Suleyman A. Gokoglu, Justin E. Niehaus, Sandra L. Olson, Daniel L. Dietrich, and Gary A. Ruff

Glenn Research Center, Cleveland, Ohio

Paul V. Ferkul and Michael C. Johnston

National Center for Space Exploration, Glenn Research Center, Cleveland, Ohio 

Prevention of Over-Pressurization 

During Combustion in a Sealed Chamber

NASA/TM—2012-217712

September 2012

AIAA–2012–3511
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Suleyman A. Gokoglu, Justin E. Niehaus, Sandra L. Olson, Daniel L. Dietrich, and Gary A. Ruff

Glenn Research Center, Cleveland, Ohio

Paul V. Ferkul and Michael C. Johnston

National Center for Space Exploration, Glenn Research Center, Cleveland, Ohio 

Prevention of Over-Pressurization 

During Combustion in a Sealed Chamber

NASA/TM—2012-217712

September 2012

AIAA–2012–3511

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

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NASA/TM—2012-217712 1

Prevention of Over-Pressurization

During Combustion in a Sealed Chamber

Suleyman A. Gokoglu, Justin E. Niehaus, Sandra L. Olson, Daniel L. Dietrich, and Gary A. Ruff

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Paul V. Ferkul and Michael C. Johnston

National Center for Space Exploration

Glenn Research Center

Cleveland, Ohio 44135

Abstract

The combustion of flammable material in a sealed chamber invariably leads to an initial pressure rise 

in the volume. The pressure rise is due to the increase in the total number of gaseous moles (condensed 

fuel plus chamber oxygen combining to form gaseous carbon dioxide and water vapor) and, most 

importantly, the temperature rise of the gas in the chamber. Though the rise in temperature and pressure 

would reduce with time after flame extinguishment due to the absorption of heat by the walls and contents 

of the sealed spacecraft, the initial pressure rise from a fire, if large enough, could lead to a vehicle overpressure and the release of gas through the pressure relief valve. This paper presents a simple lumpedparameter model of the pressure rise in a sealed chamber resulting from the heat release during 

combustion. The transient model considers the increase in gaseous moles due to combustion, and heat 

transfer to the chamber walls by convection and radiation and to the fuel-sample holder by conduction, as 

a function of the burning rate of the material. The results of the model are compared to the pressure rise in 

an experimental chamber during flame spread tests as well as to the pressure fall-off after flame 

extinguishment. The experiments involve flame spread over thin solid fuel samples. Estimates of the heat 

release rate profiles for input to the model come from the assumed stoichiometric burning of the fuel 

along with the observed flame spread behavior. The sensitivity of the model to predict maximum chamber 

pressure is determined with respect to the uncertainties in input parameters. Model predictions are also 

presented for the pressure profile anticipated in the Fire Safety-1 experiment, a material flammability and 

fire safety experiment proposed for the European Space Agency (ESA) Automated Transfer Vehicle 

(ATV). Computations are done for a range of scenarios including various initial pressures and sample 

sizes. Based on these results, various mitigation approaches are suggested to prevent vehicle overpressurization and help guide the definition of the space experiment.

Nomenclature

Af area of the flame over the fuel-sample surface, m2

Aw area of the total available surfaces heat is convected to, m2

Cv,g molar specific heat of gas at constant volume, J/mol-K

FP average fire power obtained from the integration of qcomb over τ, W

L characteristic length for convection, m

Nu Nusselt number for heat transfer 

Pi pressure, atm

Pr Prandtl number 

Q thermal energy accumulation, J

ReL Reynolds number based on characteristic length L

Tf average flame temperature, K
NASA/TM—2012-217712 2

Tg average gas temperature, K

Tp fuel pyrolysis temperature, K

Tw wall temperature, K

Vf flame volume, m3

Vt total available gas volume of the sealed chamber or vehicle, m3

aP Planck mean absorption coefficient, m-1

dt time step, s

hw heat transfer coefficient, W/m2

-K

ng total number of moles in chamber/vehicle, mol

qcomb heat release rate due to combustion, W

qcond heat loss due to conduction, W

qconv heat loss due to convection, W

qrad heat loss due to radiation, W

sf stand-off distance of the flame from the fuel-sample surface, m 

t time, s

η sensitivity parameter of model, Equations (8) and (9)

λg thermal conductivity of gas, W/m-K

ξj, ξk parameter j and k of model in Equation (1), Table I and Table II

σ Stefan-Boltzmann constant, W/m2

-K4

τ total duration of the combustion event (burn-time), s

Subscripts

max maximum

o baseline case

Introduction

The objective of NASA’s Advanced Exploration Systems Program is to advance and demonstrate 

technologies such that they can be implemented on future exploration systems. Because of the importance 

of fire safety technologies in spacecraft design, a project titled Spacecraft Fire Safety Demonstrations was 

recently initiated with the sole purpose of closing the technology gaps by conducting a fire safety 

experiment in an orbiting vehicle.

The work conducted to date has shown that fire behavior in low-gravity is very different from that in 

normal-gravity, with differences observed for flammability limits, spread rates, and flame structures

(Ref. 1). As a result, the prediction of the behavior of fires in reduced gravity is at present not validated.

The proposed fire safety experiment, titled Fire Safety-1, seeks to address this gap in the knowledge 

through the use of an unmanned but pressurized cargo transfer vehicle.

