes (<j>).

3. MODELS OF THE PHYSICAL PROCESSES

3.1 The Burning Object

As stated above, Mark 5 allows for three types of fires: a gas burner, a

pool fire or a growing fire. The growing fire algorithm is the most general,

the other two are specializations of this. The growing fire model is for a

centrally ignited horizontal slab of material. It was experimentally observed

that, for foamed polyurethane, the fire radius increases exponentially with

time [14]. We assume that the spread rate depends on the net impinging flux

in such a way that the experimentally-observed exponential growth rate for a

small fire is reproduced. Reradiation and convective heating of the burning

surface are taken into account in calculating the net impinging heat flux.

This leads to the spread-rate expression for the fire radius,

r r

2 R = AC (1 + T + o ) , R< °* 95 R ( 1 ) ^ 2 3

' - m

-6 -
where C = <}>/aT^ ( 2 )

and A is a spread-rate parameter specific to the material. <j> is the net heat

flux impinging on the pyrolyzing surface, and is the flame temperature. It

will be seen that the right hand side of equation (1) represents the first

three terms in the expansion of log(l-C). This was done in order to avoid the

singularity at C = 1.

When the radius R approaches the input maximum radius, Rm , the spread

rate evidently must go down, and so we take

R = (R - Rl/10, R > 0.95 R (3) m 1 m

R is integrated to find the radius, R(t).

The pyrolysis rate is then given by

raf = ~ tiR2

(J./H (A)

f

Y v

where H

y

is the heat of pyrolysis (or vaporization). The negative sign is

included because m^(t) is the mass of the fuel.

An important point is that <j> includes all the radiation incident on the

surface, including that from the hot layer, walls, and its own flame and other

fires. This feedback produces an acceleration of burning in the room,

relative to burning in the open where only radiation from the objects own

flame would be present.

- 7 -
Combustion in the diffusion flames found in fires is typically quite

inefficient. Only a fraction of the pyrolyzed fuel in fact burns, the rest

going off as soot, CO, and unburned hydrocarbons. Furthermore, when the hot

upper gas layer is so low that it keeps the fire plume from entraining much

air, the fire becomes starved for oxygen, and the burning rate may go lower

still. Thus the burning rate is

= min (- x m

f

, rWy) (5)

where m^ is the rate of entrainment of air into the plume, y

is the effective

air/fuel mass ratio in burning, and x

is the fraction of pyrolyzed fuel which

actually burns (completely). This is found from experiment to be about

14.45. The chemical energy released then in either case is

q

= m

b

H

c> (6)

where H = the heat of combustion

c

The burner and pool fires are rather simpler, and will not be described here.

3.2 The Flame

The flame is modeled by a homogeneous, isothermal gray cone of gas, of

semi-apex angle, ij*. When the fire is starved for oxygen, or when near fuel

exhaustion, the cone becomes squatter, thereby emitting less radiation. In

Recalculation in 1985 showed that y is closer to the stoichiometric value,

9.85.

-8-
the absence of other limiting factors the cone angle is \p 30°. When oxygen

o starvation or burnout reduce the burning rate, then

( 8 )

The flame gas temperature is taken to be 1260°K, and its absorption

[15] and Orloff [16]. Radiation per unit area to the flame base is then given

by

where V = cone volume, A = bounding area, and £ = shape factor (or order

0.9). Radiation from the flame to other targets is complicated by the fact

that the slab on which it "sits" may shade targets lying below it.

Expressions for the flux to ceiling, targets (horizontal or vertical) and that

absorbed by the hot layer, are given in references [3] and [13]

.

The plume model used is that due to Morton, Taylor and Turner [17] with

the heat source a virtual point below the surface of the fuel at a distance

such that the plume radius at the surface matches the fire radius:

coefficient k = 1.55 m in agreement with measurements made by Markstein

(7)

3.3 The Fire Plume

x = R/l . 2a (9)

- 9 -
Here, a “ the entrainment coefficient, taken to be 0.1

the plume into the hot layer is

The mass flow from

m

p

where p = ambient air density (1.177 kg/m^ at 300°K)

