NISTIR 7013

The Global Combustion Behavior of 1 MW to 3 MW 

Hydrocarbon Spray Fires Burning in an Open 

Environment 

Anthony Hamins

Alexander Maranghides

George Mulholland
2

U.S. DEPARTMENT OF COMMERCE

Donald L. Evans, Secretary

TECHNOLOGY ADMINISTRATION

Phillip J. Bond, Under Secretary of Commerce for Technology

NATIONAL INSTITUTE OF STANDARDS AND TECHNOLOGY

Hratch G. Semerjian, Acting Director

June 2003

The Global Combustion Behavior of 1 MW to 3 MW 

Hydrocarbon Spray Fires Burning in an Open 

Environment 

Anthony Hamins

Alexander Maranghides

George Mulholland

Building and Fire Research Laboratory

NISTIR 7013
Abstract 

A series of experiments were conducted in order to determine the global combustion 

behavior of a number of liquid fuels burning in large (1 MW to 3 MW) spray fires in an 

open environment. The experiments described here provide a characterization of the 

global fire characteristic of the liquid spray burner, which is a standard fixture in the 

NIST Large Fire Laboratory. The fuels tested include n-heptane, toluene, a commercial 

blend of heptane isomers, Jet A, and a heptane/toluene fuel mixture. The fuel flow was 

controlled. Measurements were made of the radiative emission to the surroundings, the 

heat release rate, and the emission of soot, CO2, and CO. These measurements were 

normalized by the mass burning rate to determine the radiative heat loss fraction, the 

combustion efficiency, and the yields of soot, CO2, and CO.

1. Introduction

Global fire properties are needed as input for CFD fire models. Although there is some

information available in the literature regarding the global combustion behavior of 

hydrocarbon pool fires, there is little data on large (>1 MW) fires, and almost nothing on 

large spray fires. 

A series of experiments were conducted in order to determine the global combustion 

behavior of a number of liquid fuels burning in a spray flame in an open environment. 

Measurements were made of the radiative emission to the surroundings, the heat release 

rate and the yields of soot, CO2, and CO. Through control of the fuel mass burning rate 

and measurement of the heat release rate, the combustion efficiency was determined. The 

mass burning rate information and measurement of the emitted radiation allowed 

determination of the fractional radiative heat loss. The soot yield was determined from 

knowledge of the mass burning rate ( ) and through extractive sampling and subsequent 

analysis of the mass of soot relative to CO and CO

m&

2 in the fire plume.

The experiments described here provide a characterization of fires in the liquid spray 

burner, which is a standard fixture in the Large Fire Laboratory, for heat release rates 

between 1 MW and 3 MW. The burner has been used in a number of large fire 

experiments including the International Fire Model Benchmarking and Validation 

Exercise sponsored by the Nuclear Regulatory Commission [Hamins et al., 2003]. The 

fuels selected here include the fuels used in those experiments. 

This report is organized into three Sections. In the remainder of Section 1, the definitions 

of combustion efficiency and radiative fraction are provided. In Section 2, the 

experimental apparatus, procedures, and measurement uncertainty are described. The 

measurement results are discussed in Section 3. Each Section addresses the 

measurements of interest including the heat release rate, the radiative fraction, and the 

yields of soot, CO, and CO2. 

3
1.1 Definitions 

The radiative heat loss fraction from a fire (χr) is defined as the ratio of the rate of 

radiative energy emitted to the surroundings (Q ) to the idealized heat release rate 

( ·H

r

&

m& c): 

χr = Q&

r / ( m& ·Hc) (1) 

where Hc is the net heat of combustion of the fuel (in units of MJ/kg). In the spray burner, 

unlike a pool fire, the value of m was controlled such that it was a constant value during

the tests. 

&

The heat release rate of a fire is a critical experimental parameter. The heat release rate 

represents the amount of energy per unit time that is generated by the fire. It is the value 

of the heat release rate that controls the thermal environment and drives the radiative and 

convective heat transfer, the fluid flow, the thermal insult onto secondary items such as 

structural members, the rate of fire spread and growth, the volume of smoke and toxic 

products, and ultimately the hazard associated with a fire. The heat release rate (Q ) is the 

product of the mass burning rate of the fuel (m ), the heat of combustion of the fuel (H

&

& c) 

and the combustion efficiency (χa). 

