NBSIR 75-706

Calculations of Radiant Heat

Flux in the Proposed Floor

Covering Flame Spread Test

Apparatus

James Quintiere and Kevin Bromberg

Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

December 1975

Final Report

U S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 75-706

CALCULATIONS OF RADIANT HEAT

FLUX IN THE PROPOSED FLOOR

COVERING FLAME SPREAD TEST

APPARATUS

James Quintiere and Kevin Bromberg

Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

December 1975

Final Report

U.S. DEPARTMENT OF COMMERCE, Rogers C.B. Morton, Secretary

James A. Baker, Hi, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science arid Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler. Acting Director

CONTENTS

Page

LIST OF FIGURES iv

1. INTRODUCTION 1

2. ANALYSIS AND RESULTS 2

2.1. Radiant Heat Flux from Panel to Specimen

Plane 2

2.2. Effect of Panel Edge Surface on Heat Flux . 4

2.3. Effect of Panel Temperature on Heat Flux. . 4

2.4. Comparison of Calculated Heat Flux with

Measured Flux 5

2.5. Effect of Enclosure on Heat Flux 6

3. OTHER CALCULATED HEAT FLUX PROFILES 7

4. CONCLUSIONS 7

5 . REFERENCES 8

iii
LIST OF FIGURES

Page

Figure 1. Panel geometry and orientation with respect

to the specimen plane 9

Figure 2. Basic configuration (applies to eq. [2]) . 10

Figure 3. Schematic of radiant panel showing hot spot

region as approximated in calculations.

(Dimensions are in cm) 11

Figure 4. Comparison of calculated and measured heat

flux distributions for condition C . . . . 12

Figure 5. Comparison of calculated and measured heat

flux distributions for condition D . . . . 13

Figure 6. Comparison of calculated and measured heat

flux distributions with the enclosure

surfaces removed for condition C 14

Figure 7. Comparison of calculated and measured heat

flux distributions with the enclosure

surfaces removed for condition D 15

Figure 8. Calculated heat flux distributions for

various panel temperature, orientations,

and presence of enclosure surfaces .... 16

\
CALCULATIONS OF RADIANT HEAT FLUX IN THE

PROPOSED FLOOR COVERING FLAME SPREAD TEST APPARATUS

James Quintiere and Kevin Bromberg

Calculations have been made to determine the

radiant heat flux distribution to the test specimen

in the proposed radiant panel flame spread test for

floor covering materials. Comparison with measured

heat flux indicates a significant heat transfer contribution from the enclosure of the test apparatus.

Also, nonuniformities in the temperature of the

radiant panel affect the resultant flux distribution. Based on these results, it is expected that

two similar test apparatuses would not have identical heat flux profiles along the specimen. Additional calculations were made to illustrate possible

heat flux profiles capable with the present apparatus under various panel temperatures and orientations.

Key words: Floor covering; heat flux; radiant

panel test method.

1. INTRODUCTION

The purpose of this report is to analyze the radiant

heat transfer characteristics of the proposed radiant panel

test for measuring floor covering flammability [1,2]1. In

the test apparatus, a gas-fired porous refractory burner is

enclosed in a rectagular chamber. The burner is oriented at

an angle to the horizontal and faces downward. A test specimen is mounted in a horizontal plane below the burner. The

analysis considered in this report will be directed at the

radiant heat exchange between the radiant panel, specimen,

and the surrounding surfaces of the enclosure. This analysis

does not consider heat transfer effects associated with flame

spread along the specimen. It is primarily concerned with

the initial radiant heat flux distribution to the specimen.

The specific objectives of this analysis are: (1) to

identify and quantify the sources of radiant heat flux to the

specimen, (2) to determine the relative importance of the

different factors which influence the incident radiant flux,

and (3) to compare the theoretically determined radiant heat

fluxes with measured results.

Numbers in brackets correspond with the literature references

listed at the end of this paper.

1
By accomplishing these objectives, the resultant information should be helpful in the development and interpretation of the proposed test method.

2. ANALYSIS AND RESULTS

The primary source of radiant heat transfer to the

specimen plane is the gas-fired panel. Several factors

influence the magnitude of this flux and will be considered

in the analysis to follow. Radiation from the panel depends

on the temperature distribution over its face. The face of

the burner consists of a porous burner region which is heated

by the combustion process, and an "inactive" perimeter which

is heated basically by conduction. The temperature distribution over the combustion zone of the panel and its edges

will influence the emitted radiant heat transfer.

