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NBSIR 83-2712

A Simple Correlation for

Predicting Temperature in a Room

Fire

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

June 1 983

100 I S. DEPARTMENT OF COMMERCE

, U56 ATIONAL BUREAU OF STANDARDS

83-2712

1983

C . 2

NATIONAL btreau

of STANDARDS

library

JUL 2 1 19 OcrVcXCJC-r oin^C.

O-Q— \O0

.LX'bV*

NBSIR 83-2712

A SIMPLE CORRELATION FOR

PREDICTING TEMPERATURE IN A ROOM

FIRE

James G. Quintiere

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

June 1 983

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CD

TABLE OF CONTENTS

Page

List of Tables iv

List of Figures v ,

Nomenclature vi

Abstract 1

1. INTRODUCTION 1

2. DEVELOPMENT OF CORRELATION 3

2.1 Example 1: Factory Mutual Bedroom Fire (1973) 11

2.2 Example 2: Factory Mutual Second Bedroom Fire (1974) 14

2.3 Example 3: Factory Mutual Room Test No. 4 - Open Door

and Window 15

2.4 Example 4: Factory Mutual Room Test No. 5 - Steady PMMA

Fire 16

2.5 Example 5: NBS/PRC Room Test W-4-1 - Four Wood Cribs 17

2.6 Example 6: NBS/PRC Room Tests - Peak Burning of Plastic

Cribs 19

2.7 "Flashover" Conditions by Peacock Using the Harvard

Computer Fire Code I 21

3. SUMMARY OF RESULTS 23

4. REFERENCES 23

iii
List of Tables

Page

Table 1. Data sources used in developing the correlation 25

Table 2. Thermal properties of lining materials 26

Table 3. Results for example 1: Factory Mutual bedroom fire 27

Table 4. Results for example 2: Factory Mutual second bedroom

fire * 28

Table 5, Results for example 3: Factory Mutual room test no. 4 ... 29

Table 6. Results for example 4: Factory Mutual room test no. 5 ... 30

Table 7. "Flashover" criteria by Thomas [15] 31

iv
TABLE OF CONTENTS

Page

List of Tables iv

List of Figures v

“

1

' t

' i

' : "jf

1 Nomenclature vi

Abstract 1

1. INTRODUCTION 1

2 . DEVELOPMENT OF CORRELATION »'. . 3

2.1 Example 1: Factory Mutual Bedroom Fire (1973) 1 11

2.2 Example 2: Factory Mutual Second Bedroom Fire (1974) 14

2.3 Example 3: Factory Mutual Room Test No. 4 - Open Door

and Window 15

2.4 Example 4: Factory Mutual Room Test No. 5 - Steady PMMA

Fire 16

2.5 Example 5: NBS/PRC Room Test W-4-1 - Four Wood Cribs 17

2.6 Example 6: NBS/PRC Room Tests - Peak Burning of Plastic

Cribs 19

2.7 "Flashover" Conditions by Peacock Using the Harvard

Computer Fire Code I 21

3. SUMMARY OF RESULTS 23

4. REFERENCES 23

iii
List of Tables

Page

Table 1. Data sources used in developing the correlation 25

Table 2. Thermal properties of lining materials 26

Table 3. Results for example 1: Factory Mutual bedroom fire 27

Table 4. Results for example 2: Factory Mutual second bedroom

fire. 28

Table 5. Results for example 3: Factory Mutual room test no. 4 ... 29

Table 6. Results for example 4: Factory Mutual room test no. 5 ... 30

Table 7. "Flashover" criteria by Thomas [15] 31

iv
List of Figures

Page

Figure 1. Problem definition 32

Figure 2. AT correlation with floor heat loss taken from Ref. [ 6 ],

X| and X2 given in eq. (7) 33

Figure 3. Example 1, Factory Mutual first bedroom fire 34

Figure 4. Example 2, Factory Mutual second bedroom fire 33

Figure 5. Example 3, room with an open door and window 36

Figure 6 . Example 4, pool fire fuel source 37

Figure 7. Example 5, fire conditions and configuration 38

Figure 8. Example 5, temperature distribution - wood cribs

(measured values apply to positions from ceiling to

floor, 9-23; calculated values from Ref. [13] for upper

and lower layers; estimated result from eq. (16) 39

Figure 9. Example 6 , peak temperatures as a function

of door width - plastic crib fires

0 = 4, = 3, A = 2, = 1 crib 40

Figure 10. Example 7, room fire conditions for AT = 500°C 41

Figure 11. Comparison of "flashover" (AT = 600°C) predictions 42

v
Nomenclature

A

c

8

h

hk

H

o k

m

m

•m

o

Q

T

T

o

t

t P

W

o x

x

, x2

6

AH

AT

P

P o

surface area of enclosure

area of vent

specific heat of solid

specific heat at constant pressure

specific heat at constant volume

gravitational acceleration

effective heat transfer coefficient

effective enclosure conductance

vertical vent dimension

thermal conductivity

mass

mass rate of fuel supply

rate of mass flow out of vent

rate of energy release

temperature of upper gas

initial or ambient air temperature

time

thermal penetration time, eq. (6)

width of vent

dimensionless groups, eq. (7)

enclosure material thickness

heat of reaction

temperature rise of upper gas

density

density of ambient air

vi
A Simple Correlation for Predicting Temperature in a Room Fire

J. Quintiere

National Bureau of Standards

Washington, D.C. 20234

The use of a simple formula for predicting upper

compartment gas temperature in a fire is demonstrated. The

formula is given in terms of energy release rate, vent

geometry, and compartment lining material properties. It

treats discrete fires within the room. Several examples are considered to show the versatility of the formula and its

general level of accuracy.

Keywords: Compartment fires; energy release rate; modeling;

prediction temperature; vent effects, wall effects.

1. INTRODUCTION

The gas temperatures within a compartment which result from fire in that

compartment depend on many factors. Temperatures within the flame zone will

be very high, approaching theoretical flame temperatures at most. In

contrast, air entering openings will be at ambient temperature and will be

heated slightly as it flows towards the flame. Also, combustion products

flowing away from the fire will cool due to mixing with colder gases and heat

transfer to surfaces. Despite this extreme range of spatially varying gas

temperatures in a compartment fire, a simplified description is reasonably

adequate for the process. This description is based on a zone model which

assumes a uniform temperature upper gas region within the compartment, a lower

region at ambient (air) temperature, and the fire plume represented as a localized heat source. It is a good description for small fires in conventional size rooms. For larger fires (fully involved room fires) and for fires

in large compartments, temperature variations in this upper zone could be

large. Nevertheless, the estimation of an average upper gas temperature could

still have some utility in characterizing the severity of the compartment

1
fire. In general, buoyancy and recirculation promote a distinct uniform

temperature zone while heat transfer and combustion effects promote temperature variations in this upper region.

The concept of a zone model for compartment fires has been used by

several investigators [e.g., 1-4] to predict various aspects of fire growth.

