Heat Release Rate of Objects 

Burning in Cargo Compartments 

Richard E. Lyon Ph.D 

David Blake 

April 2005 

DOT/FAA/AR-TN05/9 

This document is available to the public through the National 

Technical Information Service (NTIS), Springfield, Virginia 22161. 

U.S. Department of Transportation 

Federal Aviation Administration

ote technical note technic

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NOTICE 

This document is disseminated under the sponsorship of the U.S. 

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thereof. The United States Government does not endorse products or 

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because they are considered essential to the objective of this report. This 

document does not constitute FAA certification policy. Consult your local 

FAA aircraft certification office as to its use. 

This report is available at the Federal Aviation Administration William J. 

Hughes Technical Center’s Full-Text Technical Reports page: 

actlibrary.tc.faa.gov in Adobe Acrobat portable document format (PDF). 
Technical Report Documentation Page 

1. Report No.

DOT/FAA/AR-TN05/9 

2. Government Accession No. 3. Recipient's Catalog No.

5. Report Date 

April 2005 

4. Title and Subtitle

HEAT RELEASE RATE OF OBJECTS BURNING IN CARGO COMPARTMENTS 6. Performing Organization Code

7. Author(s)

Richard E. Lyon Ph.D and David Blake 

8. Performing Organization Report No.

DOT/FAA/AR-TN05/9 

9. Performing Organization Name and Address 10. Work Unit No. (TRAIS)

Federal Aviation Administration 

William J. Hughes Technical Center 

Airport and Aircraft Safety 

Research and Development Division 

Fire Safety Branch 

Atlantic City International Airport, NJ 08405 

11. Contract or Grant No.

12. Sponsoring Agency Name and Address

U.S. Department of Transportation 

Federal Aviation Administration 

13. Type of Report and Period Covered

Technical Note 

Office of Aviation Research 

Washington, DC 20591 

14. Sponsoring Agency Code

ANM-110 

15. Supplementary Notes

16. Abstract

The heat release rate of objects burning in a relatively large, simply ventilated cargo compartment is reconstructed from the 

oxygen consumption history of the exiting gas stream, assuming perfect mixing of the combustion gases in the compartment. The 

model was calibrated using a premixed propane gas burner to generate a variety of well-defined heating histories. Qualitative 

agreement between actual and computed heat release rate histories is obtained when the duration of the burning is on the order of 

1/2 of the mixing time of the compartment. This research supports efforts by the Federal Aviation Administration to develop new 

certification requirements for aircraft cargo compartment fire detectors. 

17. Key Words

Cargo compartment, Fire, smoke, Heat release rate, Smoke 

detector 

18. Distribution Statement

This document is available to the public through the National 

Technical Information Service (NTIS), Springfield, Virginia 

22161.

19. Security Classif. (of this report)

Unclassified 

20. Security Classif. (of this page)

Unclassified 

21. No. of Pages

11 

22. Price

Form DOT F1700.7 (8-72) Reproduction of completed page authorized 
TABLE OF CONTENTS 

Page 

INTRODUCTION 1 

MIXING MODEL 1 

EXPERIMENTAL 3 

RESULTS 3 

CONCLUSIONS 6 

REFERENCES 6 

iii
LIST OF FIGURES 

Figure Page 

1 Compartment Fire Model 2 

2 Cargo Compartment Used for Full-Scale Testing 3 

3 Step Change HRR History in Cargo Compartment Compared to Equation 6 

With (τ = 28 min) and Without (τ = 0) Deconvolution of the Oxygen 

Consumption Data 4 

4 Square Wave HRR History in Cargo Compartment Compared to Equation 6 With 

and Without the Use of a Circulation Fan 5 

5 Multistep HRR History in Cargo Compartment Compared to Equation 6 With 

(τ = 28 min) and Without (τ = 0) Deconvolution of Oxygen Consumption Data 5 

6 Multistep HRR History in Cargo Compartment Compared to Equation 6 With 

and Without Deconvolution of Oxygen Consumption Data 6 

LIST OF TABLES 

Table Page 

1 Comparison of Calculated and Best-Fit Parameters for Propane Burner 

Calibration of Cargo Compartment Model 4 

iv
INTRODUCTION

To support the development of more reliable fire detectors and facilitate their certification for 