3

b = 1.2 ahp is the plume radius at the hot-cold layer interface

hp = h

r - hf - h

L + x is the height of the plume above the

virtual source. Note that the plume height shown in figure 1

is h = h' - x. P p

h

r = room height

h^ = height of the fire base

h

L

= depth of the hot gas layer

1/3 u = (C

Q

/hp) is the axial flow velocity at the hot-cold

layer interface

1/3 U£ = (C

q

/x) is the axial flow velocity at the fire base

C

0 = 25 gQ/48 *o

2

C

p

T

a

P a

T

a = ambient temperature

Cp = ambient air specific heat

g = acceleration of gravity

Q

= rate of heat release in the plume

a = the entrainment coefficient =0.1

Enthalpy is carried into the hot layer by the plume at the rate

E = m C T + Q- E (16)

P P P a pr

- 10-
where E is t pr

percent of Q).

is the energy lost by the plume via radiation (of the order of 35

3.4 The Hot Layer

In common with most zone models, two gas layers are assumed. The upper

gas layer is homogeneous and isothermal, and the lower layer consists of

ambient air. The interface between the two layers is assumed to be a horizontal plane. In reality, of course, there is seldom a distinct homogeneous

"upper layer" —the temperature and species concentrations vary from point to

point; a first simplification of reality would be to assume a single smoothly

varying vertical profile for all locations within the room (except within the

fire plumes). The step-function profile assumed for current two-layer models

is a further simplification, but it seems adequate, so far.

An energy balance for the hot layer yields

(17)

where E = the energy added from the fire plumes

EE = the energy carried out through the vents by mass flow

v

^E^ = the energy convected into the walls

ET „ = the net loss of energy by radiation

L K.

Similarly, the layer mass changes according to

• _ • • til = £ m — m ( 18 ) L

P

- 11 -
where nip = the mass added from the fire plumes

= the rate at which mass leaves the room via the vent(s)

The layer mass and energy are then found by integrating equations [17] and

[18].

Since we can also write

E

L

= Wl = KV Cl\ »L

Ah

L

C

L

T

L

(19)

(where A is the cross-sectional area of the room, is the specific heat of

the hot layer gases, h^ is the layer depth, and its (mass) density), we

have

h

L

= el /aVlt

l

= et /act p t

L w a a

( 20 )

where the second equality follows from the ideal gas law. If we ignore the

(small) difference between and Cp (the specific heat of ambient air, at

constant pressure), it is clear that the layer depth is a function only of the

layer energy. It also becomes clear that the total gas energy in the room is

(essentially) constant: as energy is added, enough gas is pushed out by gas

expansion, to leave the total energy unchanged. Finally, the layer

temperature is found from

t

l

e

l

/c lm

l

( 21 )

- 12 -
The oxygen concentration in the layer is readily found as the solution of the

equation

m = 0.2318 T dl - y 1 - Y m (22) ox L L s d

j o u

where Y = m /nr (23)

o ox L

is the mass fraction of oxygen in the hot layer and y is the stoichiometric

s air/fuel mass ratio (9.85 for polyurethane); 0.2318 is, of course, the mass

fraction of oxygen in air, and m^ , m . and m^ have all been defined already.

As for the other chemical species, each burning material is assumed to

generate a constant fraction of CO, CO2 , ^0, soot, and hydrocarbons per unit

mass of fuel pyrolyzed. Values for these fractions are taken from measurements [18] and the species concentrations in the hot layer thus become

calculable. These concentrations, in turn, permit evaluation of the layer's

absorptivity, k, which is then used in various radiation calculations. Two

alternative routines are used to evaluate k. The simpler one assumes that all

the absorption is due to (grey) soot absorption:

k = 265 Y (24)

s

where Y = m /mT (25)

s s L

is the soot mass fraction. The more complicated one also takes into account

the band absorption of CO2 and l^O.

- 13-
3.5 The Vents

The mass flows through each vent are calculated according to a hydraulic

model [19] , with an efflux coefficient of 0.68. The pressure at the floor in

the center of the room is used as an auxiliary variable. As a result of

assuming the gas layers to be, separately, homogeneous, the pressure difference across a vent is a piecewise linear function of height. The vent is

divided into horizontal strips corresponding to each linear variation, and

include any place where Ap drops to zero (a neutral axis) as a strip boundary.