The current concept is to conduct this experiment in an ISS resupply vehicle such as the ATV, 

Cygnus, HTV, or Dragon, after it departs the ISS and before it experiences significant g-forces as it enters 

the atmosphere. While the requirements are still being developed, the current concept focuses on 

conducting two types of material flammability tests that would be performed sequentially and can proceed 

autonomously. The first set of tests would consist of up to nine samples of varying materials, each having 

dimensions of approximately 10 cm wide by 30 cm long. These samples emulate the configuration used 

in NASA Standard 6001 Test 1. There would be an external air flow from the bottom of the samples to 

the top and each sample would be ignited at the bottom using a hot wire. Minimal diagnostics would be 

required for these tests as the intended result is primarily to determine whether the flame propagates or 

self-extinguishes.

The second test will investigate flame spread over a panel of thin material approximately 0.5 m wide 

by 1.0 m long. As in the previous tests, the ignition method would be a hot wire along the upstream edge.

This material will be expected to burn at the anticipated cabin atmosphere. The objective of this test is to 

quantify the flame development over a large sample in low-gravity. This sample will be more heavily 
NASA/TM—2012-217712 3

instrumented with multi-view video, thermocouples, radiometers, etc. so that the data can be used to 

verify numerical simulations of fire spread and development in low-g.

To ensure safe reentry of the orbiting vehicle, the combustion event in the proposed Fire Safety-1 

experiment must not raise the internal pressure of the vehicle above the allowed limits. The pressure rise 

from this experiment is most readily controlled by limiting the amount of fuel that is available to burn. 

Given the low mass of air in the vehicle, if all of the energy from a fire went to heat the gas-phase, the 

pressure rise could be quite high. Much of the heat, however, is absorbed by surrounding objects where it 

causes an insignificant increase in their temperature. Consequently, accurate prediction of the pressure 

rise resulting from a combustion test requires good estimates of the fraction of the heat that is directly 

absorbed by the vehicle walls and physical objects contained in the vehicle. At this point in the 

development of the experiment, many of these parameters can only be estimated. The necessary thermal 

modeling to provide a robust prediction of the pressure transient caused by the flame is underway. In the 

meantime and while the experiment is being better defined, a more practical, but rational, approach has 

been taken to estimate and manage the pressure rise during the flame event.

In this paper, we describe this practical model, our approaches to validate it with limited groundbased, normal-gravity experiments, and our attempts to predict pressure profiles and maximum pressures

anticipated in the Fire Safety-1 experiment assuming that the experiment will be conducted in the 

European Space Agency (ESA) Automated Transfer Vehicle (ATV). Various scenarios and mitigation 

approaches will be presented in order to prevent over-pressurization in the ATV vehicle.

Model Description

The model accounts for the energy gain and loss mechanisms that occur during the combustion 

process. A transient energy balance includes the energy gain due to the burning rate and the associated 

energy release rate for a typical fuel material (qcomb) to be identified. The energy losses are due to heat 

transfer by radiation from the flame to the vehicle walls (qrad), by convection from the heated gases 

(which expand as well as get convected) to the vehicle walls (qconv), and by conduction from the flame to 

the fuel-sample holder (qcond). The resulting expression for energy accumulation in the vehicle is

d(Q)/dt = qcomb – qrad – qconv – qcond (1)

The transient term on the left-hand side can be written as 

d(Q)/dt = Cv,g d(ngTg)/dt (2)

where Cv,g is the molar specific heat of the gas (air) at constant volume, ng is the total number of gaseous 

moles in the chamber/vehicle and varies with time during combustion due to reaction stoichiometry, and 

Tg is the gas temperature averaged over the chamber/vehicle volume.

For determining the energy gain during combustion, Huggett’s recommended heat release factor of 

13,100 kJ/kg-O2 has been used (Ref. 2). The heat release rate qcomb has been related to the burning rate of the 

fuel via this heat release factor. The basic chemical unit of the fuel has been assumed to be cellulose with a 

molecular formula of C6H10O5 and burning stoichiometrically; i.e., C6H10O5 + 6O2  6CO2 + 5H2O.

The time-dependent burning rate profile of the fuel in ground-based, normal-gravity experiments has 

been inferred from visual observations of flame behavior in recorded videos of the combustion event

conducted in sealed chambers of various volumes filled with air. Typically, the flame grows to a steady 

size soon after the fuel is ignited and diminishes in a brief period to flame out. The observed flame 

behavior has been described as an approximate function of time for the duration of the burn, which in turn 

has been used to get an indirect estimate of the instantaneous burning rate, and hence, the instantaneous 

heat release rate qcomb. The integrated average of qcomb over the total duration (burn-time) of the 

combustion event, τ, is an important parameter which we call the fire power, FP. The O2 consumption,
NASA/TM—2012-217712 4

and CO2 and H2O generation rates have been calculated from the inferred fuel burning rate, the chemical 

composition of the fuel, and assuming a stoichiometric combustion process.

For predicting the pressure rise in the ATV under microgravity conditions, the energy release is

estimated using the area density of a potential thin fuel and burning rate is estimated conservatively by 

using correlations developed for microgravity flame spread rates of a lower area density fuel (i.e., 

Kimwipe (Ref. 3).

The radiative heat loss to the walls of the chamber/vehicle can occur both by the solid particulate 

matter (smoke and soot) generated during combustion and gas-phase radiation, primarily from CO2 and 

H2O. The current calculations neglect particulate radiation (usually the larger fraction), and hence are 

more conservative. The radiative loss term is expressed as 

qrad = aP Vf σ (Tf

4 – Tw4

) (3)

where aP is the Planck mean absorption coefficient, Vf is the radiating flame volume, σ is the StefanBoltzmann constant, Tf is the flame temperature averaged over flame volume, and Tw is the temperature 

of the wall the flame is radiating to.