A secondary source of radiant heat transfer which is

expected to contribute to the heat flux on the specimen plane

originates from the heated walls and ceiling of the enclosure.

This contribution depends on the temperature distribution

along the enclosure surfaces. This contribution will not be

directly predicted since it would involve a more complex

analysis than is required to meet the objectives of this

analysis. However, the magnitude of the enclosure heat flux

contribution will be determined by comparison of measured

specimen fluxes with and without enclosure walls.

2.1. Radiant Heat Flux from Panel to Specimen Plane

The incident radiative heat flux on the specimen due to

the panel is determined by

where Fgp is the configuration factor from a differential specimen area to the panel,

a is the Stefan-Boltzmann constant,

and Tp is the effective blackbody temperature of

the panel burner.

The configuration factor is a function of orientation and

geometry. The arrangement of the panel with respect to the

specimen plane is shown in figure 1. The constraints on the

NBS apparatus are such that height of the specimen plane can

2
be varied, and the panel inclination can be varied about the

lower edge as an axis of rotation. The active burner area of

the panel is 30.5 cm wide (b = 15.3 cm) and 45.7 cm long

(a2 - ^1 = 45.7 cm) . The inactive perimeter of the panel

face is 1.9 cm in width. The configuration factor between

an element dAg on the centerline of the specimen and the

panel face, P, is determined from the configuration factor

relationship for the basic arrangement shown in figure 2 [3]

where Fi2 =

jj^ jtan"^ [j-] + V coscj) - tan ^ V

(2)

where V = n2 + - 2NLcoS(!)

-1/2

W = 1 + S in2 ^)'A

N =

and

Configuration factor algebra [3] is then used to determine Fgp. The basic configuration factor F12 can be considered as a function of a, b, and c. It can be shown that

Fgp = 2 I Fi 2 ( a2 , b, Hcotcl) + 8.9 cm + x

- F

[

12(^1' t). Hcotd) + 8.9 cm + X (3)

where F12 = ^12 (a/b,c) is given by equation (2).

3
Two test conditions have been used extensively with this

apparatus and have been referred to as conditions C and D

[1] . The parameters defining these conditions are listed in

table 1. These conditions will be referred to in the following discussion.

Table 1.

Parameters Defining Condition C and D

T H

P

Condition (^C) (cm) (deg.)

C 490 14. 0 30

670 8.6 30

2.2. Effect of Panel Edge Surface on Heat Flux

A calculation was made to determine the effect of the

inert perimeter region of the panel which is heated by conduction. The inert region was assumed to be at the same

temperature as the combustion zone of the panel. That is,

the radiating area was increased to include the edge region.

In this manner, equation (1) was used to evaluate the edge

effect. It was found that for both conditions C and D, the

edge contribution could be, at most, between 4% at x = 0 and

18% at x = 90 cm, where x is the position along the test

sample. Since this edge temperature is expected to be lower

than the effective panel temperature Tp in practice, it was

concluded that its effect on heat transfer is small; and

consequently, will be neglected in all subsequent calculations. (In effect, this influence can be absorbed into the

enclosure influence discussed in 2.5.)

2.3. Effect of Panel Temperature on Heat Flux

It has been recognized that two factors influence the

temperature, Tp, of the radiant panel [4]. In one case, the

nature of the porous burner is such that a nonuniform surface

temperature is likely to occur. In fact, Adams has found

that a "hot spot" existed over the lower left corner of the

burner used in the NBS apparatus [4] . Based on these temperature measurements, this hot spot effect was included in

our calculations by dividing the panel surface into two zones

of uniform temperature. This is shown in figure 3. The

temperature of the "hot spot" was taken as 35 "C above the

4
average panel temperature in condition D. The incident

radiant flux on dAg from the panel with a "hot spot" is

given as

^Sp = ^SP ^^P ^SH ^ (^P ^^h)' (4)

where SP

is the configuration factor between dAg and

the panel face minus the hot spot region.

is the configuration factor between dAg and

the hot spot region.

and AT.H

is the increase in temperature of the hot

region above the average panel temperature.

The configuration factors F^p and F^^^ can be found by using

equation (2) and configuration factor algebra.