Q& = χa · m& · Hc (2) 

The combustion efficiency was determined by measuring Q , controlling , and 

knowledge of the value of H

& m&

c. The combustion efficiency is known to vary for different 

fuels, and is limited by definition to values between 0 and 1. 

1.2 Fuel Properties 

The fuels tested included n-heptane, toluene, heptane, Jet A, and a heptane/toluene fuel 

mixture. Toluene, heptanes, and Jet A are commercially available fuels. Heptane is a 

blend of heptane isomers. The value of Hc was known or was determined for each of the 

fuels. Table 1 lists the value of Hc as well as other properties required to characterize the 

fuels, including the liquid density at ambient temperature and the value of the heat of 

combustion per unit mass of oxygen consumed (Hc/ro), where ro is the mass of oxygen 

consumed per unit mass of fuel. The parameter (Hc/ro) is an important parameter used in 

calorimetry [Bryant et al., 2003]. 

2. Experimental Apparatus and Procedure

The fuel system was designed to deliver a uniform liquid fuel flow. The system consisted 

of a fuel storage container and a magnetic drive positive displacement gear pump. The 

pump was controlled by a variable frequency driver. Fuel was delivered through two 

atomizing spray nozzles oriented down onto a 1 m by 2 m stainless steel pan. The spray 

nozzles were located about 0.6 m above the pan. The pan was 7 cm deep. The nozzles 

had a 90o

 spray angle. A plan view of the experiments is shown in Fig. 1. The fuel flow 

was calibrated with a graduated cylinder and stopwatch. 

Measurements were made for at least 2 min after the fire had reached steady state 

burning. The fuel mass burning rate was controlled. Because of this, steady burning 

4
required much less time to achieve than for a typical pool fire, taking as little as 1⁄2 min 

as determined from the measurements of the radiative flux from the fire. 

Since all of the measurements results are normalized by the fuel mass burning rate ( ), 

uncertainty its measurement is a major factor in an analysis of the uncertainty in the 

determination of the fire radiative fraction and combustion efficiency. The value of 

was determined at least three times before and three times after each experiment. The 

average value of the standard deviation was equal to 1 %, with its value ranging from 0.1 

% to 2.4 %. 

m&

m&

Table 1. Fuel Properties 

Fuel Density (kg/m3

) 5 Hc (J/kg) 7 Hc/ro (MJ/kg O2) 

Heptane 1 688.5 ± 0.4 44.5 8 12.67 10

Heptane/Toluene Mix 2 866.9 ± 0.5 43.2 9 12.8 9

Toluene 3 871.2 ± 0.5 41.2 8 13.0 11

Jet A 4 805.6 ± 0.5 45.6 8 13.1 12

n-Heptane 683.7 6 44.56 6 12.68 6

 1. not pure n-heptane; a commercial product composed of heptane isomers 

 2. the fuel mixture was composed of 60 % heptanes and 40 % toluene by mass. 

 3. not pure toluene; a commercial product. 

 4. assumed to have properties like kerosene.

 5. measured at 22 o

C. 

 6. Babrauskas, V., Appendix A in the Fire Protection Handbook, (Ed.: A.E. Cote) 18th

Ed., 1997. 

 7. net heat of combustion with water as a gaseous (not liquid) combustion product. 

 8. Galbraith Labs [2003]. The expanded uncertainty is not reported, but conversations with 

scientists from Galbraith Laboratories suggest that it is typically 5 %.

 9. estimate based on component properties. 

10. assumed to be equal to the value for n-heptane. 

11. assumed to be equal to the value for pure toluene. 

12. estimate. 

2.1 Radiative Heat Flux to the Surroundings 

The radiative heat flux ( q ) was measured using calibrated Gardon total heat flux sensors 

positioned at a distance of 6 m to 14 m from the center of the fire pan and positioned 2 m 

above the burner, which was approximately 1⁄2 of that expected for the time-averaged fire 

height. Measurements were made for at least 2 min at a sampling rate of 10 Hz, which 

was saved as a running 1 s average. Instrument time response was approximately 1⁄2 s. 

Background signal was taken before and after every measurement. The gauges had a 

" &

5
150o

 view angle. The sensor surface was sprayed with a high emissivity (=0.95) paint that 

was spectrally flat. 

It was assumed that the fire was symmetric about every quadrant around the pan center. 