The convective heat loss term is expressed as 

qconv = hw Aw (Tg – Tw) (4)

where hw is the convective heat transfer coefficient between the heated gas and walls of the 

chamber/vehicle, and Aw is the total surface area of the walls available for convective heat transfer. The 

heated gas carried downstream by buoyant convection in normal gravity or by forced convection in the 

planned space flight experiments is expected to circulate inside the chamber/vehicle, so we assume that

for our purposes, a flow-over-a-flat-plate type of correlation would be sufficient to approximate the 

convective heat transfer coefficient. Therefore, we use the following average Nusselt number correlation

NuL = hw L / λg = 0.664 Pr1⁄3 ReL

1⁄2 (5)

where L, the distance from the leading edge of the flat plate, is conveniently taken in this analysis as the 

known diameter (i.e., the characteristic length) of the chamber/vehicle, λg is the thermal conductivity of 

the gas (air), Pr is the Prandtl number of the gas (air), and ReL is the Reynolds number based on the 

characteristic length L. The properties of the gas have been evaluated at an average temperature and 

pressure during the combustion event and usually taken as their initial values prior to combustion unless 

their variations are non-negligible. The Reynolds number is a function of the expected gas velocities 

which have either been estimated from buoyant convection in ground-based, normal-gravity experiments 

or from anticipated operational speeds of the fans to be used in the space flight experiment (~ 15 cm/s).

The estimates for conductive heat losses have been guided by ground-based experiments conducted at 

NASA Glenn Research Center using various candidate fuel materials for the flight experiment. For some 

of these experiments, the fuel sample and the fuel-sample holder configuration do not warrant a 

consideration of conductive losses. However, when a specific fuel-sample material developed in-house is

burned then the qcond term is non-negligible and needs to be accounted for. In this case, the fuel sample is 

woven into a non-burning, flexible matrix material for ease of handling and mounted on both sides to 

high-conductivity metallic strips. The conductive heat loss term is then expressed as 

qcond = λg (Tf – Tp) (Af /sf ) (6)

where λg is the thermal conductivity of the gas (air) evaluated at an average temperature between Tf and 

Tp, Tp is the pyrolysis temperature of the cellulosic fuel (~ 900 K), Af is the area of the flame over the fuel 

sample, and sf the flame stand-off distance from the fuel sample. The video images of the ground-based 

experiments help determine the approximate length of the propagating flame over the fuel sample and, 

knowing the fuel sample width, allows us to estimate the flame area Af. In the absence of side-view 
NASA/TM—2012-217712 5

images of propagating flames, the flame stand-off distance has also been estimated to be in the order 

millimeters. 

There is also no straightforward way to estimate Tf for the purposes of the practical model outlined 

here. Whenever it is necessary to account for conductive heat loss qcond then a flame temperature estimate 

of 1800 K is used in Equation (6).

Similar to the approximations involved in estimating Tf, estimating the flame volume Vf is just as 

challenging. An approach would be to estimate Vf from the assumed flame size which in turn is related to 

the qcomb. The smaller flame volume would result in higher average species concentrations despite a 

higher flame temperature. However, this introduces another unknown variable into the formulation which 

for this analysis has been deemed unnecessary. Therefore, the more readily accessible quantities have 

been substituted in Equation (3). The radiating volume Vf is assumed to be the sealed volume of the 

chamber/vehicle Vt. The Planck mean absorption coefficient aP for the gas in the chamber/vehicle is 

computed using the volume-average mole fractions for CO2 and H2O vapor (Ref. 4) in Vt at the volumeaverage mean gas temperature Tg. As such, the radiative loss term has been approximated as

qrad ≈ aP Vt σ (Tg

4 – Tw4

) (7)

Using the above definitions of each term in Equation (1), the energy balance equation can be

integrated and the average gas temperature rise can be calculated as a function of time. The corresponding 

instantaneous pressure rise has been calculated using the ideal gas law for the constant volume of the 

chamber/vehicle. 

Model Calibration and Validation

The transient lumped-parameter model described above has a number of variables which require 

estimations for making predictions. One way to avoid some of the uncertainties in the estimations is to 

anchor the model prediction to an experimental result by tuning the values of the model variables until a 

reasonably good fit between the model and experiment is obtained.

The approach has been to utilize the pressure versus time profile measured in a sealed cylindrical 

chamber of ~37 liters by burning Whatman 44 ashless filter paper of dimensions 5 cm by 18 cm. Igniter is 

located at the bottom for upward flame propagation, i.e., concurrent with buoyant convection but with no 

forced convection. Some of these experiments used a thin holder on the sides of the paper while one case 

was without a holder, basically holding the paper from one of its corners hanging in the chamber. Since 

there was nothing else inside the chamber and the experimental results indicate that the presence of the 

holder practically has no effect on the measured pressure-time trace except towards the end and after flameoff, the conductive loss term expressed by Equation (6) can be confidently eliminated from the model. For 

the amount of fuel burned, the total amount of energy released is calculated to be about 10.75 kJ. Even then, 

there are a number of variables that can be adjusted in the model to match the predictions to the experiment, 

so the calibration of the model does not give a unique answer for the best fit.

Figure 1 shows the experimental curves and the best fit of model predictions based on our visual, 

qualitative judgment. This fit is obtained by (a) taking the total burn-time as 8 s (the experiment reports an 

estimated burn-time less than 10 s), (b) applying a heat release rate versus time profile such that the power 

rises linearly to its maximum level of 2.38 kW in 3 s (37.5 percent of total burn-time), stays at the maximum 

level for 1 s (12.5 percent of total burn-time), and decays linearly to flame-off in 4 s (50 percent of total 

burn-time), and (c) using a convective heat transfer coefficient, hw, of 44 W/m2

-K. Note that the applied heat 

release rate profile satisfies the total energy release of 10.75 kJ calculated for this amount of fuel. If the 

chamber walls were adiabatic the calculated maximum pressure for this experiment would be 31.5 psia, 

indicating that about 74 percent of the total energy is lost to the environment.

