ABSTRACT 
 
 
 
 
Title of Dissertation: High Temperature Radiation Absorption of Fuel 
Molecules And An Evaluation of Its Influence 
on Pool Fire Modeling   
  
 Kaoru Wakatsuki 
Doctor of Philosophy, 2005 
 
Dissertation Directed By: 
 
Associate Professor, Jungho Kim 
Associate Professor, Greg Jackson 
Department of Mechanical Engineering 
 
 
Infrared absorption coefficients of various gas and liquid fuels (propane, n-
heptane, methanol, toluene, propylene and methyl methacrylate) were measured using 
high temperature Fourier transform infrared spectroscopy (FTIR) for a range of 
temperatures up to 1000 K in order to facilitate calculation of radiative absorption of fuel 
molecules in large-scale, non-premixed flames. Spectrally resolved fits as a function of 
temperature (up to 600 K) were calculated using a semi-empirical expression derived 
from quantum theory.  These fits provided a basis for calculating infrared spectra for the 
fuels from 300 K to 1400 K.  Extrapolating the fit to high temperature gave integrated 
total absorption coefficients with errors ? 20 % temperature up to 1000 K for measured 
hydrocarbon fuel specie.  Highly resolved infrared absorption coefficient database of 
fuels and combustion products (H
2
O, CO
2
, and CO from HITEMP database, and soot 
from modeling) were created.  Comparison of Planck mean absorption coefficients as a 
function of temperature indicated unique behavior with respect to molecular structure of 
 
fuels.  Directional radiation intensity at the fuel surface of 0.3 m methanol, heptane and 
toluene pool fires were solved using a one dimensional radiative transport equation for 
line of sight at flame centerline using the new radiation absorption coefficient database. 
The solution of transport equation predicted radiation intensity at fuel surface within 2 % 
for non-sooty methanol pool, but under predicted < -100% for sooty pool fires of heptane 
and toluene.  Flame structure impacted importance of absorption and emission.  Soot 
within the flame, which has continuous band absorption at entire infrared region, 
absorbed much more radiation than other species, which has particular discrete band 
absorption, and resulted in low radiation intensity at the fuel surface.         
 
 
 
 
 
 
 
 
 
 
HIGH TEMPERATURE RADIATION ABSORPTION OF 
FUEL MOLECULES AND AN ENVALUATIOIN OF ITS 
INFLUENECE ON POOL FIRE MODELING 
 
 
 
By 
 
 
       Kaoru Wakatsuki 
 
 
 
 
 
Dissertation submitted to the Faculty of the Graduate School of the  
University of Maryland, College Park, in partial fulfillment 
of the requirements for the degree of 
Doctor of Philosophy 
2005 
 
 
 
 
 
 
 
 
 
 
Advisory Committee: 
Professor  Jungho Kim, Chair         
Professor  Greg Jackson, Co-Chair   
Professor  Kenneth Yu, The Dean?s representative 
Professor  James G. Quintiere 
Professor  Anthony Hamins 
Professor  Marc R. Nyden 
 
 ii
 
 
Acknowledgements 
 
I would like to express my deepest gratitude to my advisors, Drs. Jungho Kim and 
Greg Jackson, who gave me to the opportunity to work for their project from the Building 
and Fire research laboratory (BFRL) in National Institute of Standards and Technology 
(NIST) and led me to complete my PhD program.   I greatly appreciate Drs. Anthony 
Hamins and Marc Nyden of BFRL in NIST, who gave me the interest of thermal energy 
feedback in a fire and supported me technically and financially.  To Dr. James Quintiere, 
who first taught me how to play with fire and the fear of fire, and always cheered my 
wife and me to accomplish our goal in the U.S., I deeply appreciate his advice.  I thank to 
Dr. Kenneth Yu for serving my dissertation as the Dean?s representative, and to Dr. S. 
Paul Fuss of Alcohol, Tobacco, Firearms and Explosives (ATF) who gave me the 
opportunity to continue his project, and advised me to run and fix the high temperature 
FTIR in NIST. 
To my friends of Department of Fire Protection Engineering (ENFP), Nathasak 
Boonmee, Yunyong Utiskul (Pock), Tingguang Ma, and Yi Wang, I thank to them all 
their help for my study and grateful discussion.  To Drs. Francine Amon and Takashi 
Kashiwagi of BFRL at NIST, who supported me personally, and worked together for 
their projects, I greatly appreciate them. To Dr. Tomohiro Naruse of Building Research 
Insitute (BRI) in Japan, who worked with me during his two years stay in ENFP and gave 
me many advice for my study and a job search, I am so thankful to him, too. 
 
 iii
To my wife, Kayo, I would like to give her my deepest appreciation. With her 
support and understanding for my dream, I have completed the academic program in the 
U.S.  This degree is the achievement between Kayo and me.  Finally, my special thanks 
go to Mr. and Mrs. William and Toshiko Lofquist, my relatives in law, for their support 
of our life in the U.S.  
 
 
 iv
Table of Contents 
 
List of Tables ?????????????????????????????vii 
List of Figures????????????????????????????...viii 
CHAPTER 1 INTRODUCTION .............................................................................. 1 
1.1 Radiation feedback study in fire ......................................................................... 1 
1.1.1 Background..................................................................................................... 1 
1.1.2 Previous work ................................................................................................. 3 
1.1.2.1 Radiation feedback in fires ..................................................................... 3 
1.1.2.2 Absorption coefficient measurements..................................................... 8 
1.2 Vibration and rotation infrared spectroscopy principle .................................... 10 
1.2.1 Vibration with harmonic oscillator model .................................................... 13 
1.2.2 Rotation......................................................................................................... 15 
1.2.3 Vibration-Rotation with harmonic oscillator................................................ 16 
1.2.4 Vibration with anharmonic oscillator model ................................................ 17 
1.2.5 Vibration-Rotation with anharmonic oscillator ............................................ 18 
1.2.6 Vibration and rotation of a polyatomic molecule ......................................... 20 
1.3 Line broadening ................................................................................................ 20 
1.3.1 Collision broadening..................................................................................... 21 
1.3.2 Doppler and Natural broadening................................................................... 22 
1.4 Absorption coefficient ...................................................................................... 22 
1.4.1 Absorption coefficient theory ....................................................................... 22 
1.4.2 Temperature dependence on absorption coefficient ..................................... 24 
1.5 Problem description .......................................................................................... 25 
1.6 Objective and brief summary of the thesis ....................................................... 27 
 
CHAPTER 2 EXPERIMENTAL APPARATUS.................................................... 30 
2.1 Introduction....................................................................................................... 30 
2.2 Challenges of high temperature absorption measurement................................ 30 
2.3 Experimental setup............................................................................................ 34 
2.4 Window cooling effect on the absorption coefficient....................................... 39 
2.5 Sample preparation ........................................................................................... 42 
2.5.1 Gas fuels........................................................................................................ 42 
2.5.2 Liquid fuels ................................................................................................... 43 
2.6 Conclusion ........................................................................................................ 48 
 
 v
 
CHAPTER 3 ABSORPTION DATA ANALYSIS................................................. 49 
3.1 Introduction....................................................................................................... 49 
3.2 Gas fuels............................................................................................................ 49 
3.2.1 Propane (C
3
H
8
).............................................................................................. 49 
3.2.2 Propylene (C
3
H
6
) .......................................................................................... 52 
3.3 Liquid Fuels ...................................................................................................... 55 
3.3.1 Heptane (C
7
H
16
)............................................................................................ 55 
3.3.2 Toluene (C
7
H
8
).............................................................................................. 57 
3.3.3 Methanol (CH
3
OH)....................................................................................... 61 
3.3.4 Methyl Methacrylate (MMA, C
5
H
8
O
2
)......................................................... 64 
3.4 Extrapolation technique .................................................................................... 68 
3.4.1 Concept and background............................................................................... 68 
3.4.2 Verification ................................................................................................... 71 
3.4.2.1 HITEMP database................................................................................. 71 
3.4.2.2 Carbon Monoxide ................................................................................. 72 
3.4.2.3 Carbon Dioxide..................................................................................... 75 
3.4.2.4 Water vapor........................................................................................... 79 
3.4.3 Experimental data ......................................................................................... 79 
3.4.3.1 Propane ................................................................................................. 79 
3.4.4 Application of extrapolation technique......................................................... 84 
3.4.4.1 Effect of fuel pyrolysis.......................................................................... 86 
3.5 Conclusion ........................................................................................................ 89 
 
CHAPTER 4 DEVELOPMENT OF A RADIATION ABSORPTION DATABASE
 ???????????????????????????????? 91 
4.1 Introduction....................................................................................................... 91 
4.2 Current database................................................................................................ 91 
4.2.1 HITRAN and HITEMP................................................................................. 91 
4.2.2 RADCAL ...................................................................................................... 92 
4.3 New database .................................................................................................... 93 
4.3.1 Concept and database structure..................................................................... 93 
4.3.2 Fuel absorption database............................................................................... 93 
4.3.3 Combustion product database (CO
2
, H
2
O, and CO)..................................... 94 
4.3.4 Combustion product database (Soot)............................................................ 95 
4.3.5 Planck mean absorption coefficient.............................................................. 97 
4.3.5.1 Hydrocarbon fuels................................................................................. 98 
4.3.5.2 Other fuels........................................................................................... 101 
4.4 Conclusion ...................................................................................................... 105 
 
 
 vi
CHAPTER 5 THERMAL RADIATION FEEDBACK ANALYSIS AND 
CALCULATION ??????????????????????????. 107 
5.1 Introduction..................................................................................................... 107 
5.2 Solution of 1D radiative transport equation (line of sight)............................. 107 
5.2.1 Transport equation ...................................................................................... 107 
5.3 Radiation intensity at fuel surface by line of sight analysis............................ 110 
5.3.1 Data set and processing procedure.............................................................. 110 
5.3.2 Methanol pool fire analysis......................................................................... 111 
5.3.3 Heptane pool fire analysis.......................................................................... 116 
5.3.4 Toluene pool fire analysis........................................................................... 122 
5.3.5 Radiation transport between gas phase and condensed phase .................... 128 
5.4 Conclusion ...................................................................................................... 130 
 
CHAPTER 6 CONCLUSION............................................................................... 132 
6.1 Summary of Results........................................................................................ 132 
6.2 Recommendation for Further Research .......................................................... 134 
 
Reference ??????????????????????????. 136 
 
 vii
List of Tables 
 
Table 1-1: An example of an absorption coefficient database currently used in 
combustion calculation ............................................................................................. 27 
Table 2-1: Thermal properties of typical optical materials adopted from Ref. [56]......... 32 
Table 2-2: Temperature used for uncertainty analysis of absorption coefficient due to 
window cooling......................................................................................................... 41 
Table 2-3: Antoine equation parameters for heptane, methanol, toluene, and methyl 
methacrylate.............................................................................................................. 45 
Table 2-4: List of experimental condition for gas and liquid fuels................................... 46 
Table 3-1: Summary of errors in the HITEMP extrapolations. ........................................ 76 
Table 3-2: Errors in the integrated absorption coefficients for propane at 1 cm
-1
 resolution.
................................................................................................................................... 84 
Table 3-3: Errors of the integrated absorption coefficients in the HITEMP fitting at 550 K.
................................................................................................................................... 86 
Table 4-1: Spectral ranges used in the absorption coefficient database for fuels............. 94 
Table 4-2: Spectral ranges used in the absorption coefficient database for water vapor, 
carbon dioxide and carbon monoxide by HITEMP. ................................................. 95 
Table 4-3: Values for 4th order polynomial fits with equation 4 to Planck mean 
absorption coefficient data of hydrocarbon. ........................................................... 100 
Table 4-4: Values for 4th order polynomial fits with equation 4 to Planck mean 
absorption coefficient data of other fuels................................................................ 105 
 
 viii
List of Figures 
 
Figure 1-1: Energy transition due to absorption and emission: (a) Absorption and (b) 
Emission.................................................................................................................... 11 
Figure 1-2: Energy transition due to induced emission. ................................................... 12 
Figure 1-3: Potential energy curve for anharmonic oscillator; anharmonic oscillator (? ), 
harmonic oscillator (----)........................................................................................... 14 
Figure 1-4: Rotational-vibrational spectrum (?=0? 1) of the P and the Q branches of HCl.
................................................................................................................................... 19 
Figure 1-5: Temperature/Fuel contour plot of 1m Heptane pool fire using NIST Fire 
Dynamics Simulator.................................................................................................. 26 
Figure 2-1: Spectral transmissivity of infrared materials: (a) sapphire and (b) zinc 
selenide. .................................................................................................................... 33 
Figure 2-2: Picture of a zinc selenide window (a) clean and (b) oxidized at high 
temperature ............................................................................................................... 33 
Figure 2-3: Diagram of the high temperature test rig. ...................................................... 36 
Figure 2-4: Picture of high temperature FTIR test rig. ..................................................... 36 
Figure 2-5: Picture of experiment setup, Left: Entire setup, Right: Cooling line............. 37 
Figure 2-6: Temperature measurement of a ZnSe window with a K-Type thermocouple.
................................................................................................................................... 38 
Figure 2-7: Temperature distribution within a gas cell..................................................... 38 
Figure 2-8: Window temperature as a function of cooling velocity. ................................ 39 
Figure 2-9: Absorption coefficient and pathlength used for uncertainty analysis of 
absorption coefficient due to window cooling.......................................................... 40 
Figure 2-10: Uncertainty of absorption coefficient for CO
2
 due to window cooling at 600 
K, 800 K, and 1000 K. .............................................................................................. 42 
Figure 2-11: Picture and diagram of a fuel bubbling device. ........................................... 45 
Figure 3-1: The measured spectral absorption coefficient of propane (C
3
H
8
) at 296 K and 
the temperature dependent normalized blackbody spectral emissive power as a 
function of wavenumber. .......................................................................................... 51 
 
 ix
Figure 3-2: Measured temperature-dependent spectral absorption coefficient of C
3
H
8
; (a) 
C-H bending and (b) C-H stretching region. ............................................................ 52 
Figure 3-3: The measured spectral absorption coefficient of C
3
H
6
 at 296 K and the 
temperature-dependent normalized blackbody spectral emissive power as a function 
of wavenumber.......................................................................................................... 53 
Figure 3-4: The measured temperature dependent spectral absorption coefficient of 
Propylene (C
3
H
6
); (a) =CH
2
 out of plane bending (b) C-H in plane and out of plane 
bending, and C=C stretching and (c) CH
3
- and =CH
2
 stretching. ............................ 54 
Figure 3-5: Measured spectral absorption coefficient of n-C
7
H
16
 at 293 K and the 
temperature dependent normalized blackbody spectral emissive power as a function 
of wavenumber.......................................................................................................... 55 
Figure 3-6: The measured spectral absorption coefficient of n-heptane; (a) C-H bending 
and (b) C-H stretching. ............................................................................................. 56 
Figure 3-7: Measured spectral absorption coefficient of toluene (C
7
H
8
) at 300 K and the 
temperature dependent normalized blackbody spectral emissive power as a function 
of wavenumber.......................................................................................................... 58 
Figure 3-8: The temperature dependent spectral Planck mean absorption coefficient of 
toluene (C
7
H
8
); (a) phenyl =CH out of plane bending (b) phenyl =CH in plane 
bending, (c) phenyl C=C stretching, (d) overtones of (b) and (e) CH
3
- and =CH 
stretching................................................................................................................... 60 
Figure 3-9: Measured spectral absorption coefficient of methanol (CH
3
OH) at 293 K and 
the temperature dependent normalized blackbody spectral emissive power as a 
function of wavenumber. .......................................................................................... 62 
Figure 3-10: The temperature dependent spectral absorption coefficient of methanol 
(CH
3
OH); (a) C-O stretching, (b) C-H bending, (c) C-H stretching, and (d) O-H 
stretching region........................................................................................................ 64 
Figure 3-11: Measured spectral absorption coefficient of Methyl-methacrylate (MMA, 
C
5
H
8
O
2
) at 297 K and the temperature dependent normalized blackbody spectral 
emissive power as a function of wavenumber. ......................................................... 65 
 
 x
Figure 3-12: The temperature dependent spectral absorption coefficient of methyl 
methacrylate (C
5
H
8
O
2
); (a) =CH
2
 out of plane bending (b) C-O stretching and CH
3
- 
bending (c) C=C and C=O stretching, and  (d) CH
3
- and =CH
2
 stretching.............. 67 
Figure 3-13: Comparison of CO spectral absorption coefficient between HITEMP and 
data calculated using eqn. 3.3 with fit parameters at 1cm
-1
 resolution: (a) 300K and 
(b) 1000K.................................................................................................................. 73 
Figure 3-14: Residual (?
Fit
 ? ?
Hitemp
) for CO at 1000 K. This represents the difference 
between the data sets shown in Figure 3-13. ............................................................ 74 
Figure 3-15: Comparison of CO spectral absorption coefficient between HITEMP and 
data calculated using eqn. 3.3 with fit parameter at 4cm
-1
 resolution: (a) 300 K, (b) 
1000 K....................................................................................................................... 74 
Figure 3-16: Comparison of CO
2
 spectral absorption coefficient at 300 K between 
HITEMP and data calculated using eqn. 3.3 with fit parameters at 0.5 cm
-1
 
resolution: (a) 300K, (b) 1000K................................................................................ 77 
Figure 3-17: Residual (?
Fit
 ? ?
Hitemp
) for CO
2
 at 1000 K.  This represents the difference 
between the data sets shown in Figure 3-16. ............................................................ 77 
Figure 3-18: Comparison of CO
2
 spectral absorption coefficient at 1000 K between 
HITEMP and data calculated using eqn. 3.3 with fit parameters at 4 cm-1 resolution: 
(a) 300K, (b) 1000K.................................................................................................. 78 
Figure 3-19: Comparison of water vapor spectral absorption coefficient between 
HITEMP and data calculated using eqn. 3.3 with fit parameters at 1cm
-1
 resolution: 
(a) 300K, (b) 1000K.................................................................................................. 80 
Figure 3-20: Residual (?
Fit
 ? ?
Hitemp
) for H
2
O at 1000 K. This represents the difference 
between the data sets shown in Figure 3-19. ............................................................ 80 
Figure 3-21: Comparison of C
3
H
8
 spectral absorption coefficient between experiment and 
data calculated using eqn. 3.3 with fit parameters at 1 cm
-1
 resolution: (a) 
Extrapolation, (b) Experiment. ................................................................................. 82 
Figure 3-22: Comparison of C
3
H
8
 spectral absorption coefficient between experiment and 
data calculated using eqn. 3.3 with fit parameters at 1 cm
-1 
resolution: (a) 800K, (b) 
1000K........................................................................................................................ 83 
 