Measurements were simultaneously made at several angles (θ =0o

, 30o, 60o, 90o in Fig. 1), 

using several gauges to determine the dependence of flux with angle. At one location, 

three gauges were positioned in very close proximity to facilitate the uncertainty analysis. 

The value of the total radiative flux emitted by the fire (Q ) was determined assuming 

that the spray fire was symmetric about the center of the rectangular pan: 

r

&

 

Qr

& = 8 R2 ∫

/ 2

0

π

" q& (θ) dθ (3) 

where R is the distance between the center of the fire pan, and is the measured 

radiative heat flux as a function of angle, θ (see Fig. 1). 

" q&

The value of χr was determined using the measured results for and in conjunction 

with Eqs. 1 and 3. The assumption of point source radiative emission has been found to 

be an acceptable approximation for pool fires, providing that the distance between the 

heat flux gauge and the fire is greater than five times the fuel pan radii [Modak, 1976; 

1977]. The point source assumption was tested at a number of angles by comparing the 

product of and R

" q& m&

" q& 2

 determined from gauges at various values of R for a particular value 

of θ. The flux measurements were integrated about the pan and the value of in Eq. 3 

was determined. The value of χ

Qr

&

r was then determined using Eq. 1 and the mass burning 

rate data. 

2.2 Heat Release Rate 

The fire heat release rate ( ) was measured using oxygen consumption calorimetry in 

the standard manner through measurement of exhaust products in the 6 m by 6 m hood 

[Bryant et al. 2003; 2004]. The exhaust products from the compartment flowed into the 6 

m exhaust duct where the gas flow was characterized. This form of fire calorimetry is 

based on the fact that the oxygen deficit in the exhaust duct flow (relative to ambient air) 

is a measure of the heat release rate of a fire. The calorimeter measurement system in the 

6 m hood measures the velocity, temperature, and concentrations of oxygen, CO, and 

CO

Q&

2. This data was used to determine the heat release rate. A correction is made for 

ambient humidity. This system was calibrated before each test using carefully measured 

flows of natural gas, with fires as large as 2 MW. A detailed analysis of the combined 

expanded uncertainty in the measurement yields a value of approximately 11 % for 

fires in the Q =1 MW range [Bryant, 2003]. Further details can be found in Bryant et al.

[2003; 2004], which includes a thorough description of the experimental methodology, 

hardware, instrumentation, procedures, and uncertainty. 

Q&

&

6
6 m

6 m

2 m

1 m atomizing 

fuel nozzles

R

radiometer

(90−θ)

extractive sampling 

of soot, CO & CO2 in 

fire plume

exhaust hood 

footprint 

fire pan 

radiometer

Figure 1. Plan view of experiments designed to determine global combustion parameters for a 

number of liquid fuels. Radiative flux measurements were made for several values of θ and R, 

while gas samples were extracted above the fire plume. 

2.3 Soot, CO and CO2 Yields 

The yields of soot, CO and CO2 were measured just above the visible fire, in the plume. 

The yield is defined as the number of grams of a compound emitted per gram of fuel 

burnt. The soot yield was determined by using the carbon balance method applied to 

measurements of soot, CO, and CO2. 

Two collection probes were positioned over the center of the burner at a height of 4.15 m

above the pan (see Fig.1). The probes were mounted parallel to each other and were 

separated by 23 cm. Each probe has a nominal 1 mm bead size thermocouple near the 

sampling point of the probe. Qualitatively, the plume seemed to angle slightly toward the 

north wall and the Probe 1 TC reading was almost always higher than the Probe 2 

reading. 

The tests consisted of turning on the burner, achieving steady state conditions, sampling 

from the filter attached to Probe 1 for a period of time, and then at a later time sampling 

with the filter attached to Probe 2. Initially, an ambient bypass flow was introduced just 

downstream of the filter that flows through the gas analyzers. Then, the by-pass solenoid 

is closed and the Probe 1 solenoid is opened. At the completion of collecting the first 

sample, the Probe 1 solenoid is closed and the bypass is opened to allow the gases in the 

long sampling line to be measured by the gas analyzers. The second filter sample is 

collected after the gas analyzers have reached their background value, and the burner is at 

steady state at a second Q . &

7
The sampling time for the thermocouple and the Q measurement, and the approximate 

time interval for the smoke collection were 2 min. The burner was nominally steady 

when the measurement began. A mass flow controller was used to maintain a constant 

rate of sample extraction from the plume. The flow was sampled at 5.00 cm

&

3

/s (3.00 

L/min) at 1 atm pressure and 21oC. The smoke entered the 3.6 m long stainless steel 

probe at the plume temperature in the range 100 o

C to 200 oC. A water-jacket heat 

exchanger surrounded the last 60 cm of the sampling line to control the temperature of 

the smoke entering the filter at near 60 o

C. This prevented condensation of moisture on 

the filter. 