Figure 2 shows a similar fit to the experimental curves by another possible combination of model 

parameters. This time, the heat release rate profile follows a path rising linearly to its maximum level of 

2.15 kW in 25 percent of burn-time (2 s), staying at the maximum level for 25 percent of burn-time (2 s), 
NASA/TM—2012-217712 6

Figure 1.—Experimental pressure profiles and our best 

matching prediction by calibrating model parameters; 

Whatman 44 ashless filter paper, 5- by 18-cm.

Figure 2.—Experimental pressure profiles and another 

close fit by a different calibration of model parameters; 

Whatman 44 ashless filter paper, 5- by 18-cm.

and decaying linearly to flame-off in 50 percent of burn-time (4 s), but also satisfying the total released 

energy constraint of 10.75 kJ. Matching the maximum peak pressure is accomplished by using a hw value 

of 42 W/m2

-K. Though this calibration can also be viewed as acceptable, it has a faster initial rise and 

underpredicts the later stages of pressure decay. Given the model assumptions employed for describing 

the process, a more rigorous quantitative measure of judging the goodness of the fits is deemed to be 

unwarranted. We have therefore settled on the first set of model parameters resulting in the pressure trace 

depicted in Figure 1 for our calibration of the model.

Next, the calibrated model is used to predict transient pressure profiles measured in the same chamber 

but for different types and quantities (masses) of fuel of the same size; i.e., 5- by 10-cm. Even though the 

fuel material is bleached cheesecloth for all cases and it can be described as a cellulosic fuel with a basic 

molecular unit of C6H10O5, the experiments have employed types of cheesecloth materials with different 

area densities or burned different number of pieces stacked on top of each other with no glue or binding 

material in-between. The measured pressure traces of all of these various cases are depicted in Figure 3.

The first two cases burn single pieces of cheesecloth of the same dimensions but of different mass due to 

differences in their area density while the third case in the legend uses two pieces in a stack. It is 

experimentally observed that the thicker the fuel stack is the more incomplete and sooty the burn is. Also, 

as fuel stack gets thicker the final pressure at the end of the experiment starts to fall lower than the initial 

starting pressure. This may be due to the formation of condensable hydrocarbons from incomplete and 

O2-lean combustion of the fuel when stacked, although the amount of leftover O2 after burning the 

thickest stack (i.e., four pieces with a total of 856 mg of fuel) is calculated to be not less than 

18.5 percent; i.e., not vitiated relative to the flammability limit of ~11.5 percent. Note that while the 

measured peak pressure values of the thinner stacks increase with the amount of burnt fuel mass the 

values of the thicker stacks with three or four pieces do not consistently increase with the total energy 

released, even though all samples have the same length. Also notice that the positions of the reported 

spread and total burn times relative to the observed peak pressure position is not always the same, neither 

are they apart from one another in a consistent manner.

The top three cases in the figure legend display a long-time pressure behavior similar to the 

calibration cases in that final pressures settle at a level close to the initial pressures. The last two cases use 

three and four pieces of stacked 90 grade bleached cheesecloth and their final pressures fall significantly 

below their initial pressures, though both seem to interestingly settle at the same long-term value. We 

have picked only the two single-piece cases plus one case which is only double-stacked as an acceptable 

borderline situation (i.e., the top three cases in the figure legend) for comparison with our predictions. 

0

0.5

1

1.5

2

2.5

14

15

16

17

18

19

20

-10 0 10 20 30

Fire Power (kW)

Chamber Pressure, psia

Time, s 

no holder

thin holder 1

thin holder 2

thick holder

Model

Fire Power

0

0.5

1

1.5

2

2.5

14

15

16

17

18

19

20

-10 0 10 20 30

Fire Power (kW)

Chamber Pressure, psia

Time, s 

no holder

thin holder 1

thin holder 2

thick holder

Model

Fire Power
NASA/TM—2012-217712 7

Figure 4 compares the model prediction against the second experimental case where a single piece of 

90 grade bleached cheesecloth is burned. This material has a total mass of 214 mg with total energy 

release of 3.32 kJ. The experimentally reported spread time is 4 s. The model does an excellent job of 

predicting both the peak pressure value and the full pressure profile. The final long-term pressure 

predicted by the model comes down to the initial level while the experimental curve remains slightly 

higher. If the chamber walls were adiabatic the calculated maximum pressure for this experiment would 

be 19.7 psia, indicating about 63 percent heat loss to the environment. 

Figure 5 compares the model prediction against the third experimental case where two stacked pieces 

of 90 grade bleached cheesecloth are burned. This time, the fuel has a total mass of 428 mg and the total 

energy release is 6.64 kJ. For the reported spread time of 10 s, the experimentally observed pressure peak 

Figure 3.—Experimental pressure profiles for various types and quantities of 

fuel; bleached cheesecloth, 5- by10-cm.

Figure 4.—Comparison of experimental pressure profile 

and calibrated model prediction; bleached cheesecloth, 

5- by10-cm.

Figure 5.—Comparison of experimental pressure profile 

and calibrated model prediction; bleached cheesecloth, 

5- by10-cm.