These include flame spread and burning of various materials and even the

computation of the fire effects on other rooms of the building. These studies

predict many variables in the fire growth process, and consequently require a computer solution for the many coupled governing equations. For a complete

understanding of the contribution by materials to fire growth and of the

impact of fire on its surroundings, these computer solutions will be

necessary. In some cases, a more easily implemented solution may be possible.

Indeed, the purpose of the current study is to explore the use of a simple

solution for upper gas temperature in a room fire. Its accuracy and applicability will be demonstrated by illustrative examples for various fire conditions.

Before proceeding with the details of this simple solution, some background will be presented to explain its development. McCaffrey [2,5]

discovered that the gas temperatures measured in the upper part of the room could be correlated in a power law relationship involving the energy release

rate of the f ire (Q) , the ventilation factor for the opening (A

q

i/h^) , and a room geometric scale factor. These data applied to steady gas burner fires

and to the peak burning conditions for wood or plastic crib fires. The corre- lation was so successful that it inspired a further study of its application.

The results of that study by McCaffrey, Quintiere and Harkleroad [6] led to a more general correlation which included the additional parameters of room

surface area and its thermal properties. This more comprehensive result was developed from an analysis of over 100 data sets for a wide range of fires.

That development will be reviewed here and examples will be presented to

illustrate applications of the correlation.

2
2. DEVELOPMENT OF CORRELATION

The problem being addressed Is shown schematically in figure 1 along with

the significant variables that apply. The fire is considered to be in the

lower portion of the room such that it has direct access to the air flowing

into the compartment. Ceiling fires would not be within the scope of this

analysis. The objective is to predict the upper gas temperature rise (AT) in

terms of the variables listed in figure 1. The rate of energy release (Q) is an important input variable, but is not known a priori under fire growth

conditions. To make a complete prediction, Q as well as T would have to be

derived. Alternatively, Q will have to be estimated or derived from experimental results to predict T in this problem. These aspects will be discussed

further in the examples to follow. The other variables in figure 1 should be

consistent with a general view of the problem. They involve room geometry,

opening dimensions and thermal properties of the materials of construction.

All of these variables can be easily determined.

The variables used in the AT correlation were derived by applying the

conservation of energy equation to the flame and upper gas region shown in

figure 1.

q

= C + m c AT + hAAT (1) v dt op

Rate of Rate of

” Rate of energy enthalpy ” Rate of

energy = stored in + flow out + heat lost

_ released_ the gas of the _ by the ga s _ openings

The terms are defined below.

Q

= rate of energy release within the compartment by the fire

m = mass of the heated gases within the compartment

T = temperature of the heated gases within the compartment

3
AT = temperature rise above the initial or ambient temperature, T

Q

t = time

c y,Cp = specific heats for the gas at constant volume and constant

pressure, respectively

m

Q = gas flow rate out of the opening

h = an effective heat transfer coefficient for the enclosure walls,

ceiling and floor

and A = the corresponding wall, ceiling and floor areas for heat

transfer.

The rate of energy stored in the gas is small compared to the other terms

in eq. (1) for most fire situations. By neglecting it, eq. (1) can be solved

for AT to yield

AT

T

o 1 + hA/ (cm ) P o The intention is to formulate the dependence of

dimensionless variables. The quantities m

Q

and

workable expressions to achieve this objective,

flow rate can be represented as

( 2 )

AT/T

q

into easily computed

h need to be transformed into

It can be shown that the gas

4

o = A</*£ • + (T

> V "o'

(3)

where <J> is a dimensionless function of T, Q, A

Q and H

Q [1,6]. For small AQ

, m

Q

is nearly directly proportional to A^/h^ (the ventilation factor), but in

general <f> must be known to compute m

Q

. The effective heat transfer coefficient, h, involves many heat transfer processes. Radiation and convective

heat transfer occur at the enclosure solid boundaries (walls, etc.) followed

by conduction into these surfaces; also radiative heat loss occurs at

openings. The convective and radiative processes will depend on T, Q and

A
geometric factors; while the "wall" conduction depends on its thickness (6)

and thermal properties (k, conductivity; c, specific heat; and p, density).

The effective heat transfer coefficient will therefore be represented as follows

:

h = h^ • *KT, Q, A

q

, ...) (4)

where ^ represents the radiative and convective effects and will depend on

a number of variables in the problem,

and h^ represents the "wall" or enclosure conductance.

This "wall" conductance term is given by a convenient approximate

expression [1,6]:

/kpc/t , t _< t h

k

- p

k/6 , t > t — P

where the solid thermal penetration tLme, tp, is given by

(5)

( 6 )

Equation (5) combines the initial heating solution of an infinitely thick wall

with the steady-state heat conduction result for a wall of thickness 6.

By substituting eqs. (3) and (4) into eq. (2) it can be seen that functionally AT/T

q can be expressed in terms of easily determined quantities.

However, the functions <|> and i|; are not generally known; and even if they were, an explicit solution for AT would not be possible. Nevertheless, it can be

said that the functional form of the solution would be

AT/T

q = f(X

x

, X

2

) (7)

where

5
and

Xl = q/(/5 p0

c p

T

o A

o/iT),

X. = h.A/(/g p c A /h~

)

2 k o p o o

Thus, through this analysis the relevant dimensionless groups, and X£, have

been derived. This result could have been developed by other methods, but

perhaps the analysis used here has revealed more of their physical significance. Moreover, a solution in the form of eq. (7) should account for

phenomena not explicitly described, such as gas flow rate through the opening,

and radiative and convective heat transfer processes. The objective now is to

develop an explicLt relationship for the function of Xj and X£, and establish

its accuracy. This was done by McCaffrey et al. [6] and their result will be

described.

The strategy for seeking a relationship for f(Xj, X£) was to consider a power law variation in the form of

The values for C, n and m were determined a best-fit with experimental

results. The source of that data was eight experiments which are summarized

in table 1 [6]

.

In most cases the peak (or nearly steady) burning conditions

were used. For Data Set 6, data were analyzed during the fire spread period.

Judgment was used in the interpretation of the most representative measure of

the average upper gas temperature; however, it is not uncommon to find temperature variations in the layer to be within 20% of the temperature rise at a single location. Another uncertainty is the determination of Q. All of the

data considered were estimated to lie within the fuel-controlled burning

regime in which sufficient air flow entered the compartment to burn all of the

fuel released. The flow rate of fuel was monitored by flowmeters for gaseous

fuels and by continuous weight sensors for solid fuels. Therefore, the

instantaneous mass rate of fuel supplied m(t) times the heat of reaction for

the fuel (AH) gives Q:

AT/T

o

( 8 )

Q(t ) = m(t) AH (9)

6
For solid fuels, WH in the flaming state is generally less than the theoretical heat of combustion for complete burning. The values of WH used in this

analysis were the best available estimates and are listed in table 1. Uncertainties, of the order of 20%, are possible for the solid fuels listed

there.