Before presenting the result of this calculation, one

other effect on panel temperature, which was accounted for in

the calculations, should be discussed. The panel temperatures

given in table 1 are nominal values, initially measured with

a pyrometer viewing the panel through the open bottom of the

enclosure. After the bottom of the enclosure is closed with

the specimen holder, it has been found that the average panel

temperature increases [4] . The increase was measured to be

about 12 °C for condition C and 18 °C for condition D. Hence,

when the heat flux distribution is measured with the specimen

holder in place, the water cooled heat flux sensor views a panel which is hotter than that seen by the pyrometer initially.

In comparing calculations with measured heat flux, it was

then necessary to use the increased panel temperature in

equation (4 )

.

2.4. Comparison of Calculated Heat Flux with Measured Flux

Figures 4 and 5 illustrate a comparison of the calculated

radiative heat flux distributions with measured values for

conditions C and D, respectively. The calculated values are

based on equation (4) with two results shown; one for the

initial panel temperature, and one for the increased panel

temperature after it has reached a new equilibrium, due to

closing the bottom of the enclosure. The measured values

were determined using a total heat flux sensor which is water

cooled and hence is a cold target relative to its hot surroundings. Since a total heat flux meter was used, convective

5
heating to the sensor cannot be precluded. However, measurements with a radiometer indicated that convective heating is

likely insignificant [4] . The deviation between calculated

fluxes and measured values must be due to the added radiation

received from the heated walls of the enclosure.

In order to determine that the walls were responsible

for the difference between calculated and measured values, a

profile of heat flux was determined with the walls and ceiling

removed from the apparatus. The measurements are included

for comparison in figures 6 and 7. Two calculated curves are

shown, one at the initial panel temperature and the other at

the increased panel temperature after it would come to equilibrium with the enclosure and specimen in its test position.

It was estimated that the specimen surface has the dominant

influence on increasing the panel temperature. Hence, the

curves calculated for the increased temperature are more

appropriate for comparing results with the measured values

even for the case where the walls were removed. Except for

specimen positions close to the radiant panel for condition

D, the calculated flux from the panel agrees well with the

measured heat flux with the enclosure removed. The inability

of the calculation to predict the measured flux in D could be

due to a convective heating effect or a temperature variation

effect of the panel unique to condition D.

2.5. Effect of Enclosure on Heat Flux

As shown above, the enclosure accounts for a significant

portion of the heat flux to the specimen. For example, under

flux conditions C and D, 40% or more of the total incident

flux to the sample comes from the heated enclosure for distances beyond 60 cm (see figs. 6 and 7). This contribution

increases relative to the flux from the panel with increasing

distance from the panel. In order to predict the radiative

heat flux component due to the heated enclosure, the temperature distribution must be known. If the enclosure temperature is assumed to be uniform, T^, then the incident heat

flux to the specimen element dAg would be given as

q" = o Fgp T^ + a (1 - Fgp) T^ (5)

If the measured heat flux is substituted into equation (5)

,

an effective enclosure temperature can be calculated corresponding to each specimen position x. This was done and

yielded effective enclosure temperatures which decreased

from 200 °C at x = 10 cm to 80 °C at x = 90 cm for condition

C. Measurements of side wall temperatures for conditon C

6
indicated 154 °C at x = 40 cm and 99 at x = 70 cm. These

measurements were made with thermocouples located on the side

wall midway between the specimen plane and the ceiling. The

corresponding calculated effective temperatures were 139 °C

and 93 °C. Thus, these calculations yield results which

confirm the effect of enclosure walls on heat flux to the

specimen

.

3. OTHER CALCULATED HEAT FLUX PROFILES

In the development of the test apparatus, it is likely

that the present flux conditions (C and D) may be modified.

Several considerations are likely to affect this decision.

Among these considerations is that the flux should span a

range of values that are relevant to real fire conditions.

Also, the flux should decrease slowly with x initially and

gradually decrease more rapidly as x is increased. This

feature is desirable in order to minimize transient effects

associated with ignition and a relatively high rate of flame

spread at the start of the test, and to minimize test time.

In anticipation of a modification of the flux distribution,

some calculations were made to estimate the flux distribution

for several conditions. These results are shown in figure 8.