The smoke yield was determined by the carbon balance method. This method required a 

determination of the ratio of the smoke mass in a given volume to the total mass of carbon 

in the form of gas or particulate in the same volume. This was accomplished by dividing 

the smoke mass collected on a filter by the sum of the smoke mass and the mass of carbon 

contained in the forms of CO and CO2. Laboratory scale studies with ethene indicate that

for free burning conditions the contributions of unburned vapor phase hydrocarbons 

account for about 2 % or less of the carbon [Leonard et al., 1994]. The unburned 

hydrocarbons are neglected in this analysis, but are included in the uncertainty analysis. 

The equation for calculating the smoke yield (ys) in terms of the CO2 and CO concentrations is given by: 

 . [ m +1 n ( (CO )+ (CO )]

f m

y = s t

s

s 2 ∆φ 2 ∆φ (4) . 

The quantity f is the carbon mass fraction of the fuel, ms is the mass of the smoke sample

collected on a filter and on the wall of the sampling probe, nt is the number of moles of gas 

sampled, and the constant 12 represents the molar mass of carbon in grams. The quantities 

∆φ(CO) and ∆φ (CO2) are the volume fractions of CO and CO2 of the gas sample taken 

during the test minus the ambient background volume fractions of these gases. The yield 

for CO is given by a similar formula: 

 [ m +1 n ( (CO )+ (CO )]

fn ( (CO )

y = s t

t

CO

φ φ

φ

∆ ∆

∆

2 2

28

 (5) 

where 28 is the molecular weight of CO. For n-heptane and the heptane blend, the CO 

concentration was not measurable above the background. In these cases we estimate that 

the CO yield is less than 8 × 10-3 based on a minimum detectable CO volume fraction of 

2 × 10-5. 

The measured mass concentrations of soot correspond to the values at the sample location 

and the corresponding temperature. The value is computed using the following formula: 

( ) smoke

f c c

s V T

m C m

M

+ = , (6) 

where mf is the mass of smoke collected on the filter, mc the mass collected on the walls

of the sampling tube, C a correction factor based on the amount not removed by the first 

wiping of the cloth, and V is the volume of smoke sampled at temperature Tsmoke. The 

concentration in the flame itself will be greater. The volume fraction of soot is obtained 

8
by dividing the mass concentration by the density of soot, which is taken to be 1.8 g/cm3

. 

This represents the volume of the condensed phase soot per volume of gas at the 

sampling point. This value can be expected to be higher in the flame. 

The volume of gas sampled at the probe inlet was somewhat greater than 3 L/min, 

because the gas temperature at the sampling point was greater than 21 o

C. The ideal gas 

equation was used to compute the volume sampled with the measured temperature. For 

Probe 1, the temperature used in the calculation of the volume was 231 oC (averaged over 

the first filter collection), while for Probe 2 the temperature used was 126 o

C. 

Uncertainty Analysis for Soot, CO2, and CO yields

The estimated standard uncertainty in the volume fraction of the measured CO2 and CO, 

uI(CO2) and uI(CO) are 15 × 10-5 and 3 × 10-5. These estimates are based on using two 

sets of span gases (span 1volume fractions: 0.180 for CO2, 0.0700 for CO; span 2 volume 

fractions: 0.0151 for CO2, 0.000152 for CO) and analysis of the instrument noise and 

drift. These estimates were more than an order of magnitude lower than the nominal gas 

analyzer uncertainty. 

The law of propagation of uncertainty was used to compute the total uncertainty in the 

smoke yield arising from the quantities appearing in Eq. 4. As indicated in Table 2 

below, the dominant sources of uncertainty are the smoke mass, the mole fraction of CO2, 

and the molar gas flow. The resulting relative total standard uncertainty was 0.064. To 

compute the relative combined standard uncertainty of the mean, the total uncertainty is 

combined in quadrature with the relative standard uncertainty of the mean of the repeat 

measurements. Finally, the expanded uncertainty was computed using a coverage factor 

of two. The results are presented in Table 4. 