From these experiments, numerical results for 112 data groups were derived in order to determine the power law constants. It was felt that the

variations in the experimental conditions were sufficiently broad to provide a basis for a fairly general correlation. Fuel ranged from gas, to wood, to

plastics. Scale ranged from conventional room sizes down to nearly 1/8 of

that. Both door and window openings were included. The construction

materials used for the compartments were all essentially noncombustible and

had a wide range of properties. Table 2 lists these properties

(k, p, c, a = k/pc and kpc) for the construction materials in table 1 and

other representative room lining materials. It should be noted that the

computation of h^A in X

2 must account for all of the materials used in the

floor, walls and ceiling. The following procedure should be used for

computing h^A:

(1) Each area of enclosure lining having a different construction must be

considered separately, then summed.

S (h. A)

i

K

.-i

( 10)

where A.^ is the surface area of that region; e.g., it could be the

wall, ceiling or floor area.

(2) h^

^ is computed for the ith region consistent with eqs. (5) and

(6). If it is a single material, this is exactly as given. If it is

a composite construction, then eqs. (5) and (6) should be applied as appropriate for a series of thermal conductors. For a composite

consisting of j-layers:

h

k - 1/8 t . <>»

J k,j

7
where

/ t/(kpc)

j

, 0 -< t < t . “ P,1

(5/k)

x

’ 1 >— 1 P>1

0 , 0 —< t < t — p, 1 / t/ (kpc)

2

, t < t < (t

P,1 - - P,1

(S/k)

2

» t 1 (t

1 + t p , 1 P »

2

( 12 )

and h^

j can be found accordingly. Thus, the h^A values were computed for

each of the 112 data groups analyzed in reference [6]. The specific

analysis derived for each experiment Ls described in that reference. Once

those computations were completed, values for AT/T

q

, and X

2 were substituted into eq. (8) and the constants C, n and m were determined by

regression analysis.

A correlation was developed for two cases. In one case the floor was

Ignored as a heat transfer region, and in the second case it was included

along with the walls and celling. The motivation for this is that in the

early stage of fire growth at low upper gas temperature, there would be little

heat transfer to the floor; in the later period of fire development, at high

temperatures, floor heat transfer would become significant. Figure 2 shows

the result of the regression analysis for the case of floor heat loss; the

other case yields a similar result. The corresponding equations are, for no

floor heat loss:

AT/T = 1.32 X*?’ 624

X

0,315

o 12 (13)

and for the floor included:

AT/T = 1.52 X°*

65° X 0,387

o 1 z (14)

An alternative form of these equations, motivated by results from plume theory

is

8
AT/T (15)

o 1.63

Equation (15) will be used throughout the remainder of this presentation, and

will be interpreted to include the floor heat loss. A more convenient form of

eq. (15) in specific units is given by

AT

where

~\ 1/3

6.85

(A /H~)(h A)

o o k

in U C

Q is in kW,

2 A

q

, A are in m , H

q

is in m,

h^ is in kW/m^-K,

(16)

2 3 and the constant quantities have been taken as g = 9.8 m/s , P Q = 1.2 kg/m , T

c = 295 K, and Cp = 1.05 kJ/kg-K. This will be the working equation for the

subsequent examples. It should be applied as follows:

(1) Q(t) represents the instantaneous rate of energy release within the

compartment at time t.

(2) A /T is the sum for all openings in the walls to the ambient at T

o o o under natural ventilation conditions.

(3) h^A is the appropriate sum of the wall, ceiling and floor effects

based on eqs. (10-12).

A series of examples illustrating the application and accuracy of eq.

(16) will now be presented. In each case the example is based on experimental

results or results derived from mathematical models. No absolute measure of

accuracy will be possible to ascribe to eq. (16) from these comparisons since

uncertainties exist relative to the experiments and the mathematical models.

But favorable agreements in these comparisons will give more confidence in the

general applicability of the empirical correlation (eq. (16)). This should

follow since all of the examples to be considered have new or different

features from the data base which established the correlation. Hence, this

9
exercise could be viewed as a test of its validity; not just an explanation of

its application. A summary description of the examples along with a distinguishing feature for each is given below:

Examples 1 and 2 - These examples display the application of the formula to a spreading fire on a bed. The room fire configuration is

similar to those experiments considered in the development

of the correlation. However, the formula will be used to

predict the temperature response over time, in contrast to

peak or steady-state temperature data used in the derivation of the formula.

Example 3 - This is an exercise to examine the results from applying the

correlation formula to a spreading fire within a room having both

an open door and window.

Example 4 - In this example the fire consists of a fixed diameter pool of

polymethyl methacrylate beads which is uniformly ignited. Therefore changes in the burning rate are only due to transient

effects of the fuel bed and room thermal feedback.

Example 5 - The formula is applied to predict the transient temperature

response due to a room fire consisting of four wood cribs. Ihe

results are compared to both experimental data and results from a computer-based zone method fire growth model.

Example 6 - This example is an extension of the previous example. Here the

peak results are examined for a series of experiments involving

plastic crib fires and room door widths, both of which varies in

size. The formula is used to estimate the temperature at the

ventilation limit condition. This corresponds to the point for

which the air supply to the room is equal to that required to

burn all the available fuel.

10
Example 7 - Some investigators have suggested that the achievement of a critical temperature rise (500-600°C) can be used to indicate the

onset of flashover or potential full-involvement of the remaining

fuel in the room. The formula is applied in order to determine

the relationship between the corresponding critical energy

release rate and room geometric parameters. Results from a specific example are compared with results derived from using the

Harvard Room Fire Code.

2.1 Example 1: Factory Mutual Bedroom Fire (1973) [7]

The experiment [7] consisted of a typically furnished bedroom with a closet and a single doorway open to the surroundings. The fire was initiated

on the bed, consuming initially the mattress. A decay in the growth then

briefly occurred, followed by involvement of other items near the bed leading

to full-involvement of the room furnishings. The floor material was plywood,

and the walls and ceiling were sheetrock on studs and joists. These investigators [7] performed an energy balance from their measurements in order to

estimate the energy release by the fire Q(t). This is a difficult estimation

to perform accurately, and some negative values computed at the start of the

fire demonstrate that uncertainty. Nevertheless, their positive values will

be considered valid for the purpose of estimating AT. This computed temperature will then be compared to two measured temperatures—0.24 m from the

ceiling, between the bed and the doorway, and 0.13 m from the top of the

doorway. The computations are summarized below:

Ventilation Factor

H

q = 2.03 m

W

Q = 0.74 m A /H~ = W H

3/2 = 2.13 m

5/2

o O o o

11
Heat Loss Factor

1. Wall/celling material - sheetrock

O Area of walls and ceLling including closet, Aj = 47.7 m Thickness, 6

^ = 0.0159 m

(k/pc ) 1 = 0.16 x

10"6 m

2 /s

.*. t = 395 s P,1

/(kpc)