A. U Then for the i cn strip, the pressure drop at the top of the strip:

(26)

where Ap. is the pressure drop at the bottom of the strip, p is the ambient

1 3

air density, p that of the hot layer, and Ah^ the height of the strip. The

mass flow through that strip then is

where

m. „ b + /ab + a

“

i = -

/ b + /a

5 |

A

P± | , b = |Ap 1+1

(27)

(28)

and G

i = (sign Ap^ (2/3) C

d

B At^ /2 gp^p (29)

Here C . = 0.68 and B is the width of the vent. When Apc1 is correctly

a r loor

chosen, all the flows are such that mass balance for the room is satisfied:

m

out m

in

h

C T

P a

- Ef

ra„ (30)

- 14 -
3.6 Radiation

There are eight radiation subroutines which calculate the most important

radiation exchanges among the flame(s), objects, hot layer, and hot

wall/ceiling. Some are quite simple, like equation (7). Most others are

complex, and will not be listed here; the interested reader should see

reference [3].

The convective heat exchanges between the hot layer and walls, and that

between layer(s) and objects, are found assuming a simple (but temperaturedependent) film coefficient. For heat transfer to ambient air, Mark 5 takes

and T

g is the temperature of the surface being cooled (outside of walls, or

objects in the room). For heat transfer from the hot layer,

3.7 Convective Heat Transfer

(31)

where

(32)

where h . = min

l [50,5 + 0.45 (Tl - T

a

)] (33)

In the steady state, the heat loss rate to the walls and ceiling therefore is
(34) ®LW ~ \ \

where = 2 (L + W) h

L + LW - A

v (35)

where L and W are the length and width of the room, and Ay is that part of the

vent area intersected by the hot layer. Here T0 of equation (32) is taken to

be T^, the inner wall/ceiling temperature, assumed to be uniform. As the fire

grows, however, the layer thickens and, in order to (artificially) maintain a

uniform temperature, extra heat has to be supplied to the newly exposed wall

areas. This must be done such that the newly heated wall immediately acquires

the same temperature profile throughout its thickness as the rest of the

heated wall. Hence for the growing layer, equation (34) is replaced by

- Vw + 2 <L w> t" \ (\ > 0) (30)

where q" = / (q” + q^w

) dt (37)

o

is the energy per unit area stored in the wall, and q" is given by equation

AW

(31), with T = T . , £ .It follows from equation (20) that

s outside wall surface

h

L

= h

L

E

L

/E

L

(38)

When the layer decreases in depth, we evidently must use equation (34) r.ither

than equation (36).

-lb-
3.8 Conductive Heat Transfer

Walls and objects are assumed to be finite-thickness slabs insulated at

their edges. Thus the one-dimensional heat-conduction equation can be used.

3T

3T (39)

is solved numerically with a simple algorithm. Although this finds the

temperature profile through the object as a function of time, most of that

information is neglected, as we are (currently) only interested in the surface

temperatures and the integral of the profile.

This completes the brief outline of the physics included in the model.

The numerical methods by which the resulting equations are solved will

not be discussed since this is done in detail in CFC III [9] and CFC V [13].

For those readers who are not familiar with these papers, we might mention

that two alternative algorithms are used: a Gauss-Seidel successive substitution method is normally used; when convergence is not achieved with that

method, a multivariate Newton technique is used. This combination works very

well, 95 percent of the time.

4 . THE TESTS

In 1977, Factory Mutual Research Corporation carried out [20] a series of

eight well-instrumented full-scale room fire tests, against which the Mark 5

program can be checked. The eight tests were systematic variations of a

- 17 -
a standard room. The standard configuration is shown in figure 2; it is a

2.44 by 3.66 by 2.44 m room (8* x 12' x 8') with an open doorway 0.76 x 2.03 m

(30" wide by 80" high); a slab of polyurethane (P.U.) foam, measuring 1.52 x

1.52 x 0.10 m (5' x 5' x 4") is in one corner; its top surface is 61 cm from

the floor (this models a foam mattress). A P.U. foam target 1.22 x 0.30 x

0.10 m (4' x 1* x 4") is in the near adjacent corner; its top surface is 25 cm

(10") above that of the primary fuel slab. The primary slab is ignited at its

center, and the fire followed.