They were determined using equation (1) for the configurations without a surrounding enclosure, and equation (5) for

the configurations with an enclosure. The wall temperature

distribution was approximated by an effective wall temperature distribution similar to that determined for condition D.

4. CONCLUSIONS

Calculations and measurements indicate that the enclosure

can produce a significant contribution to the specimen heat

flux. About 10 to 60% of the incident heat flux in conditions C and D originates from the heated enclosure. Hence,

for test apparatuses with differing enclosure materials or

geometry, it is expected that the heat flux distribution on

the specimen will differ accordingly for the same panel

temperature and orientation. In addition, nonuniformity of

temperature over the burner face will perturb the heat flux

distribution to specimen. Consequently, in the specification

of a test method, it is important to require a record of the

flux distribution for each apparatus. It is not likely, nor

should it be expected for the current state of the apparatus,

that the heat flux profiles would be the same for all apparatuses .

7
/ The implication of these conclusions bears on the case

concerned with flame spread along a specimen in the test.

Ideally, during a test, the externally applied radiative heat

flux to the specimen should remain constant, and the only

additional specimen heating should result directly from the

spreading flame on the specimen. The results of this report

have shown that the initial external heat flux is sensitive

to the enclosure surface temperature, and that the panel

temperature can increase due to radiative exchange with hot

surfaces. Thus, during flame spread it is expected that the

panel temperature will change and the enclosure surface will

become hotter. Specimen smoke production, flame height

impingement on the panel, and energy release rate will influence the extent of these changes. It is noted that for a

similar gas-fired radiant panel, used in a vertical flame

spread test, Buschman [5] found a significant increase (about

20%) in panel emitted radiative heat flux due to the presence

of an adjacent burning specimen. Hartzell [1] found in his

study of the floor covering test, that panel temperature

could increase or decrease during a flame spread test. These

factors indicate a need for experiments to determine the

influence of specimen flame spread on the initially applied

external radiative heat flux.

. . : 5. REFERENCES

[1] Hartzell, L.G. , Developing of a Radiant Panel Test for

Flooring Materials, Nat. Bur. Stand. (U.S.), NBSIR 74-495

(May 1974)

.

[2] Quintiere, J. and Huggett, C, An Evaluation of Flame

Spread Test Methods for Floor Covering Materials, Fire

Safety Research, Proceedings of a Symposium held at the

National Bureau of Standards, Aug. 22, 1973, Nat. Bur.

Stand. (U.S.), SP-411 (Nov. 1974).

[3] Hamilton, D. C. and Morgan, W. R. , Radiant Interchange

Configuration Factors, NACA Tech. Note 2836 (Dec. 1952).

[4] Adams, C.H., Private Communications, National Bureau of

Standards, 1974.

[5] Buschman, A. J., Ignition of Some Woods Exposed to Low

Level Radiation, Second Progress Report, Nat. Bur. Stand.

(U.S.) NBS Report 7848 (Apr. 1963).

8
9
Figure 2. Basic configuration (applies to eq. [2]).

10
Figure 3. Schematic of radiant panel showing

hot spot region as approximated in

calculations. (Dimensions are in cm)

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NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 75-7062. Gov't Accession

No.

3. Recipient's Acces.-^ion No.

4. TITLE AND SUBTITLE

Calculations of Radiant Heat Flux in the

Proposed Floor Covering Flame Spread Test Apparatus

5. Publication Date December 197 5

6. Performing Organization Code

7. AUTHOR{S)

James Quintiere and Kevin Bron.berg

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4915676

11. Contract/Grant No.

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

same as No. 9

13. Type of Report & Period Covered

Final Report

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-woTd or /ess factual summary of most si^ificant information. If document includes a significant

bibliography or literature survey, mention it here.) . Calculations have been made to determine the radiant heat flux

distribution to the test specimen in the proposed radiant panel flame

spread test for floor covering materials. Comparison with measured

heat flux indicates a significant heat transfer contribution from the

enclosure of the test apparatus. Also, nonuniformities in the temperature of the radiant panel affect the resultant flux distribution.

Based on these results, it is expected that two similar test apparatuses would not have identical heat flux profiles along the specimen.

Additional calculations were made to illustrate possible heat flux

profiles capable with the present apparatus under various panel temperatures and orientations.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons

Floor covering; heat flux; radiant panel test method

18. AVAILABILITY Unlimited

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