1 /t = /0. 18/ t , t < 395 s h

l k /6 = 0.17 x 10

_2

/0 .0159 = 1.07 x

10"2

, t > 395 s

2. Floor material - plywood

Area of floor including closet,

Thickness, 62 = 0.0159 m

( k/pc ) 2 = 0.089 x 10~ 6 m

2 /s

. *

. t 0 = 710 s

I

P,

2

^0.16/t , t < 710 s

0.12 x 10~3

/0 .0159 = 0.75 x 10

"2

,

Finally, from eq. (10)

A

2 = 9.38 m'

kW/m -K

t > 710 s

kW/m 2 K

hkA = (hA ) 1 + (hA ) 2

From the values of Q estimated by these experimenters [7] and the values

of and h^A given above, AT can be computed using eq. (16). These

results are tabulated in table 3 along with the selected measured room and

doorway temperature rises. The temperature rise is plotted as a function of

time in figure 3. The computed results are connected by a smooth curve for ease in illustrating the trend. Although a sharp temperature rise occurs just

after 16 minutes, flashover was defined to occur at 17 min. 40 s. in this

experiment. It is significant, for the purposes of estimating Q(t), that they

[7] estimated that the heat flux to the burning fuel did not exceed 20% of its

free burn value before flashover. That means that the mass loss rate (m(t),

eq. (9)) of the bed until flashover, was nearly at a value that could have

12
been determined from burning it outside of the room. The general establishment of this fuel response characteristic would enable a practical method for

estimating ra(t) and then Q(t) for complex fuel arrangements in order to

predict room temperature. After flashover occurs, and a fully-developed fire

results, room heat transfer can enhance the mass loss rate many times over its

free burn value, or ventilation limited conditions can reduce the mass loss

rate relative to free burn levels. Mass loss rate will depend directly on surface heat transfer rate and air supply rate or oxygen concentration.

Qualitatively, this can be expressed for a given fuel as

m = m, + f

1 (02

) + f

2 (q") (17)

where m is the free burn value, 00 9 f^ is the effect of 0>2 and f-2 the effect of heat flux to the fuel.

The functions fj and f£ are not completely understood, and more research is

needed to formulate them completely. Nevertheless, since f^CC^) will have a negative effect as A

Q

/lP is reduced or the fire grows,

m < m^t) (18)

during the growth period to flashover provided f

2 (q") is not a significant

value before flashover. Complete resolution of this issue has not yet been

made. A lesser, but non-trivial, issue is the estimation that Q

= mAH. If

eq. (18) holds, then Q = rn^AH is an upper limit if AH is taken as the theoretical heat of combustion for the fuel. Better accuracy will undoubtedly

require the determination of an "effective" AH consistent with the actual fire

process. Perhaps this digression on computing Q has given some insight on how

best to make that estimate for the intended application of eq. (16).

It should be clear now that an assessment of the accuracy of eq. (16), as displayed by the comparisons in figure 3, is not straight forward. The

inability to reconcile the concept of a computed average upper gas temperature

with point-wise varying temperature measurements, and the uncertain accuracy

of Q(t) preclude a precise assessment. Nevertheless, general agreement of

13
these temperatures in this example and those to follow will provide some perspective on this question. Only in this way can the confidence in the

validity of approximate fire models be developed. The remaining examples will

be presented in decreasing illustrative detail. The reader is encouraged to

complete the steps in order to gain an appreciation and understanding of the

analysis. High precision was not maintained in these illustrations so that

alternative computations may lead to slightly different numerical results.

2.2 Example 2: Factory Mutual Second Bedroom Fire (1974) [8]

This experiment [8] had an arrangement similar to that of Example 1. A

bed was the item ignited as previously, but the spread was more rapid in this

case. This, of course, underscores our inability to accurately predict Q(t).

Fortunately, the determination of Q(t) in this test appears to have yielded

more accurate results based on the quantity and consistency of the data displayed [8], Since the test conditions were the same as in Example 1, the same values of h, A and A /H~ should be used with the new values for Q. However, k o o since the plywood floor area is small relative to the area of the walls and

ceiling, and since the sheetrock properties are similar to the plywood, a reasonable approximate is to use the sheetrock properties throughout. It can

be shown that the results are as follows:

AT = 1.85 [Q

2/t] 1/3

, t < 395 s and

AT = 6.05 Q

2/3

, t > 395 s

in the units of eq. (16) (T in °C, Q in kW). The results of the computations

and the measured temperatures are listed in table 4 and shown in figure 4.

The same measurement positions as in Example 1 were selected. In contrast to

Example 1, flashover occurred earlier and the fire was extinguished after 7.5

minutes. The agreement between results compared up to that time is seen to

be, remarkably, excellent.

14
2.3 Example 3: FM Room Test No. 4 - Open Door and Window [9]

This example is taken from a series of room fire tests conducted jointly

by FMRC and Harvard University [9], The room structure (Marinite XL*,

6 = 0.0254 m) and size (2.4 x 3.7 x 2.4 m high) remained fixed throughout the

series. In this test, the primary fuel consisted of a polyurethane slab

located 0.6 m above the floor and a smaller remote "target" of the same material located 0.25 m above the slab height. The slab was ignited at the

center and fire spread over Lts surface. The target would become involved

later by spontaneous ignition under sufficient radiative heating. This target

ignition could be construed as the inception of "flashover". The distinguishing feature of Test No. 4 is that both an open doorway (0.775 m x 2.04 m high)

and window (0.76 m x 0.97 m high) were incorporated. The computation proceeds

as follows based on the data available [9]

:

h

fc A = 14.7//t kW/K for t < 1008 s.

The value for Q was estimated by eq. (9) where AH was given [9] as 18.7 kJ/g

and m was determined from continuous mass loss measurements of both the

primary fuel slab and the target. It can be shown that on substitution of the

above information into eq. (16)

A /iT = (0.775)(2.04) 3/2 + (0.76) (0.97) 3/2 = 299 m

5/2

o o

6 = 0.0254 m

k/pc = 0.16 x 10

-6 m

2 /s

From eq. (6), tp = 1008 s.

Since t < 362 s in this example, then from eq. (5),

or

AT = 13.7 (m

2/t)

1/3

, (°C)

*The use of trade names does not constitute an endorsement by NBS.

15
where m is in g/s and t is in s. The variables are listed in table 5 along

with the defined [9] average upper gas temperature based on measurements 0.72 m below the ceiling. The results are plotted in figure 5.

It is interesting to note that the mass loss rate of the primary fuel

dropped after the target became involved. Eventually the total mass loss rate

dropped and a sprinkler extinguished the fire at 384 s.

2.4 Example 4: FM Room Test No. 5 - Steady FMMA Fire [10]

This test [10] is another in the series described in the previous

example. In this case, the differences from Test No. 4 are that only the door was open, and the primary fire element was a 0.73 m diameter pool of polymethyl methacrylate (PMMA) beads which were uniformly ignited. The objective

was to consider a non-spreading fire which would tend to reach a steady

burning level. Steady-state occurred in approximately 1000 s. In order to

compute the temperature rise the following calculations are made:

A /h~ = 0. 775(2. 04) 3/2 = 2.26 m

5/2

o o

h^A = 14.7// t for t < 1008 s

From eq . (5) , h^A = k . (0.125 x 10

3 kW/m-K) , 2.