Tests #0, 1, and 2 were all meant to be identical—the standard

configuration. Test 3 had the doorway narrowed to 19 cm; test 4 added a

window; test 5 had a pool of PMMA beads replacing the foam; test 6 had a

window instead of a door, and test 7 had the door reaching up to the ceiling.

Comparing the results of calculations with the results of these experiments

shows that the "predictions" vary from excellent to fair for most of the

variables. Although comparisons have been made for all the tests, for brevity

only two of these will be discussed: the standard configuration and test

#6. These show the best and poorest agreements between the predictions of the

model and the actual fires.

5. RESULTS

The rate of mass loss of the fuel (while it is burning) is shown for runs

0, 1, and 2, in figure 3. These are curves A, B, and C, respectively. We see

that A and B agree very well, although there is a good deal of statistical

fluctuation for t < 150 sec. For test #2 (on July 8) fire development was

more rapid, as can be seen from curve C—it looks as if ignition occurred

- 18 -
about 40 seconds early. Note that these are semilog plots, as is also true

for figs. 6, 11, 12, and 13.

The thickness (or depth) of the hot gas layer for each of these first

three tests is shown in figure 4. Up to t = 200 sec, curves A and C (tests 0

and 2) track together very well, whereas curve B (the dotted curve,

corresponding to test 1) begins its descent some 50 sec earlier; this

contrasts with the behavior in fig. 3, where ignition appeared to have

occurred earlier for test 2, rather than test 1. Beyond 200 sec, B and C

switch - that is, curve C leads the other two by about 40 sec (consistent with

the mass-loss rate shown in fig. 3), while A and B track together quite well.

This holds up to t = 310 sec; after that, there are substantial deviations,

curve B displaying marked oscillations whose nature is not clear. These two

figures serve to show how much variation there can be in reasonably wellcontrolled experiments—so that we should not expect calculated results to

agree any better than this, with any one experimental fire.

Test #1 (July 6) was used as the standard for comparison, partly because

a roof leak appeared during test #0, and it is, therefore, suspect. The

target ignited 310 seconds after ignition of the primary slab, and the

sprinkler was turned on at t = 326 sec.

Figure 5 shows how differences in the handling of the data can also lead

to rather different results. The solid curve shows "the temperature" T^(t) of

the hot layer as a function of time, as obtained by taking an average of the

readings of 8 thermocouples located at different places in the room, all at a

height 1.71 m from the floor—(70 percent of the distance to the ceiling).

- 19-
This was the value of T^Ct) used by Factory Mutual in their data analysis. We

made a different evaluation of T^Ct), using the temperature profiles as a

function of height at three places in the room; this gave the dashed curve.

As can be seen, the latter method gives a peak temperature 150°C lower than

the FMRC method does.

6. PREDICTION VS EXPERIMENT

Figure 6 shows the pyrolysis rate for test 1H (July 6). The calculation

generally agrees with experiment, though the maximum is some 50 percent high.

Figure 7 shows the hot layer temperature for the same test. As we see, the

calculation agrees quite well with experiment, out to 310 sec., but then falls

below the experimental value. Incidentally, no meaningful comparisons can be

made after t = 326, when the sprinkler was turned on—the program does not yet

simulate extinguishment. Note that the calculated peak temperature is low

even though the burning rate is over- predicted at this point.

In figure 8 the layer height calculation is shown to agree very well with

experiment out to t = 290; the subsequent disagreement occurs in part because

in Mark 5, the layer cannot descend below the level of the base of the fire.

It is possible, moreover, that late in the fire the interface between the hot

and cold layers is not, in fact, a plane: it may be that the surface rises

locally, near the fire, and is lower elsewhere; because of the way in which it

was obtained the data would only reflect the lower part of the surface.

The outflow rate of hot gas is shown in figure 9

again, the calculation

is in excellent agreement with experiment out to t = 300 sec.; beyond that,

-20-
the hotter layer produces greater buoyancy (recall figure 7), and therefore

greater flow. The target temperature (not shown) also agrees very well with

calculation.

Figure 10 shows that the oxygen concentration in the layer is reasonably

well calculated. The fact that the real minimum is lower than the calculated

minimum is of course consistent with the temperature and mass flow curves,

though a possible alternative explanation will be given when we discuss test

# 6 .

Other species concentrations are shown in figure 11; the calculated CO2 concentration agrees very well with experiment, but the CO does not.