13.5

14

14.5

15

15.5

16

16.5

17

0 10 20 30 40

Chamber Pressure, psia

Time, seconds from igniter on

1x10 grade - 100 mg

1x90 grade - 214 mg

2x90 grade - 428 mg

3x90 grade - 642 mg

4x90 grade - 856 mg

spread time

total burn time

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

13.5

14

14.5

15

15.5

16

16.5

17

0 10 20 30 40

Fire Power (kW)

Chamber Pressure, psia

Time, s

1x90 grade - 214 mg

Model

Fire Power

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

13.5

14

14.5

15

15.5

16

16.5

17

0 10 20 30 40

Fire Power (kW)

Chamber Pressure, psia

Time, s

2x90 grade - 428 mg

Model

Fire Power
NASA/TM—2012-217712 8

Figure 6.—Comparison of experimental pressure profile 

and calibrated model prediction; bleached cheesecloth, 

5- by 10-cm; hw = 22 W/m2

-K for heat loss.

is slightly higher than the two previous experimental cases. Again, the model does a very good job of 

predicting both the peak and the full profile of the experimental pressure curve. The final long-term 

values of both experimental and predicted pressures return to the initial starting level. For this case, 

adiabatic combustion would result at a maximum pressure of 25.0 psia, indicating about 79 percent heat 

loss to the environment. 

Figure 6 depicts the first experimental case where a single piece of 10 grade bleached cheesecloth is 

burned. This material has a lower area density with a total mass of 100 mg for the same fuel sample size.

It burns relatively quickly reported to last for about 3 s. The total energy release is only 1.55 kJ, and the 

experimentally observed pressure peak is lower than the other measurements in the same series. If the 

same heat release rate profile obtained from the calibration and the same convective heat transfer 

coefficient of 44 W/m2

-K best describing the calibration cases were used also for this case then the model 

tends to overpredict the peak pressure value observed in the experiment. It is speculated that this 

discrepancy is mostly due to the fact that this light material which burns in a flash does not create 

sufficient gas expansion and buoyant convective motion in the chamber to generate as much heat loss as 

the other cases. In fact, when the model is run with the same heat release rate profile but with a smaller 

convective heat transfer coefficient of 22 W/m2

-K to reflect the smaller heat losses then the model 

captures the experimental pressure profile very accurately and predicts the peak value perfectly. Both the 

experimental and predicted final long-term pressure values come down to the initial level. The maximum 

pressure for adiabatic combustion in this case would be 16.9 psia, indicating a smaller heat loss of about 

36 percent to the environment

Given the issues discussed about the experiments above, it seems that that the model can predict the 

pressure curves reasonably well covering a range of released total energies of 1.55 to 10.75 kJ. The next 

challenge would be to check the model for predictions of pressure profiles both in a different enclosure of 

much larger volume so that the heat losses would be different and for sizes, masses, and types of fuels so 

that the energy contents and heat release rates would be different. Experiments in such an environment 

are currently underway using one of our in-house sealed facility chambers, namely VF-13. This chamber 

has basically a cylindrical shape with a diameter of ~1.5 m and a height of 3.6 m, resulting in an 

approximate total internal surface area of 18.73 m2 and volume of 6.35 m3

. As such, VF-13 is more than 

two orders of magnitude larger than the 37-liter chamber we use here to calibrate our model. Our 

intention is to validate the performance of our model against the experiments conducted in VF-13, and 

improve it if necessary, as soon as the data becomes available.

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

13.5

14

14.5

15

15.5

16

16.5

17

0 10 20 30 40

Fire Power (kW)

Chamber Pressure, psia

Time, s

1x10 grade - 100 mg

Model

Fire Power
NASA/TM—2012-217712 9

Sensitivity Analysis of Model Predictions

Given the level of estimations involved in determining the parameters of the model, it’s important to 

understand the sensitivity of model predictions with respect to uncertainties in employed parameter 

values. Such an analysis would guide us in focusing our attention to the accuracy of the most critical ones 

among these parameters for the purpose of more reliably predicting the transient pressure profile as well 

as the maximum pressure in the enclosure. Moreover, it would also give indications on which parameters 

are most effective for preventing over-pressurization.

The solution of Equation (1) enables the prediction of transient temperature profiles, and via the use 

of the ideal gas law, the instantaneous pressure in an enclosure. We define a sensitivity parameter, η, 

based on the logarithmic change in the predicted maximum pressure relative to a logarithmic change in a 

given model parameter, ξj, when all other parameters, ξk, are held constant, i.e.,

η = [∂(lnPmax)/∂(lnξj )]ξk=constant (8)

Equation (8) can be approximated as 

η ≈ (ξi/Pmax)o [(ΔPmax)/(Δξj)]ξk=constant (9)

where the subscript “o” refers to the values for the baseline case. Logarithmic change allows normalizing 

the corresponding change in pressure with respect to a change in a given parameter such that each 

resulting sensitivity value can be compared to another on an equal and non-dimensional basis. We have 

varied the values of various, and mostly estimated, relevant parameters of the model by about ± 5 percent

of their baseline values (i.e., Δξj = ± 5 percent ξj) to calculate the corresponding changes of predicted 

maximum pressures. We have also tried changes in the range from ± 2.5 to ± 25 percent ascertaining the 

nearly linear behavior of the corresponding changes. Also note that some of these parameters may be 

interrelated; for example, a given characteristic length of the enclosure may define the surface area and 

volume of the enclosure. However, the sensitivity analysis ignores the interrelationships of parameters 

such that when one parameter is varied all other parameters are kept constant at their baseline values.

A baseline case is chosen from a typical experiment to be conducted in VF-13. We assume burning a 

fuel with a constant heat release rate of 10 kW and a total burn-time of about 60 s, i.e., a total energy 

release of 600 kJ and an average fire power, FP, of 10 kW. To give a feel of what these values mean, note 

that burning about 8 sheets of regular paper (8.5- by 11-in.) in a minute would have an equivalent energy 

release and fire power. We take the initial temperature as 293 K and pressure as 0.95 atm (963 hPa). For 

the calculation of convective heat loss rates, we assume a velocity of 15 cm/s and a characteristic length 

of 1.5 m, i.e., the diameter of VF-13.