6 A = (0.0254 m) (47 m }

= 0.230 kW/K for t > 1008 s.

From eq. (9), Q = m(t)AH

where m is in g/s as given [10] and AH was taken as 24.2 kJ/g for PMMA [11].

Therefore, eq. (16) yields

AT

17.8(m

2 /t)

1/3

, t < 1008 s

71.3 m

2/3

, t > 1008 s

16
The results are compared to the average measured upper layer gas temperature

in table 6 and figure 6.

A sprinkler was activated at 1780 s and terminated the fire. The target

did not ignite for the PMMA primary fuel; and in the free burning condition,

the mass loss rate achieved 8.5 g/s [12]. Hence, the room enhancement effect

was approximately

(m - moo )/moo = (10 - 8.5)/8.5 = 0.176

or roughly 18%. Thus, computations based on a free burn mass loss rate would

have given slightly lower values of AT. Another point to consider is the

"discontinuity" in the AT prediction at 1008 s. This, of course, comes from

the change in h^ inherent in its approximate form. Despite that effect, the

overall results do not appear to suffer much.

2.5 Example 5: NBS/PRC Room Test W-4-1 - Four Wood Cribs [2,13]

This example is based on a series of room fire experiments involving wood

(sugar pine) or plastic (rigid polyurethane) of nearly the same density. They

were conducted at the National Bureau of Standards [13] and sponsored by the

Products Research Committee. The room had a single door opening whose width

(WQ

) was varied. The room size was 2.18 x 2.18 x 2.41 m high and lined on the

walls and ceiling with calcium silicate board of 0.019 m thickness, the floor

was concrete. The peak burning condition results were used to generate the

correlation, eqns. (13-15) [6] whereas computations over time will be made

here. The case of four wood cribs with the standard (largest) door width will

be considered. The mass loss rate of the cribs was determined from the

measurements. Here, a heat of reaction was selected as 13 kJ/g compared with

15 kJ/g used in the previous analysis [6]

.

This reflects the uncertainty in

this value [2], and the lower value is consistent with more recent computations performed by a more complete computer-based model [2,13]. The nature of

this problem and the results for AT are summarized in figure 7. The required

steps in the computation are shown below.

A /IT = W H

3/2

= (0.79)(1.83)

3/2

= 1.96 m

5/2

o o o o

17
For these enclosure materials, Lt can be shown that t will be greater than or equal to the limit of these calculations—t = 600 s. Hence, from eqs. (5) and

(10) and for enclosure parameters of

(1) calcium silicate walls and ceiling:

A^ = 26.2 m

2

(kpc)

1 = 0.098 (kW/m 2 -K) 2-s

(2) concrete floor:

A

2 = 4.75 m

2

(kpc)^ = 2.9 (kW/m 2-K) 2 -s

it follows that

h

k

A = 26.2/0.098/t + 4.75/2. 9/t

h^A = 16.3//t kW/K with t in s.

From eqs. (9) and (16) with T = 21 °C

o

T = 21 + 11.9(m2 /t)

1/3 °C

with m in g/s and t in s. The results of this computation ("estimate") are plotted in figure 8 along with experimental results and results from a more

complete model [13]. The experimental results [2] show the temperature variation of equally spaced ceiling to floor (9-23) thermocouples, numbered 9-23,

and surface thermocouples numbered as 8 and 25. Down to thermocouple 13 (0.75 m from the ceiling) and above the floor to thermocouple 19 (0.75 m from the

floor) the variation is slight. Thus, two distinct gas layers (zones) are revealed in room fires with a transition zone in between. The more complete

model [2,13] is based on a two zone characterization for the gases in the

enclosure and those predicted temperatures (T , T Z) along with their

8 y u 8 y corresponding solid boundary surface temperatures (Tw u , Tw

Z) have been

plotted in figure 8. The estimated results are too low as computed by eq.

(16). The computer model predictions are in better agreement with the

measurements and give a more complete thermal characterization.

18
2.6 Example 6: NBS/PRC Room Tests - Peak Burning of Plastic Cribs [2,13]

These results are taken from the same series of experiments described in

O Example 5. In this case, the plastic (rigid polyurethane, 340 kg/m ) fires

will be examined at their peak burning conditions in each test. The computed

results for AT (T = 21°C) will be compared with both the experimental results

and the results of the more complex zone model described earlier [2,13]. That

zone model incorporates a specific pyrolysis (burning) rate expression, as given by eq. ( 17 ) • It accounts for heating effects between adjacent cribs,

radiative heat flux to the crib surfaces, and reduced pyrolysis due to a lowering of oxygen concentration in the vitiated air flowing into the base of

the cribs. Fortunately, for items which burn like cribs (internal channel

dominated pyrolysis), the free burn rate (m^) is a good approximation to the

pyrolysis rate in a compartment provided the ventilation (air-controlled)

limit is not reached. Eq . (16) can still be used until the ventilation limit

is reached with m^ taken as nominally 8 g/s per crib. The limit condition

which gives the maximum temperature for a fixed A

q

/h^ and corresponding fuel

load (n-cribs) can be estimated as follows:

The maximum air flow rate (m ) for small openings or fully-involved enclosure

Si fires was shown by Kawagoe [1] to be

m = k A /H~; k = 0.5 kg/m^^-s. (19)

a o o o o

The maximum possible energy release rate within the compartment is therefore

0 = m AH (20)

inax a a

where AH = 3 kJ/g air consumed, approximately. This number is fairly

cl constant for the range of combustibles in fires. Substituting eq. (19) and

(20) in eq. (16), the limit temperature is estimated for the boundary between

ventilation-limited and fuel-limited fires. For the same fuel load, the AT

for either larger or smaller openings (A

q /H values) will be lower. Hence,

AT.. , = 896[A /H~/(h,A)] 1/3 (°C) (21)

limit L o o k

J

19
with (S.I.) units as used in eq. (16).

The fuel-controlled (non-air-limited) temperatures are calculated as usually. For this example, the following is done:

(1) The height (H

Q

) of the opening was fixed at 1.83 m, and the door

width (W

Q

) was varied.

(2) The heat of reaction was taken as AH = 19 kJ/g.

(3) The mass loss rate was taken as m = 8n(g/s) where n is the number of

cribs.

(4) Peak burning conditions were nominally reached at t = 250 s, therefore h^A = 16.3//t kW/K was computed at this peak time

condition.

Substituting all of the above into eq. (16) yields

AT = 142(n

2 /W ) 1/3 (°C)

o

where W

Q

Ls in m. Correspondingly, the limit temperature rise was computed

from eq. (21) so

AT,. . = 1190 W

1/3

, lrmi t o

Hence, for each W

Q

, there is some number of cribs which correspond to the

maximum possible AT rise for that opening.