 xi
Figure 3-23: Residual (?
Fit
 ? ?
Experiment
) for C
3
H
8
 at 1000 K.  This represents the 
difference between the data sets shown in Figure 3-22. ........................................... 83 
Figure 3-24: Comparison of (a) CO, (b) Water, and (c) CO
2
 spectral absorption 
coefficient between HITEMP and fitted data at 550 K............................................. 86 
Figure 3-25: Calculated normalized fuel volume fraction of hydrocarbon fuels remaining 
after residence in gas cell as a function of temperature. ........................................... 88 
Figure 3-26: Comparison of the extrapolated and experimentally measured spectral 
absorption coefficient of heptane (C
7
H
16
) for the C-H stretching band at 1000 K. The 
difference between extrapolated (----) and measured (? ) spectrum is due to 
pyrolysis.................................................................................................................... 89 
Figure 4-1: The modeled spectral absorption coefficient of soot. .................................... 97 
Figure 4-2: Planck mean absorption coefficient of CH
4
 (from HITRAN), C
3
H
8
, n-C
7
H
16
, 
and C
3
H
6
 (from fitting and extrapolation of measurements). ................................. 100 
Figure 4-3: Spectral absorption coefficients for C-H bending peaks for methane 
(HITRAN), and propane and heptane (experimental) at 296 K.............................. 101 
Figure 4-4: Planck mean absorption coefficient of methanol, and toluene, methyl 
methacrylate (MMA) (from fitting and extrapolation). .......................................... 103 
Figure 4-5: Spectral absorption coefficient of methanol, toluene and methyl methacrylate 
at room temperature. ............................................................................................... 103 
Figure 4-6: Comparison of Planck mean absorption coefficient for methyl methacrylate 
(MMA) with results from Park et al [14]................................................................ 104 
Figure 5-1: Spectral directional radiation intensity along the flame centerline from flame 
to fuel surface for 0.3 m methanol pool fire. .......................................................... 114 
Figure 5-2: Integrated directional radiation intensity by all species and methanol, and the 
ratio of methanol to all species intensity as a function of height for 0.3 m methanol 
pool fire................................................................................................................... 114 
Figure 5-3: Integrated directional radiation intensity, mole fraction of each species (X
i
), 
and temperature as a function of height for 0.3 m methanol pool fire.................... 115 
Figure 5-4: Spectral radiation intensity of C-H stretching of methanol about 3.4 mm 
(3000 cm
-1
) as a function of height ......................................................................... 115 
 
 xii
Figure 5-5: Comparison of radiation intensity of 0.3 m methanol pool fire calculated by 
temperature dependent and independent methanol absorption coefficient and 
temperature dependent methane absorption coefficient.......................................... 116 
Figure 5-6: Spectral directional radiation intensity along the flame centerline from flame 
to fuel surface for 0.3 m heptane pool fire.............................................................. 119 
Figure 5-7: Integrated directional radiation intensity by all species and heptane, and the 
ratio of heptane to all species intensity as a function of height for 0.3 m heptane pool 
fire. .......................................................................................................................... 119 
Figure 5-8: Spectral directional radiation intensity along the flame centerline from flame 
to fuel surface for 0.3 m heptane pool fire with blackbody intensity as an initial 
condition. ................................................................................................................ 120 
Figure 5-9: Mole fraction of species (X
i
) and soot volume fraction (ppm), and 
temperature as a function of flame height for 0.3 m heptane pool fire................... 120 
Figure 5-10: Comparison of radiation intensity of 0.3 m heptane pool fire calculated by 
heptane and methane absorption coefficients, and by species and blackbody 
emission at 1400 K as boundary conditions. .......................................................... 121 
Figure 5-11: Comparison of spectral radiation intensity of C-H stretching peak about 3.4 
?m (3000 cm
-1
) at heptane pool surface between heptane and methane absorption 
coefficient (Specie emission boundary condition).................................................. 121 
Figure 5-12: Spectral directional radiation intensity along the flame centerline from flame 
to fuel surface for 0.3 m toluene pool fire............................................................... 125 
Figure 5-13: Integrated directional radiation intensity by all species and toluene, and the 
ratio of toluene to all species intensity as a function of height for 0.3 m toluene pool 
fire. .......................................................................................................................... 125 
Figure 5-14: Mole fraction of species (X
i
) and soot volume fraction (ppm), and 
temperature as a function of flame height for 0.3 m toluene pool fire. .................. 126 
Figure 5-15: Comparison of radiation intensity of 0.3 m toluene pool fire calculated by 
toluene and methane absorption coefficients, and by specie emission as a boundary 
condition. ................................................................................................................ 126 
Figure 5-16: Comparison of spectral radiation intensity from 3 to 11 ?m at toluene pool 
surface by toluene and methane absorption coefficient.......................................... 127 
 
 xiii
Figure 5-17: Spectral directional radiation intensity along the flame centerline from flame 
to fuel surface for 0.3 m toluene pool fire with blackbody boundary condition..... 127 
Figure 5-18: Transmissivity of methanol infrared spectrum; (a) gas phase and (b) 
condensed phase from NIST Webbook [58]........................................................... 129 
Figure 5-19: Transmissivity of heptane infrared spectrum; (a) gas phase and (b) 
condensed phase from NIST Webbook [58]........................................................... 129 
Figure 5-20: Transmissivity of toluene infrared spectrum; (a) gas phase and (b) 
condensed phase from NIST Webbook [58]........................................................... 129 
 
 1
 
CHAPTER 1  INTRODUCTION 
1.1  Radiation feedback study in fire 
1.1.1  Background 
Energy to volatilize solid and liquid fuels in fires is transported by conduction, 
convection and radiation. With small fires less than 0.1 m in base diameter, conduction 
dominates the heat transfer to the fuel source, whereas convection tends to dominate for 
fires with diameters between 0.1 and 0.3 m.  Above about 0.3 m, radiation heat transfer is 
typically the largest source of heat feedback to the fuel source [1].  Because of the 
dominance of radiation for large fires, an accurate assessment of radiation absorption 
within the fuel rich core of the fire becomes imperative for assessing heat feedback to the 
fuel source.   
For large fires, radiation dominates external heat transfer to the surroundings as 
well as internal heat transfer to the fuel source. Hamins et al. [2] reported that radiation 
heat transfer provides 96%, 80% and 55% of total heat feedback to the fuel source for 0.3 
m diameter (D) pool fires of toluene, n-heptane and methanol respectively. Because 
external heat transfer from these and large fires are typically dominated by radiation, 
assessment of fire damage depends on accurate models of radiative heat transfer emitted 
from fires, which in turn depends on the flame temperature.  Flame temperature may be 
impacted by the absorption of radiation by both soot and the fuel rich core just above the 
fuel surface in a fire. Since the incident radiative heat flux controls fuel volatilization in 
 
 2
fires, accurate assessment of the effects of gaseous fuel molecules on radiative exchange 
is needed. 
In most previous studies, combustion products such as carbon dioxide (CO
2
), 
water vapor (H
2
O), carbon monoxide (CO) and soot have been the focus of radiative 
transport [3-5]. Studies on the radiative absorption of these molecules have provided 
absorption coefficients over a broad range of temperatures, and one can obtain this data 
through HITEMP [6]. To include contributions of fuels and other decomposition products 
to radiative transport in fires, absorption coefficients for these molecules must be known 
over a broad range of temperatures characteristic of the fuel rich core, from 300 K to 
1000 K [7, 8].  
Many studies incorporating radiative transport in fires or combustion utilize a 
gray gas assumption to calculate radiation attenuation. The gray gas emissivity 
approximation is often based on empirical fits to external radiation intensity 
measurements, e.g., in fires of volatilized plastics [9].  The effective emissivity and 
corresponding absorptivity will vary significantly with flame temperature particularly for 
sooty flames depending on how close the peak of the broadband flame emissions falls 
relative to the strong absorption bands of the vaporized fuel molecules [10].  To date, 
only a few studies have attempted to provide data for assessing the temperature 
dependent absorption coefficients of fuel molecules to temperatures as high as 1000 K.  
Notable studies in this area include the work of Tien and coworkers on hydrocarbon fuels 
and methyl-methacrylate (MMA) [11-14], and Fuss et al. on paraffin hydrocarbons and 
acid gases [15-17].  Difficulties in measuring high-resolution infrared absorption 
coefficients at high temperature arise because of the temperature limitations of most 
 
 3
infrared window materials and issues associated with high temperature vacuum seals. 
This study has been undertaken to build a database for absorption coefficients for several 
hydrocarbon molecules for temperatures up to 1000 K.  Infrared absorption coefficients 
of the hydrocarbons propane (C
3
H
8
), n-heptane (C
7
H
16
), and propylene (C
3
H
6
) were 
measured by Fourier transform infrared spectrometer (FTIR) in a unique experimental 
facility that facilitates measurements to 1000 K.  These measurements are analyzed and 
compared to existing data for methane (CH
4
) in the HITRAN [18] database.   
 
1.1.2 Previous work 
1.1.2.1  Radiation feedback in fires 
A pool fire is a basic experiment to study characteristics of a fire. Application of 
the pool fires experiments includes fire growth in enclosures, such as compartment fires 
[19], tunnel fires [20], smoke management [20-23], fire suppression [20, 24-33], and oil 
tank fires [34-36].  Laboratory scale pool fire experiments are generally up to 1 m [2, 7, 
10, 37, 38].  Several pool fire experiments in outdoors [35, 39] have been conducted so 
far, but the fires were affected by wind and weather, and cannot be correlated with 
predictions of a large pool fire extrapolated from small fire experiment. Although large 
pool fire experiments are necessary to determine the separation distance of oil tanks and 
tactics to extinguish oil tank fire practically, there is unfortunately little information on 
large pool fires.  Computer modeling such as NIST?s fire dynamics simulator (FDS) [40] 
is being developed to study large fires.  Several fire modelers have tried to mimic small 
and large pool fires [41-43]. One of the current problems is that the computer model does 
not predict mass (fuel) evaporation rate well since radiation feedback from flame to fuel 
 
 4
surface is not calculated correctly. Radiation absorption by fuel molecules in the 
relatively cool fuel rich core above the fuel surface plays a significant role in controlling 
the amount of the energy reaching the fuel surface. For example, De Ris [44], Brosmer et 
al. [7], and Novozhilov et al [42]. used a gray gas absorption coefficient to calculate 
energy feedback on pool fire. Hostikka et al. [41] modeled methanol pool fires using 
NIST Fire Dynamics Simulator (FDS) [45] with RADCAL database [46]. Therefore, it is 
very important to resolve the role of fuel absorption on determining thermal energy 
feedback to fuel surface and mass burning rate for fire modeling.  A summary of previous 
studies on energy feedback study on pool fires follows. 
Buckius and Tien [3] first studied the radiation contribution of combustion 
products on monomer-polystyrene (PS, C
8
H
8
), monomer-poly-methylmethacrylate 
(PMMA, C
5
H
8
O
2
), and monomer-polyacetal (PA, CH
2
O) fires. They discovered soot is 
dominant in sooty fires such as PS , soot and product species are important in moderate 
sooty fires such as PMMA, and product species such as carbon dioxide, water, and 
carbon monoxide are dominant in non-sooty fires such as PA. They also found non-
homogeneous and non-gray models predict the relationship between radiance and 
pathlength accurately.  
De Ris [44] investigated energy feedback to a polymer (PMMA, PE, and PS) pool 
surface. He evaluated the validity of three radiation models, such as Hottel?s emissivity 
charts, narrow-band statistical models and wide-band models [47], to predict emissivity 
of non-homogeneous and non-gray path within a fire. He stated that the narrow band 
approach is accurate, but needs expensive computation. The wide band model is 
moderately accurate significantly less computational demand for combustion simulations.  
 
 5
He assumed sooty and moderately sooty fires can use the gray gas radiation absorption.  
However, he first proposed that radiation absorption of vaporized fuel gas on condensed 
surface controls burning rate. He further concluded that it is necessary to develop fuel 
absorption coefficient database to handle the fuel rich core since radiation attenuates 
within the fuel core.  
Modak [48] analyzed absorption coefficient and temperature distribution within 
the fuel rich core of a 0.73 m PMMA pool fire. Cross sectional temperature profiles 
showed a cool fuel rich core near the PMMA surface (from 0.02 m to 0.03 m thick). 
Absorption coefficient near the pool surface significantly increased at the center of the 
pool fire. As the fire size increases, absorption coefficient and species concentration 
within the fire became distributed non-homogeneously. Especially for large fires, non-
isothermal and non-homogeneous conditions should be included to determine the incident 
heat flux to the fuel surface, which is proportional to fuel burning rate, when pool heating 
is ignored or very small. 
Brosmer and Tien [49] assumed two separate zones exist in a fire; a relatively 
cool fuel rich core and a high temperature zone. They used 900 K and a gray absorption 
coefficient for fuel calculated from soot absorption in their fuel core, and 1350 K and the 
gray absorption coefficient of combustion products (CO
2
, H
2
O and soot) as their 
combustion region. Their prediction based on this two region model for mass evaporation 
rate of PMMA had good agreement up to 0.73 m pool diameter. Although their two 
region model predicted the fuel burning rate well, they stated non-isothermal and non-
homogeneous assumptions should be incorporated as the fire size becomes larger. 
 
 6
Hamins et al. [2, 38] measured radial variation of mass burning rate, and radiative 
and net heat flux in pool fires of heptane (C
7
H
16
), toluene (C
7
H
8
), methanol (CH
3
OH), 
and methylmethacrylate (MMA, C
5
H
8
O
2
) with pools up to 0.38 m in diameter.  Radiation 
heat transfer was measured to provide 96%, 80% and 55% of total heat feedback to the 
fuel source for 0.3 m diameter pool fires of toluene, n-heptane and methanol respectively.  
The intensity was distributed uniformly on the pool for toluene, was slightly decreased 
toward to pool edge (approximately 25 % less than at the center) for heptane, and reduced 
gradually quarters of the pool diameter (approximately 25 % less than at the center) and 
significantly dropped toward to the pool edge (approximately 85 % less than at the 
center) for methanol. The highest radiation intensity for all fuels was observed at the 
center of the pool. The paper also concluded that all pool fires with 0.3 m < D < 1 m have 
a small convection effect on energy feedback (< 20 %), and the radiation dominates 
completely the energy feedback to the fuel surface of larger pool fires.   
Gritzo et al. [50] investigated energy feedback of a large JP-8 pool fire (20 m 
diameter) under several wind conditions both experimentally and numerically.  Their 
radiation heat flux distribution and fuel burning rate were affected by wind speed and 
wind induced vortices.  They observed the lowest heat flux region was at the center of 
fuel surface. This is opposite to the result of small-scale fires by Hamins.  As the fire size 
increases, the fuel rich core with soot increased the relatively cold temperature region and 
resulted in the lowest heat flux at the center of the pool.  The lowest heat flux region was 
also shifted by the wind speed from the center toward to the pool edge. The magnitude of 
lowest and highest heat flux increased with wind speed.  The existence of a fuel rich core 
 
 7
region was confirmed by their low wind velocity test, and fuel and soot radiation 
absorption reduced the radiation heat flux on the fuel surface.  
Klassen et al. [37] measured local radiation intensity and transmissivity of small 
toluene pool fire (D = 7.1 cm) as a function of radial and height position using a He-Ne 
laser and two band pass filters.  Based on the intensity and transmissivity measurements, 
they estimated local temperature and soot volume fraction.  Results showed little 
emission near the pool surface at height 1.4 cm and radial distance 40% from the center 
at 2.8 cm from the pool surface.  As the height from the surface increased, the highest 
radiation intensity position shifted closer to the pool center.  They also observed visually 
that soot particles near the pool surface moved up and down with a low frequency motion.  
Soot volume fraction estimated by transmission measurement showed that almost the 
same amount of soot at the flame tip was above the pool surface.  Low emissivity at the 
pool surface suggested that relatively cold soot and toluene fuel vapor absorption were 
blocking the radiation feedback from flame toward fuel surface. 
 Hostikka et al. [41, 51] used NIST?s fire dynamics simulator (FDS) to model 
methanol and heptane pool fires.  Since FDS did not at the time include methanol and 
heptane absorption information, methane absorption data was used instead absorption 
data for the two fuels.  Six and nine separated band models were used to calculate Planck 
mean absorption coefficient, and incorporated into FDS to conduct radiation transport 
calculation.  Fuel burning rate, radiative and convective heat fluxes as a function of pool 
diameter, and temperature distribution within the fire were reported.  The fuel burning 
rate as a function of D showed qualitative agreement, but quantitavely overpredicted it.  
They commented that more absorption information and band models should be 
 
 8
investigated, and more than 20 grid cells should be set within the pool diameter to obtain 
good results. 
Novozhilov and Koseki [42] developed a CFD model including both gas and 
liquid phase interface to calculate fuel burning rates of methanol, heptane, and toluene.  
Their model used a dense mesh at the gas and liquid interface and along the flame 
centerline.  Their modeled data was compared to previous experimental data done by 
Hamins [38], Klassen [8], Janssen [52], and Koseki [53].  The prediction agreed 
qualitatively for mean flame temperature, fuel burning rate of different pool size, 
radiation heat flux on fuel surface, and radiation contribution to total energy feedback 
toward the fuel. The absorption coefficient calculation was done using a simple gray gas 
simple formula including all gases absorption according to Fletcher et al. [20].  Average 
error of a fuel burning rate was about 17%, and toluene fire had the worst discrepancy 
due to strong dependency on soot absorption. 
 
1.1.2.2  Absorption coefficient measurements 
Many researchers have conducted temperature dependent absorption coefficient 
measurements since the 1960?s. Most of the studies in the 1960?s and 1970?s were 
combustion product measurements such as carbon dioxide, carbon monoxide, water and 
methane.  Ludwig?s NASA report summarizes results for the 1970?s [4].  Tien and his 
coworkers made great contributions in the 1980?s on the absorption coefficient 
measurement on fuels such as methane, propylene, acetylene, and methyl-methacrylate 
[11-14]. Their spectral resolution permitted the use of wide band and narrow band models 
 
 9
to optimize line broadening and temperature dependency of infrared spectrum. Their data 
is still used to calculate radiation transport equation in combustion and fire simulations.  
 Grosshandler and his coworkers constructed the narrow band radiation absorption 
coefficient database ?RADCAL? [46] in 1993 based on Ludwig?s report and the date of 
Tien et al.  Current fire modeling programs such as FDS use this program to tabulate 
radiation absorption coefficient as a function of temperature and species concentration.  
HITRAN and HITEMP database [6, 18] edited by Rothman is also currently used to 
calculate absorption coefficients. HITRAN has line-by-line spectral information for 37 
species and its accuracy has been verified with experiments up to 600 K. HITEMP has 
three combustion product species (H
2
O, CO
2
 and CO), with spectral information 
experimentally verified up to 1000 K. The HITEMP database will be used to make a new 
radiation absorption coefficient database for H
2
O, CO
2
 and CO as a part of this thesis 
Tien and his coworkers measured temperature dependent infrared spectra of 
acetylene (C
2
H
2
), methane (CH
4
), propylene (C
3
H
6
), and methyl methacrylate (MMA, 
C
5
H
8
O
2
) [11-14].  They constructed a simple infrared spectrometer with a globar source, 
a chopper, a monochromometer, a gas cell with a temperature controlling furnace, and 
infrared windows. Two combinations of infrared windows were used; Barium Fluoride 
(BaF
2
) and Sodium Chloride (NaCl) windows for short wavelengths, and Potassium 
Bromide (KBr) for long wavelengths. Low-resolution infrared spectra were analyzed by 
both wide and narrow band models to correlate low-resolution data to high resolution 
ones. Their work includes temperature dependent infrared spectra, wide band and narrow 
band fitting parameters, and Planck mean absorption coefficients.  They found that a 
statistical narrow band model with equal spacing (Elasser model) gave good agreement 
 
 10
with high-resolution data for methane. The data are still used to calculated radiative 
transport of fuels 30 years later.  
Fuss et al. measured the infrared spectra of methane (CH
4
) with 4 cm
-1
 resolution 
from 296 K to 900 K [15]. They used an FTIR and a temperature controlled gas cell like 
Tien. Infrared spectra were obtained by the instrument with BaF
2
 windows and 4 cm
-1
 
and 32 cm
-1
 resolution. They investigated the effect of resolution on Elasser?s narrow 
band parameters. They found that band resolution impacts individual narrow band 
parameters, but the results showed that total (integrated) absorptivity did not have a 
strong dependency on spectral resolution. They concluded that resolution dependency 
impacts the modeling the absorptivity of multi component gas mixtures.  Fuss et al. also 
reported temperature dependent ethane (C
2
H
6
), propane (C
3
H
8
) and butane (C
4
H
10
) 
spectra [16], in addition to methane, with the same temperature condition. Universal 
functions on total absorptivity for four fuels as a function of temperature were established 
and correlated with their experiment results. Two formulas for each species were 
distinguished due to optically thin and thick condition. The results showed that total 
absorptivity per unit C-H bond of ethane, propane, and butane were similar, but that of 
methane was about 40% and 60% lower than the other three species at 296 K and 900 K, 
respectively.   
 