The major terms contributing to the uncertainty in the CO yield are the uncertainty in the 

CO volume fraction, which affects the numerator of Eq(5), and the volume fraction of

CO2, which is the dominant term in the denominator. The relative total standard 

uncertainty in the CO yield, ut(yCO), is equal to the root-sum-square of the relative 

standard uncertainties for CO and CO2 measurements. 

( )

1/ 2

2

2

1

2

1 ( y ) u (CO) u (CO ) ut CO = r + r (7) 

The relative uncertainty u1r = uI/φ, where φ is the volume fraction of the gas. From this 

result, the expanded uncertainty was computed using the same general approach as 

above. The results are given in Table 4. 

The uncertainty in the yield of CO2 was small, because the numerator and denominator of 

the yield equation were dominated by the volume fraction of CO2. The largest 

uncertainty was for toluene, for which the ratio of the mass of soot to the mass of carbon 

in the generated CO2 is approximately 0.25. For CO, the ratio was about 0.05. Even in 

this case, the estimated total uncertainty is only 3 % of the mean value. This value 

includes a 2 % contribution for unburned hydrocarbons. For heptane, there was little 

smoke production, and the uncertainty was even less, with an estimated value of 2 %. 

9
There is an additional uncertainty component for the jet A, the heptane blend, and the 

heptane/toluene mixture because the composition of the mixtures are not exactly known. 

In these cases, the uncertainty in f was taken to be 1 % of the estimated value (f=0.84, 

heptane, 0.913, toluene, 0.88, Jet fuel, 0.84 heptane blend, 0.87, 40 % toluene.60 % 

heptane blend by volume) The resulting expanded uncertainties were 2 % of the mean for 

the heptane blend, and 2.5 % for the jet fuel and the toluene/heptanes mixture. As above, 

the expanded uncertainty was estimated by combining in quadrature the total uncertainty 

with the uncertainty of the mean from repeat measurements, and then multiplying by a 

coverage factor of 2. Finally, the total uncertainty for mass concentration was computed 

based on Eq. 6. The major individual uncertainties and the total relative standard 

uncertainty is presented in Table 3. 

Table 2. Major Contributors to the Uncertainty in the Smoke Yield 

Variable Typical Value Relative standard 

uncertainty 

Mass of smoke 1.945 mg 0.044 

Volume fraction of CO2 0.0050 0.030

Moles of gas sampled 0.373 moles 0.036 

Smoke yield 0.076 0.064* 

* This value, the relative total standard uncertainty, is computed as the root-sum-squares of

the three individual values of uncertainty.

Table 3. Major Contributors to the Uncertainty in the Mass Concentration.

Variable Typical Value Relative standard 

uncertainty 

mass on the filter 1.5 mg 0.021 

mass on cloth 0.35 mg 0.04 

cleaning efficiency correction factor 1.27 0.173 

mass on tubing wall 0.445 mg 0.178 

mass of smoke 1.945 mg 0.044 

volume of smoke sampled 0.00816 m3 0.040 

mass concentration of smoke 0.238 g/m3 0.059* 

* This value, the relative total standard uncertainty, is computed as the root-sum-squares 

of the uncertainties in the mass of smoke and the volume.

3. Results and Discussion 

3.1 Heat Release Rate 

Table 4 summarizes the heat release rate measurement results. The Table includes the 

mass flow of fuel ( ), the idealized , the mean measured Q , the combustion 

efficiency, and the expanded uncertainties for each of these parameters. The mass flow of 

fuel was the product of the measured volumetric fuel flow and the fuel density listed in 

Table 1. The idealized value of Q was the product of and H

m& Q& &

& m& c, which were taken from

Table 1. The expanded uncertainty was computed with a coverage factor, k=2, which 

defines an interval estimated to have a level of confidence of 95% and represents two 

10
times the standard deviation, σ, of the uncertainty. Based on measurement 

reproducibility, the relative expanded uncertainty of the mean fuel flow measurement was 

taken as 1% for all tests. The relative expanded uncertainty of the mean heat release 

measurement was typically 5% for all tests, except for the jet fuel, which has an 

uncertainty of approximately 7 %, due to a particularly large uncertainty in the value of

Hc/ro (see Table 1). The relative expanded uncertainty in the idealized heat release rate is 

lowest for the experiments using n-heptane, where Hc is well established. 