Initially, we have neglected the conductive heat loss and implemented Equation (7) for the integration 

of Equation (1) and predicting the pressure profile. This baseline case gives a maximum pressure of 

1.22 atm (1234 hPa) and maximum temperature of 376 K. It should be mentioned that the corresponding 

maximum pressure and temperature if this process were adiabatic would be 1.33 atm (1346 hPa) and 

408 K. The calculations indicate that about 70 percent of the total energy has been gained by the gas in 

the enclosure and 30 percent has been lost to surroundings. The total contributions of individual heat loss 

terms for this specific situation, obtained by integrating instantaneous heat loss by convection and 

radiation over the burn-time, are 76 percent by convection and 24 percent by radiation. Table I provides

the model sensitivity parameter, η, with respect to each of the model variable. The model sensitivity for 

predicting maximum pressure is highest, by definition, to the initial pressure, Pi. It is also understandable

that the next most sensitive parameters are average fire power (FP), total internal volume of the enclosure 

(Vt), and burn-time (τ) since they directly relate to the total amount of energy input to the enclosure as 

well as to heat release per unit volume and time. Sensitivities with respect to the parameters related to the 

heat losses from the system (Aw, U, and L) are smaller relative to those parameters related to heat input to 

the system.
NASA/TM—2012-217712 10

TABLE I.—MODEL SENSITIVITY (ONLY CONVECTIVE AND RADIATIVE HEAT LOSSES)

Parameter, ξj

Radiation by Equation (7) Radiation by Equation (3)

Pi FP τ Vt Aw U L Tf Vf

0.86 0.21 0.14 –0.15 –0.05 –0.03 0.03 –0.05 –0.01

We have then explored the effect of substituting Equation (3) for Equation (7) for the treatment of the 

radiative loss term in Equation (1). For a fair comparison of these two different treatments the total 

contribution of radiative loss is kept the same such that the resulting maximum pressure from either 

treatment still gives the same value of 1.22 atm. This constraint as well as the chosen baseline Tf value of 

1800 K defines the baseline value for Vf. The last two columns of Table I provide the sensitivity values 

with respect to both Tf and Vf. It is not surprising that radiative heat loss which depends on the fourth 

power of the flame temperature is more sensitive to Tf than on Vf. Based on the sensitivities tabulated in 

Table I, the accurate determination of Tf and the management of total internal surface area available for 

convective heat transfer are key variables for a more reliable prevention of over-pressurization in the 

enclosure. 

Finally, we include the effect of conductive heat loss in the model in order to account for situations 

where, for example, the woven structure of the fuel into a non-burning matrix material and/or the fuel 

holder warrants the consideration of a conductive heat loss mechanism. From visual observations of 

burning an experimental thin fuel of dimensions 5- by 180-cm with equivalent energy release and fire 

power as before, we estimate the length of the flame (Lf) propagating upward over the fuel to be about 

20 cm and take the flame stand-off distance (sf) to be 1 mm for our baseline calculation. Here, the 

determination of flame characteristics (i.e., Vf, Lf, sf, etc.) are based on direct visual examinations of 

flame video images and not correlated, for example, with heat of combustion or flame power. The flame 

temperature (Tf) is assumed again to be 1800 K. This baseline case, with the simpler treatment of the 

radiative term by using Equation (7), gives a maximum pressure of 1.20 atm (1213 hPa) and maximum 

temperature of 369 K, both expectedly lower than the aforementioned case where only the convective and 

radiative heat losses are considered. For this case, the calculations indicate that about 65 percent of the 

total energy has been gained by the gas in the enclosure and 35 percent has been lost to surroundings. The 

total contributions of individual heat loss terms for this specific situation, obtained by integrating 

instantaneous heat loss by convection and radiation over the burn-time, are 59 percent by convection, 

18 percent by radiation and 23 percent by conduction. The resulting sensitivity values are tabulated in 

Table II.

TABLE II.—MODEL SENSITIVITY (ALL HEAT LOSSES ACTIVE)

Parameter, ξj

Radiation by Equation (7)

Pi FP τ Vt Aw U L Tf Lf sf

0.87 0.21 0.14 –0.14 –0.05 –0.03 0.03 –0.03 –0.02 0.02

The model sensitivity is highest again to the initial pressure, followed by average fire power, 

enclosure gas volume, and burn-time. Convective heat transfer is the most important heat loss 

mechanism. It is noteworthy that while incorporation of conductive losses helps bring the maximum 

pressure down, the reported sensitivities of Tf, Lf, and sf are small relative to other parameters for 

worrying about their accuracy in our estimations. Conductive losses would play an insignificant role for 

drawing prudent conclusions from this analysis for preventing over-pressurization. Similarly, radiative 

loss is also secondary relative to convective loss. Among the convective loss parameters, the sensitivity is 

greatest to the available internal surface area (Aw). Therefore, for a given energy input and heat release 
NASA/TM—2012-217712 11

rate, it is recommended that attention is focused more on maximizing the area of convective heat transfer 

surfaces inside the enclosure for preventing its over-pressurization. 

Projections for Fire Safety-1 Experiment in ATV

Despite its limited capabilities and insufficient validation, and until a more detailed and multidimensional thermal model is developed, the current model can still be used as a practical tool to guide us 

in designing the Fire Safety-1 experiment to be conducted on an orbiting vehicle such as the ATV.

We use our model for first-cut predictions of the transient pressure profiles and maximum pressures 

attainable in the ATV based on some preliminary definition of the Fire Safety-1 experiment. For the ATV 

vehicle constraints given in References 5 to 7, some mitigation approaches are suggested for safely 

conducting the experiment.