1.2  Vibration and rotation infrared spectroscopy principle 
Radiation absorption coefficients for any gas species can be related to molecular 
structure and modes of energy storage in the individual molecules.  A molecule has four 
modes of energy states such as translational, electronic, rotational and vibrational. All 
 
 11
energy modes are quantized, which means that transitions between two discrete energy 
levels shown in Figure 1-1 are associated with absorption or emission of photons at 
particular energy levels of frequency. When the ground energy level of a molecule, say 
E
1
, jumps up to one energy level higher, say E
2
, the molecule absorbs photons with 
certain energy ?E (= E
2 
- E
1
). The same amount of energy ?E is emitted in a photon when 
the higher energy level returns to the original level.  These two processes are called 
?absorption? and ?emission?, respectively.  Absorption and emission from translational 
energy transitions occur at such low energy due to the closely packed nature of the 
energy levels, translational energies do not impact absorption or emission relevant for 
radiative heat transfer.  
 
?E
excitation
(a) (b)
?E
emission
E
1
E
2
E
1
E
2
 
Figure 1-1: Energy transition due to absorption and emission: (a) Absorption and (b) 
Emission. 
 
Induced emission shown in Figure 1-2 is different from the previous emission 
process.  This emission is caused as follows: when the photons from a certain direction 
with the same frequency as quantized energy transition strike (encounter) a molecule with 
an excited energy state, and the molecule emits a photon in the same direction and 
frequency as the stimulating photon.  
 
 12
?E
excitation
?E
emission
?E
stimulation
E
1
E
2
E
1
E
2
 
Figure 1-2: Energy transition due to induced emission. 
 
The theory of vibration and rotational spectroscopy is summarized in Banwell and 
McCash [54], and Modest [47], respectively.  Max Planck introduced Planck constant h 
to relate the energy transition ?E to photon frequency ? (s
?1
). 
?hE =?   (1.1) 
Since the amount of energy due to state transition is different for each electric, rotational, 
and vibrational modes (?E
rot
 < ?E
vib
 < ?E
elec
), a frequency for each mode can be easily 
calculated by eqn. 1.1.  In spectroscopy, wavenumber v  (cm
-1
) and wavelength ? (?m) 
are commonly used to describe an electromagnetic wave. The definition of wavenumber 
and wavelength are: 
 
100100 ?=?=
hc
E
c
v
v   (1.2) 
100
10000
?==
E
hc
v
?   (1.3) 
 
 
 
 13
1.2.1  Vibration with harmonic oscillator model 
A chemical bond between two atoms can be represented to a first approximation 
by a mass-spring system, which gives a harmonic oscillator.  The harmonic oscillator 
potential energy well is parabolic, which only works as a good approximation for 
relatively low energy levels near the ground state shown in Figure 1-3. Since the 
harmonic oscillator assumes that vibration between two atoms in a molecule has 
displacement, for instance a diatomic molecule, the Schr?dinger wave equation is applied 
to calculate vibrational energy between two atoms. Also, a vibrating spring obeys 
Hooke?s law.  Combination of the Schr?dinger and Hooke?s equations gives the 
quantized vibrational energy equation. 
One-dimensional Schr?dinger wave equation for the potential well V(x)=1/2*k(x-
x
0
)
2
 gives  
 
() 0
2
12
2
2
2
=
?
?
?
?
?
?
?+ xkxE
dx
d
?
??
h
  (1.4) 
where  E(x): Total energy for a harmonic oscillator. 
 h : Modified planck constant (=h/2?). 
 ?: Reduced mass. 
 ?(x):  Spatial amplitude of the wave. 
 
The energy level in equation 1.4 serves as an eigenvalue for the differential equation and 
solutions for ?(x) only exist at discrete value of E given by equation 1.5. 
 
 
 14
??
??
?
?
?
?
h
k
h
k
E
?
?
?
?
?
?
+=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+=
?
?
?
?
?
?
+=
2
1
2
1
2
1
2
1
h   (1.5) 
 
where ?: Quantum number (?= 0, 1, 2, 3?.) 
 
 Since the Schr?dinger equation only permits energy transition between two 
adjacent energy levels, so called ?specific selection rule (?? = ?1)?, the vibrational 
energy transition due to absorption and emission is given as: 
 
   ?
????
hEEE
absorption
=?=?
++? 11,
 (1.6) 
   ?
????
hEEE
emission
?=?=?
+?+ 11,
 (1.7) 
 
? = 0
? = 1
? = 2
J= 0
J= 1
J= 3
J= 2
J= 0
J= 1
J= 3
J= 2
?? = 1
?J= +1 ?J= -1
Vibrational transition
Rotational transition
Internuclear separation distance
Energy
E
?=0
E
?=1
E
?=2
?? = 2
x
x=0
Energy
 
Figure 1-3: Potential energy curve for anharmonic oscillator; anharmonic oscillator (? ), 
harmonic oscillator (----). 
 
 15
 
1.2.2  Rotation 
The energy levels of a rigid rotator are assumed to explain rotational motion of a 
diatomic molecule. Two atoms have their own mass m
1
 and m
2
, and fixed separation 
distance from the center of two masses, respectively.  When the diatomic molecule 
rotates about the center of the two masses at a frequency ?
r
, kinetic energy K of the 
rotator is expressed as: 
 
????
2222
22
2
11
2
1
2
1
2
1
rIrmrmK ==
?
?
?
?
?
?
+=   (1.8) 
where I is the moment of inertia and ? is the effective reduced mass. 
 
The Schr?dinger equation for a rigid rotator with polar coordinates ? and ? is  
 
() ()????
???
?
??
,,
sin
1
sin
sin
1
2
2
2
2
2
EYY
I
=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
+
?
?
?
?
?
?
?
?
?
?
?
h
  (1.9) 
 
Solving this partial differential equation gives eigenvalues for E as follows: 
 
()1
2
+= JJ
I
E
rot
h
   (1.10) 
where, J is Rotational quantum number (J=0, 1, 2, 3?). 
 
 
 16
The energy due to absorption and emission between two adjacent rotational energy levels 
(J and J+1) by the selection rule are written as 
 
() () ()121
4
1
2
22
1,
+=+=+=?
+?
JBhJ
I
h
J
I
E
JJabsorption
?
h
   (1.11) 
() () ()121
4
1
2
22
1,
+?=+?=+?=?
?+
JBhJ
I
h
J
I
E
JJemission
?
h
  (1.12) 
 
where B is rotational constant (
I
h
B
2
8?
= ). 
1.2.3 Vibration-Rotation with harmonic oscillator 
Simple rotational transitions for most low-lying states occur at frequencies in the 
microwave region, and they are not as important in radiative heat transfer as vibrational  
transition. However, when a molecule absorbs photons at vibrational transition, rotational 
transition may also be simultaneously induced.  This so-called ?Vibration-Rotation? 
transition plays a significant role for spectral broadening of a vibrational absorption band, 
and impacts the radiation transport calculation. Total energy by vibration and rotation is 
 
()12
2
1
++
?
?
?
?
?
?
+=+ JBhJhEE
rotvib
??    (1.13) 
where, ?=0, 1, 2, 3? and  J=0, 1, 2, 3? 
 
When a molecule absorbs radiation, two combinations of selection rule for vibration-
rotation are considered; (1) (?, J) ?  (?+1, J+1) and (2) (?, J) ?  (?+1, J-1).   
 
 17
Transition energy of selection rules (1) and (2) is expressed in terms of frequency and 
wavenumber as 
For rule (1), 
() ( )12 ++=+? JBhhvEE
rotvib
  (1.14) 
()
()12
0
++=
+?
JBv
hC
EE
rotvib
  (1.15) 
 For rule (2) , 
()BhJhvEE
rotvib
2?=+?    (1.16) 
()
JBv
hC
EE
rotvib
2
0
?=
+?
   (1.17) 
Since typical values of v  and B  are about the order of 10
3
 cm
-1
 and 1 cm
-1
, energy level 
spacing associate with rotational levels is 1/1000 of the vibrational levels shown in 
Figure 1-3. 
 
1.2.4 Vibration with anharmonic oscillator model 
In previous sections, the harmonic oscillator model was introduced to simply 
understand the relationship between molecule motion and energy transition.  However, in 
reality the molecule has anharmonicities because of the non-parabolic nature of the true 
energy well as indicated in Figure 1.3. One potential energy curve for approximations 
anharmonic oscillator transitions is the Morse function as: 
 
( )[ ]
2
exp1 axDE
eq
?=   (1.18) 
 
 
 18
where a is a constant for a particular molecule and D
eq
 is the dissociation energy 
between two atoms. Substituting the potential energy on anharmonic oscillator into 
Schr?dinger equation in eqn. 1.4, vibrational energy on anharmonic oscillator at different 
energy levels is found to be as polynomial form: 
L?
?
?
?
?
?
?
++
?
?
?
?
?
?
+?
?
?
?
?
?
?
+=
ee
vib xxE
32
2
1
2
1
2
1
???    (1.19) 
 
where x
e
 is anharmonic constant (approx. = 0.01) 
This expression gives unequally spaced vibrational energy levels, and the selection rule 
on anharmonic oscillator can expand to K3,2,1 ???=?? .  Each transition ? = 0 ?  1, ? 
= 0 ?  2, and ? = 0 ?  3 is named fundamental, first overtone, and second overtone, 
respectively.  However, the overtones progressively becomes less intense with higher ??. 
 
1.2.5 Vibration-Rotation with anharmonic oscillator 
As for the harmonic oscillator model, the total energy by vibrational and 
rotational mode is expressed as: 
 
rotvibtot EEE +=    (1.20) 
 
Rotational energy for the anharmonic oscillator is  
 
() ( ) ( ) L?+++?+=
3322
111 JJHJJDJJBE rot   (1.21) 
 
 
 19
and the selection rule for this rotational transition is 1?=?J . Substituting rotE  and vibE  
into total energy equation, equation 1.20 becomes: 
 
() () ()LL ?+++?+?
?
?
?
?
?
?
++
?
?
?
?
?
?
+?
?
?
?
?
?
?
+=
3322
32
111
2
1
2
1
2
1
JJHJJDJJBxxE
ee
tot ???  
  (1.22) 
 
Rotational spectrum induced by vibration comes out on both the left from the 
band center (P branch, ?J = -1) and the right from the band center (R branch ?J = +1). 
Rotational-vibrational spectrum (?=0? 1) of HCl is shown in Figure 1-4 as an example, 
which presents the P and the Q branches. 
   
Figure 1-4: Rotational-vibrational spectrum (?=0? 1) of the P and the Q branches of HCl. 
 
P Q 
 
 20
1.2.6  Vibration and rotation of a polyatomic molecule 
When two atoms in a molecule bond have different electronegativity, a dipole 
moment between the two atoms forms due to a charge distribution imbalance. Infrared 
absorption happens if the dipole moment is non-zero, but not if the dipole moment is zero.   
For example, in C-Cl bonds, chlorine has more electronegativity than carbon so chlorine 
plays negative and carbon is positive within a dipole moment. In C-H bonds, carbon 
plays negative and hydrogen is positive. However, homonuclear diatomic molecules like 
H
2
, N
2
, and O
2
 do not have dipoles because nuclei equally attract. One of vibration 
motions of a diatomic molecule CO
2
, also doesn?t have infrared absorption since the net 
dipole vector is zero.    
A polyatomic molecule has 3 (non-linear molecule) and 2 (linear molecule) 
degrees of freedom for rotational, and 3N-6 (non-linear molecule) and 3N-5 (linear 
molecule) degrees of freedom for vibrational modes (where, N is the number of atoms).  
Within the vibrational mode, N-1 is for vibrational stretching and 2N-5 or 2N-4 are for 
vibrational bending.  For example, methane (CH
4
, N=5) has 6 degrees of freedom for 
vibration: three for stretching and also three for bending.  Since the frequency of each 
different bond is unique, the characteristic band group of stretching and bending motion 
of bonds are tabulated and applied to identify the chemical bond and motion within a 
molecule.  
 
1.3  Line broadening 
Theoretical emission or absorption takes place monochromatically at a frequency 
?
0
 obtained by energy transition.  Line distributions cause peaks to occur over a range of 
 
 21
frequencies. Line broadening and overlap, can arise from collision, Doppler and natural 
broadenings.  The width of the distribution is dependent on temperature, pressure 
(population of molecules), and pathlength, and impacts the total amount of energy 
absorbed by a molecule. 
 
1.3.1  Collision broadening 
For fire temperatures up to 2000 K, collision broadening is the most important 
broadening of the three broadenings. Since the molecule is releasing electro magnetic 
waves continuously, molecular collisions disrupt the wave and changes the phase.  
Although the collision doesn?t change the frequency of transition, it changes the phase of 
the electromagnetic wave at a transition frequency.   
An absorption coefficient ?
?
 including collision broadening gives a Lorentzian 
profile with respect to ?, which is expressed by 
 
()
22
0 c
c
v
bvv
bS
+?
=
?
?    (1.23) 
 
where S is line intensity, b
c
 is line half width with a collision broadening, ?
0
 is the center 
of the line spectrum, and ? is an arbitrary wavenumber within the Lorentzian profile.  
The line half width b
c
 is calculated from kinetic theory as 
 
2
1
0
0
0
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
T
T
p
p
bb
cc
    (1.24) 
 
 22
where subscript 0 is standard condition. The line half width of collision broadening 
increases with pressure P, but decreases with temperature.    
 
1.3.2  Doppler and Natural broadening 
Doppler broadening happens at high temperatures (high velocity), and low 
pressures (low probability of collision).  Comparing the frequency of the transition and 
the one due to molecular velocity, a slight shift of frequency happens while the molecule 
is moving in the line of sight, and the Doppler effect results in the broadening of the line 
width spectrum. Doppler broadening has a Gaussian profile due to the molecule velocity.  
Since the lifetime of excitation (10
-4
 to 10
-5
 second) results in a line width on the order of 
10
-7
 cm
-1
, and thus natural broadening is not relevant for radiation absorption calculations. 
 
1.4  Absorption coefficient 
1.4.1 Absorption coefficient theory 
According to the Beer Lambert law, the absorption coefficient, ?
?
, at any 
wavenumber, ?, can be expressed in terms of measurable quantities as 
 
( )
pL
?
?
?
?
ln?
=
 (1.25) 
 
where ?
?
 is the spectral transmittance, p is the partial pressure of the absorbing specie 
(Pa), and L is the measurement path length (m).  From a fundamental perspective [55], 
 
 23
the absorption coefficient is the product of line intensity (S), line shape (g(?-?
0
)) and the 
number of absorbing molecules per unit volume and pressure: 
 
() ?
?
?
?
?
?
????=
T
N
gS
L
296
0
?
??
?
  (1.26) 
 
where ?
o
 is the center of an absorbing line in wavenumber and N
L
 is Loschmidts? number 
(N
L
 = 2.447?10
19
 molecules/cm
3
/kPa at 296 K). For applications at atmospheric pressure 
and moderate temperatures, the Lorentzian line shape is generally applied assuming 
broadening is dominated by collisions; 
 
()
( )
()?
??
??
?
?
22
0
0
p
p
g
+?
=?
  (1.27) 
 
where ?
p
 is the pressure (collision)-broadened line half width: 
 
P
t
n
p
T
296
g
?
?
?
?
?
?
?=
?
.   (1.28) 
 
where P
t
 is the total pressure, g is a broadening parameter (cm
-1
/kPa), and n is the air-
broadened linewidth parameter.  The line intensity (S) corresponds to the product of the 
quantum mechanical probability for the transition and the population difference between 
the initial (absorption) and final (emission) states [10]:  
 
 
 24
10
expexp1
3
8
36
'
2
3
?
?
?
?
?
?
?
?
?
???
?
?
?
?
?
?
?
?
?
?
?
?
?????
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?
?
=
Q
kT
E
g
kT
hc
I
g
g
R
hc
S
l
a
i
l
?
?
?
r
 (1.29) 
 
Here, h and k are the Planck and Boltzmann constants, respectively, c is the speed of light, 
E? is the energy of the lower state, R
r
 is the transition moment, and hc? is the difference 
in energy between the upper and lower states.  The second bracketed term is the quantum 
mechanical transition probability, where g
l
 is the degeneracy of the lower state.  Finally, 
I
a
 is the isotope fraction, g
i
 is the nuclear spin degeneracy, and Q is the rotational 
partition sum. Combining eqns. (1.26) to (1.29) yields: 
 
?k
=
8?
3
?
3hc
? 
? 
? 
? 
? 
? 
???
R
2
l
g
? 
? 
? 
? 
? 
? 
? 
? 
? 
? 
i
?g
a?I
? 1?exp ?
hc?
kT
? 
? 
? 
? 
? 
? 
? 
? 
? 
? 
? 
? 
?
l
g ?exp ?
'
E
kT
? 
? 
? 
? 
? 
? 
?
g
?
?
296
T
? 
? 
? 
? 
? 
? 
n
?
tP L?N
?
296
T
? 
? 
? 
? 
? 
? 
Q?
36
10
? ??
0?()
2
+ g?
296
T
? 
? 
? 
? 
? 
? 
n
?
tP
? 
? 
? 
? 
? 
? 
? 
? 
2
? 
? 
? 
? 
? 
? 
? 
? 
    
        (1.30) 
 
where P
t
 is the total pressure and g is a broadening parameter (cm
-1
/kPa). 
 
1.4.2  Temperature dependence on absorption coefficient 
As temperature increases, absorption coefficients decrease around the band peaks 
but increased broadening due to rotational transitions can cause a rise in the band wings.  
The band peak decreases because the higher vibrational states become more probable 
with higher temperatures. 
 
 25
Spectral absorption coefficient in equation 1.30 at band center has contribution of 
rotational partition function Q, quantum mechanical probability of energy transition, 
probability of lower energy state to higher energy state, collision broadening band width, 
and the number of absorbing molecule decrease absorption band peaks at high 
temperature.  Rotational partition function Q on denominator is proportional to T (m = 2 
rotational degrees of freedom) in a linear molecule and T
3/2
 (m = 3) in a nonlinear 
molecule [18]. For the first exponential term, energy absorption due to the quantum 
mechanical energy transition exponentially decreases, since induced emission 
exponentially increases with temperature. Induced emission happens when the photons 
from a certain direction with the same frequency as quantized energy transition strike 
(encounter) a molecule with an excited energy state.  For the second exponential term, the 
probability of energy absorption from lower energy state to higher energy state also 
decreases exponentially. Since a molecule with highly excited energy state increases with 
temperature. Broadening parameter term and the number of absorbing molecule 
decreases as a function of 1/T. All contributions described above decrease the absorption 
coefficient with temperature.  In contrast, absorption coefficient at band wings increases 
with temperature. This is because the largest population of rotational energy states shifts 
higher as temperature increases, and vibrational energy transition at higher energy states 
?hot bands? happens at high temperature. 
 
