c/

1r

NBSIR 77-1302

A Numerical Technique to

Correct Heat Release Rate

Calorimetry Data for Apparatus

Time Delay

D. D. Evans and L. H. Breden

Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

November 1977

Final Report

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NBSIR 77-1302

A NUMERICAL TECHNIQUE TO

CORRECT HEAT RELEASE RATE

CALORIMETRY DATA FOR APPARATUS

TIME DELAY

D. D. Evans and L. H. Breden

Center for Fire Research

Institute for Applied Technology

National Bureau of Standards

Washington, D.C. 20234

November 1977

Final Report

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

Dr. Sidney Harman, Under Secretary

Jordan J. Baruch, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

CONTENTS

Page

LIST OF FIGURES iv

Abstract 1

1. INTRODUCTION 2

2. EXPERIMENTAL 3

3. ANALYSIS 5

4. TEST RESULTS 9

4.1. Approximating Peak Rate Adjustments 11

5. CONCLUSIONS 14

6. ACKNOWLEDGMENTS 14

7. REFERENCES 15

iii
LIST OF FIGURES

Page

Figure 1. Test Assembly for Time Response Measurements .... 16

Figure 2. Normalized Time Response Data 17

Figure 3. Dynamic Test Similar to Particle Board 18

Figure 4. 13 mm Balsa Wood 2.5 W/cm2 19

Figure 5. 19 mm Particle Board 2.5 W/cm2 20
A NUMERICAL TECHNIQUE TO CORRECT HEAT RELEASE RATE

CALORIMETRY DATA FOR APPARATUS TIME DELAY

D. D. Evans'*

- and L. H. Breden

Abstract

A numerical scheme is presented to correct heat

release rate measurements made with the Ohio State University rate of heat release apparatus for the effects of

inherent time delays in the measurement system. The magnitude of the correction is shown to increase with increasing

rate of change in heat release rate. Illustrative heat re- lease rate curves for particle board and balsa wood show

that corrections to the peak heat release rate of 40% and

130% respectively are necessary. Measurements of the apparatus time response to step changes in heat release rate are reported. A simple method of determining corrections to

the measured peak heat release rate is discussed.

Key words: Calorimetry; heat release rate; response time;

time delay.

At the time this work was completed D. Evans was a Postdoctoral

Research Associate for the National Research Council (NRC) at NBS.

1
1. INTRODUCTION

As part of the evolution in material fire performance testing, much

attention has been given recently to the measurement of the rate of heat

release from a material burned under various conditions. Although at

present several different methods to measure the rate of heat release of

2 materials are available [1] , the most widely used is that developed by

Smith at Ohio State University [2,3]. With this method, materials and

products are tested for the rate of heat release and rate of visible

smoke release when exposed to different levels of radiant surface

heating. This Ohio State University rate of heat release calorimeter

(OSU-RHR) measures as a function of time, the increase in temperature of

air forced through the apparatus at a constant flow rate. The increase

in temperature can be related to the rate of heat release from a burning

test sample. In addition, a rate of smoke release is determined by

measuring the obscuration produced by smoke in the exhaust gases. From

each test, typically 10 minutes in duration, two curves may be produced;

one showing the rate of heat release, and the second the rate of smoke

release as a function of time. Proposals have been made to characterize

the samples tested by selecting particular values such as the peak rate

and the time to the peak rate from the experimental curves. In addition,

an integration of the heat release rate curve is sometimes performed to

measure the total heat released during the entire test or some portion

of the test.

If one is interested in using the details of the heat release rate

curves, he should be concerned with how closely the apparatus can follow

changes in the rate of heat release from a sample. The slower the rate

at which the apparatus can respond to fluctuating heat release rates,

the more distorted the measured values will be from the actual rate of

heat release from the sample. It is for this reason that Smith suggests

that rate of heat release measurements from tests in which changes in

2 Numbers in brackets refer to the literature references listed at the

end of this paper.