The results of these estimates are compared to the data [2] and computer

model results [13] in figure 9. The lower (ventilation) limit temperatures

found by the more complete zone model reflect the reduction in the pyrolysis

rate due to local vitiation of the crib air; this likely occurs before the

estimated limit eq. (21) is reached. Although deviations exist among all the

values, the estimated results appear reasonably consistent.

20
2.7 Example 7: "Flashover" Conditions by Peacock [14] using

the Harvard Computer Fire Code V

Although this example is entitled "flashover," the term can not be

precisely defined, but is based on the subjective "eye of the beholder."

Having Seen a dramatic eruption of fire in a room, an observer shouts "flashover." To define this event in operational terms requires a complete understanding of the fire growth mechanisms responsible for its cause. Nevertheless, despite this lack of complete understanding, expedient investigators

seek simple operational measurements to signify flashover. Recently, Thomas

[15] tried to give some basis for using an upper gas temperature rise as an

indicator of "flashover." Table 7 summarizes these estimates for several

potentially promoting mechanisms —"others" are also listed to leave the issue

open. In this context. Peacock [14] decided to define AT = 500°C as the point

of flashover. He proceeded to compute conditions which would yield this

temperature for an impulsively initiated, constant energy release rate fire.

He selected the following configuration for his computations:

(1) Room height fixed at 2.4 m, but total room surface area (A) ranged

from 48 to 323 m

3

.

(2) Lining material was gypsum board with 6 = 0.0127 m and k = 0.17 x

10" 3 kW/m-K.

(3) Door height (HQ

) was fixed at 2.03 m, but the width (W

Q

) was varied.

Since a steady fire was considered and the maximum AT sought, it follows that

h

k

= k/6 = 0.0134 kW/m

2 -K.

Hence, from eq. (16) with AT = 500°C the corresponding Q values are found by

= 0.0721 (A A /iT) 1/2 in MW. x500 o o

21
The limit curve (i.e. AT^

^ = 500°C) was also computed from eq. (21). These

estimated values are compared in Figure 10 with the results given by Peacock

[14] based on the Harvard Code V. It is interesting to note that Peacock

computed down to the estimated ventilation limit line without any explicit

recognition of it; however, the Code should have dealt with it properly

depending on its input information. Agreement between the two computations

seems fair for conventional room sizes, i.e., 48-85 m . The empirical result

(Eq. (16)) springs from data taken in such rooms. The Harvard code also gives

higher Q500 va lues > especially for "small" A

q

/H^ (note, a typical door or window has an A /h~ of 2-3 m^^). This may result because that model

considers the lower room space to remaLn at its Initial temperature, thereby

becoming an excessive heat sink as enclosure temperatures increase. For the

"large" wall area compartment and "large" A

q

/h^ values, no experimental data

are available to provide credibility to each of these computed results.

Overall, both show similar trends and their utility is clear for design

purposes.

Another view of this type of analysis has been made by Thomas [15]. He

compared several formulae to predict the Q required to achieve an upper gas

temperature of 600°C in the experiments of Hagglund et al. [16]. Babrauskas

[17] derived an expression for this Q as a function primarily of A

q

/h~, and

subsequently a modified expression involving the surface area (A or A^)

.

Thomas [15] developed an independent analysis and found Q for T = 600°C to be

Q (T=600°C)

- 7 - 8 A + 378 Vs:

(kW)

with the dimensions in m. While not explicit in the Thomas formula, since he

particularized it to the Hagglund experiments, is the enclosure material

properties. Taking the present result in eq. (16) for the Hagglund experiments it can be shown that

'5(T=600»C)

/A o

/Sr

'o = 144 WM/lT) 172

in units of kW and m. As A + 0 (or more physically meaningful, h^ 0) this

result is not valid; its behavior is an artifact of the correlation. A

comparison between all of these formulae and the data of Hagglund et al. [16]

that just achieved T = 600°C is shown in figure 11. As in figure 10, it is

22
interesting to note that all of the results in figure 11 are within the fuelcontrolled (non-ventilation-limited) fire regime since from eqs. (19) and (20)

Q /A flT = 1500 kW/m 5/2

. max o o

3. SUMMARY OF RESULTS

An assessment and demonstration of using the empirically based formula

for upper gas enclosure temperature rise,

f

= 1.6 / 2

o \ /g c p T A fT

\ p o o o o

has been presented. An impression of the initial correlation (Fig. 2) and the

results of the various examples suggests it predicts experimental results

within 100°C (at worst). The uncertainties in selecting Q and the lack of

one-to-one correspondence between an average bulk computed temperature and

pointwise measurements mitigate that evaluation. The need to specify Q is a critical one. It may be resolved by using free burn data, but a complete

generalization of this approach needs to address enclosure radiative feedback

effects on fire growth. A thorough assessment of this issue is key to using

eq. (16). Nevertheless, estimates for Q from experiments have led to good

predictions of temperature in those experiments. And it has been illustrated

that these predictions appear to account well for the effects of vents,

material properties, time and scale. More complete models are certainly

needed to address the wide range of interest in fire safety; however, this

empirical formula could provide a simply derived estimate of thermal effects.

4. REFERENCES

[1] Quintiere, J. , "Growth of Fires in Building Compartments," Amer. Soc.

Test and Mater., ASTM STP 61A, 1977, p. 131.

[2] Quintiere, J. and McCaffrey, B., "The Burning of Wood and Plastic Cribs

in an Enclosure: Vol. 1," Nat. Bur. Stand., NBSIR 80-2054, Nov. 1980.

[3] Emmons, H. W. , "The Prediction of Fires in Buildings," 17th Symposium

(International) Combustion, The Combustion Institute, 1979, p. 1101.

2/3 h A

k -1/3

/g° c p a sr

p o o o

23
[4] Tanaka, T. , "A Model on Fire Spread in Small Scale Buildings, 2nd

Rept.," Building Res. Inst. (Japan), BR1 Paper No. 84, March 1980.

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

Enclosure Fires," J, of Res, of the Nat. Bur, Stand ., 82, 2, 1977.

[6] McCaffrey, B. J. , Quintiere, J. G. , and Harkleroad, M. F., "Estimating

Room Temperatures and the Likelihood of Flashover using Fire Test Data

Correlations," Fire Technol. , 17, 2, May 1981, p. 98.

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

11, 1973," Factory Mutual Research, FMRC Ser. No. 21011.4, July 1974.

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

II," Factory Mutual Research, FMRC Ser. No. 21011.4, June 1975.

[9] Alpert, R. L. et al. , "Influence of Enclosures on Fire Growth Vol. 1: Test Data, Test 4: Open Door and Window," Factory Mutual Research, FMRC

Job I.D. No. 0A0R2.BU-4, July 1977.

[10] Alpert, R. L. et al., "Influence of Enclosures on Fire Growth Vol. 1: Test Data, Test 5: Steady PMMA Fire," Factory Mutual Research, FMRC Job

I.D. No. 0A0R2.BU-5, August 1977.

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

Polymer Lc Materials," Nat. Bur. Stand. NBS-GCR-80-295 , Nov. 1980.