1.5  Problem description 
Figure 1-5 shows the temperature and fuel contour plots of a heptane 1m pool fire 
calculated by FDS. The line represents temperature, and the filled plot represents fuel 
 
 26
volume fraction. There is a cool fuel rich core above the fuel surface temperature ranging 
from 400 K to 800 K, which is consistent with Brosmer [7] and Klassen?s [8] condition. 
Radiation is most likely attenuated within this fuel core, and transmitted radiation reaches 
the liquid or solid fuel bed. Since fuel radiation absorption is not well studied, radiation 
properties of fuel species from low temperature to high temperature are needed to 
calculate radiation attenuation within the fuel core. 
Width (m)
0.0
0.2
0.4
0.6
0.8
1.0
0.0 
0.1 
0.2 
0.3 
0.4 
0.5 
0.6 
Fuel Volume
Fraction (mol/mol)
Temperature (K)
0.0
0.90.9
300
800
700
600
500
900
400
Pool 
surface
Flame Centerline
For 1-D Radiation
Transport Calcs.
 
Figure 1-5: Temperature/Fuel contour plot of 1m Heptane pool fire using NIST Fire 
Dynamics Simulator 
 
Table 1-1 is an example of an absorption coefficient database currently used in 
combustion calculations. Previous databases contain combustion product information for 
carbon dioxide, water, and carbon monoxide. However, methane is the only fuel gas in 
the databases. This small gas molecule information is not adequate to calculate radiation 
 
 27
absorption of more complex fuel molecules such as heptane, methanol and toluene. 
Different chemical structure will give differences in radiation absorption characteristics 
compared to methane and ethane.  Additional fuel absorption data is necessary for 
accurate calculations of energy feedback study in fire.   
Table 1-1: An example of an absorption coefficient database currently used in 
combustion calculation 
Moderate accuracy,
low resolution
Accurate, but needs many 
parameters
Key point
Fuel
Combustion 
products
Species
Temperature
Author
Database
N/A
3
Up to 2000K
CH
4
CO
2
,H
2
O, CO, Soot
5
Up to 2000K
Grosshandler (1993)
RADCALHITEMP
CO
2
, H
2
O, CO
Rothman et al.
(2003)
 
 
1.6 Objective and brief summary of the thesis 
The objective of this thesis is to 1) measure infrared spectra of fuel species, namely 
propane (C
3
H
8
), n-heptane (C
7
H
16
), propylene (C
3
H
6
), methanol (CH
3
OH), toluene 
(C
7
H
8
), and methyl methacrylate (MMA, C
5
H
8
O
2
), using a high temperature FTIR test rig 
in a unique experimental facility that enables measurements to 1000 K, 2) develop a 
simple extrapolation technique for absorption coefficient to high temperature, and verify 
the extrapolated results with HITEMP [6] and experimental data using the high 
temperature FTIR test rig, 3) build an absorption coefficient database RADCAL2 with 
the updated data of combustion products from HITEMP and fuels from experiment and 
existing data for methane (CH
4
) obtained from the HITRAN [18] database, and 4) 
 
 28
investigate the contribution of fuel radiation absorption on radiation feedback to the fuel 
surface using line of sight one dimensional radiative transport equation and FDS. 
 A brief summary of this dissertation is given below.  In chapter 2, the 
experimental apparatus used to obtain high temperature FTIR is described.  Thermal 
properties and spectral characteristics of infrared windows are evaluated.  A window 
cooling unit designed and installed in a gas cell is described. Cooling effect on the 
infrared window evaluated by temperature measurement on the windows.  
In chapter 3, infrared spectra of gas and liquid fuel species measured by high 
temperature FTIR apparatus are presented.  Propane, heptane, methanol, toluene, 
propylene and methyl methacrylate (MMA) infrared absorption coefficients are presented 
as a function of temperature up to 1000 K. A simplified extrapolation technique for 
absorption coefficient proposed by Fuss is evaluated by HITEMP database and propane 
spectrum.  Fuel pyrolysis at high temperature is calculated by CHEMKIN AURORA 
using detailed kinetic mechanisms to determine fuel pyrolysis during high temperature 
infrared measurement and thereby influences results. 
In chapter 4, new absorption coefficient database is created.  Combustion 
products absorption coefficient calculated by E-trans with HITEMP, modeling of soot 
absorption, and fuel absorption coefficients as a function of temperature calculated by 
extrapolation and interpolation using simplified extrapolation equation described in 
chapter 3 are shown.  Planck mean absorption coefficient of measured fuels and methane 
from the HITRAN database are calculated and fit to fourth order polynomial of Planck 
mean absorption coefficient as a function of temperature are given. 
 
 29
In chapter 5, contribution of combustion products and fuel for radiation feedback 
to fuel surface are investigated by solving the one dimensional radiative transport 
equation with new absorption coefficient database.   Mole fraction of gas species and soot 
volume fraction are calculated from FDS with old absorption coefficient data, and the 
concentration data are input to solve radiation intensity on fuel surface. The result of 
radiation intensity by new database and RADCAL are compared for methanol, heptane, 
and toluene 0.3 m pool fires. Also, radiation transport at gas and condensed phase 
interface are discussed by comparing infrared spectra of both phases. 
Finally, a summary of this dissertation and future work are presented.   
 
 30
 
CHAPTER 2  EXPERIMENTAL APPARATUS 
2.1 Introduction 
For radiation feedback study in a fire, radiation absorption coefficients of fuels 
from low temperature to high temperature in addition to combustion products are very 
important to understand how radiation attenuates within the fire.  Although absorption 
coefficient of combustion products such as H
2
O, CO
2
, CO and soot have been studied for 
a long time over wide temperature ranges, absorption coefficient for fuels are not well 
known.  Tien and his coworkers [11-14] and Fuss et al. [15, 16] studied hydrocarbons and 
methyl methacrylate. However, Tien?s data, which has been used for more than 20 years, 
are not highly resolved. Updated absorption coefficients of Tien?s fuels and other new 
fuels over a wide temperature range are necessary to model accurate radiation feedback 
within a fire. High-resolution infrared spectrum measurements at high temperature is 
challenging because the infrared windows must keep its transparency to obtain a high 
resolution infrared spectrum over many scans.  In this study, a Fourier transform infrared 
spectrometer with unique window cooling system is developed, in order to accomplish 
high temperature infrared measurement for various fuels. In this chapter, the unique FTIR 
system and gas and liquid fuel absorption coefficient measurement technique is described 
here. 
2.2   Challenges of high temperature absorption measurement 
Transmissivity of infrared window materials along the infrared beam path need to 
be carefully considered in order to take measurements of infrared spectroscopy at high 
 
 31
temperature.  Table 2-1 shows thermal properties of window materials, which are 
commonly used, in infrared spectroscopy.  Many infrared materials lose their optical 
properties from 600 K to 700 K due to oxidation, attack by steam, or thermal degradation. 
Even if the infrared material maintains its transmissivity at high temperature, the material 
cuts off spectral transmissivity at several important band groups. For instance sapphire 
[Figure 2-1 (a)], which is typically used for space engineering, sustains its optical 
transmissivity up to 2000 K, which is applicable for our temperature range of interest. 
However, sapphire cuts off the spectrum below 1700 cm
-1 
(5.6 ?m), which contains 
characteristics band groups of carbon double bonding, aromatic group, bending motion of 
C-H bending motion, etc.  Similarly, quartz is not suitable to be used along our infrared 
beam path, but its high temperature stability makes it suitable for walls and tubes not in 
the optical path.  
Zinc Selenide (ZnSe), chosen as the window in this thesis, has uniform 
transparency at mid- infrared range shown in Figure 2-1 (b) and has low thermal 
expansion. Low thermal expansion can prevent an infrared window from thermal shock 
during furnace cooling.  However, ZnSe can only be used up to 600 K without thermal 
degradation and oxidation, and window-cooling line with inert gas is necessary for higher 
temperatures.  Figure 2-2 shows a comparison between non-oxidized (clean) and oxidized 
ZnSe windows.  The oxidized window changes its color from dark yellow (clean 
condition) to white. As the result of oxidation at high temperature, the window loses its 
optical transparency.  
 
 
 
 32
 
Table 2-1: Thermal properties of typical optical materials adopted from Ref. [56] 
Thermal  
Conductivity
Thermal  
Expansion
Maximum 
Use 
Temp. 
Comments Material 
  
Symbol 
  
mW/cm?K 
?10
-6
/K 
?C   
Sodium chloride NaCl 65 44 400 slightly sensitive to thermal 
shock 
Potassium 
chloride 
KCl 65 36 400   
Potassium 
bromide 
KBr 48 43 300 sensitive to thermal shock 
Calcium fluoride CaF2 97 19 600   
Strontium fluoride SrF2 83 18 ~600   
Barium fluoride BaF2 117 18 500 sensitive to thermal shock 
Sapphire a Al2O3 240 8.4 1700   
Crystal quartz a SiO2 12 11 >1200   
Zirconia ZrO2 ~19 ~9 >1000   
Zinc sulfide ZnS 272 6.4 300   
Zinc selenide ZnSe 180 7.3 300   
Cadmium sulfide CdS 159 4.6 ~200   
Cadmium 
selenide 
CdSe ? 4.9 >200   
Cadmium 
telluride 
CdTe 63 4.5 300 opaque at high temperatures 
Diamond C 23200 0.8 >700   
Silicon Si 1490 4.2 300 opaque at high temperatures 
Silica glasses vSiO2 14 0.6 1070 immune to thermal shock 
 
 
 33
 
(a)
 
(b)
 
Figure 2-1: Spectral transmissivity of infrared materials: (a) sapphire and (b) zinc 
selenide. 
 
 
 
(a)                                                       (b) 
Figure 2-2: Picture of a zinc selenide window (a) clean and (b) oxidized at high 
temperature 
 
 
 34
2.3  Experimental setup 
A Mattson Galaxy 7020 FTIR spectrometer was modified such that the IR beam from 
a globar source passed through the interferometer and was diverted from the internal 
sample compartment and along the axis of an external quartz flow cell.  The flow cell 
was located inside a tube furnace, and the IR beam passed through the cell and into an 
external Mercury Cadmium Telluride (MCT) detector (MI0465, Graseby Infrared).  The 
detected signal fed back to the FTIR, and a Fourier transform was used to generate the 
spectrum.  Winfirst FTIR software by Mattson was used to operate the FTIR and analyze 
the infrared spectrum.  Absorption spectra were measured at 1 cm
-1
 resolution with the 
signal averaged over 128 scans. A diagram and a picture of the experimental setup are 
shown in Figure 2-3 and Figure 2-4.   
The entire optical path, including the spectrometer and external detector chamber was 
purged with N
2
 (99.995 % min. purity) from a liquid nitrogen tank (200 liter) to eliminate 
absorption from ambient water vapor and CO
2
.  The interferometer was equipped with 
corner-cube optics which minimized the effect of sample emission on the transmission 
measurements [57].  This was confirmed by measuring the emission with the source 
blocked from the heated (1000 K) cell containing propane gas, which was found to be 
negligible.  The furnace (Lindberg/Blue M HTF53347C) had three heating zones 
designed to maintain a uniform temperature over the full length (31.75 ? 0.01 cm) of the 
cell (inner diameter = 2.54 cm).  Gas temperatures were measured with K-type 
thermocouples (probe diameter = 0.05 cm o.d.) at the inlet and outlet of the cell.  The set 
point was adjusted to keep the inlet and outlet of gas line temperature within 5 K, which 
was considered acceptable for the purposes of this investigation.  Temperature difference 
 
 35
at inlet and outlet was observed when the furnace temperature was low (400 K, 450 K, 
500 K, and 600 K), and the set point was adjusted by monitoring the temperature on the 
data acquisition system. Before the infrared measurement at a given temperature, the 
furnace and cell condition were stabilized for 30 minutes. This lead time helped to yield a 
stable background spectrum, although the spectrum changed slightly during the 
measurement.  
 The ends of the quartz cell were sealed with zinc selenide (ZnSe) laser grade 
windows (0.3 cm thickness, ISP optics).  Sealing between the ZnSe window and the 
quartz cell was performed using graphite gasket and high tension springs to absorb 
thermal expansion of the materials at high temperature. Although maximum temperature 
for ZnSe is reported to be 600 K [56], the ZnSe window (CVD grade, ISP optics) kept its 
transparency up to 700 K.  To prevent oxidation of the ZnSe, the temperature of the 
windows was kept below about 700 K by directing a jet of N
2
 on the outside of the 
windows as indicated in Figure 2-3.  This cooling permitted high-resolution infrared 
measurement at high temperature with many scans. The pressure inside the cell was 
monitored by an absolute pressure transducer (Omega engineering, PX303-050) and 
regulated to maintain 101 kPa ? 1 kPa during the measurements. 
Convection cooling with nitrogen jet gas from a liquid nitrogen tank (200 liter) on the 
window center was incorporated into the FTIR test rig.  Figure 2-5 shows a picture of the 
cooling line.  Stainless tube (O.D. 1/4?) was welded at on angle of 30 degree to the center 
of a ZnSe window from outside of the gas cell.  After cooling the window, the nitrogen 
pushed out air within beam path of a stainless tube and prevented carbon dioxide and 
water vapor from affecting the infrared spectrum.   
 
 36
Sample
In
Sample
Out
N
2
Cooling In
N
2
Cooling In
Quartz Cell
ZnSe
windows
Out
Out
ZnSe
windows
Sample Stream
Furnace
Sour
ce
De
tector
Thermocouple
L
31.75 ? 0.01 cm
Sour
ce
De
tector
 
Figure 2-3: Diagram of the high temperature test rig. 
  
 
 
 
Figure 2-4: Picture of high temperature FTIR test rig. 
  
 
 
 37
 
Figure 2-5: Picture of experiment setup, Left: Entire setup, Right: Cooling line. 
  
 
To find the proper cooling gas volume flow rate (velocity), K-type thermocouples 
were temporarily installed on the ZnSe window with zirconia?s based adhesive 
(Cotronics Co. Ltd., type: RESBOND 940).  Figure 2-6 shows the picture of temperature 
measurement on the ZnSe window.  In order to verify that this did not affect the gas 
temperature within the gas cell, gas temperature measurement was conducted by 
traversing a K-type thermocouple wire from the inlet to outlet of the gas cell.  Figure 2-7 
shows the gas temperature within the cell and Figure 2-8 shows the inside and outside of 
ZnSe window temperature.  These figures indicate that the cooling system did not affect 
the gas temperature on the streamline within the cell, while keeping the window 
temperature below the temperature limit. However, the temperature on the inside surface 
was lower than gas temperature on the streamline.  There was a small temperature 
gradient.  Temperature gradient effect on absorption coefficient will be discussed in the 
next chapter.  
 
 
 38
 
Figure 2-6: Temperature measurement of a ZnSe window with a K-Type thermocouple. 
 
024681012
0
100
200
300
400
500
600
700
800
900
Te
mp
era
t
ure
 (K)
Distance from inlet of the cell (inch)
 400 K w/ cooling
 400 K w/o cooling
 600 K w/ cooling
 600 K w/o cooling
 800 K w/ cooling
 800 K w/o cooling
 
Figure 2-7: Temperature distribution within a gas cell. 
 
 
 39
300
400
500
600
700
800
900
1000
0 5 10 15 20 25 30
Inside, 400 K
Outside, 400 K
Inside, 600 K
Outside, 600 K
Inside, 800 K
Outside, 800 K
Inside, 1000 K
Outside, 1000 K
Temperature (K)
Velocity (m/s)
 
Figure 2-8: Window temperature as a function of cooling velocity. 
2.4 Window cooling effect on the absorption coefficient 
To estimate the uncertainty of variations in absorption coefficient due to 
temperature variation near the cooled windows, effective absorption coefficients were 
calculated based on the measured axial temperature profile with window cooling and 
compared to the absorption coefficients found assuming a uniform temperature in the gas 
cell.   The analysis was performed using Beer's law for the uniform temperature, which 
can be expressed as Beer?s law of uniform temperature for entire beam path is expressed 
as: 
 
() ( ) ( )PLILI ??= exp0    (3.1) 
 
 
 40
Figure 2-9 shows the elements based on temperature measurement, and Table 2-2 shows 
the temperature used for this uncertainty analysis.  Uniform medium pressure P for each 
element was assumed. Based on this assumption, equation 3.1 can be modified as: 
 
 () ( ) ( )[ ]
2211
2exp0 PLPLILI ?? +?=   (3.2) 
 
where, coefficient 2 on absorption coefficient ?
1
 represents that the same temperature 
gradient near the window for both side is assumed as a result of temperature 
measurement.  Using equation 3.2, HITEMP carbon dioxide data was used to estimate the 
uncertainty of absorption coefficient due to window cooling for 600 K, 800 K and 1000 
K.  
 
0 1.5 30.25 31.75
Pathlength L
L
1
L
2
L
1
Absorption coefficient ?
?
1
?
2
?
1
I
0
I
 
Figure 2-9: Absorption coefficient and pathlength used for uncertainty analysis of 
absorption coefficient due to window cooling. 
 
 41
 
Table 2-2: Temperature used for uncertainty analysis of absorption coefficient due to 
window cooling. 
Element 1 Element 2 Element 1
543 K 600 K 543 K
706 K 800 K 706 K
871 K 1000 K 871 K
600 K
800 K
1000 K
600 K
800 K
1000 K
 
 
 Figure 2-10 shows the error between absorption coefficients for uniform 
temperature and for a temperature gradient due to window cooling.  Carbon dioxide has a 
characteristic peak at about 2350 cm
-1
.  The error shows about + 2 % error is at the band 
center for all temperature, and ? 3.5 % to ? 6 % error at the band wings for 600 K and 
1000 K, respectively. Therefore, the uncertainty of absorption coefficient due to the 
window cooling can be expected within  ? 4 %, ? 5 %, and ? 6 % for 600 K, 800 K, and 
1000 K, respectively.  As the pathlength of uniform temperature increases, the error of 
absorption coefficient decreases.  In other word, a short pathlength results in a huge 
uncertainty on absorption coefficient.   
 
 
 42
2400 2300 2200 2100
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
Uncertainty of absorption coefficient for CO
2
Er
r
o
r (%
)
Wavenumber (cm
-1
)
 600 K
 800 K
 1000 K
 
Figure 2-10: Uncertainty of absorption coefficient for CO
2
 due to window cooling at 600 
K, 800 K, and 1000 K. 
 
2.5 Sample preparation 
2.5.1  Gas fuels 
CP grade (99.0 %) propane (Matheson gas), CP grade  (99.0 %) propylene 
(Matheson gas), and acetylene infrared spectra at temperature ranging from 300 K to 
1000 K were taken (300 K, 400 K, 450 K, 500 K, 600 K, 800 K and 1000 K).  Mixtures 
containing 1000 ? 20 ppm, 2500 ? 50 ppm, and 4000 ? 80 ppm of propane in N
2
 
(99.999% Super Dry), and 15000 ? 300 ppm, 10000 ? 200 ppm, and 5000 ? 100 ppm of 
propylene in N
2
 (99.999% Super Dry) were made by regulating the flow of these gases 
into the cell using mass flow controllers (MKS 1479A, 20 sccm for propane, 200 sccm 
for propylene and 1000 sccm for N
2
).  In order to calibrate the volume flow rate for each 
fuel, a NIST certified volume flow calibrator (Dry Cal DC-Lite, BIOS international Co.) 
Band center
 
 43
was used.  The mass flow controllers were operated by a data acquisition system 
(Strawberry Tree Inc., currently supported by IO Tech Inc.), which continuously 
monitored the concentration, temperature within a gas cell, and pressure of gas line.  The 
diluted gas was introduced into the gas cell, and then out to the exhaust.   
 