The radius of the fire as a function of time is well predicted by the

program, as is the radiative flux at the center of the floor (most of the

radiation comes from the hot layer); see figure 12. (The calculated flux

rises too slowly beyond t = 305 because the calculated layer temperature rises

too slowly there.)

In sum, the standard run reproduces the results of tests 0 and 1 quite

well, the principal disagreement being the failure to reproduce the

temperature peak, and the consequences which flow therefrom.

Next, consider test #6, where the doorway was replaced by a window about

1 m high, m^, T^, h^, m^, Tw

and y( 02 ) will be used for comparison.

-21 -
The pyrolyzation rate, m

f

, (see fig. 13) is in excellent agreement up to

t = 300, but the calculated peak again continues to rise beyond the experimental peak. In spite of that, the calculated temperature, T^, rises more

8 lowly than the experimental value, as seen in figure 14, and dies out much

faster, beyond t = 360.

The layer depth in the room, h

L , is shown in figure 15, and is seen to

agree reasonably well with experiment between t = 90 and t = 230. Beyond that

point, the layer is again quite a bit deeper than calculated. The disagreement is bad after t = 360, just as it is for the temperature; however, the

experimental values are themselves suspect out here.

The resulting gas outflow rate, m^, is shown in figure 16, and is in

surprisingly good agreement with experiment out to t = 210. The first calculated maximum, at 280 seconds, is due to oxygen starvation: the layer is so

low that not enough fresh air is drawn in by the plume to permit burning as in

the open. The second maximum (at t = 350) is due to the beginning of burnout

of the primary fuel. The third peak, at t = 380, is not understood.

In figure 17, we show the average temperature of the ceiling and upper

part of the walls (that part in contact with the hot layer) T

y

. As could be

expected, the curves are similar to the layer temperature curves (see fig.

14) —that is, the calculated wall temperature lags behind the measured temperature by about 15 sec, out to t = 290, then falls behind more dramatically.

The oxygen concentration at the window, y(02), is shown in figure 18 as a

function of time for probes at different heights. Note that in this figure

-22 -
-he heights refer to distance down from the ceiling. Thus the curve marked

0.2H gives the oxygen concentration 20 cm below the ceiling. The stratification of the layer, which was not evident in test #1, is brought out most

strikingly, here. It is clear from examination of the test data that there

may well have been variations along the length of the room. (The

stratification, incidentally, has important implications for burning in the

vitiated layer.) Were the layer to be well stirred, the mean oxygen

concentration would evidently be a weighted average of the experimental

values. This average was not taken, but it is probable that the calculated O

2 concentration would agree reasonably well with such a mean.

Finally, the fact that the oxygen concentration at the fire base is

ambient throughout most of the burn in spite of the fact that the layer has

fallen below the base of the fire, is not consistent with the assumption that

the layer is flat everywhere. It is much more likely that it rises locally,

near the fire, as mentioned earlier.

7. DISCUSSION

The Mark 5 growing fire algorithm predicts the radius of the fires quite

well. The same is true of the pyrolysis rates early in the fire; however, the

predicted peaks tend to be too high, and the resulting burnout too swift.

The vent routine is quite good, and gives mass flow rates in excellent

agreement with measurement provided the layer temperature is well predicted.

-23-
The plume model we use, though crude, seems satisfactory, judging only by

the amount of air entrained and the resulting oxygen and CO2 concentrations in

the layer. The flux from the hot layer to the floor agrees well with experiment, suggesting that the layer emissivity is reasonably well estimated, and

therefore that the smoke concentration is reasonably well predicted.

On the other hand, the wall temperatures are a bit low, suggesting that

radiation from the flame plus convection from the layer are under-estimated.

This suggests that the flame model is not quite adequate. This impression is

reinforced when we note that the flux to the targets is low in some cases (but

not in others).

The burnout of the fuel was made _ad hoc , and turns out to be poor. This

is not of central significance at the moment, but clearly has to be improved.

Because CO is a major hazard of fire the failure of the model to predict

its concentration well is a major weakness. CO production in diffusion flames

is not well understood and the model reflects this. Fortunately, research

currently in progress shows promise that a better understanding of the physics

and chemistry of CO production will soon be available.