[12] Modak, A. T. (ed.), "Influence of Enclosures on Fire Growth Vol. II - Analysis," Factory Mutual Research, Job I.D. No. 0A0R3.BU, July 1978.

[13] Quintiere, J. , Steckler, K. and McCaffrey, B., "A Model to Predict the

Conditions in a Room Subject to Crib Fires," Nat. Bur. Stand., presented

at the First Spec. Meeting (Int.) of the Combustion Institute, Univ.

Bordeaux, France, July 1981.

[14] Peacock, R. D. and Breese, J. N. , "Computer Fire Modeling for the

Prediction of Flashover," Nat. Bur. Stand., NBSIR 81-2516, October 1981.

[15] Thomas, P. H. , "Testing Products and Materials for their Contribution to

Flashover in Rooms," Fire and Materials , Vol. 5, No. 3, 103-111,

September 1981

[16] Hagglund, B., Jansson, R. and Ornermark, B., "Fire Development in

Residential Rooms after Ignition from Nuclear Explosions," FOA Rep.

C 20016-D6( A3) , Forsvarets Forskingsanstalt , Stockholm, Nov. 1974.

[17] Babrauskas, V., "Estimating Room Flashover Potential," Fire Technol ., 16, May 1980, p. 94.

24
TABLE

Is

DATA

SOURCES

USED

IN

DEVELOPING

THE

CORRELATION

rH CM cn ^3* >3

m NO

00 0 3 0) 0) 05 Wl 9 a> u •H AJ AJ 0 <D C > G rH CO CO a> aj > •H 0 0) •H O a >

cn 05 0 cn 0 cn . 0 0) •H •H 0 cn

rH CD rH 3 CM rH 0 O rH »H rH • X cn • rH cn • 0 m •H CM •H ON O

CO »H CO

O 1 CM HD (0 cn CO rH • u 0) CO O O O CD 05 O C O 0 O 0 u 1 • AJ H3 • u • 0 • 3 aj 0 • Q • HD 0 0) aj <d <D <0 AJ \ <D 3 3 0

rH

u 3 HD

H AJ aj

u V) *T3

u *H HD *H HD 0

Pm a>

uO U»

O c Vu <DU 0 u

U

MO Am

g 3 E CO

C •rH <d 3 X CO

OG rH CO rH CO cd 0 aJ O O CO X 0 05 0 rH O c0 O CO O rH CO CJ O HO O Ph (0 0 < .0 Oh O O X cj X aON m rH cn CM u O rH m 0 <D •» • O c >% CM >

-N 0 • vO 0 0 H3 0 a>

O 0 0 HD 1—i

•H rH 0) AJ HD

'w' *H

M HD

O AJ rH

O 0)

M cn

05

X CO V< CO CO CO Vj cO rH

05 rHm

O cO 1— rH <4-4 0 O

O

O 05 *H CM X O e 3 0 0 c X •

a) 0 X 3 05 3 3 rH cn 0 c • 0) 10 G C O X X rH 0 a) 0) AJ 05 a *rt *H •H AJ O AJ AJ vO 0 HD cO CO O >N 0 AJ O CO • HD c0 CO vO

*H

C

OO AJ oc 05 3 CO rHa CU

O

OO

X. cO •H

H 05 05 rH rH

O •H HD AJ •H •H

O

H rH rH 0)

X CO CO 3 rH

O CO rH

H

O 60 •H •H rO rH 05 05 •H O u •H •H • rH c 05 05 05 <u 60 H G 05 05 0) CO 05 ^ CO •H 1 CO CL 0) •H CO 1 CO 0

•H rH CO 0 1 >v 05 > rH CO rH 0 co 3

V4 •H 3 3 AJ 4J 3 O 60

G

a •• 3 c c

<u a> •H •H

G

O <r «H 05 •H •H «H

AJ 0 6 O 0) P u

m vO

X 0 rH

O 0 0

CO 3 rH i a> CM

O AJ 3 <u rH rH 3 3 X rH CO 9 > *H O O •H rH > (0 CO rH rH c CJ CJ 0 • • 5 < 0 3 CJ < cO m m rH

tcc

•H3

O)04 o 3 0 E 0

00

CMmrHOm

CM

CM

onoCM

cn

00

cn

cnON

ON

CM I m

rH

rv /-n 3• W• m

on r-*. O O• • CM rH

ON

ON ^• >-/ I 1^ m cn

cn

cm •

cn

GO

cn • 00 rH

rH <n

*3-

VO

IT» ao CM

m

rHm 0 m vO co • CM cn cn cn cn CM 3 e ocn o O

cn

o\

cn ON

cm

<r

CM

00CM

SC 6 ocn

CM

*3- cn

CM CM CM

cn

rH

CM

cn*o 00 tH X X ^< 2 m cn

rH CM om

vOMf om

CO om

05

a rO 9 05 -H X -Q H

AJ *H

O

0) rH 0 a o)

CDG 05 05 3 rH <D CO CO 3 G X 60 60 X •H 4J AJ Ou a) rH 0) rH

CD 05 Vm CO 3 3 0 AJ H 3 U 3 J-t >% <D <0 >\ 3 a. 3

rH a; Ci) rH AJ 0 AJ 0 X 3 O co M 3

Dm (JO C/5 Pm Z Pm Z

(0 •HO

hdoo5

CO X<0 rH

GO03 r-s O 3

1+4

U

•H

<D <A4 c

(0 00 X C

AJ -H

0) HD M (0 3 CD >> H

rH O- o CO Pm

0)c

CO •C

i-J 0) z

co a» O c/5

a)eo

14 IM S C HS•H CO 3 *-» • 3

/-N s> 3 (0 C- H oz meg
TABLE

2:

THERMAL

PROPERTIES

OF

LINING

MATERIALS

O)od

CDd

a)