2.5.2  Liquid fuels 
Vaporized heptane (99.0 % Mallinckrodt), methanol (99.98 % J.T. Baker), 
toluene (99.999 % J.T. Baker), and methyl methacrylate (MMA, 99.9 %, Aldrich) 
infrared spectra were taken over temperatures ranging from 300 K to 1000 K as well as 
the gas fuel measurement.  Since vaporized liquid fuels have to be supplied continuously, 
a fuel bubbling unit was set up within a lab hood.  Figure 2-11 shows a picture and 
diagram of the fuel bubbler.  Two K-type thermocouples (one for water bath, and the 
other for the fuel bubbler) were installed.  Temperature data measured by a thermocouple 
in the fuel bubbler was used to calculate vapor pressure of fuel.  The vapor pressure of 
each fuel was calculated using the Antoine equation with three parameters obtained by 
NIST web book (http://webbook.nist.gov).  Fuel vapor pressure is expressed by Antoine 
equation as: 
 
()
?
?
?
?
?
?
?
?
+
?=
CT
B
AEBarP
fuel
fuel
0.1     (2.1) 
 
where, T 
fuel
,, A, B, and C are liquid fuel temperature (K), and Antoine parameters for 
each fuels shown in Table 2-3, respectively. 
 
 44
Nitrogen was introduced into the bubbler and mixed with additional nitrogen at 
the mixing point for dilution, then delivered to the gas cell.  Three concentrations shown 
in Table 2-4 were adjusted not to exceed the saturation of transmittance (0% 
transmittance) infrared spectrum. Therefore, the first attempt for each fuel infrared 
measurement was to set the concentration of each fuel at ambient temperature.  The gas 
phase infrared spectrum data on NIST webbook [58] was used to estimate the maximum 
concentration not to saturate the spectral transmissivity 0, and minor adjustment was 
made with the smaller fuel flow mass flow controller.   At least three samples and 
maximum 5 samples were taken for each concentration of fuel and nitrogen mixture to 
verify that the spectrum was stable at each temperature.  Infrared measurements were 
conducted from highest concentration to lowest one. The repeatability of the spectrum 
using low to high concentration and also high to low concentration was checked and both 
orders gave the same result.   
 
 45
N2
Thermocouple
for reference 
temperature using 
Antoine eqn.
Thermocouple
Thermocouple (Water)
Gas Cell
Bubbler
Dilution
Mixing
Fuel
Water
MFC 1
MFC 2
 
Figure 2-11: Picture and diagram of a fuel bubbling device. 
 
Table 2-3: Antoine equation parameters for heptane, methanol, toluene, and methyl 
methacrylate. 
Fuel Temperature (K) A B C 
Heptane 
 (C
7
H
16
) 
299.1-372.43 4.02832 1268.636 -56.20 
Methanol 
(CH
3
OH) 
288.0-256.83 5.20409 1581.341 -33.50 
Toluene 
(C
7
H
8
) 
273.13-297.89 4.23679 1426.448 -45.957 
Methyl 
methacrylate 
(C
5
H
8
O
2
) 
312.3-362.3 5.37785 1945.560 -7.569 
 
 
 
 
 
 
 
 
 
 46
Table 2-4: List of experimental condition for gas and liquid fuels. 
Gas fuels 
Propane
Temperature (K)
295 1000 2500 4000
396 1000 2500 4000
435 1000 2500 4000
513 1000 2500 4000
578 1000 2500 4000
790 1000 2500 4000
1009 1000 2500 4000
Volume Fraction (x 10
-6
)
 
Propylene
Temperature (K)
296 5000 10000 15000
390 5000 10000 15000
444 5000 10000 15000
491 5000 10000 15000
594 5000 10000 15000
793 5000 10000 15000
1003 5000 10000 15000
Volume Fraction (x 10
-6
)
 
 
 
Liquid fuels 
Heptane
Temperature (K)
293 474 985 1554
400 458 951 1500
450 480 982 1564
490 474 964 1561
593 479 992 1588
794 468 952 1389
1000 548 971 1149
Volume Fraction (x 10
-6
)
 
 
Methanol
Temperature (K)
293 1570 2256 2912
396 1590 2323 2935
443 1445 2235 2960
483 1540 2213 2857
570 1574 2286 2904
804 1692 2472 3193
1000 1543 2302 3055
Volume Fraction (x 10
-6
)
 
 
 47
Toluene
Temperature (K)
300 4278 3183 2548
396 3929 3021 2552
440 3446 2666 2340
477 3964 3032 2617
587 3729 3026 2557
795 4021 3043 2627
999 4345 3260 2821
Volume Fraction (x 10
-6
)
 
MMA
Temperature (K)
297 3162 2474 1716
396 3217 2413 1670
441 2978 2330 1600
483 3011 2337 1613
597 3044 2350 1626
803 3324 2551 1746
1014 3596 2767 1883
Volume Fraction (x 10
-6
)
 
 
 48
2.6 Conclusion 
An experimental apparatus for high temperature FTIR measurement was developed.  
Thermal properties and spectral characteristics of infrared windows were evaluated and 
ZnSe were chosen as the infrared window.  A window cooling unit was designed and 
installed in a gas cell to protect the ZnSe windows from oxidation and thermal 
degradation and keep its spectral transmissivity at high temperature.  Cooling effect on 
the infrared window was evaluated by temperature measurement inside and outside of the 
windows by thermocouples, and the necessary cooling velocity on the window was 
determined.  Two mass flow controllers, one for fuel delivery and the other for fuel 
dilution, were installed to supply gas fuels and nitrogen mixture continuously to optical 
cell. In order to investigate an infrared spectrum at gas phase of liquid fuels, a water bath 
was used to vaporize liquid fuels by nitrogen bubbling. A thermocouple in the liquid fuel 
determined the vapor pressure of liquid fuel using the Antoine equation. All 
concentrations of fuel and nitrogen mixture were determined by the ratio of fuel volume 
flow rate to total volume flow rate. 
 
 
 49
 
CHAPTER 3 ABSORPTION DATA ANALYSIS  
3.1 Introduction 
In the previous chapter, the unique high temperature infrared spectrometer and 
measurement technique for gas and liquid fuels were introduced.  In this chapter, infrared 
spectrum of various fuels is first presented for characteristic band groups for each fuel.  
Next, a simplified extrapolation technique of infrared absorption coefficient at high 
temperature from several lower temperatures is introduced. This technique is very useful 
to take an infrared measurement at high temperature (> 700 K), which cannot usually be 
measured by infrared spectrometers, and also for fuels, that are thermally unstable at high 
temperature.  Last, verification of the extrapolation technique using HITEMP database 
and infrared spectra of propane and fuel pyrolysis problem at high temperature are 
presented.   
 
3.2  Gas fuels 
3.2.1  Propane (C
3
H
8
) 
Figure 3-1 shows the absorption coefficient of propane at 296 K, which illustrates a 
typical absorption spectrum for a paraffin hydrocarbon.   The temperature dependent 
normalized blackbody spectral emissive power is also plotted as a function of 
wavenumber to show how characteristic bands of such fuels impacts absorption of 
blackbody radiation for a range of temperatures.  Propane contains a CH
3
- stretching peak 
 
 50
centered at 2960 cm
-1
 and bending peaks at 1460 and 1380 cm
-1
 as well as -CH
2
- 
stretching peaks at 2930 and 2850 cm
-1
, and a bending peak at 1470 cm
-1
.  Figure 3-2 (a) 
and (b) show the spectral absorption coefficient of the propane stretching and bending 
band regions as a function of T.  The plots show the characteristic decline with increasing 
T in absorption coefficients near the band centers and the broadening causing a rise in 
spectral absorption with increasing T near the edges of the band. 
The location of the peak blackbody emission shifts to larger wavenumber (shorter 
wavelength) as T increases as indicated in Figure 3-1.  The low wave number absorption 
bending bands thus have a larger impact on emission and absorption of blackbody 
radiation at low T ? 400 K.  On the other hand for high temperature (T ? 800 K), the 
higher frequency C-H stretching peaks fall nearer to the peaks of blackbody emission and 
thus play the dominant role in fuel-based radiative absorption.  In addition to a decrease 
of absorption coefficient and an increase the height of band wing, the spectrum at high 
temperature looks noisy.  Taine and Soufiani [59] provide a good explanation of infrared 
spectrum at high temperature.  As temperature increases, the probability of energy 
transition between higher energy levels of both vibration and rotation increase. Finally, a 
spectrum at the higher energy level tends to appear clearly. Since a spectrum shows the 
sum of all possible energy transition in a molecule, a spectrum at high temperature 
presents many noisy tiny waves.     
 
 
 51
Wavenumber (cm
-1
)
1000200030004000
Normali
zed Blac
kbod
y
 
Sp
ec
tral 
E
m
i
s
s
i
v
e
 P
ower
 (1
/
c
m
-1
)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Abs
o
rption coef
f
i
c
i
ent
 (Pa
-1
m
-1
)
0.000
0.005
0.010
0.015
0.020
0.025
400 K
800 K
1200 K
 
Figure 3-1: The measured spectral absorption coefficient of propane (C
3
H
8
) at 296 K and 
the temperature dependent normalized blackbody spectral emissive power as a function 
of wavenumber. 
1600 1550 1500 1450 1400 1350 1300
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
Absorpt
ion coef
f
i
cient
 (Pa
-1
m
-1
)
Wavenumber (cm
-1
)
  295 K
  396 K
  578 K
  790 K
 1009 K
 
(a) 
 
 52
3200 3100 3000 2900 2800 2700
0.000
0.005
0.010
0.015
0.020
0.025
A
b
sorption coefficient
 
(Pa
-1
m
-1
)
Wavenumber (cm
-1
)
  295 K
  396 K
  578 K
  790 K
 1009 K
 
Figure 3-2: Measured temperature-dependent spectral absorption coefficient of C
3
H
8
; (a) 
C-H bending and (b) C-H stretching region. 
 
3.2.2 Propylene (C
3
H
6
) 
Figure 3-3 shows the absorption coefficient of propylene at 296 K and the 
temperature dependent normalized blackbody spectral emissive power as a function of 
wavenumber. Propylene has a large set of characteristic band groups such as a bending 
group (1420 cm
-1
), stretching of =CH
2 
(3080 cm
-1
), C-H out of plane bending (1860 cm
-1
), 
C=C stretching (1645 cm
-1
), and =CH
2 
out of plane bending (990 cm
-1 
and 910 cm
-1
), in 
addition to a C-H stretching group (2960 cm
-1
 for CH
3
-).  Propylene?s =CH
2 
out of plane 
bending enhances radiation absorption and emission at lower temperatures.  Figure 3-4 
(a), (b), and (c) show the spectral absorption coefficient of propylene =CH
2 
and C-H out 
of plane bending peaks, and C=C stretching, and C-H in and out of plane bending and 
=CH
2
 stretching peaks as a function of temperature.  
(b) 
 
 53
  
Wavenumber (cm
-1
)
1000200030004000
Normalized Bla
ckbody
 Spectral 
Emiss
i
ve Pow
e
r
 (
1
/cm
-1
)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
A
b
sorpt
i
on coeff
i
ci
ent
 (Pa
-1
m
-1
)
0.000
0.002
0.004
0.006
0.008
0.010
400 K
800 K
1200 K
 
Figure 3-3: The measured spectral absorption coefficient of C
3
H
6
 at 296 K and the 
temperature-dependent normalized blackbody spectral emissive power as a function of 
wavenumber. 
 
 
 
1100 1000 900 800
0.000
0.002
0.004
0.006
0.008
0.010
Absorp
tio
n
 co
efficien
t (Pa
-1
m
-1
)
Wavenumber (cm
-1
)
  296 K
  390 K
  594 K
  793 K
 1003 K
 
(a) 
 
 54
1900 1800 1700 1600 1500 1400 1300
0.0000
0.0005
0.0010
0.0015
0.0020
Ab
sorpti
on
 coe
f
fi
cie
n
t (P
a
-1
m
-1
)
Wavenumber (cm
-1
)
  296 K
  390 K
  594 K
  793 K
 1003 K
 
3200 3100 3000 2900 2800 2700
0.000
0.001
0.002
0.003
0.004
0.005
A
b
s
o
rpt
i
on co
eff
i
cie
n
t (P
a
-1
m
-1
)
Wavenumber (cm
-1
)
  296 K
  390 K
  594 K
  793 K
 1003 K
 
Figure 3-4: The measured temperature dependent spectral absorption coefficient of 
Propylene (C
3
H
6
); (a) =CH
2
 out of plane bending (b) C-H in plane and out of plane 
bending, and C=C stretching and (c) CH
3
- and =CH
2
 stretching. 
(c) 
(b) 
 
 55
 
3.3  Liquid Fuels 
3.3.1  Heptane (C
7
H
16
) 
 
 Figure 3-5 shows the absorption coefficient of n-heptane at 296 K and the 
temperature dependent normalized blackbody spectral emissive power as a function of 
wavenumber. Since both propane and heptane are alkanes and have the same 
characteristic band groups (CH
3
- and -CH
2
-), heptane qualitatively has the same 
absorption characteristic as propane.  Figure 3-6 (a) and (b) show the spectral absorption 
coefficient of the C-H bending and stretching peaks for heptane as a function of 
temperature.  As expected, comparison of Figures 3-3 and 3-5 shows that heptane absorbs 
more radiant energy per unit mole than propane due to the increased number of C-H 
bonds.   Furthermore, heptane, with its increased chain length, has a reduced sharpness in 
the peaks in comparison to propane. 
Wavenumber (cm
-1
)
1000200030004000
Normal
iz
ed
 Bl
ack
b
ody
 Spectral
 
E
m
i
s
s
i
v
e
 Power (1/
c
m
-1
)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Ab
so
rp
tio
n
 co
effi
ci
e
n
t (Pa
-1
m
-1
)
0.00
0.01
0.02
0.03
0.04
400 K
800 K
1200 K
 
Figure 3-5: Measured spectral absorption coefficient of n-C
7
H
16
 at 293 K and the 
temperature dependent normalized blackbody spectral emissive power as a function of 
wavenumber. 
 
 56
1600 1550 1500 1450 1400 1350 1300
0.000
0.001
0.002
0.003
0.004
0.005
Absorption coefficient (
P
a
-1
m
-1
)
Wavenumber (cm
-1
)
  293 K
  393 K
  594 K
  801 K
 1002 K
3200 3100 3000 2900 2800 2700
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
0.040
Absorption co
e
f
f
i
cient
 (Pa
-1
m
-1
)
Wavenumber (cm
-1
)
  293 K
  393 K
  594 K
  801 K
 1002 K
 
Figure 3-6: The measured spectral absorption coefficient of n-heptane; (a) C-H bending 
and (b) C-H stretching. 
 
(a) 
(b) 
 
 57
3.3.2 Toluene (C
7
H
8
) 
Figure 3-7 shows the absorption coefficient of toluene at 296 K and the 
temperature dependent normalized blackbody spectral emissive power as a function of 
wavenumber. This figure shows how characteristic bands of toluene impact absorption of 
blackbody emission. Toluene contains CH
3
- stretching peaks centered at 2940 and 2889 
cm
-1
, bending peaks at 1473 and 1392 cm
-1
, =CH stretching peaks at 3073 and 3046 cm
-1
, 
in-plane bending peaks at 1090 and 1030 cm
-1
, and a strong out of plane bending peak at 
728 cm
-1
, phenyl C=C stretching peaks at 1609 and 1500 cm
-1
, respectively.  Figure 3-8 
(a)-(e) show the spectral absorption coefficient of the toluene =CH out of plane bending, 
in plane bending, CH
3
 bending and phenyl C=C stretching, and CH
3
 and =CH stretching 
band region as a function of temperature, respectively. A phenyl =CH bending motion 
and C=C stretching have the most significant impact on emission and absorption for 
blackbody radiation from low to high temperature.  Stretching motion of CH
3
- for toluene 
at low temperature does not contribute blackbody radiation so much compared to other 
peaks, but the motion becomes important at temperature higher than 800 K. Since the fuel 
rich core temperature generally ranges from the boiling temperature to 900 K, out of 
plane and in plane =CH bending and C=C stretching peaks of toluene molecule causes 
blackbody emission and absorption mainly within the fuel rich core and C-H stretching 
motion does near the flame.    
 
 58
 
Wavenumber (cm
-1
)
1000200030004000
N
o
r
m
al
i
z
ed Bl
ac
kbody
 
Spect
r
al
 
E
m
is
s
i
v
e
 P
o
w
e
r 
(1
/
c
m
-1
)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Absorption coef
f
i
cient (Pa
-1
m
-1
)
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
400 K
800 K
1200 K
 
Figure 3-7: Measured spectral absorption coefficient of toluene (C
7
H
8
) at 300 K and the 
temperature dependent normalized blackbody spectral emissive power as a function of 
wavenumber. 
 
750 740 730 720 710 700
0.000
0.005
0.010
0.015
0.020
Absorp
tion coe
f
ficie
n
t (Pa
-1
m
-1
)
Wavenumber (cm
-1
)
 300 K
 396 K
 587 K
 795 K
 999 K
 
(a) 
 
 59
1100 1080 1060 1040 1020 1000
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
Absorpti
on coeffi
cient (Pa
-1
m
-1
)
Wavenumber (cm
-1
)
 300 K
 396 K
 587 K
 795 K
 999 K
 
1600 1500 1400 1300
0.000
0.001
0.002
0.003
Absorption coeff
i
cient (Pa
-1
m
-1
)
Wavenumber (cm
-1
)
 300 K
 396 K
 587 K
 795 K
 999 K
 
(b) 
(c) 
 
 60
2000 1900 1800 1700
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
Absorpti
on coeffi
cient (Pa
-1
m
-1
)
Wavenumber (cm
-1
)
 300 K
 396 K
 587 K
 795 K
 999 K
 
3200 3100 3000 2900 2800 2700
0.000
0.001
0.002
0.003
0.004
0.005
Ab
sorption coef
ficient 
(Pa
-1
m
-1
)
Wavenumber (cm
-1
)
 300 K
 396 K
 587 K
 795 K
 999 K
 
Figure 3-8: The temperature dependent spectral Planck mean absorption coefficient of 
toluene (C
7
H
8
); (a) phenyl =CH out of plane bending (b) phenyl =CH in plane bending, 
(c) phenyl C=C stretching, (d) overtones of (b) and (e) CH
3
- and =CH stretching. 
 
(d) 
(e) 
 
 61
3.3.3  Methanol (CH
3
OH) 
Figure 3-9 shows the absorption coefficient of methanol at 296 K and the 
temperature dependent normalized blackbody spectral emissive power as a function of 
wavenumber. This figure represents how characteristic bands of methanol impact 
absorption of blackbody emission. Methanol contains CH
3
- stretching peaks centered at 
2981 and 2844 cm
-1
, bending peaks at 1455 and 1345 cm
-1
, an -OH stretching peak at 
3680 cm
-1
, a strong C-O stretching peak at 1033 cm
-1
, and a bending peak at 1470 cm
-1
.  
Figure 3-10 (a)-(d) show the spectral absorption coefficient of the methanol C-O 
stretching, CH
3
- bending, CH
3
- stretching, and ?OH stretching band region as a function 
of temperature, respectively. A C-O stretching motion has the most significant impact on 
emission and absorption for blackbody radiation from low to high temperature.  Other 
motions such as CH
3
- bending and ?OH stretching are very small compared to C-O 
stretching, but CH
3
- stretching motion becomes more important higher than 800 K. 
Although the fuel rich core region of a methanol fire is much thinner than heptane and 
toluene fire, the C-O stretching motion of methanol molecule for blackbody emission and 
absorption occurs near the fuel surface while the CH
3
- stretching motion occurs near the 
flame.    
 
 62
Wavenumber (cm
-1
)
1000200030004000
N
o
r
m
al
i
z
ed Bl
ac
k
body 
Spe
c
t
r
al
 
E
m
i
ssiv
e
 P
o
w
e
r 
(1
/
c
m
-1
)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Absorption coef
f
i
cient (Pa
-1
m
-1
)
0.000
0.005
0.010
0.015
0.020
0.025
400 K
800 K
1200 K
 
Figure 3-9: Measured spectral absorption coefficient of methanol (CH
3
OH) at 293 K and 
the temperature dependent normalized blackbody spectral emissive power as a function 
of wavenumber. 
 