commercial aircraft, the Federal Aviation Administration (FAA) is conducting research to 

generate a complete and reproducible fire signature typical of a luggage article burning in a 

cargo compartment [1 and 2]. Aircraft manufacturers primarily use photoelectric smoke 

detectors, and to a lesser extent ionization detectors, to comply with FAA regulations for fire 

detection in cargo compartments of commercial aircraft. The photoelectric detectors rely on 

smoke particles entering a chamber where they either reflect or attenuate a light beam to produce 

an alarm. While effective at detecting smoke, these detectors also alarm when airborne particles 

or moisture are detected. The current ratio of false alarms to real fires in commercial aircraft 

cargo compartments is on the order of hundreds-to-one [3]. The low reliability (< 1%) of current 

fire detectors is costly to airlines, so detectors are being developed that alarm only after multiple 

fire products are sensed, e.g., optical extinction, temperature, carbon monoxide, hydrocarbons, 

etc. The location of the fire source and the movement of fire products within the cargo 

compartment is important for optimum placement of fire detectors. A computational fluid 

dynamics (CFD) model is being developed in combination with an experimental program to 

address this issue [1]. The CFD model requires a well-characterized fire product source. A 

composite sample was developed for this purpose, which is comprised of several different 

plastics in the approximate ratio found in passenger luggage [2]. The history of heat release rate, 

smoke density, and combustion gas composition of the plastic composite in flaming and 

nonflaming modes was measured in a bench-scale fire (cone) calorimeter to obtain its fire 

signature [2]. Full-scale testing of luggage articles and the plastic composite in a ventilated 

Boeing 707 cargo compartment revealed that the fire signature deduced from the exhaust gases 

was smeared due to volumetric mixing in the cargo compartment. Consequently, a simple 

mixing model was evaluated to determine whether time-deconvolution of the exhaust gas history 

could be used to provide the fire signature of a burning object in the (relatively) large cargo 

compartment of a commercial passenger jet. The model was evaluated by comparing known 

heat release rate histories in the cargo compartment from a premixed propane burner to those 

calculated from the mixing model using the oxygen consumption history of the exhaust gases. 

MIXING MODEL

Figure 1 illustrates the basic physical flow problem. Relevant quantities are the fixed volumetric 

flow (leak) rate, = = F, of ambient air at oxygen mass fraction = 0.23 through a 

well-mixed control volume, V

Vin

& Vout& ]O[ 2

o

o (the cargo compartment volume) at atmospheric pressure. The 

mass flow rate of oxygen leaving the control volume at constant air density ρ is 

( )

dt

d

V dt

dV

dt

Vd

mout

]O[ ]O[ ]O[ 2

2

2 ρ ρ ρ & = = + (1) 

1
HRR

[O2](t)

Volume, Vo

Vin

•

Vout

•

Pressure = 1 atm

[O2]

o

FIGURE 1. COMPARTMENT FIRE MODEL 

The mass rate of oxygen consumption by the fire having a heat release rate (HRR) (watts) 

resulting from burning fuel having heat release per mass of oxygen consumed, E (MJ/kg-O2), in 

the cargo compartment is 

E

HRR mfire

– & = (2) 

The mass flow rate of oxygen entering the control volume is 

]O[ ]O[ ]O[ 2

2

2

o

in Vin dt

d

V dt

dV m & & = ρ + ρ = ρ (3) 

since d[O2]/dt = 0 for incoming air at [O2] = O[ ] = 0.23. The mass balance for oxygen is 2

o

in mout E

HRR m& – = & (4) 

Substituting equations 1, 2, and 3 into equation 4 gives the instantaneous HRR of the fire in 

terms of the oxygen concentration of the combustion gas stream exiting the well-mixed 

compartment 

{ } EV

tHRR

V

F

dt

d

o

o

o ρ

)(– ]O[–]O[–]O[

2 2

2 = (5) 