2
heat release rate greater than 220 J/s 2 (750 Btu/min2

) [2] occur not be

considered a quantitative measurement of heat release rate and only be

used for comparative purposes. Our work shows that a substantial

distortion of the measured heat release rate as compared with the actual

values is possible at rates of change of heat release rate well below

the 220 J/s2 (750 Btu/min2

) limit.

In this work, the time response characteristics of the OSU-RHR

apparatus are reported. These are used in a simple numerical data

analysis program to correct rate of heat release measurements for the

distortions introduced by the time delays in the system. The corrected

measurements are in all cases a better representation of the actual rate

of heat release from a burning sample than the uncorrected data. Specific

examples of corrected and uncorrected heat release data from tests using

particle board, balsa wood and a programmed methane burner are presented. In addition a simple method of estimating the error in peak

rate measurements because of time delay is discussed.

2 . EXPERIMENTAL

A useful way to characterize the time response of the OSU-RHR

apparatus is to examine the output that results from a step change in

heat release rate input. For this investigation an effort was made to

simulate as closely as possible, conditions that exist during material

testing in the vertical position. Figure 1 shows a schematic representation of the equipment assembled within the test chamber of the OSU-RHR

apparatus. In the standard vertical sample holder (0.152 m x 0.152 m) a 0.01 m thick mat of lightweight (Density * 100 kg/m 3 = 6 lb/ft 3

) fibrous

refractory insulation was mounted. No backing material was used as the

insulation mat was sufficiently rigid to be held in place by the standard holder spring clip. The binder-free insulation mat simulates a sample in the holder, but releases no heat during the test. Heat

release rate for the simulation was controlled by the methane flow rate

to the burner along the bottom edge of the vertical holder. During time

3
response tests, visible flames from the burner would form a sheet along

the insulation surface contacting and rising above the top edge of the

holder. Visually this simulated what commonly occurs in routine testing

of materials. The mass of the insulation mat used in the holder was

small enough that no significant influence of it on the time response of

the apparatus was expected.

The procedure for measuring the response of the OSU-RHR apparatus

to step changes in heat release rate began by igniting a small pilot

flow rate of methane through the burner. Enough time was allowed to

stabilize a base line output of the apparatus to this small heat release

rate. Each of the small pilot flames would grow rapidly when selected

larger flow rates of methane gas were quickly added to the burner fuel

supply, effectively producing a step change in heat release rate within

the apparatus. Adding the increase fuel flow to the burner from a pressure regulated reservoir through a simple on-off valve produced a gas surge immediately after opening the valve. In trial runs, this

surge of fuel above the steady flow rate value caused the apparatus to

respond very quickly; the output reaching 90% of the steady value in

about five seconds. To avoid fuel surges and achieve an acceptable step

change in flow rate, increases in methane flow to the burner for our tests were made by switching the flow from a vented gas line to the

burner fuel supply line. The vent line was constructed such that its

resistance to gas flow was the same as the system supplying the burner,

thus minimizing any gas surge in rapid switching of the gas flow between

lines. Sharp step decreases in heat release rate were produced by

simply shutting off the extra methane flow and returning to the baseline pilot flame flow rate.

The response of the OSU-RHR apparatus to two different levels of

step increases and decreases in heat release rate (+1.51 kJ/s [86 Btu/min]

and +3-87 kJ/s [220 Btu/min]) were measured at a 25 kJ/m2 s (2.5 W/cm2

) heat flux from the radiant panel determined at the face of the sample

holder. This heat flux is the most widely used in our present testing.

4
In addition, the response to a third level of change (+4.57 J/s

[260 Btu/min]) in heat release rate was measured with the radiant panel

off. The results of these six measurements are shown in figure 2.

Despite the fact that the response of the instrument appears slightly

faster in the tests with the radiant panel off, the agreement between the

six normalized responses is good. At 240 s (4 min) after the change in

heat release rate was made, approximately 90% of the full response was measured. Full response was achieved after 1200 s (20 min).