The combustion efficiency, χa, as defined in Eq. 2 is shown in Table 4 for each of the 

tests. There is no significant difference between the measured value of χa for the same

fuel types over the heat release rates considered here. By definition, χa ≤ 1. Values of χa 

greater than one are not physical, but are indicative of measurement uncertainty. The 

value of χa reported here was based on Eq. 2. The uncertainty in χa was dominated by 

uncertainty in the measured Q . &

Table 4. The measured fuel flow, m& · Hc, the mean measured Q , the 

combustion efficiency (χ

&

a) and uncertainties (with a coverage factor of two). 

Test # Fuel 

Flow 

(L/min) 

m& · Hc 

(MW)

Q& (meas) 

(MW)

χa 

1 Jet A 3.26±0.03 1.89±0.09 1.56±0.11 0.83±0.12 

2 Jet A 5.02±0.05 2.91±0.15 2.66±0.19 0.91±0.14 

3 Jet A 3.26±0.03 1.89±0.09 1.77±0.12 0.93±0.14 

4 Jet A 5.02±0.05 2.91±0.15 2.72±0.19 0.93±0.14 

5 Jet A 3.26±0.03 1.89±0.09 1.78±0.12 0.94±0.14 

6 Jet A 5.02±0.05 2.91±0.15 2.71±0.19 0.93±0.14 

7 Toluene 3.01±0.03 1.80±0.08 1.37±0.07 0.76±0.10 

8 Toluene 4.77±0.05 2.85±0.14 2.10±0.10 0.74±0.10 

9 heptanes 2.79±0.03 1.42±0.07 1.51±0.08 1.06±0.15 2

10 heptanes 4.55±0.05 2.32±0.12 2.24±0.11 0.97±0.13 

11 n-heptane 2.79±0.03 1.42±0.02 1.58±0.08 1.11±0.12 2

12 n-heptane 4.55±0.05 2.32±0.03 2.35±0.12 1.01±0.10 2

13 Mixture 1 3.08±0.03 1.92±0.08 1.40±0.07 0.73±0.13 

14 Mixture 1 5.01±0.05 3.13±0.14 2.08±0.10 0.66±0.12 

1. the fuel mixture was composed of 60 % heptanes + 40 % toluene by mass. 

2. By definition, χa ≤ 1. χa is based on Eq. 2, in which the uncertainty in χa is 

dominated by uncertainty in the measured Q . &

11
0.0

0.5

1.0

1.5

2.0

0 30 60 90

Angle (Degree)

Flux at 6.7m (kW/m2

pan

0

45 90

1.9 MW

2.5

)

3.0

2.9 MW

Figure 2. Radiative heat flux measured at a distance of 6 .7 m from the fire as a function 

of angle about the center of the rectangular burner (see schematic on right) for 1.9 MW 

and 2.9 MW Jet A spray fires. 

3.2 Radiative Fraction

An example of the radiative heat flux measurement results are presented in Fig. 2, which 

shows the flux as a function of angle about the rectangular spray burner for 2 MW and 

3 MW Jet A fires. The flux varied as a function of angle in a fairly linear fashion. This

was consistently observed for all of the fuel types and fire sizes. 

Because of space limitations during the measurements, the burner was positioned within 

5 m of a wall. A supplementary series of measurements was conducted to determine the 

impact of reflection from the wall on the heat flux measurements. The value of χr was 

determined with and without the wall present. The results showed that wall reflection

accounted for approximately 8 % of the radiative heat flux. The radiative fraction results 

reported here were corrected for this effect. 

The point source assumption for radiative flux was tested by comparing the values of the 

product of and the square of the distance to the center of the fire (R) with the heat flux 

gauge positioned at various values of R for θ=0

" q& o

 and θ=90o (see Fig. 1). The 

measurements showed that there was less than 2 % difference in the value of the product 

of and R " q& 2

 derived from radiative flux measurements at 6 m and 13 m. 

Several factors contributed to the estimated measurement uncertainty for χr, including 

measurement variance and the uncertainty associated with calibration, which was taken 

as approximately 5 % (with a coverage factor of two). The uncertainty in the correction 

factor for wall reflection (for fuels other than heptane) also contributed to the estimated 

uncertainty.

Table 5 shows that there was no significant difference in the radiative fraction for the fire 

sizes tested here (refer to Table 4 for fire heat release rate). For the same fuel type, the 

12
Table 5. The measured radiative fraction (χr) and uncertainties (with a 

coverage factor of two). 