A system response time is defined as τ = Vo/F and a heat release constant as C = ρVoE. The 

oxygen consumption is defined as θ(t) = ]O[ − [O 0

2 2](t), such that dθ/dt = – d[O2]/dt so that 

equation 5 takes the simplified form 

{ } { } dt

d EF

dt

C d tHRR θ τθρ θ τθ

τ

( ) +=+= (6) 

2
The model parameters C and τ were evaluated using a propane burner in the cargo compartment 

to generate known HRR histories 

)( )( (7) 0= ρχ &

pcp tVhtHRR

where V&

p (m3

/s) is the instantaneous propane flow rate and ρp = 1.83 kg/m3 (STP), = 46.36 

MJ/kg, and χ are the density, net heat of complete combustion, and combustion efficiency of 

propane, respectively. The combustion efficiency χ was assumed to be unity for the premixed 

propane-air burner. 

0

hc

EXPERIMENTAL

Testing was conducted in a B-707 cargo compartment shown schematically in figure 2. The 

cargo compartment has volume V0 = 25.8 m3

 and contains a perforated duct that is used to 

extract air and combustion products out of the compartment at a rate F = 0.012 m3

/s using a 

calibrated exhaust fan. This arrangement is meant to simulate an in-flight air leak from the cargo 

compartment through the cargo door seals due to the pressure difference at altitude. A 

combustion gas sample was drawn from the exhaust duct outside the compartment and filtered 

before passing through a continuously reading oxygen analyzer (Rosemount OM11EA). Oxygen 

concentration data were recorded electronically at 2-second intervals. A premixed propane gas 

burner was placed in the center of the cargo compartment, as indicated in figure 2, for model 

validation testing. For some experiments, a 0.5-m-diameter electric fan was placed in the cargo 

compartment to improve circulation (mixing). 

FIGURE 2. CARGO COMPARTMENT USED FOR FULL-SCALE TESTING 

RESULTS

Figure 3 compares the cargo compartment model to a step change in HRR followed by a gradual 

but monotonic decrease over the test interval. Equation 6 was fit to the data for the oxygen 

concentration history extracted from the cargo compartment exhaust gases during the test with 

τ = 28 minutes and C = 447 MJ giving the best visual representation. The response time was 

3
defined as the time required for the oxygen concentration to reach (1–1/e) = 63% of the 

equilibrium value after a step change in HRR. In all cases, the total heat calculated from oxygen 

consumption was within a few percent of the nominal value for the mass of propane burned for 

the test. These empirical (best-fit) values for C and τ are compared in table 1 to calculate values 

C = ρV0E and τ = V0/F assuming ρ(air) = 1.35 kg/m3

 (STP), and E = E (propane) = 12.78 MJ/kgO2 is the ratio of the net heat of combustion of propane (46.4 MJ/kg) to the oxygen/propane mass 

ratio (r = 3.629). 

The empirical value for C is well within the uncertainty of the calculated value, assuming 5% 

accuracy of the tabulated and measured quantities. However, the empirical response time τ is 

significantly less than the calculated value, suggesting that the hot, buoyant combustion products 

from the propane burner improved mixing. The heat release rate of the propane burner estimated 

from the oxygen concentration of the exhaust gases without deconvolution (τ = 0 on the righthand side of equation 6) is also plotted in figure 3, showing the extent of HRR smearing due to 

volumetric mixing in the compartment. 

TABLE 1. COMPARISON OF CALCULATED AND BEST-FIT PARAMETERS FOR 

PROPANE BURNER CALIBRATION OF CARGO COMPARTMENT MODEL 

Parameter Calculated Fit of Equation 6 

C 445 MJ 447 MJ 

τ 36 min 28 min 

0

2

4

6

8

10

0 10 20 30 40 50 60 70 80

Rate of Heat Release, kW

Time, minutes

Equation 6 (τ = 0)

Equation 6 (τ = 28 min)

Propane burner

FIGURE 3. STEP CHANGE HRR HISTORY IN CARGO COMPARTMENT COMPARED 

TO EQUATION 6 WITH (τ = 28 min) AND WITHOUT (τ = 0) DECONVOLUTION OF THE 

OXYGEN CONSUMPTION DATA 

Figure 4 compares a 10-minute square wave HRR history in the cargo compartment to the 

deconvoluted HRR history computed from the oxygen consumption data using equation 6 (τ = 

28 minutes) with and without the use of the circulation fan. Figure 4 shows that forced 

circulation of the air and combustion products inside the cargo compartment reduces the mixing 

(response) time by a few minutes, as evidenced by the higher fidelity of the computed HRR. 