Analytically the time response is represented well by the expression

where E(t) is the fraction of the total response with t measured in

seconds. This expression suggests that the time response of the apMost OSU-RHR apparatus in operation today are augmented by digital

data logging equipment with computerized data reduction. The continuous

analog outputs from the apparatus are usually sampled by the data

logging system once every few seconds and the data stored for later

processing. In most cases processing of the data presently involves

simple multiplication of raw data by appropriate calibration constants

to produce data in acceptable units for tabulation and/or plotting as a function of time. The computer assisted data reduction while performing

the above task efficiently can be further utilized to correct the data

for apparatus time delay. While staying within the capabilities of the

laboratory oriented mini-computer a better representation of the actual

heat release rate of a tested material can be calculated from the test

( 1 )

paratus is a combination of a fast response possibly associated with the

thermocouples and a slower response influenced by the mass of the

apparatus

.

3. ANALYSIS

data.

5
There are several techniques that can be employed to correct heat

release rate data. Smith and Heibel [4] employ a combination of a fast and slow dynamic correction. The fast correction is performed

with a derivative lead compensation on smoothed experimental data,

approximating the system response as first order and linear. The

slow dynamic compensation utilizes a two parameter model of the

system.

The method employed here uses the experimentally measured response

to a step change in heat release rate directly to correct test data.

It also exploits the fact that within acceptable accuracy the time

response of the apparatus to a step change in heat release rate is

insensitive to the magnitude and direction of the change, and to the

panel heat flux. This fact, supported by experimental observations

discussed in the previous section, justifies the treatment of the

OSU-RHR apparatus as a linear dynamic system.

In a linear system, any overall system response may be represented

as the sum of many partial responses. In particular, one may build up

the time varying heat release rate output as the sum of many step inputs

for which the response of the apparatus is known. Mathematically we may

represent this statement by:

0(t) is the experimental output from the OSU-RHR apparatus,

C(t) is the actual heat release rate of the burning sample

and may be thought of as the corrected output or corrected 0 (t)

,

E(t) is the measured fractional time response of the

apparatus to a step change in heat release rate,

6

t

0(t) E(t - t) dx ( 2 )

o where

:
t is the time in seconds measured from the beginning of

the test , and

t is the dummy variable of integration.

For special cases of E(t) equation (2) may be solved exactly for

the corrected output, C(t), in terms of 0(t), the uncorrected experimental results. In particular, if E(t) results from a simple first

order lag in the system E(t) = 1 - exp (- at) , the solution would be:

C (t) * °(t)+7^p- (3)

Equation (3) is essentially the same as that used by Praul and

Hmurcik [5] to correct thermocouple measurements for time lag.

For the case of the OSU-RHR, the response of the instrument to a step input, E(t), is given by equation (1). This case is more complicated than the simple first order lag system discussed above. An analytic

solution to equation (2) for C(t) using equation (1) for E(t) can still

be obtained but is considerably more complicated than equation (3) and

involves second derivatives of the experimental curve 0(t). These two

factors render it impractical for direct use. Instead we have chosen to

obtain and approximate solution to equation (2) numerically. The recursive calculation to be performed on experimental data, sampled at a fixed interval, to correct them for time delay associated with the

apparatus will be developed from equation (2).

Writing equation (2) at time equal to t + At yields:

t + At

0 (t + At) * / E(t + At - t) dt

J

(4)

Dividing the interval of integration into two parts and approximating

E(t + At) as E(t) + — At gives:

O L

7
0(t + At)

L /

dC(r)

dx

E(t - x) dx + /W Hh1

*•) dx +

/

t + At

dC(x)

t + At

dx

E(t - x) dx +

( 5 ) dx

Retaining only terms of order At or greater eliminates the last term on the right hand side of equation (5). Then recombining the first and

second integral and approximating all integrals with summations yields:

j - i - 1

0(t

i + i

> ‘2 C(t ) - C(t

_ x

) At

j = 0

E(t. + ! - t ) At +

( 6 )

C(t.) - C(t.