The contingency pressure limit of the ATV is given as 1048 hPa, but it is recommended that the

engineering limit of 1035 hPa not be exceeded. The Fire Safety-1 experiment currently plans to run 

flammability tests for nine small thin-fuel samples of dimensions 10- by 30-cm and one large thin-fuel 

sample of dimension 50- by 100-cm. Instead of considering the most conservative but unlikely possibility 

of burning all fuel samples simultaneously, we consider here the more realistic scenario of burning the 

large sample alone, given that small samples would result in smaller pressure rises. The resulting data 

obtained from our model is summarized in Table III for four possible conditions.

TABLE III.—RESULTS OF PRELIMINARY PRESSURE RISE 

CALCULATIONS FOR FIRE SAFETY-1—LARGE SAMPLE ONLY

Condition Large Sample Fuel mass,

g

Estimated 

burn-time,

s

To, 

K

Po, 

hPa

Conductive 

loss area,

cm by cm

Tmax, 

K

Pmax,

hPa

Average 

rate of

pressure 

rise

hPa/s

Width,

cm

Length,

cm

1 50 100 45.0 105 294 1023 N/A 309 1075 0.50

2 50 100 45.0 105 294 1023 50 by 20 299 1039 0.15

3 50 100 45.0 105 294 950 N/A 309 997 0.45

4 25 50 11.3 53 294 1023 N/A 300 1041 0.34

For Condition 1, it is assumed that there are no conductive heat losses and the predicted peak pressure 

exceeds the ATV maximum limit of 1048 hPa. The other conditions show that various mitigation 

approaches can be employed to keep the maximum pressure at an acceptable level. Condition 2 assumes 

some level of conductive heat loss to the vehicle contents, such as to the experimental hardware (e.g., fuel 

sample holder, filters, etc.), and demonstrates that such a heat loss management scheme can be devised to 

prevent excessive pressure rise. For Conditions 3 and 4, no additional heat loss is assumed except to the 

external ATV walls. Condition 3 points out the obvious benefit of reducing the pressure prior to initiating 

the experiment without adversely affecting the fundamental flame behavior. Condition 4 assumes a 

scenario where the fuel sample is one-quarter of the original size (or mass) used for the baseline Fire 

Safety-1 experiment. Condition 4 depicts that reducing sample mass is another possible remedial 

approach to stay below the ATV contingency pressure, although it leads to pressure levels slightly above 

the ATV engineering limit of 1035 hPa under the assumed conservative conditions.
NASA/TM—2012-217712 12

The following is the list of assumptions in current model predictions of transient pressure profiles in 

the ATV for the planned Fire Safety-1 experiment taking into consideration the conservative limiting 

conditions from References 5 to 7:

• The ATV free volume is assumed to be 29.7 m3

, i.e., smallest possible.

• The initial temperature is 21 °C.

• The initial pressure is 1023 hPa, except for Condition 3 where an operational scenario of reducing 

the initial pressure prior to 950 hPa is explored.

• Though the area densities of candidate fuel sample materials are larger than that of Kimwipes by 

at least a factor of two, their burning rates are conservatively estimated from microgravity spread 

rate correlations developed for Kimwipes (Ref. 3); i.e., with the fastest spread rate possible. The 

burn-times reported in the table are obtained from spread rates assuming 15 cm/s concurrent flow 

and 21 percent O2 at 1 atm.

• The fuel mass is calculated by assuming a fuel area density equal to that of the in-house 

developed candidate fuel (18.05±0.02 mg/cm2 with a thickness of 0.31±0.02 mm, composed of 

50 percent cotton and 50 percent fiberglass by mass). The area densities of current candidate fuel

materials are smaller than that of this in-house developed fuel, and hence, the tabulated fuel 

masses are conservative. The baseline large sample size for the Fire Safety-1 experiment is 50- by

100-cm.

• The current transient model accounts for the heat release from the fuel sample and heat loss from 

the gas to the vehicle walls by convection and radiation. Convective and near-field radiative 

losses to the experiment hardware and ATV internal structure have not been considered explicitly 

but have been accounted for by conductive losses to the sample holders. Once the variation of 

temperature with respect to time is determined, the pressure is calculated from the instantaneous 

temperature using the ideal gas relationship for constant volume. 

• The total energy release is estimated by using Huggett’s heat release factor2 of 13,100 kJ/kg-O2, 

typical for a hydrocarbon fuel like C6H10O5. The corresponding fire power is assumed to apply at 

a constant rate throughout the given burn-time; i.e., a constant burning rate with instantaneous 

ignition and flame-out. 

For all conditions, the maximum pressure is reached at the end of the combustion event (shown as the 

estimated burn-time in Table III). At this point, the rate of pressure rise is found to be at its minimum. A 

typical model prediction of pressure and temperature profile is shown in Figure 7 for Condition 2. The 

average values for the rate of pressure rise dP/dt and temperature rise dT/dt are obtained by simply 

dividing the difference between their corresponding maximum and initial values by the burn-time.

Therefore, these average rates reported in the table are conservative for evaluating the volume expansion 

rates and associated mass release rates by the relief valve. 