1200 1100 1000 900
0.000
0.005
0.010
0.015
0.020
0.025
A
b
s
o
r
p
ti
on
 c
o
e
f
f
i
ci
en
t 
(P
a
-1
m
-1
)
Wavenumber (cm
-1
)
  293 K
  396 K
  570 K
  804 K
 1000 K
 
(a) 
 
 63
1500 1400 1300 1200
0.000
0.001
0.002
Ab
so
rp
ti
o
n
 co
effi
ci
e
n
t 
(Pa
-1
m
-1
)
Wavenumber (cm
-1
)
  293 K
  396 K
  570 K
  804 K
 1000 K
 
3200 3100 3000 2900 2800 2700
0.000
0.001
0.002
0.003
0.004
0.005
0.006
A
b
s
o
r
p
ti
on
 c
o
e
f
f
i
ci
en
t 
(P
a
-1
m
-1
)
Wavenumber (cm
-1
)
  293 K
  396 K
  570 K
  804 K
 1000 K
 
(b) 
(c) 
 
 64
3800 3750 3700 3650 3600
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
Abs
o
rp
ti
o
n
 co
e
ffi
ci
e
n
t (Pa
-1
m
-1
)
Wavenumber (cm
-1
)
  293 K
  396 K
  570 K
  804 K
 1000 K
 
Figure 3-10: The temperature dependent spectral absorption coefficient of methanol 
(CH
3
OH); (a) C-O stretching, (b) C-H bending, (c) C-H stretching, and (d) O-H 
stretching region. 
 
3.3.4  Methyl Methacrylate (MMA, C
5
H
8
O
2
) 
Figure 3-11 shows the absorption coefficient of methyl methacrylate at 296 K and 
the temperature dependent normalized blackbody spectral emissive power as a function 
of wavenumber. This figure shows how characteristic bands of methyl methacrylate 
impact absorption of blackbody emission. Compared to methanol and toluene, methyl 
methacrylate has more bands. Methyl methacrylate contains CH
3
- stretching peaks 
centered at 2970 and 2864 cm
-1
, bending peaks at 1450 and 1332 cm
-1
, =CH stretching 
peaks at 3114 and 3001 cm
-1
, and out of plane bending peaks at 941 and 1030 cm
-1
, a 
C=C stretching peak at 1651 cm
-1
, a C=O stretching peak at 1748 cm
-1
, and C-O 
stretching peaks at 1202 and 1170 cm
-1
.  Figure 3-12 (a)-(d) show the spectral absorption 
coefficient of the methyl methacrylate =CH
2
 out of plane bending, C-O stretching and 
(d) 
 
 65
CH
3
- bending, C=C and C=O stretching, and CH
3
- and =CH
2
 stretching band region as a 
function of temperature, respectively. C-O and C=O stretching and CH
3
- bending 
motions have the most significant impact on emission and absorption for blackbody 
radiation of methyl methacrylate from low to high temperature.  Stretching motion of 
CH
3
- for methyl methacrylate at low temperature does not contribute the blackbody 
radiation as much compared as other peaks, but the motion increases at temperature 
higher than 800 K. The C-O and C=O stretching motions play an even more important 
role for emission and absorption of blackbody radiation at 800 K. Since the fuel rich core 
temperature generally ranges from the boiling temperature to 900 K, C-O and C=O 
stretching and CH
3
- bending motions of methyl methacrylate molecule occupy regions of 
high blackbody emission and absorption mainly within the fuel rich core, and C-O, C=O, 
CH
3
- and =CH
2
 stretching motions does near the flame. 
Wavenumber (cm
-1
)
1000200030004000
N
o
r
m
al
i
z
ed Bl
ac
k
body
 Spec
tr
al
 
Em
i
s
s
i
v
e
 Power
 (
1
/c
m
-1
)
0.00
0.05
0.10
0.15
0.20
0.25
0.30
Absor
p
tion coef
f
i
cient (Pa
-1
m
-1
)
0.000
0.005
0.010
0.015
0.020
0.025
0.030
400 K
800 K
1200 K
 
Figure 3-11: Measured spectral absorption coefficient of Methyl-methacrylate (MMA, 
C
5
H
8
O
2
) at 297 K and the temperature dependent normalized blackbody spectral emissive 
power as a function of wavenumber. 
 
 66
 
1050 950 850 750
0.000
0.001
0.002
0.003
0.004
0.005
0.006
A
b
sorpt
i
on coeff
i
cient (P
a
-1
m
-1
)
Wavenumber (cm
-1
)
  297 K
  396 K
  597 K
  803 K
 1014 K
 
1500 1400 1300 1200 1100
0.00
0.01
0.02
0.03
Ab
sorp
ti
on
 co
effi
ci
e
n
t
 (P
a
-1
m
-1
)
Wavenumber (cm
-1
)
  297 K
  396 K
  597 K
  803 K
 1014 K
 
(a) 
(b) 
 
 67
1950 1900 1850 1800 1750 1700 1650 1600 1550
0.000
0.005
0.010
0.015
0.020
0.025
0.030
Abso
rp
t
i
on co
ef
ficient (Pa
-1
m
-1
)
Wavenumber (cm
-1
)
  297 K
  396 K
  597 K
  803 K
 1014 K
 
3200 3100 3000 2900 2800 2700
0.000
0.001
0.002
0.003
0.004
0.005
0.006
A
b
so
r
p
ti
o
n
 co
e
ffi
cie
n
t 
(P
a
-1
m
-1
)
Wavenumber (cm
-1
)
  297 K
  396 K
  597 K
  803 K
 1014 K
 
Figure 3-12: The temperature dependent spectral absorption coefficient of methyl 
methacrylate (C
5
H
8
O
2
); (a) =CH
2
 out of plane bending (b) C-O stretching and CH
3
- 
bending (c) C=C and C=O stretching, and  (d) CH
3
- and =CH
2
 stretching. 
 
(c) 
(d) 
 
 68
3.4  Extrapolation technique 
3.4.1  Concept and background 
Absorption measurements at temperatures above 700 K are difficult to make due 
to the thermal properties of infrared transmitting materials.  Materials that transmit well 
in the infrared are generally not sufficiently robust to characteristic bands of methanol 
impact absorption of blackbody emission.  One way to circumvent these limitations is to 
extrapolate the data collected at lower temperatures.  This extrapolation technique was 
developed by Fuss and Nyden, and Wakatsuki [60].  The focus of this investigation, 
therefore, was to develop a semi-quantitative method to extrapolate absorption coefficient 
data, obtained for temperatures up to about 700 K, to the higher temperatures 
(approaching 1000 K) that are required to describe the transfer of radiation between the 
flame zone and fuel-rich core in fires.     
The approach taken in this study was to simplify a quantum mechanical 
expression of general absorption coefficient described in eqn. 1.30 at chapter 1 to a form 
suitable for fitting the absorption coefficients measured over a range of temperatures. 
This was achieved by reducing eqn. 1.30 to an expression containing three fit parameters 
(S
0
, E?, and ? ) and two variables (? and ?).  The values of the absorption coefficients at 
higher temperatures, which are difficult to measure, can then be estimated by 
extrapolation. 
Recall, absorption coefficient is expressed as 
 
 69
()
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?+???
?
?
?
?
?
?
?
?
??
?
?
?
?
?
??
?
?
?
?
?
?
?
?
???
?
?
?
?
?
?
?
?
?
?
?
?
???
?
?
?
?
?
?
?
?
?
?
?
?
??
?
?
?
?
?
?
?
=
2
2
0
36
'
2
3
296
10
296296
expexp1
3
8
P
T
gQ
T
NP
T
g
kT
E
g
kT
hc
I
g
g
R
hc
k
t
n
Lt
n
l
a
i
l
?
?
?
?
?
?
?
  (1.30) 
 
The terms with negligible temperature or frequency dependence were consolidated into 
S
0
 as indicated in eqn. (3.3). 
 
?
?
?
?
?
?
?
?
?
?
???
????
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
=
?
2
361
2
2
0
10
296
3
8
m
t
n
L
l
a
i
l
T
Q
P
g
N
g
I
g
g
R
hc
S
?
    (3.3) 
 
In the denominator, it includes all but T
m
 and the temperature dependence of the partition 
sum Q.  The rotational partition function is presumed to be proportional to T (m = 2 
rotational degrees of freedom) in a linear molecule and T
3/2
 (m = 3) in a nonlinear 
molecule.  With this in mind, all powers of T that were not contained in the exponential 
terms were included in the temperature exponent, n.  Including the temperature 
dependency on the number of absorbing molecule and rotational partition function, the 
constraint of power n was set from 0 to 2.  As a first approximation, the explicit 
contributions from overlapping rotational lines are ignored by setting ? = ?
0
 so that the 
effects of the Lorentzian line shape functions are effectively subsumed into the S
0
 and T
n
 
terms.  Since the temperature dependence of each rotational transition is unique, this 
approximation is likely to result in larger errors when the resolution of the measurements 
 
 70
is not sufficient to differentiate between the individual lines.  After substituting E? = hc?
r
 
= 1.439 ?
r
 for the energy of the lower state, eqn. (1.30) becomes: 
 
 
T
S
k n
r
TT
?
?
?
?
?
?
?
? ?
??
?
?
?
?
?
?
?
?
?
?
?
? ?
????
=
?
?
?
?
439.1
exp
439.1
exp1
0
 (3.4) 
 
In this expression temperature, T (K), and wavenumber, ? (cm
-1
), are independent 
variables and the parameters S
0
, ?
r
, and n were fit over a range of temperatures at each 
wavenumber. 
Equation 3.4 ignores minor temperature dependencies of some terms in the full 
quantum expression by lumping them into a constant S
0
, but provides a reasonable 
approximation to the full equation with respect to temperature.  The three parameters S
0
, 
?
r
, and n are optimized using a least squares approach to fit measured spectral absorption 
data such that ?
?
 can be extrapolated and interpolated for any range of temperatures.  The 
fits do very well at capturing the falloff with temperature of the various absorption bands, 
but have limited accuracy for the wings of strong bands where slight increases in ?
?
 with 
temperature can arise due to line broadening at high temperatures.  However, the wings 
typically account for very small amounts of the total integrated ?
p
 and thus the fitted 
equations provide sufficiently accurate values for ?
?
?s to use, and for finding ?
p
 as a 
function of T. 
 
 
 71
3.4.2 Verification 
3.4.2.1  HITEMP database 
Absorption data for CO, CO
2
, and H
2
O were obtained for temperatures up to 1000 
K from the HITEMP database [6].  HITEMP is the high temperature extension of the 
HITRAN database, which is compilation of molecular line absorption data for 39 species 
[18].  The accuracy of the spectra derived from the HITEMP database for applications to 
combusting systems at temperatures exceeding 1000 K has already been examined by 
others [61].  The parameters (S
o
, ?
r
, ? ) were fit to eqn. 3.3 for absorption coefficients 
obtained from the database at 300 K, 400 K, 450 K, 500 K, and 600 K.  Using these 
parameters, an extrapolation was performed to 1000 K and comparisons were made to 
absorption coefficients calculated from spectra generated directly from the HITEMP 
database at 1000 K. As a first attempt, the accuracy of the extrapolation procedure was 
examined without introducing complications due to experimental errors. This exercise 
provides an estimate of the magnitude of the errors resulting from the simplifications 
introduced in representing eqn. 1.30 by eqn. 3.4. 
The accuracies of the extrapolations are assessed according to eqn. 3.6.  The 
relative errors are determined by taking the ratio of the difference between the integrated 
absorption coefficients obtained from the extrapolations and the ?actual? values obtained 
(either from HITEMP for CO, H
2
O, and CO
2
 or experimental spectra for C
3
H
8
) and 
dividing by the ?actual? values.   
 
()
() ()
()
100% ?
?
??
?
=
?
??
?
?
?
?
?
?
??
????
d
dd
Error
ExperimentorHITEMP
ExperimentorHITEMPFit
(3.6) 
 
 72
 
3.4.2.2  Carbon Monoxide 
Parameters were fit for the R branch of the 4.7 ?m CO band, over the range from 
2150 cm
-1
 to 2270 cm
-1
.  The data were generated at a resolution of 1 cm
-1
, resulting in an 
average spacing of 0.482 cm
-1
.  This was sufficiently high that the individual lines in the 
band were resolved.  Figure 3-13 (a) is a comparison of the extrapolated absorption 
coefficient from eqn. 3.5 to the one from HITEMP at 300 K.  The difference in the 
integrated absorption between the original and fit data, obtained from eqn. 3.6, is less 
than ?0.1 %.  The small error is expected because the reference spectrum was included in 
the training set.  In Figure 3-13 (b), however, the extrapolated absorption coefficients are 
compared to the HITEMP data at 1000 K, which is 400 K above the highest temperature 
spectrum used in the fitting procedure. The difference in the integrated absorbance at this 
temperature is still only 3.6 %.  While this agreement may be a little misleading because 
there is clearly a cancellation of errors, the magnitudes of the residuals (Figure 3-14) are 
on average at least an order of magnitude smaller than the absorbance values. 
The spectra of heavier molecules are not as well resolved at elevated temperatures 
as is the CO spectrum shown in Figure 3-15.  Closely spaced broadened lines will, in 
effect, smear out distinguishable line structure.  Since this is the case for many fuels, it is 
important to investigate the effect of reducing the resolution on the accuracy of the 
extrapolations.  Figure 3-15 (a) and (b) compare the extrapolated absorption coefficients 
and HITEMP data at 1000 K and 4 cm
-1
 resolution.  At this resolution, the CO line 
structure is gone and the band appears as a continuous absorption.  The fit procedure was 
carried out using these data with similar results as the higher resolution case.  The 
 
 73
integrated absorbance at 1000 K using the fit parameters differed from the HITEMP data 
by only ?0.28 %.  The errors in the temperature extrapolations for CO appear to remain 
small for de-resolving the spectrum even though the contributions from overlapping 
rotational lines were not explicitly accounted for in the derivation of Eqn. 3.4.   
Wavenumber (cm
-1
)
2150217021902210223022502270
Absor
p
tion coef
f
i
ci
ent (
P
a
-1
 
m
-1
)
0.000
0.002
0.004
0.006
0.008
0.010
Fit
HITEMP
(a)
 
Wavenumber (cm
-1
)
2150217021902210223022502270
Abs
o
r
p
t
i
on c
oeff
i
c
i
ent
 (
P
a
-1 
m
-1
)
0.0000
0.0004
0.0008
0.0012
0.0016
0.0020 Fit
HITEMP
(b)
 
Figure 3-13: Comparison of CO spectral absorption coefficient between HITEMP and 
data calculated using eqn. 3.3 with fit parameters at 1cm
-1
 resolution: (a) 300K and (b) 
1000K. 
 
 74
 
Wavenumber (cm
-1
)
2150217021902210223022502270
R
e
si
dual (Pa
-1 
m
-1
)
0.0000
0.0004
0.0008
0.0012
 
Figure 3-14: Residual (?
Fit
 ?  ?
Hitemp
) for CO at 1000 K. This represents the difference 
between the data sets shown in Figure 3-13. 
 
 
Wavenumber (cm
-1
)
2150217021902210223022502270
A
b
sor
p
ti
on c
oeff
i
c
i
ent
 (
P
a
-1
 
m
-1
)
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
0.0030
Fit
HITEMP
(a)
 
 
Wavenumber (cm
-1
)
2150217021902210223022502270
Absor
p
ti
on coef
f
i
ci
ent (Pa
-1
 
m
-1
)
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
Fit
HITEMP
(b)
 
Figure 3-15: Comparison of CO spectral absorption coefficient between HITEMP and 
data calculated using eqn. 3.3 with fit parameter at 4cm
-1
 resolution: (a) 300 K, (b) 1000 
K. 
 
 75
 
3.4.2.3  Carbon Dioxide 
The accuracy of the extrapolation method for the 4.3 ?m band in CO
2
 over the spectral 
range 2250 cm
-1
 to 2350 cm
-1
 (P branch) was also examined.  The procedure was carried 
out using data at two resolutions: 0.5 cm
-1
 and 4 cm
-1
, resulting in average data spacing of 
0.241 cm
-1
 and 1.93 cm
-1
, respectively.  The HITEMP and fit data at 300 K and 0.5 cm
-1 
resolution are compared in Figure 3-16 (a).  In this case the difference in the integrated 
absorption coefficient was ?2.1 %, compared with ?1.1 % at 4 cm
-1
 resolution.  At 1000 
K, the difference at 0.5 cm
-1
 resolution was only ?0.7 %.  The HITEMP and fitted spectra 
are compared in Figure 3-16 (b).  While the error in the integrated absorbance is small, a 
frequency resolved comparison, as indicated by the residual spectrum in Figure 3-17, 
does reveal a small, but noticeable systematic error between 2270 cm
-1
 and 2300 cm
-1
.  
At 4 cm
-1
 resolution (and 1000 K), the difference in the integrated absorption coefficient 
at 1000 K is 1.3 %.  The discrepancies are apparent in the comparison shown in Figure 
3-18.   
A summary of the integrated and residual RMS errors for the extrapolations of the 
HITEMP data is presented in Table 3-1.  Chu et al. [62] report uncertainties on the order 
of 2 % - 3 % for the measurement of absorption coefficients in the NIST Quantitative 
Infrared Database.  Additionally, their study reports that line intensity variations on the 
order of ? 10 % can frequently be found in comparisons of quantitative reference spectra.  
Although the cancellation of positive and negative errors makes it difficult to discern a 
pattern in the discrepancies between the integrated absorption coefficients obtained from 
direct calculation and the extrapolation, it does appear that the RMS errors grow more 
 
 76
rapidly with temperature in the extrapolations from the lower resolution spectra.  
However, in either case, the errors in the extrapolations are comparable to the 
experimental uncertainties reported by Chu. 
 
Table 3-1: Summary of errors in the HITEMP extrapolations. 
Error in integrated 
values 
RMS of the 
residual 
Molecule 
(resolution) 
Reference 
Data 
Integration 
Range (cm
-1
)
300 K 1000 K 300 K 1000 K
CO (1 cm
-1
) HITEMP 2150 ? 2270 -0.1 % 3.6 % 1.33 E
-3
 1.11 E
-3
CO (4 cm
-1
) HITEMP 2150 ? 2270 0.3 % -0.3 % 2.04 E
-4
 1.10 E
-3
H
2
O (4 cm
-1
) HITEMP 3500 ? 4000 -0.02 % 3.6 % 2.09 E
-3
 4.85 E
-3
CO
2
 (0.5 cm
-1
) HITEMP 2250 ? 2350 -2.1 % -0.7 % 3.06 E
-2
 1.45 E
-2
CO
2
 (4 cm
-1
) HITEMP 2250 ? 2350 -1.1 % 1.3 % 1.36 E
-2
 1.18 E
-1
 
 
 
 
Wavenumber (cm
-1
)
225022702290231023302350
Absorption coef
f
i
ci
ent (
P
a
-1
 
m
-1
)
0.000
0.005
0.010
0.015
0.020
0.025
0.030
0.035
Fit
HITEMP
(a)
 
 
 77
Wavenumber (cm
-1
)
225022702290231023302350
Ab
sorptio
n
 coe
f
f
icien
t (Pa
-1 
m
-1
)
0.000
0.003
0.006
0.009
0.012
0.015
0.018
Fit
HITEMP
(b)
 
Figure 3-16: Comparison of CO
2
 spectral absorption coefficient at 300 K between 
HITEMP and data calculated using eqn. 3.3 with fit parameters at 0.5 cm
-1
 resolution: (a) 
300K, (b) 1000K. 
   