_ x

)

At

E (At) At

Solving for C(t^) gives for i _> 0

C(t.) = c(t

i _ x

) +

with C(t.) * 0 for i < 0

l

j - i - 1

j

E- 0

0(t

i H- 1> y, I C(t

J

> - C(t

j - 1*]

E(t

i + 1 " t

j

)

E(At)

(7)

8
Equation (7) is the basis of the numerical technique used in our correction for OSU-RHR data. Notice that O(t^) are experimental points

and that the experimental response of the apparatus to a step input,

E(t), is used directly. The presence of the summation in equation (7)

will result in a longer run time for this correction technique compared

to that of Smith and Heibel's correction [4]. The direct use of the

easily obtained response to a step input, E(t), makes our technique very

easy to apply to any individual rate of heat release apparatus. In

fact, if storage space is available, only the experimental values of

E(t) at the time differences to be used in the calculation need be

retained, thus eliminating the need to curve fit this data.

Using this technique, experimental heat release rate data may be

processed to yield a better representation of the actual sample performance in the test. Specific comparisons between corrected and uncorrected

test results will be presented in the next section.

4 . TEST RESULTS

To verify that corrections to measured heat release rate curves using the above technique are meaningful, measurements were made on a controlled heat release rate input. For this modest effort, the con- trolled heat release rate input similar in shape to data for particle

board was achieved using a rotameter to manually control the methane

flow to the burner shown in figure 1. The heat release rate was manually matched to the input curve shown in figure 3 at five-second intervals

with smooth transitions between points. In figure 3 the metered heat

release rate curve is shown as the broken line rising at a rate of 22

J/s 2 (75 Btu/min2 ), leveling off shortly at 930 J/s (53 Btu/min) , then

decreasing to 720 J/s (41 Btu/min) until the methane flow was shut off

at 150 seconds after the beginning of the simulation. We feel that the

desired input curve was reproduced to within +0.02 kJ/s (1.1 Btu/min)

using the manually controlled rotameter to adjust the fuel flow rate.

9
Two measurements (corrected and uncorrected) of the controlled

heat release rate curve are also shown in figure 3. The corrected data

based on a five-second data sampling interval agrees well with the known

input. The uncorrected curve shows the distortions introduced by the

apparatus time delay. As the correction process enhances fluxuations in

the uncorrected data, the corrected data can be made more attractive by

smoothing techniques one of which is discussed by Smith and Heibel [4],

The peak rate of heat release, a commonly used parameter of each

heat release rate curve, for the corrected data of 920 J/s (52 Btu/min)

agrees well with the actual rate of 930 J/s (53 Btu/min). In contrast

the uncorrected data has a peak rate of 690 J/s (39 Btu/min) approximately 26% below the actual rate. This discrepancy in measured and

known peak rates of heat release occurs at the termination of a constant

rate of change of heat release rate 1/10 the maximum limit given for

quantitative measurements 220 J/s 2 (750 Btu/min2

) in the ASTM Draft

Procedure [2].

Integration of each curve in figure 3 with time yields the total

heat released by the sample during the test. This total energy release

was found to be conserved among the three curves within estimated

experimental and calculational errors, thus serving as an additional

check on the calculation.

In detail, integration of the corrected data curve yields a total

heat release of 102 kJ (97 Btu) during the test. This is in good agreement with the 98.6 kJ (93 Btu) total heat release calculated by integrating the uncorrected curve including the portion of the tail beyond

215 seconds not shown in figure 3. Of the total heat release calculated

from the uncorrected curve, 23% is contributed by the long tail of the curve. Integration of the test input curve yields 105 kJ (99 Btu) total

energy release which also compares favorably with the value calculated

from the corrected data.

10
For illustrative purposes corrected and uncorrected heat release

rate curves for balsa wood and particle board evaluated at 25 kJ/m2 s (2.5 W/cm2

) panel heat flux are shown in figures 4 and 5 respectively.

Both sets of data were taken at four-second intervals. In each case the

corrected curve is significantly above the uncorrected curve.