Current estimates, while preliminary and obtained from conservative analyses, show that the Fire 

Safety-1 experiment is feasible within ATV pressure limits. More refined and validated models will guide 

the future efforts. Tests are planned to obtain direct measurements of pressure rise in a large sealed 

volume (VF-13) to validate the model predictions. In these experiments, we will investigate the effect of 

sequentially burning the small and large samples on the peak pressure rise as well as quantifying the heat 

loss mechanisms that play a significant role in the energy balance. The contingency plan is to reduce the 

initial pressure of the ATV while attempting to mitigate the risk in the uncertainty in the initial pressure 

through sample selection and sample size reduction. These efforts at NASA Glenn will be augmented by 

our collaboration with the ESA science team.
NASA/TM—2012-217712 13

Summary and Conclusions

A lumped-parameter transient model is described which accounts for the energy gain due to the 

burning and its associated heat release of a typical thin fuel material in a sealed enclosure and the energy 

losses due to heat transfer by radiation from the flame to the walls, by convection from the heated gases to 

the enclosure, and by conduction from the flame to the fuel-sample holder. The temperature and 

associated pressure profiles during and after the combustion event are predicted. The model is first 

calibrated against an experimentally measured pressure profile obtained from burning one type of fuel in 

a closed chamber. It is then used to predict pressure profiles obtained from burning a different type and 

various quantities of fuel material. The calibrated model predictions are found to be quite reasonable both 

in terms of the full pressure profile and determining the maximum pressure for fuel energy contents 

varied by a factor of seven. 

A sensitivity analysis is performed for the predictions of maximum pressure with respect to 

uncertainties in parameter values employed by the model. It is determined that the model sensitivity is

highest to the initial pressure, followed by average fire power, total internal gas volume of the enclosure, 

Figure 7.—Predicted pressure and temperature profiles in ATV for Fire Safety-1 

experiment, Condition 2 in Table III.

ATV initial pressure

ATV engineering max

ATV maximum pressure
NASA/TM—2012-217712 14

and burn-time. Among the heat loss parameters, the sensitivity is greatest to the available internal surface 

area and to the flame temperature. Therefore, for a given energy input and heat release rate, the 

maximization of total internal surface area available for convective heat transfer and accurate 

determination of the flame temperature are key variables for a more reliable prevention of overpressurization in the enclosure.

Albeit its limited capabilities and validation, the current model is used as a practical tool to guide us 

in the design of the Fire Safety-1 experiment proposed to be conducted on an orbiting vehicle such as the 

ATV. The first-cut model predictions of the transient pressure profiles and maximum pressures attainable 

in the ATV show that the Fire Safety-1 experiment is feasible within the ATV vehicle constraints.

Various scenarios and mitigation approaches are suggested to prevent over-pressurization. The 

development of more refined models and their validation by tests in larger sealed chambers are currently 

underway for the safe conduct of the experiment in any potential orbiting vehicle.

References

1. Ross, H. D. (ed.), Microgravity combustion: fire in free fall, San Diego, CA, Academic Press (2001). 

2. Huggett, C., Estimation of Rate of Heat Release by Means of Oxygen Consumption Measurements, 

Fire Mater. Vol. 4, 61-65 (1980).

3. Olson, S.L., Ruff, G.A., and Miller, F.J. “Microgravity Flame Spread in Exploration Atmospheres: 

Pressure, Oxygen, and velocity Effects on Opposed and Concurrent Flame Spread,” SAE Paper No. 

2008-01-2055, 38th International Conference on Environmental Systems, San Francisco, CA, June 29-

July 2, 2008.

4. Abu-Romia and T’ien, “Appropriate mean absorption coefficients for infrared radiation of gases,”

ASME Journal of Heat Transfer, 89C:321–327 (1967).

5. ATV Cargo Accommodation Handbook, 20 November 2004, ATV-HB-AI-0001-7, ATV-ALS-UM0001.

6. ATV ICC User Manual ATV-ALS-UM-0002, Issue 06, February 28, 2005. 

7. ATV Dry Cargo Integration Interface Definition Document, Issue 03 Rev1, 18 Jan. 2010, OPS-IDD0-200.

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Prevention of Over-Pressurization During Combustion in a Sealed Chamber 

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6. AUTHOR(S)

Gokoglu, Suleyman, A.; Niehaus, Justin, E.; Olson, Sandra, L.; Dietrich, Daniel, L.; Ruff, 

Gary, A.; Ferkul, Paul, V.; Johnston, Michael, C. 

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WBS 067463.04.05.04.03 

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National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

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13. SUPPLEMENTARY NOTES

14. ABSTRACT

The combustion of flammable material in a sealed chamber invariably leads to an initial pressure rise in the volume. The pressure rise is due to the increase in the total number 

of gaseous moles (condensed fuel plus chamber oxygen combining to form gaseous carbon dioxide and water vapor) and, most importantly, the temperature rise of the gas in 

the chamber. Though the rise in temperature and pressure would reduce with time after flame extinguishment due to the absorption of heat by the walls and contents of the 

sealed spacecraft, the initial pressure rise from a fire, if large enough, could lead to a vehicle over-pressure and the release of gas through the pressure relief valve. This paper 

presents a simple lumped-parameter model of the pressure rise in a sealed chamber resulting from the heat release during combustion. The transient model considers the 

increase in gaseous moles due to combustion, and heat transfer to the chamber walls by convection and radiation and to the fuel-sample holder by conduction, as a function of 

the burning rate of the material. The results of the model are compared to the pressure rise in an experimental chamber during flame spread tests as well as to the pressure falloff after flame extinguishment. The experiments involve flame spread over thin solid fuel samples. Estimates of the heat release rate profiles for input to the model come from 

the assumed stoichiometric burning of the fuel along with the observed flame spread behavior. The sensitivity of the model to predict maximum chamber pressure is 

determined with respect to the uncertainties in input parameters. Model predictions are also presented for the pressure profile anticipated in the Fire Safety-1 experiment, a 

material flammability and fire safety experiment proposed for the European Space Agency (ESA) Automated Transfer Vehicle (ATV). Computations are done for a range of 

scenarios including various initial pressures and sample sizes. Based on these results, various mitigation approaches are suggested to prevent vehicle over-pressurization and 

help guide the definition of the space experiment.

15. SUBJECT TERMS

Combustion; Fire; Fire prevention; Fire safety; Combustion chamber 

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