Perhaps the most puzzling question is why the layer temperature is well

predicted for most of the burn, but underpredicted late in the fire. There

are at least five possible reasons for this:

-24 -
1. Mark 5 may overestimate the rate of heat loss by the layer.

2. There may be burning in the layer itself.

3. The plume model may be inadequate, calculating more ambient air

entrainment than is found in practice.

4. Mark 5 neglects heating of the lower layer; this may be important.

5. Air may be drawn up around the base of the flames. Mark 5 may limit

burning due to oxygen starvation prematurely.

Let us consider these in order: //I is very unlikely since it would lead to

wall temperatures higher than observed, rather than lower. Also, energy loss

through the vent is already underestimated. #2 is unlikely, as no thermocouple gave a reading anywhere near flame temperature. (However, the thermocouple response times may be too long.) #3 is possible, though not very

likely. Heating of the lower layer, however, ( #4 ) certainly occurs—both

because the floor is heated by radiation, thereby heating the air, and by

entrainment of the hot gases by the ambient air coming in through the vents.

This will make the upper layer hotter, too.

The other effect which has been neglected, is the raising of the hot/cold

interface at the fire. This would delay oxygen starvation, and allow more

vigorous burning to take place. These are matters to be investigated, both

theoretically and experimentally.

-25-
8. CONCLUSIONS

The overall performance of the Mark 5 simulations is satisfactory, both

in its numerical stability and convergence, and in the predictions it makes.

There are a small number of inadequacies, which are being investigated; there

is every reason to believe these difficulties will be overcome.

In spite of all their complexities, therefore, it appears that fires can

be successfully simulated by mathematical models, and it is clear that

continued efforts will lead to continued progress.

9. REFERENCES

[1] Ingberg, S.H., Q. NFPA _20, 243 (1927). ibid 43 (1928).

[2] Kawagoe, K. , Fire Behavior in Rooms (BRI Report No. 27), Building

Research Institute, Tokyo, 1958.

[3] Mitler, H.E., The Physical Basis for the Harvard Computer Fire Code,

Harvard University Home Fire Project T.R. #34 (1978).

[4] Babrauskas, V. and Williamson, R.B., Fire and Materials, Vol. 2, No. 2,

39 (1978).

[5] Heskestad, G. , Modeling of Enclosure Fires, in Fourteenth International

Symposium on Combustion, p. 1021 (1973).

[6] Quintiere, J., The Growth of Fire in Building Compartments, paper

delivered at ASTM-NBS Symposium on Fire Standards and Safety, at NBS,

Gaithersburg, MD (1976).

[7] Reeves, J.B. and MacArthur, C.D., 3-volume report, FAA-RD-120, Univ. of

Dayton Res. Inst., Ohio (1976).

[8] Pape, R. and Waterman, T. , RFIRES, Illinois Inst, of Tech. Res. Inst.,

Report J6367 (1976).

[9] Emmons, H.W. , Mitler, H.E., and Trefethan, L. (Jr.), Computer Fire Code

III, Harvard Home Fire Project T.R. #25 (1978).

-26-
[10] Friedman, R., Status of Mathematical Modeling of Fires, Factory Mutual

Research Corp. Technical Report RC81-BT-5 (1981).

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

U.S. -Japan Panel on Fire Research and Safety, Building Res. Inst., Tokyo

(1978).

[12] Emmons, H.W., The Prediction of Fires in Buildings, 17th International

Symposium on Combustion (1979), p. 1101.

[13] Mitler, H.E. and Emmons, H.W., The Fifth Harvard Computer Fire Code,

Harvard Home Fire Project T.R. #45 (1980).

[14] Orloff, L., Preliminary Testing of Polyurethane Slab, Factory Mutual

Research Corp. Technical Report, May 23, 1977.

[15] Markstein, G.H., Scanning Radiometer Measurements of the Radiance

Distribution in PMMA Pool Fires, 18th International Symposium on Combustion (1980), The Combustion Institute, p. 537.

[16] Orloff, L., Simplified Radiation Modeling of Pool Fires, 18th

International Symposium on Combustion (1980), p. 549.

[17] Morton, B.R., Taylor, G.I., and Turner, J.S., Turbulent Gravitational

Convection from Maintained and Instantaneous Sources, Proc. of Royal

Society (London), Vol. A234, 1 (1956).