Test # Fuel χr

3 Jet A 0.40± 0.08 

4 Jet A 0.40± 0.08 

7 Toluene 0.43± 0.08 

8 Toluene 0.37± 0.08 

9 Heptanes 0.44± 0.06 

10 Heptanes 0.47± 0.06 

11 n-heptane 0.45± 0.08 

12 n-heptane 0.45± 0.08 

13 mixture * 0.35± 0.08 

14 mixture * 0.34± 0.08 

* the fuel mixture was composed of 60 % heptanes and 40 % toluene by 

mass.

yields of soot, CO, and CO2 for the various tests showed little difference. Table 6 shows 

the mean measured values for the yields of soot, CO, and CO2 for the different fuel types. 

Table 6 also shows the averaged measurement results as a function of fuel type for the 

combustion efficiency and the radiative heat loss fraction. The radiative heat loss fraction 

for the spray fire studied here was larger than a pool fire with a similar Q burning the 

same fuel. The value of χ

&

r for a heptane or toluene pool fire has been reported to be 0.35 

and 0.36, respectively [Hamins et al., 1996]. The larger value of the radiative fraction for 

the spray flames is attributed to differences in the structure of these fires, as fuel 

atomization plays a role in the effective fuel burning surface, the rate of fuel evaporation, 

and fuel burning. 

Table 6. The average yields of soot, CO and CO2, the combustion efficiency, and the radiative 

heat loss fraction for different fuel types. (expanded uncertainty for soot, CO, and CO2) 

Fuel Combustion

efficiency 

Radiative 

fraction 

Soot yield CO yield CO2 yield

Heptanes 1.01 ± 0.14 0.45± 0.06 0.0149 ± .0019 <0.008 3.03 ± 0.12 

Toluene 0.75 ± 0.10 0.40± 0.08 0.195 ± 0.052 0.070 ± 0.017 2.52 ± 0.22 

n-heptane 1.06 ± 0.14 2 0.45± 0.08 0.0108 ± 0.0014 <0.008 3.04 ± 0.12 

Jet A 0.93 ± 0.14 0.40± 0.08 0.097 ± 0.016 0.030 ± 0.009 2.82± 0.15 

Heptanes/

Toluene1

0.70 ± 0.13 0.35± 0.08 0.114 ± 0.022 0.042 ± 0.016 2.70 ± 0.15 

1. the fuel mixture was composed of 60 % heptanes and 40 % toluene by mass. 

2. By definition, χa ≤ 1. χa is based on Eq. 2, in which uncertainty in χa is dominated by

uncertainty in the measured Q . &

13
0.00

0.05

0.10

0.15

0.20

0.25

0.4 0.6 0.8 1.0

Soot Yield

χa

 

Figure 3. The soot yield as a function of the combustion efficiency for the 1 MW to 

3 MW fires burning the fuels considered in this study. Uncertainties are listed in Table 6.

Table 6 also shows the combustion efficiency, χa, for the various fuels studied here. As 

expected, the combustion efficiency is lowest for toluene, which is a very smoky fuel. 

Tewarson [1986] found similarly low values of the combustion efficiency for toluene. 

The relationship between the measured soot yield and the combustion efficiency is shown 

in Fig. 3. As expected, as the soot yield increased, the combustion efficiency decreased. 

This is consistent with the results of Tewarson [1986], who measured increases in soot 

yield and decreased combustion efficiency as a function of smoke point height in small–

scale experiments. The figure includes a best fit line to the data, which does not 

adequately represent the data, but does capture its trend. 

4. Conclusions 

The magnitude of the uncertainty associated with the determination of χa is relatively 

large, due to the inherently large uncertainty of the heat release rate measurement. 

Significant innovation in the measurement approach is needed to reduce the χa

uncertainty . One possible approach may be to measure the detailed combustion products 

and consider changes in the heats of formation of the reactant and product yields, relative 

to complete combustion. At a minimum, such an approach would assure that χa was less 

than unity. 

 

Acknowledgements

The authors are grateful to Edward Hnetovsky, Lauren DeLauter, and Mike Selepak, for

providing expert technical assistance, and to Dr. Matthew Bundy, Dr. Rodney Bryant, 

Mr. Rik Johnsson, and Ms. Michelle Donnally for very helpful discussions. 

14
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