4.1. Approximating Peak Rate Adjustments

In the illustrations above, it is clearly seen that because of the

inherent time delay associated with the measurement of heat release rate

with the OSU-RHR apparatus, measured rates are commonly different from

the actual rates of heat release. It has been shown that with a modest

effort these differences can be corrected through a numerical analysis

of test data. To determine if the correction procedure is necessary for

any particular set of heat release test data, it would be useful to be

able to simply approximate how much difference will exist between the

uncorrected set of data and its corresponding correction. Under certain

conditions that are commonly satisfied, a good approximation to the

difference between corrected and uncorrected peak rates of heat release

can be simply calculated. This predicted difference can be used as a guide in determining whether or not the uncorrected data can be used

satisfactorily in a given situation.

To obtain approximation to the peak rate correction one should

consider the testing of an idealized material that releases heat at a linearly increasing rate with time. For this material, the corrected

data would be

C(t) = bt (8)

where t * time in seconds

b * rate of change of the rate of heat release

11
To find the corresponding expected output from the OSU-RHR apparatus,

one must solve equation (2) using equations (1) and (8) as:

0(t) - /b

[

1 - rv ('e

-

( t - T )/8 + 0>4e

-(t - t)/200

')] dT (9) o

Equation (9) may be solved using Laplace transforms noting that the

right hand side is a convolution integral:

Usually experimental rate of heat release rate data show a rise

from zero to a peak rate and then decay towards zero. Often a linear

increase can be used as an approximation to the actual rise in heat

release rate before the peak rate is reached. This rise to the peak

rate is often of a duration greater than 10 seconds and thus equation

(11) applies. During this rise in heat release rate, the exponential

function in equation (11) does not vary greatly; therefore, the rate of

change of the corrected heat release rate data, b, will be approximately

equal to the slope of the experimental data, 0(t). For this approximation, the representative slope of the experimental data increasing to

the peak rate will be used to obtain a value for b from the test data.

Then the difference between the corrected and the experimental (uncorrected) peak rate of heat release becomes:

0(t)

(

/ 200

( 10 )

Considering times greater than 10 seconds, the second term in the

parenthesis may be neglected compared to the other terms in the

parenthesis. With this constraint equation (10) becomes:

0 (t) = bt - 57b (1.1 - e

- t/200

) (ID

C(t) - 0 (t) = ARHR = 57b (1.1 - e-At/200

) ( 12 )

12
where ARHR = approximate difference between the corrected

and uncorrected peak rate.

At = the duration of the representative linear

rise to the peak rate in experimental data (s)

b = the slope of the representative linear rise

to the peak rate in experimental data (RHR/s).

This expression may be checked against the corrected and uncorrected

curves for balsa wood and particle board. In the case of particle

board, we find an approximately linear rise in uncorrected heat release

rate at a rate of b = 3.31 kJ/m2 s

2 (17.5 Btu/ft 2 min/s) for a At = 40

seconds. We would expect from equation (12) that the difference between

the corrected and uncorrected peak rates would be 53.1 kJ/m2 s (280 Btu/ft 2 min) which compares well with the 56.8 kJ/m2 s (300 Btu/ft 2

min) observed in figure 5. For balsa wood the linear portion of the rise

to the peak rate is less than the 10 seconds suggested in the use of

equation (12). Under these conditions, equation (12) is likely to be an underestimate of the difference in peak rates. From the uncorrected

curve for balsa wood figure 4, the two parameters needed for equation (12) are b = 11 kJ/m2 s

2 (58 Btu/f2 min/s) and At = 8 seconds. The estimated

difference between the corrected and uncorrected peak rates is 87 kJ/m2 s (460 Btu/f

2 min) which is low compared to the 117 kJ/m2 s (620 Btu/f2 min)

shown in figure 4.

It has been shown that equation (12) provides a good rule of thumb

to estimate the expected difference between measured and actual rate of

heat release from materials tested in the OSU-RHR apparatus.

13
5. CONCLUSIONS

The time delay inherent in heat release rate measurements made with

the OSU-RHR (containing electric muffle furnace radiant panels) has

been quantified by measurements of the apparatus response to step changes

in heat release rate.