[18] Tewarson, A., Heat Release Rates from Burning Plastics, J. Fire and

Flammability, Vol. 8, 111 (1977); and in several technical reports for

Factory Mutual Research Corp.

[19] Prahl, J. and Emmons, H.W., Fire-Induced Flow Through an Opening,

Combustion and Flame, Vol. 25, 369 (1975).

[20] Alpert, R.L., et al. , Influence of Enclosures on Fire Growth, Vol. I: Test Data (Tests 0-7), Factory Mutual Research Corp., Serial No. 0A0

R2.BUO-7 (1977).

[21] Mitler, H.E. and Rockett, J.A., User's Guide to FIRST, A Comprehensive

Single-Room Fire Model, National Bureau of Standards Internal Report,

NBSIR to be published.

[22] Parikh, J.S., et al. , Survey of the State of the Art of Mathematical

Fire Modeling, Underwriters Laboratories Report, File NC554 (1983).

[23] Mitler, H.E., Comparison of Several Compartment Fire Models: An Interim

Report, NBSIR 85-3233 (1985).

- 27 -
o

i

QJ X

C o

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1.22m

H

r

Q0254rn

- 29-

1.525m
B A SPRINKLE K S ON

- 30 -
77777777 77

- 31 -
MEAN

HOT

LAYER

TEMPERATURE,

T,

(°C)

SPRINKLER

ON

- 32 -

(°K)
- 33 -
SPRINKLER

ON

- 34 -
POSITION

OF

HOT

LAYER,

H

R

-H

L

(meters)

- 35 -
GAS

OUTFLOW

RATE,

m

u

(kg/sec)

TIME FROM IGNITION, t (sec)

- 36 -
o

>-

- 37 -

300
COMPOSITION

-MASS

FRACTION

- 38 -
TOTAL

IMPINGING

RADIATIVE

FLUX,

<£

a

(kw/m

2)

- 39-
- 40-
- 41 -
- 42 -
- 43 -

100

200

300

t

(sec)
006

TIMF

FROM

IGNITION t

(sec.)
- 45-

(sec)
H»«n*A IMV, 1^0

rrorrasrinw

December 1986

U.t. DIPT, or COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR-86/3459

1. Performing Or|«n. Rtport No,

4. TITLE AND SUBTITLE

How Accurate is Mathematical Fire Modeling?

5. AUTHOR(S)

Henri E. Mitler and John A. Rockett

6. PERFORMING ORGANIZATION (If joint or other than NBS. see In struction s)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT of commerce

Maryland 20899

7. Contract/Grant No.

I. 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 bliography or literature survey, mention it here)

It is important to be able to predict the development of a fire in an enclosure of

arbitrary complexity. A mathematical model valid for a single room, with multiple

vents and objects in it has been developed. The fifth version of the model has just

been completed; it is the Harvard Computer Fire Code V, or Mark 5 for short. In

1977, Factory Mutual Research Corporation carried out a series of eight wellinstrumented full scale room fires, against which the single room model can be

tested. The test fire room was 2.44 m x 3.66 m x 2.44 m high, with an open doorway;

a slab of polyurethane foam in one corner, and a polyurethane foam target in a facing

corner. The primary slab was ignited at its center, and the fire followed. The

other tests were variants of this one. We compare the results of the calculations

with the results of two of the experiments: the standard configuration and the case with a window replacing the doorway. The model "predictions are in good to excellent

agreement for most of the variables. The disagreements are discussed, and it is

found that the most probable causes of disagreements are failure to take heating of

the lower gas layer into account, inadequacy of the burnout algorithm, and lack of

understanding of the production mechanism of CO.

12. KEY WORDS (Six to twelve entries ; alphabetical order; capitalize only proper names; and seporote key words by sen coi m

compartment fires; computer programs; fire models; mathematical models; room tires

13. AVAILABILITY

* Unlimited

For Official Distribution. Do Not Release to NTIS

' “ Order From Superintendent of Documents, U.S. Government Printing Office. Washington. D.C.

1 20402.

Order From National Technical Information Service (NTIS). Springfield. VA. 22161

14. NO. OF

PRINTED PAGES

50

15. Pnct

$9 . 9

‘