 
 
 
 
Wavenumber (cm
-1
)
225022702290231023302350
R
e
si
dual
 (
P
a
-1 
m
-1
)
-0.005
0.000
0.005
0.010
0.015
 
Figure 3-17: Residual (?
Fit
 ? ?
Hitemp
) for CO
2
 at 1000 K.  This represents the difference 
between the data sets shown in Figure 3-16. 
 
 
 
 78
Wavenumber (cm
-1
)
225022702290231023302350
Absorption coef
f
i
cient (
P
a
-1
 
m
-1
)
0.000
0.004
0.008
0.012
0.016
0.020
Fit
HITEMP
(a)
 
 
Wavenumber (cm
-1
)
225022702290231023302350
Absorpti
o
n
 c
oef
f
i
ci
e
n
t (Pa
-1
 
m
-1
)
0.000
0.002
0.004
0.006
0.008
0.010
Fit
HITEMP
(b)
 
Figure 3-18: Comparison of CO
2
 spectral absorption coefficient at 1000 K between 
HITEMP and data calculated using eqn. 3.3 with fit parameters at 4 cm-1 resolution: (a) 
300K, (b) 1000K. 
 
 79
3.4.2.4  Water vapor 
Parameters were fit to lines in the 2.7 ?m water band, over the range between 
3500 cm
-1
 ? 4000 cm
-1
. The temperatures used were the same as those in the CO case.  
The water absorption data was generated from the HITEMP database at a resolution of 4 
cm
-1
, resulting in an average data spacing of 1.93 cm
-1
.   At this resolution, most of the 
line structure is still visible in this band.  Figure 3-19 (a) is a comparison of extrapolated 
absorption coefficient from Eqn. 3.4 to the one from HITEMP at 300 K, using the 
parameters generated in the fit.  The error from the fits at 300 K was comparable to the 
fits at 300 K for CO.  The difference in the integrated absorbance was -0.02%.  Again, a 
small error is anticipated because the parameters were fit to data at this temperature.  
However, the comparison is still favorable at 1000 K, where the difference in the 
integrated absorbance is only 3.6%.  This result is shown in Figure 3-19 (b).  The 
residuals are shown as a function of wavenumber in Figure 3-20. 
 
3.4.3 Experimental data 
3.4.3.1  Propane 
Figure 3-21 shows how the absorption coefficient for propane varies with 
temperature. The band broadens with increasing temperature as higher energy rotational 
states become populated.  Furthermore, the peak absorption drops by more than an order 
of magnitude from 300 K to 1000 K.  These changes in the shape and intensity of the 
absorption band are captured in the extrapolations. 
 
 80
Wavenumber (cm
-1
)
350036003700380039004000
Absor
p
tion coef
f
i
cient (
P
a
-1 
m
-1
)
0.0000
0.0004
0.0008
0.0012
0.0016
0.0020
Fit
HITEMP
(a)
 
 
Wavenumber (cm
-1
)
350036003700380039004000
Absorpti
on coef
f
i
cient (Pa
-1
 
m
-1
)
0.00000
0.00008
0.00016
0.00024
0.00032
0.00040
Fit
HITEMP
(b)
 
Figure 3-19: Comparison of water vapor spectral absorption coefficient between 
HITEMP and data calculated using eqn. 3.3 with fit parameters at 1cm
-1
 resolution: (a) 
300K, (b) 1000K. 
 
Wavenumber (cm
-1
)
350036003700380039004000
R
e
s
i
dual (Pa
-1
 
m
-1
)
-0.00010
-0.00005
0.00000
0.00005
0.00010
 
Figure 3-20: Residual (?
Fit
 ? ?
Hitemp
) for H
2
O at 1000 K. This represents the difference 
between the data sets shown in Figure 3-19. 
 
 81
  
The extrapolated absorption coefficients at (a) 800 K and (b) 1000 K are 
compared to the corresponding experimental values in Figure 3-22.  Although there is at 
least qualitative agreement, a more detailed comparison reveals that the extrapolations 
retain more structure at high temperature and underestimate the absorbance at the wings 
of the bands.  The residuals at 1000 K are shown as a function of wavenumber in Figure 
3-23.  The fine structure apparent in the extrapolations is presumably an artifact resulting 
from the retention of structure in the fit parameters, which are based on measurements at 
lower temperatures.  The discrepancy at the band wings is probably due to the inability of 
the extrapolations to capture the effects of ?hot bands?, corresponding to vibrational 
transitions that are not populated at the lower temperatures used in determining the fitting 
parameters. The accuracy of the extrapolations is better for frequencies in the vicinity of 
the band center (Table 3-2).  These deficiencies in the extrapolation technique lead to 
errors in the integrated absorption coefficients at 800 K and 1000 K ranging from ?20% 
to ?12 % These deficiencies in the extrapolation technique lead to errors in the integrated 
absorption coefficients at 800 K and 1000 K ranging from ?20% to ?12 %, which 
accounts for the decomposition of propane at 1000K. Based on calculations using the 
CHEMKIN AURORA [63] with the University of California, San Diego, chemical-
kinetics model [64], the decomposition of propane is negligible at 800 K and about 8.8 % 
at 1000 K.  
 
 
 
 
 82
Wavenumber (cm
-1
)
270028002900300031003200
Abs
o
r
p
ti
on c
oef
f
i
c
i
ent (
P
a
-1
m
-1
)
0.000
0.005
0.010
0.015
0.020
0.025
1000K
800K
600K
450K
300K
Extrapolation
(a)
 
 
Wavenumber (cm
-1
)
270028002900300031003200
Abso
rp
tion coe
f
f
i
cie
n
t (Pa
-1
m
-1
)
0.000
0.005
0.010
0.015
0.020
0.025
1000K
800K
600K
450K
300K
Experiment
(b)
 
Figure 3-21: Comparison of C
3
H
8
 spectral absorption coefficient between experiment and 
data calculated using eqn. 3.3 with fit parameters at 1 cm
-1
 resolution: (a) Extrapolation, 
(b) Experiment. 
 
 
 
 83
Wavenumber (cm
-1
)
270028002900300031003200
Absorpti
on coef
f
i
ci
ent (Pa
-1
m
-1
)
0.000
0.001
0.002
0.003
0.004
Extrapolation
Experiment
(a)
 
 
Wavenumber (cm
-1
)
270028002900300031003200
A
b
sorpt
i
on coe
f
f
i
cie
n
t (P
a
-1
m
-1
)
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
Extrapolation
Experiment
(b)
 
Figure 3-22: Comparison of C
3
H
8
 spectral absorption coefficient between experiment and 
data calculated using eqn. 3.3 with fit parameters at 1 cm
-1 
resolution: (a) 800K, (b) 
1000K. 
    
 
Wavenumber (cm
-1
)
270028002900300031003200
R
e
si
dual (Pa
-1
 
m
-1
)
-0.0006
-0.0003
0.0000
0.0003
0.0006
 
Figure 3-23: Residual (?
Fit
 ? ?
Experiment
) for C
3
H
8
 at 1000 K.  This represents the 
difference between the data sets shown in Figure 3-22. 
 
 84
  
 
 
Table 3-2: Errors in the integrated absorption coefficients for propane at 1 cm
-1
 resolution. 
Integrated Absorption 
Coefficient (1/Pa/m) 
Upper: Extrapolation 
Lower: Experiment 
Error in integrated values 
(%) 
Integration 
Range (cm
-1
) 
300 K 800K 1000 K 300 K 800K 1000 K 
0.027 0.022 0.020 2700 ?2850 
(Right Wing) 0.025 0.037 0.033 
6.5 -41.1 -40.8 
0.656 0.324 0.244 2850 ? 3050 
(Band Center) 0.703 0.385 0.255 
-6.7 -15.9 -4.3 
0.015 0.013 0.011 3050 ? 3200 
(Left Wing) 0.013 0.027 0.026 
18.5 -53.7 -59.0 
 
 
 
 
 
3.4.4  Application of extrapolation technique 
 
The simple extrapolation method has great advantage in that absorption 
coefficient data can be extrapolated to high temperature, which is difficult to measure. It 
can also be calculated at any arbitrary temperature.  
Figure 3-24 shows the comparison between fitting and HITEMP data of carbon 
monoxide, water vapor and carbon dioxide at 550 K. From the figures and errors in the 
table, the simplified extrapolation equation is seen also to work well to calculate 
absorption coefficient at any arbitrary temperature.  
 
 
 85
Wavenumber (cm
-1
)
22002205221022152220
Absorption coefficient (Pa
-1
m
-1
)
0.0000
0.0005
0.0010
0.0015
0.0020
0.0025
0.0030
0.0035
Fit
HITEMP
 
Wavenumber (cm
-1
)
38603880390039203940
Absor
p
tion
 coe
ffici
ent (Pa
-1
m
-1
)
0.0000
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
Fit
HITEMP
 
 
(a) 
(b) 
 
 86
Wavenumber (cm
-1
)
23002305231023152320
Absorption c
oeffic
i
ent (Pa
-1
m
-1
)
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
0.018
Fit
HITEMP
 
Figure 3-24: Comparison of (a) CO, (b) Water, and (c) CO
2
 spectral absorption 
coefficient between HITEMP and fitted data at 550 K 
 
Table 3-3: Errors of the integrated absorption coefficients in the HITEMP fitting at 550 K. 
0.3
CO
0.3
H
2
O
0.8Error (%)
CO
2
550 K
 
 
 
3.4.4.1 Effect of fuel pyrolysis 
 
Because the current study explored very high temperatures both experimentally and 
with fit extrapolations, it is important to consider how fuel pyrolysis influenced the 
measurements and subsequent calculations for Planck mean absorption coefficient. 
Pyrolysis of the fuels of interest were calculated using the Aurora program in CHEMKIN 
[63] for temperatures up to 1800 K.  
(c) 
 
 87
Figure 3-25 shows results of the normalized volume fraction for the fuels. The 
chemical kinetics model was based on the UC San Diego, chemical-kinetics model for 
propane, heptane, methanol [64] and MIT model for toluene [65].  The experimental cell 
conditions with the calculated residence times (ranging from 15 s at 300 K down to 
around 3 s at 1000 K) were input into Aurora [63] and pyrolysis of each species within 
the cell was calculated. Figure 3-25 shows that heptane begins pyrolyzing at about 900 K, 
and is about 77% degraded at 1000 K.  Figure 3-26 compares the heptane infrared 
spectrum obtained by experiment and the extrapolation at 1000 K.  The extrapolated data 
was obtained by using the simplified extrapolation technique [60]. It was assumed that no 
fuel pyrolysis occurred at any temperature. This plot indicates that significant heptane 
pyrolysis has occurred at 1000 K, which is consistent with the results from Ref. [63]. For 
the other species, pyrolysis of methane, propane, and propylene begins at 1200 K, 900 K 
and 950 K, respectively.  Radiation calculations using Planck mean absorption 
coefficients above a fuel?s pyrolysis temperature should be modified to account for fuel 
pyrolysis. 
In general, the measurements suggest that the significance of various fuel species 
absorption in a fire will in part depend on the temperature character of the radiation.    
Since 800 K is not atypical for internal temperatures of large fires, it is clear that detailed 
radiative transport calculations including temperature effects may be necessary to resolve 
heat feedback to fuel sources.    
Another important question regarding radiation feedback involves the question of fuel 
pyrolysis products and how they impact overall absorption.  In this regard, propylene and 
methane are interesting molecules as both can be prominent pyrolysis products during the 
 
 88
breakdown of larger hydrocarbons such as heptane.  In fact two C
3
H
6
 molecules plus one 
CH
4
 molecule has the same number of C?s and H?s as C
7
H
16
, and at least at high 
temperature (T > 800 K), the sum of Planck mean absorption coefficients for the smaller 
molecules is only slightly higher than that of the larger heptane molecule.   At lower 
temperature (T < 600 K), the smaller molecules have much higher Planck mean 
absorption coefficients whereas the larger n-heptane does not.  This suggests that if 
pyrolysis products find their way either through diffusion or convection into cool regions 
of the flame core, the impact of pyrolysis on hydrocarbon radiation absorption may be 
very significant.  This is an area for further study, both with additional data collection and 
with detailed modeling of large-scale pool fires in which chemically resolved fuel rich 
cores and detailed radiation transport calculations are developed. 
Temperature (K)
400 800 1200 1600 2000
No
rm
a
liz
ed Volu
m
e
 Fra
c
tio
n
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Methane
Propane
Heptane
Propylene
 
Figure 3-25: Calculated normalized fuel volume fraction of hydrocarbon fuels remaining 
after residence in gas cell as a function of temperature. 
 
 
 89
Wavenumber (cm
-1
)
270028002900300031003200
A
b
sorption coef
f
i
cient (P
a
-1
m
-1
)
0.000
0.002
0.004
0.006
Extrapolation
Experiment
 
Figure 3-26: Comparison of the extrapolated and experimentally measured spectral 
absorption coefficient of heptane (C
7
H
16
) for the C-H stretching band at 1000 K. The 
difference between extrapolated (----) and measured (? ) spectrum is due to pyrolysis. 
 
3.5 Conclusion 
Infrared spectra of gas and liquid fuel species measured using unique high 
temperature FTIR introduced in chapter 2 were presented.  Propane, heptane, methanol, 
toluene, propylene and methyl methacrylate (MMA) infrared absorption coefficients were 
presented as a function of temperature from 300 K to 1000 K. As temperature increases, 
absorption coefficients for each fuel decrease around the band peaks, but the band wings 
are increased due to shifted and broadened rotational transition.  The characteristic band 
peak for each fuel molecule decreased and became noisy because lower vibrational states 
become less probable with higher temperatures and the spectrum featured vibrational and 
rotational energy transition at higher energy levels.  A simplified extrapolation technique 
for absorption coefficient was developed and evaluated by HITEMP database and 
 
 90
propane spectrum.  Uncertainty of extrapolating the fit to high temperature was ? 20 % 
and interpolation within the temperature measurement window was ? 10 %.  The fuel 
pyrolysis problem at high temperature was investigated by CHEMKIN AURORA, and 
evaluated the possibility of fuel pyrolysis during high temperature infrared measurement.  
All fuels studied are not expected to undergo significant (> 10%) pyrolysis with the 
exception of n-heptane at 1000 K.  The extrapolation technique is expected to enable an 
infrared spectrum to be obtained up to 1000 K, but not for higher temperatures due to fuel 
pyrolysis changing the characteristics of the infrared absorption spectra. 
 
 91
CHAPTER 4  DEVELOPMENT OF A RADIATION ABSORPTION 
DATABASE  
4.1 Introduction 
The radiation absorption coefficient databases, currently used in combustion and 
fire modeling, have been used for 20 years.  Highly resolved combustion products 
absorption coefficient database has been updated, but fuel information has not.  To model 
and predict radiation feedback study within various fires, it is critical to develop and 
update the absorption coefficient database.  In this chapter, current databases (HITRAN, 
HITEMP, and RADCAL), and the concept and the design of a new radiation absorption 
database (RADCAL2) are introduced. Finally, the new database is used to derive Planck 
mean absorption coefficients for fuels under fire conditions.  
4.2  Current database 
4.2.1  HITRAN and HITEMP 
The HITRAN database was first developed in the 1960?s at Air Force Cambridge 
Research Laboratory to investigate deeply the infrared spectra for the atmosphere. 
HITRAN started from seven species and has now expanded to 39 species in the 2004 
edition [66].  This database is used for infrared sensing such as qualitative analysis for 
atmosphere and space and quantitative analysis for environmental gases.  HITRAN offers 
the parameters obtained by experiment and calculation to obtain line-by-line intensity 
with high resolution.   
 
 92
HITRAN can calculate temperature dependent line intensity based on 296 K data 
up to 3000 K, but the high temperature data is verified experimentally only up to 600 K, 
since HITRAN misses the information regarding vibrational transition hot bands, which 
happen at high temperatures above 1000 K.  HITEMP, which include this vibrational 
transition, was developed in 2000 to include these high temperature bands for H
2
O, CO
2
, 
and CO. Modest et al. [67] and Fleckl et al. [61] verified the high temperature line 
intensities experimentally up to 1550 K. The line intensity is generated to incorporate the 
database into other program, but user friendly commercial programs such as E-Trans can 
calculate spectral transmissivity and absorptivity by input of concentration, temperature, 
resolution, and pathlength.  
 
4.2.2  RADCAL 
The RADCAL [46] was developed in the 1970?s and the 1980?s. (Current version 
was in 1993) to calculate spectral transmissivity, radiation intensity, and several mean 
absorption coefficients, such as the Planck mean, wall-incident mean, and effective mean, 
of non-isothermal gas mixtures at line of sight with the current version completed in 1993 
[46].  This database uses both experimental and modeled data of H
2
O, CO
2
, CO, and soot 
with a 25 cm
-1
 resolution.  RADCAL utilizes narrow band models to calculate detailed 
absorption coefficients from 25 cm
-1
 resolution data.  Accuracy is less than HITRAN and 
HITEMP, but the input files and user-friendly programming makes combustion modeling 
easily adapted for engineering radiation calculation.  FDS uses RADCAL to calculate the 
Planck mean and effective mean absorption coefficient as a function of temperature and 
mixture fraction. 
 
 93
 
4.3  New database 
4.3.1  Concept and database structure 
A new RADCAL database was programmed with additional new fuel species 
absorption coefficients for methane (updated), propane, heptane, methanol, toluene, 
propylene, and methyl methacrylate, and the updated absorption coefficient data for CO
2
, 
H
2
O, CO, and soot. The database was incorporated into a one dimensional radiation 
transportation analysis in order to verify how updated radiation information affects 
incident heat flux on the fuel surface.   The database had been made ready for complete 
integration into NIST?s FDS simulation package, which is expected to be completed in 
2005.  
The current input file style of RADCAL (temperature, species concentration and 
path length), was not changed since the problem of the current version is the number of 
fuel specie, and resolution. High resolution (1 cm
-1
 with 0.48 cm
-1
 line spacing) and low 
resolution (16 cm
-1
 with 7.9 cm
-1
 line spacing) tabulated databases as a function of 
wavenumber from 50 cm
-1
 (200 ?m) to 25000 cm
-1
 (0.4 ?m) and temperature from 300 K 
to 2400 K with 50 K increments were created for well-resolved spectral 1-D radiation 
transportation analysis and for radiation calculation in FDS.  
 
4.3.2 Fuel absorption database  
A fuel database was created using an interpolation and extrapolation absorption 
coefficient program written in Matlab. The program uses three fitting parameters and two 
 
 94
variables described in the extrapolation technique section in 3.4.1, and generates tables 
for spectral information of absorption coefficient, transmissivity, absorptivity, and 
integrated value of absorption coefficient and Planck mean absorption coefficient for 
seven fuels obtained by experiment and HITRAN.  Input parameters are series of 
temperatures, concentrations, and pathlengths, as well as the current and new RADCAL. 
 
Table 4-1: Spectral ranges used in the absorption coefficient database for fuels. 
Specie 
Methane
*
 
Propane 
Heptane 
Methanol Toluene MMA Propylene 
Spectral 
range 
Wavenumber 
(cm
-1
) 
1300 ? 1600 
1150 ? 1600
*
 
2700 - 3200 
900 - 1600 
2700 - 3200
3600 - 3800
700 - 800 
1000 - 1150
1300 - 1900
2700 - 3200
750 - 1950 
2700 - 3200 
750 - 1150 
1250 - 1950
2700 - 3200
 
 
4.3.3  Combustion product database (CO
2
, H
2
O, and CO) 
E-trans with HITEMP database by Spectrasoft Inc., was used to make a spectral 
absorption coefficient database for CO
2
, H
2
O, and CO.  Temperature (from 300 K to 
2400 K), total pressure (760 mmHg), species concentration (1000 ppm), pathlength 
(0.3175 m), and resolution (1 cm
-1
 or 16 cm
-1
) were input parameters.  Spectral 
transmittance for each species was calculated by E-trans, and converted to spectral 
absorption coefficient. Wavenumber range to make the absorption coefficient table is 
described in Table 4-2.   
 