It has been demonstrated that the apparatus time delay is often

responsible for the introduction of significant distortions in the

measurement of heat release rate from burning materials. These distortions can occur in tests in which the rate of change of heat release

rate is well below the presently accepted limit for quantitative

measurements of 220 J/s 2 (750 Btu/min2

)

.

A numerical technique has been shown effective in correcting

experimental heat release rate measurements from vertical material tests

for the effects of the apparatus time delay.

A simple analytic expression has been developed to estimate peak

rate of heat release corrections. This expression can serve as a tool

to aid the researcher in making a judgment about the necessity of

correcting a given set of experimental data.

6. ACKNOWLEDGMENTS

The authors are grateful for the collaboration of Mr. S. I. Adams

and Mr. J. A. Fisher of Union Carbide’s Safety Research Laboratory in

this study. The authors would also like to thank Mr. J. W. Raines of

NBS for his assistance in coding the data reduction programs.

14
7. REFERENCES

[1] Chamberlain, D. L., Rate of Heat Release - Tool for the Evaluation

of the Fire Performance of Materials, Paper presented at joint

meeting of the Central States & Western States Section of the

Combustion Institute, San Antonio, Texas, April 21-22, 1975.

[2] Draft of a Proposed ASTM Test Method ASTM E5.02.30, Test Method

for Heat and Smoke Release Rates, Feb. 6, 1976.

[3] Smith, E. E., Heat Release Rate of Building Materials, Ignition,

Heat Release, and Noncombustibility of Materials, ASTM STP 502,

American Society for Testing and Materials (1972), pp. 119-134.

[4] Smith, E. E. and Heibel, J. T., Evaluating Performance of Cellular

Plastics in Fire Systems, Final Report, PRC Project No. RP-75-1-36

(1977), Part II, pp. 18-27.

[5] Praul, S. H. and Hmurick, L. V., Instantaneous Temperature

Measurements, Review of Scientific Instruments, Vol. 44, No. 9

(Sept. 1973), pp. 1363-1364.

15
Test Assembly for Time Response Measurements

16

Figure 1.
Full

Raapnnae

-

2Q

Min

17

QQ

a

H

Figure

2.

Normalized

Time

Response

Data
UNCORRECTED

OUTPUT

inuj/nia

co

co LU

S

s/M 31VM 3SV313H 1V3H

18

Figure

3.

Dynamic

Test

Similar

to

Particle

Board
Figure 4. 13 nun Balsa Wood 2.5 W/ cm 2

19

BTU/ft

2

min.
20

BTU/ft

2

min.
85 1 UA (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBSIR 77-1302

2. Gov’t Accession

No.

3. Recipient’s Accession No.

i. TITLE AND SUBTITLE

A Numerical Technique to Correct Heat Release Rate

Calorimetry Data for Apparatus Time Delay

5. Publication Date November 1977

6. Performing Organization Code

. AUTHOR(S)

D. D. Evans and L. H. Breden

8. Performing Organ. Report No.

, PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 491 4100

11. Contract/Grant No.

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

National Bureau of Standards

Department of Commerce

Washington, D.C. 20234

13. Type of Report & Period

Covered

Final Report

14. Sponsoring Agency Code

i. SUPPLEMENTARY NOTES

I

i. ABSTRACT (A 200-word or less (actual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

A numerical scheme is presented to correct heat release rate measurements

made with the Ohio State University rate of heat release apparatus for the

effects of inherent time delays in the measurement system. The magnitude of

the correction is shown to increase with increasing rate of change in heat

release rate. Illustrative heat release rate curves for particle board and

balsa wood show that corrections to the peak heat release rate of 40% and 130%

respectively are necessary. Measurements of the apparatus time response to

step changes in heat release rate are reported. A simple method of determining

corrections to the measured peak heat release rate is discussed.

1

i

I

. 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) Calorimetry; heat release rate; response time;

time delay.

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