4
However, despite the moderate (≈ 10%) improvement in HRR fidelity, the fan was not used in 

subsequent experiments to preserve the natural pattern and history of smoke movement in the 

compartment. 

-2

0

2

4

6

8

0 5 10 15 20

Heat Release Rate, kW

Time, minutes

Fan

No Fan

Propane Burner

FIGURE 4. SQUARE WAVE HRR HISTORY IN CARGO COMPARTMENT 

COMPARED TO EQUATION 6 WITH AND WITHOUT THE USE OF A 

CIRCULATION FAN 

Figures 5 and 6 compare equation 6 with and without deconvolution of the oxygen consumption 

data to different multistep HRR histories in the cargo compartment generated by the propane 

burner without forced circulation. Equation 6 cannot capture transient data for which the 

duration of the event Δt is significantly less than the mixing time of the compartment, i.e., Δt << 

τ, as evidenced by attenuated HRR for short duration pulses in figures 5 and 6. 

-1

0

1

2

3

4

5

6

0 5 10 15 20 25 30 35 40

Heat Release Rate, kW

Time, minutes

Propane 

Burner

Equation 6 

(τ = 28 min)

Equation 6 (τ = 0)

FIGURE 5. MULTISTEP HRR HISTORY IN CARGO COMPARTMENT COMPARED TO 

EQUATION 6 WITH (τ = 28 min) AND WITHOUT (τ = 0) DECONVOLUTION OF 

OXYGEN CONSUMPTION DATA 

5
-1

0

1

2

3

4

5

6

7

0 5 10 15 20 25 30 35 40

Heat Release Rate, kW

Propane Burner Equation 6 

(τ = 28 min)

Time, minutes

Equation 6 

(τ = 0 min)

FIGURE 6. MULTISTEP HRR HISTORY IN CARGO COMPARTMENT COMPARED TO 

EQUATION 6 WITH AND WITHOUT DECONVOLUTION OF OXYGEN 

CONSUMPTION DATA 

The average correlation coefficient between the actual and deconvoluted HRR histories plotted 

in figures 3 through 6 is R = 0.7, which is a reasonable estimate of the fidelity of the technique 

for the conditions of this test. Regardless of HRR fidelity, the total heat release (J) computed 

from the time integral of equation 6 was always within a few percent of the nominal value 

obtained by multiplying the mass of propane burned during the test by its net heat of complete 

combustion. 

CONCLUSIONS

A perfect mixing model was used to reconstruct the heat release rate history, HRR(t), of an 

object burning in a constantly ventilated compartment using the oxygen consumption history of 

the exhaust gases. Reasonable HRR fidelity (≈ 70%) can be obtained when the duration of the 

burning event is on the order of one-half the volumetric mixing time of the compartment. Under 

these conditions, the model reproduces fire signatures of burning objects reasonably well using 

the physical dimensions and ventilation rate of the compartment. 

REFERENCES

1 Suo-Anttila, J., Gill, W., Gallegos, C., and Nelson, J., “Computational Fluid Dynamics 

Code for Smoke Transport During an Aircraft Cargo Compartment Fire: Transport 

Solver, Graphical User Interface, and Preliminary Baseline Validation,” FAA report 

DOT/FAA/AR-03/49, May 2003. 

2 Speitel, L.C., “Fourier Transform Infrared Analysis of Combustion Gases,” Journal of 

Fire Sciences, Volume 20, No. 5, pp. 349-372, 2002. 

3 Eklund, T.I., “Estimated Detection System False Alarms from Cargo Compartment Fire 

Extinguisher Discharge Statistics,” FAA Technical Note DOT/FAA/AR-TN96/56, June 

1996. 

6