>4-1 CD Pi

EC

X cn

m co CO

m EC CM UO

CO cs__

Ov CO rv cm 00 CO vO o 1—1 rH rH o o

CL tsr*

CM e m CN CM i—1 rH o o o

rH 00 o 00 rH m vO rH rH

m CO Ov • rH CO o o

rH rH o i o o o o

vO • • • • o o COO

vOO

-HI

CM * b i s

CO 1J

LT) 00

rH CM 00 vO vO

O

ov

m co vr iH cm

Ov

oo

m o O rH in CM

00I <r

00

iHm

C". CO

COo.^L- b 1J

VO VO r-l OCM .H rH

CO rv vO

O CM 00 I"' H H CM rH O

m vo st

rH CM tH

iHI

COmO rHI''- VI- CO CO o o

vO

(VI 1 E4 1 U 'I <J\ in <fr m vO VO CM m A

CJ

d 00 o 00 00 rH CO

m CM OV o rH CM rH 00

m

r* 1

00 ^ 1 rH o rH CM rH rH rH rH

V * • rH 1 o O O O O O O o o o 00 O

rHO

O o o vom <r o o m o

l-v -d- i—1

vO Ov OV OVm 00m VO rv

CM CM CM CM ,H o o

vt vO

CM CM o o

vO CM

d

d

d

d

O o X d K cO O •H CD a cO /V O rH 4-J d o o t-3 X X co CD rH -Q (H d

rO CD CDd CDd >v cv 4-1 4-J CO 4-1 CD o 4-J CO u

CD

d CD CD o co 4-> •H cO

d CO

d CD S s 4-1

d 4-> CJ •H 4J

O •H >v 0 g >v CD d d o CO H d cO •H r-H CL CD > d d d d CD T—t

•H rH rH CD o

v_/

O

d cj cO cO o X •H

d

d

H * d CL 1 CD d O O d o CO CO cO CO CO X

g CD CO

X o X

X

d co

g

d rH •H

d 3 P o NmS o d d cO d 1 B •H cO o IH CD c CD 4-1 V b <d O O CD 4-> S d o d

•H J-i CO

d r* JxJd

H

O

X •d

d

H

d CD •H & CO

d & O CD d CJ cj CO CO § CL cO CD CJ d d S o CO cO § d X cO H •H O- CO !>> •H d G iH cO X d cO CO CL rH o CO O d d rH rH rd (D CD cO o •H rH (H M c CJ < CQ PQ O P* CL U C CJ CJ X fd < CJ w

dH* 1 -s

1C

H

H CM CO

CD

4-1 Oz

de

name -

implies

no

endorsement

by

NBS.

Handbook

values

(concretes

based

on

density).
Table 3

Results for Example 1: FM Bedroom Fire (1973)

Experimental Values

t h

l h

2 hkA Q AT AT^ (door) AT

44

(ro

min (kW/m2-K) (kW/m2 -K) (kW/K) (kW) (°C) (°C) (°C)

2 0.0387 0.0365 2.16 99.9 88.6 9 0

4 0.0274 0.0258 1.53 264 190 82 51

5 0.0245 0.0231 1.37 331 229 120 98

6 0.0224 0.0211 1.25 538 326 185 161

7 0.0107 0.0195 0.687 711 481 235 219

8 0.0107 0.0183 0.676 694 475 465 327

10 0.0107 0.0163 0.657 360 307 255 275

11 0.0107 0.0155 0.650 347 300 217 242

13 0.0107 0.0075 0.574 50 87 143 167

16 0.0107 0.0075 0.574 145 177 220 194

17 0.0107 0.0075 0.574 1199 723 699 445

27
Table 4

Results for Example 2: FM Second Bedroom Fire 1974 [8]

Experimental Values

t Q AT AT (door) AT (rc

(min) (kW) (°C) (°c) (°C)

0.5 -0.50 — 0 0

1.0 0.15 1.0 0 0

1.5 1.09 4.2 2 2 2.0 0.88 3.8 3 2 2.5 1.80 6.3 5 4

3.0 3.50 10.1 8 7

3.5 7.70 17.6 12 12

4.0 15.70 28.9 21 19

4.5 42.20 57.0 43 39

5.0 82.40 90.6 71 72

5.5 176.30 153.0 137 147

6.0 218.70 179.0 139 162

6.5 953.00 484.0 467 452

7.0 2185.00 852.0 723 749

7.5 2342.00 903.0 777 833

28
Table 5 Results for Example 3: FM Room Test No. 4 - Open Door and Window [9]

t m

(8) (g/s)

10 0.012

100 0.328

200 3.040

300 44.000

320 63.600

362 52.7 (65.7)*

AT AT

measure (°c) (°C)

1.0 0.5

14.0 2.0

69.5 42.6

442.0 316.0

571.0 563.0

514 (595) 595.0

* Corresponds to contribution by the target item following its ignition at

350 s.

29
Results for Example 4:

Table 6

FM Test No. 5 - PMMA Steady Pool

t

•m AT ^(measured)

(s) (g/s) (°C) (°C)

100 3.17 83 124

200 6.01 142 169

300 7.21 172 204

400 8.48 201 219

600 9.06 225 244

1000 9.85 259 273

1200 10.03 332 288

1400 10.09 333 294

1600 9.74 325 297

30
Table 7

"Flashover" criteria by Thomas [15]

Mechanism Critical

• Thermal feedback/instability

• Ignition threshold of solids

• Gas phase ignition

(others)

300 -

^ 600

> 400

AT (°C)

650

- 500

31
32

Fig.

1.

Problem

definition
0.0

100.0

200.0

300.0

400.0

S00.0

600.0

700.0

800.0

Fig. 2. AT correlation with floor heat loss

taken from Ref. [6], X

1 and X

2 given

in eq. (7)

33
Fig.

3.

Example

1,

FM

first

bedroom

fire

34

TIME

(min.)
Fig. 4. Example 2, FM second bedroom fire

TIME (min)

35
700

600

500

400

300

200

100

0

Figure 5. Example 3, room with an open

door and window

36
Figure

6.

Example

4,

pool

fire

fuel

source

37
Figure

7.

Example

5,

fire

conditions

and

conf

iguration

38
400

350

300

250

200

150

100

50

0

Figure 8. Example 5, temperature distribution - wood cribs (measured values

apply to positions from ceiling

to floor, 9-23; calculated values

from Ref. [13] for upper and lower

layers; estimated result from

eq. (16)

PRC7-W-4-1

TEMPERATURE

ROOM

MEASURED

PREDICTED

ESTIMATED

CEILING TEMP.

UPPER WALL TEMP.

300 450 600 750

TIME (s)

39

150 900
‘igure

9.

Example

6,

peak

temperatures

as

function

of

door

width

-

plastic

crib

fires

0

=

4,0

=

3,

A

=

2,0

=1

crib

(3o) 3Unitfd3dM31 SV9

40

DOOR

WIDTH

(m)
Fig.

10.

Example

7,

conditions

for

AT =

500°C

A„/Ho

(m

5/2 )
600°C)

predictions

u

n3 II a

S H

o <

O

00

•H

( 2/fi ui/M>l)^ 0

V/D

42

(m'

1/2

)
NBS-114A (REV. 2 - 80 ) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR 83-2712

2. Performing Organ. Report No. 3. Publication Date June 1983

4. TITLE AND SUBTITLE

A Simple Correlation for Predicting Temperature in a Room Fire

5. AUTHOR(S)

James G. Quintiere

6. PERFORMING'ORGANIZATION (If joint or other than N BS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

S. 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

bibliography or literature survey, mention it here) The use Q f a simple formula for predicting upper

compartment gas temperature in a fire is demonstrated. The formula is given in terms

of energy release rate, vent geometry, and compartment lining material properties.

It treats discrete fires within the room. Several examples are considered to show

the versatility of the formula and its general level of accuracy.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

Compartment fires; energy release rate; modeling; prediction temperature;

vent effects; wall effects

13. AVAILABILITY

Unlimited

Q^j For Official Distribution. Do Not Release to NTIS

r —I Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

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

14. NO. OF

PRINTED PAGES

48

15. Price

$8.50

USCOMM-DC 8043-P80