 
 
 95
Table 4-2: Spectral ranges used in the absorption coefficient database for water vapor, 
carbon dioxide and carbon monoxide by HITEMP. 
Specie Water vapor Carbon dioxide Carbon monoxide 
Spectral range 
 (cm
-1
) 
0 ? 2600 
2800 - 4500 
4700 ? 6000 
6500 - 7700 
550 ? 900 
2100 ? 2450 
3300 - 3800 
1750 - 2400 
4.3.4  Combustion product database (Soot) 
Although an infrared active material has discrete characteristic wavelengths 
which represents the motion of the molecule structure, soot emits and absorbs continuous 
thermal radiation in the infrared region. Therefore, the amount of soot volume fraction 
strongly affects the entire infrared radiation emission and absorption both inside and 
outside a fire.  
Spectral soot absorption coefficient was generally modeled by the Rayleigh limit 
expression since the largest soot particle size is smaller than infrared wavelengths and 
negligible against scattering [47].  The Rayleigh limit expression is written as 
 
()
?
?
?
?
1
42
36
22
2
22
?
++?
=
knkn
nk
    [m
-1
] (4.1) 
         
where n is refractive index, k for absorptive index and ? for wavelength (m), respectively. 
Many researchers have investigated optical properties of soot. Notable work about 
soot properties are Dalzell and Salofim (propane soot) [68], Lee and Tien (polystylene 
and PMMA) [5], Chang and Charalampopoulos (propane soot) [69], and Felske and 
coworkers (propane soot) [70].  Comparison of soot optical properties on these authors 
was summarized by Modest [47], and absorption coefficient based on each authors? value 
were compared at 3 ?m. Modest reported that the optical properties of these authors 
 
 96
except Felske were given in close agreement, and that Felske?s value is the lowest due to 
a low value of k.   
Spectral refractive index n and absorptive index k are functions of wavelength. 
Chang and Charalampopoulos [69] for propane soot has polynomial expression for both n 
and k, as functions of wavelength (?m) and convenient to make various resolution soot 
spectral absorption coefficient. Therefore, soot absorption coefficient database were 
made based on equation 4.1 to 4.3.  Expressions for refractive and absorptive indexes are:  
 
For refractive index, 
???
32
ln0417.0ln0270.0ln1263.08110.1 +++=n    (4.2) 
For absorptive index, 
???
32
ln0100.0ln2309.0ln1213.05821.0 ?++=k    (4.3) 
where, ? is wavelength (?m). 
 
Figure 4-1 shows the spectral absorption coefficient of propane soot modeled by 
equations 4.1 to 4.2. 
Although soot may have a temperature dependency on the absorption coefficient 
at low temperature according to Lee and Tien [5], a temperature independent absorption 
coefficient was adopted for the new absorption coefficient database because optical 
properties taken by Chang was temperature independent.  
 
 97
0 5000 10000 15000 20000 25000
0
2
4
6
8
Absorpt
i
on co
ef
ficient (m
-1
)
Wavenumber (cm
-1
)
 
Figure 4-1: The modeled spectral absorption coefficient of soot. 
 
 
4.3.5  Planck mean absorption coefficient 
The intensity of thermal radiation from flames is diminished by absorption and 
augmented by emission as it travels through the atmosphere of a fire. The emissivity of 
the participating medium (at temperature T) is given by Planck mean absorption 
coefficient, which is expressed as an integral of the product of the spectral absorption 
coefficient ?
?
 and the blackbody Planck function E
b?
 over all wavenumber ? [71]: 
 
4
0
T
dE
bv
p
?
??
?
?
?
=
?
    (4.4) 
 
 
 98
Here ? denotes the Stephan-Boltzmann constant. Since Planck mean absorption 
coefficient is a function only of temperature, it can be easily presented in tabular form 
[72].   
Approximate values for ?
p
 are obtained by numerical integration and the accuracy 
increases with the resolution of the spectral measurements.  Accurate ?
p
 are important in 
combustion and fire modeling for solution of the radiative transport equation without 
employing computationally expensive calculations. Use of ?
p
 approach is limited by the 
scarcity of temperature dependent data ?
?
. The ?
p
 is calculated for a range of fire 
conditions and the impact of hydrocarbon absorption on radiation from large-scale fires is 
discussed.  
 
 
4.3.5.1 Hydrocarbon fuels 
Figure 4-2 shows ?
p
 for methane (obtained from HITRAN), propane, heptane, and 
propylene (interpolated and extrapolated from the experimental data), as a function of 
temperature up to 1400 K in 50 K increments.  Table 4-3 summarizes the fourth order 
polynomial fits to the data (Eqn. 4.5) shown in Figure 4-2.  
 
4
4
3
3
2
210
TaTaTaTaa
p
++++=?
   (4.5) 
 
Figure 4-2 show that both propane and heptane have similar characteristics.  The number 
of -CH
2
- groups impacts the magnitude of the absorption coefficient, but it does not 
influence the general trend of ?
p
. Methane exhibits a peak in ?
p
 at much lower 
 
 99
temperatures than the two larger alkanes due to an increased proportion of its absorption 
occuring in the low-frequency bands.  Figure 4-3 shows the absorption coefficient of C-H 
bending peaks for methane, propane, and heptane at 296 K. Since the absorption 
coefficient of the bending motion within a methane molecule is larger than that of 
propane and heptane at 1300 cm
-1
, the methane ?
p
 is larger compared to propane up to 
about 400 K and similar to heptane at 300 K.    
Propylene has the largest ?
p
 from 300 K to 500 K of hydrocarbon fuels due to 
contributions of =CH
2
 and CH
3
- bending, but the effect of the bending band on the mean 
absorption coefficient
 
is diminished above 800 K where blackbody emissions peak well 
above the frequency of those bands. In contrast, the CH
3
-, CH
2
- and =CH
2
 stretch bands 
contribute to emission and absorption of blackbody radiation. For temperatures above 
800 K, propane with the two extra C-H bonds, has a slightly higher absorption coefficient 
than propylene because for the extra low frequency bands for propylene contribute very 
little to the blackbody radiation. The results for propylene from the experiments in this 
paper compare very favorably with previous studies by Brosmer et al. [13].  Since 
transmittance of the ZnSe window used in the gas cell experiments in this study rapidly 
falls off below 700 cm
-1
 (above 14.3 ?m) as temperature increases [73], the absorption 
spectrum of the low frequency 578 cm
-1
 band was not measurable in the current study. 
Brosmer et al. [13] calculated Planck mean absorption coefficient of propylene with and 
without the 578 cm
-1
 band by approximation from the result of Load et al. [74] and Silvia 
et al. [75]. They estimated the inclusion of the band gave 15 %, 10 %, and 5 % of the 
total absorption for blackbody emissions at 300 K, 400 K and 550 K respectively and 
rapidly dropped below 1 % for higher temperatures.  The ?
p
 of propylene was corrected 
 
 100
to include the 578 cm
-1
 band and results showed that the current Planck means absorption 
coefficient was typically 15 % higher than those of the previous study for the range of 
temperatures measured.  
 
Table 4-3: Values for 4th order polynomial fits with equation 4 to Planck mean 
absorption coefficient data of hydrocarbon. 
Methane Propane Heptane Propene
300 K - 1400 K 300 K - 1400 K 300 K - 1400 K 300 K - 1400 K
a0 -1.8267E-05 -9.2136E-05 -1.5179E-04 3.3532E-04
a1 3.9617E-07 4.6676E-07 6.6905E-07 -3.4358E-07
a2 -7.7619E-10 -1.7967E-10 3.4879E-10 -1.5077E-10
a3 5.7857E-13 -2.4935E-13 -1.1117E-12 3.5885E-13
a4 -1.5283E-16 1.3570E-16 4.4372E-16 -1.3216E-16
R
2
9.9196E-01 9.9527E-01 9.9507E-01 9.9823E-01
 
 
Temperature (K)
200 400 600 800 1000 1200 1400 1600
Planck
 mean abs
or
ption
 c
oef
fic
i
ent (P
a
-1
m
-1
)
0.00001
0.0001
0.001
Methane
Propane 
Heptane 
Propylene 
 
Figure 4-2: Planck mean absorption coefficient of CH
4
 (from HITRAN), C
3
H
8
, n-C
7
H
16
, 
and C
3
H
6
 (from fitting and extrapolation of measurements). 
 
 
Propylene 
 
 101
Wavenumber (cm
-1
)
12001300140015001600
Absorption
 coe
f
f
i
cient
 (Pa
-1
m
-1
)
0.000
0.002
0.004
0.006
0.008
0.010
0.012
Methane
Propane 
Heptane 
Propylene 
 
Figure 4-3: Spectral absorption coefficients for C-H bending peaks for methane 
(HITRAN), and propane and heptane (experimental) at 296 K. 
 
4.3.5.2  Other fuels 
Planck mean absorption coefficient for methanol, toluene and methyl 
methacrylate (interpolated and extrapolated from the experimental data), as a function of 
temperature up to 1400 K in 50 K increments are shown on Figure 4-4.  Table 4-4 
summarizes the fourth order polynomial fits to the data (Eqn. 4.5).  Figure 4-4 shows that 
methanol, toluene and methyl methacrylate have similar characteristics, due to many 
bands at low wavenumber range. This is in contrast to the alkanes, which have primarily 
C-H related bands.  
Figure 4-5 shows the absorption coefficient of methanol, toluene and methyl 
methacrylate at room temperature. Since methyl methacrylate has the largest number of 
characteristic bands with large absorption coefficient at low wavenumber up to 1800 cm
-1
 
 
 102
of all fuels, methyl methacrylate has the largest Planck mean absorption coefficient over 
the entire temperature range.  
It is also interesting to compare methanol and toluene, since both have the same 
CH
3
-, but each has different bonding (C-O and -OH or phenyl carbon double C=C, 
respectively) in their chemical structure. From 300 K to 1100 K, methanol has a larger 
Planck mean absorption coefficient than toluene. This is mainly due to the contribution of 
a C-O stretching peak. In contrast, the effect of CH
3
-, and =CH stretch bands of toluene 
increases higher than 1100 K. Planck mean absorption coefficient of heptane increases up 
to 800 K, but is smaller than toluene up to 550 K and methanol up to 700 K.     
Since the transmittance of the ZnSe window starts falling below approximately 
700 cm
-1
 (14.3 ?m) and drops dramatically below 625 cm
-1
 (16 ?m) as temperature 
increases [73], the absorption spectrum of phenyl out-of and in-plane bending peak 
around 460 cm
-1
 band were not measurable. Figure 4-6 shows the comparison of our 
results and previous work done by Park et al. [13, 14].   There is an error of 19.3 % min. 
at 400 K and 31.1 % max. at 800 K between the two results. They used the total 
absorbance to generate Planck mean absorption coefficient because of their low-
resolution spectrum, compared to our high-resolution analysis. Therefore, the difference 
between our result and previous work on methyl methacrylate is attributed to the 
experimental resolution and calculation method for Planck mean absorption coefficient.  
 
 
 
 103
Temperature (K)
200 400 600 800 1000 1200 1400 1600
Pl
anck
 m
e
an absorption
 coef
ficient
 (Pa
-1
m
-1
)
0.00001
0.0001
0.001
0.01
Methanol 
Toluene 
MMA 
 
Figure 4-4: Planck mean absorption coefficient of methanol, and toluene, methyl 
methacrylate (MMA) (from fitting and extrapolation). 
 
Wavenumber (cm
-1
)
1000150020002500300035004000
Absorption coefficient (Pa
-1
m
-1
)
0.000
0.005
0.010
0.015
0.020
0.025
0.030
Methanol 
Toluene 
MMA 
 
Figure 4-5: Spectral absorption coefficient of methanol, toluene and methyl methacrylate 
at room temperature. 
 
 
 104
Temperature (K)
200 400 600 800 1000 1200 1400 1600
Planck
 m
e
an absorption
coef
f
i
cient (Pa
-1
m
-1
)
0.0001
0.001
Current Study
Park et al.
 
Figure 4-6: Comparison of Planck mean absorption coefficient for methyl methacrylate 
(MMA) with results from Park et al [14]. 
  
 
 105
 
Table 4-4: Values for 4th order polynomial fits with equation 4 to Planck mean 
absorption coefficient data of other fuels. 
Methanol Toluene MMA
300 K - 1400 K 300 K - 1400 K 300 K - 1400 K
a0 3.3374E-04 4.9459E-04 -5.7555E-05
a1 9.3528E-07 -1.2630E-06 7.2282E-06
a2 -3.0573E-09 1.8963E-09 -1.6559E-08
a3 2.6760E-12 -1.3674E-12 1.3318E-11
a4 -7.6382E-16 3.5996E-16 -3.6529E-15
R
2
9.9735E-01 9.9964E-01 9.9601E-01
 
 
 
4.4 Conclusion 
Highly resolved infrared absorption coefficient database of fuels and combustion 
products (H
2
O, CO
2
, and CO from HITEMP database, and soot from modeling) were 
created.  Planck mean absorption coefficients of measured fuels and methane absorption 
coefficients calculated from the HITRAN database were fitted to 4
th
 order polynomial 
equations as a function of temperature and compared with each other. Large differences 
in the absolute values of the coefficients were obtained for the different hydrocarbon 
molecules. Based on this observation, it is clear that an accurate description of radiative 
transfer in fires will require temperature dependent absorption coefficients for all fuels. 
As the carbon number increases, similar trends in Planck mean absorption coefficients as 
a function of frequency were observed. However, at lower temperatures, propylene shows 
a large contribution for absorption and emission due to bending motion of the C=C bond 
and the associated =C-H bond.  Other fuels such as toluene, methanol and methyl 
methacrylate, which contain characteristic band groups that absorb at low wavenumber as 
 
 106
well as propylene, had a large Planck mean absorption coefficient compared to 
hydrocarbons such as methane, propane, and heptane.  
 
 107
 
CHAPTER 5 THERMAL RADIATION FEEDBACK ANALYSIS AND 
CALCULATION 
5.1 Introduction 
Understanding of thermal radiation feedback using the new radiation absorption 
coefficient database described in the previous chapter is the final objective.  Line of sight 
radiation transport analysis for methanol, heptane and toluene 0.3 m pool fires is 
conducted to understand the radiation contribution of combustion and fuel species within 
a fire.   Radiation is dominant for energy feedback on fuel surface at fuel center. The one 
dimensional radiative transport equation along the flame centerline from the flame to fuel 
surface is introduced and the solution of the equation for pool fires for 0.3 m pool fires is 
presented.   
 
5.2 Solution of 1D radiative transport equation (line of sight) 
5.2.1 Transport equation 
Radiation intensity change by attenuation per unit length is expressed as 
 
dI
v
dz
? 
? 
? 
? 
? 
? 
a
=??
v
I
v
    (5.1) 
where, I
?
 is spectral radiation intensity, ?
?
 is spectral absorption coefficient, and z is 
distance traveling the photons,  subscript a is absorption, respectively. 
 
 108
 
Spectral radiation intensity change by emission per unit length is also expressed as  
 
dI
v
dz
? 
? 
? 
? 
? 
? 
e
=?
v
I
b,v
    (5.2) 
 
where I
b,?
 is radiation intensity by blackbody, and subscript e is emission.  Combining 
eqn. (5.1) and (5.2) results in the general radiation transport equation, 
 
dI
v
dz
=??
v
I
v
? I
b,v
( )   (5.3) 
 
where attenuation term is the first and emission term is the second of the right hand side. 
For spectroscopy, the emission term originates from the self-emission of 
molecules, but is negligible unless the absorbing medium is of high concentration and at 
high temperature. Spectroscopy uses eqn. 5.1 to measure an absorption coefficient. This 
equation is referred to as ?Beer?s law?.  Beer?s law assumes that the medium is at local 
thermodynamic equilibrium (LTE) and that there is no interaction between molecules. 
When the photons travel from a position 0 to L within the medium having 
absorption coefficient ?, equation 5.1 becomes 
 
() ( ) )exp(0 LILI
vvv
??=     (5.4) 
 
 
 109
()
()
()%)exp(
0
vv
v
v
TL
I
LI
=?= ?    (5.5) 
 
where I
?
(0) is spectral initial intensity, I
?
 (L) is spectral intensity at L, and T
?
 is spectral 
transmittance, respectively.  Physically, equations 5.4 and 5.5 indicate that spectral 
radiation intensity decays exponentially with length. 
The radiative transport equation is integrated along the line of sight from 0 to s. 
The derivative of the radiative transport equation is given as 
 
dI
v
dz
=??
v
I
v
?I
b,v
()   (5.5) 
 
Optical depth ? is introduced as 
 
d?
v
=?
v
z
( )
dz    (5.6) 
?
v
= ?
v
dz
0
z
?     (5.7) 
 
Multiplying exp (?) to both side of eqn. 5.5 yields 
 
() ()() () ()
vvvbvvv
II
vd
dIv
????
?
? expexpexp =+   (5.8) 
()()( ) () ()
vvvbvv
II
d
d
????
?
expexp =     (5.9) 
 
 
 110
Integration of eqn. 5.9 from 0 to ? can be written as 
 
()()( ) ()()**exp*exp
00
??
=
??
?????
vvvvbvv
dIId    (5.10) 
() () () ( ) ( ) **exp*0exp
0 v
vvvbvvvv
dIII
?
=?
?
?????   (5.11) 
()()() () ()()**exp*expexp0
0
?
?+?=
?
??????
vvvvbvvvvv
dIII  (5.12) 
 
Since eqn. 5.12, a source function, cannot be solved directly, the trapezoidal rule is used 
to solve the transportation equation numerically.  
 
() () ( ) ( ) ( ) ( )[ ]
vbvvvbvvvvv
IIII ????? ?++?= exp05.0exp0   (5.13) 
 
Equation 5.13 was used to solve the radiation transport equation along the centerline of 
the fire from flame to fuel surface in the following section.  
 
 
5.3 Radiation intensity at fuel surface by line of sight analysis 
5.3.1  Data set and processing procedure 
Species and temperature distribution data is necessary to analyze the radiation 
intensity along the flame centerline from flame to fuel surface.  FDS (ver. 4.02) was used 
as a tool to model species and temperature information within pool fires for methanol, 
heptane, and toluene with 0.3 m diameter, which were then used to solve radiation 
 
 111
intensity at fuel surface.  The grid sizes for each pool fire were 2 cm x 2 cm x 2 cm.  Slice 
output files and the FDS utility (FDS2ASCII.EXE) were used to generate species and 
temperature distribution in the x and z directions, then the species and temperature data 
along the centerline of the fire were tabulated. The species and temperature table from the 
FDS and high-resolution absorption coefficients of species table were loaded into spectral 
radiation transport equation solver written in Matlab script, and radiation intensity at the 
pool surface was calculated.  Radiation intensity normal onto the pool surface and 
contribution of species absorption were analyzed by gas-phase species absorption.   
Two boundary conditions were set to solve the one dimensional transport 
equation. At first emission from species concentrations calculated by FDS at selected 
flame temperature was assumed for all fires and calculated the radiation intensity at the 
fuel surface defined as I
species
.  Second, blackbody emission at 1400 K for fuels with high 
degrees of sooting (heptane and toluene) was assumed and calculated the radiation 
intensity at the heptane and toluene pool surface defined as I
BB.
 
5.3.2  Methanol pool fire analysis 
Figure 5-1 shows the solution of the spectral radiative transport equation along the 
fire centerline from the flame to fuel surface for a 0.3 m methanol pool fire. It should be 
mentioned that the grid is far too big to capture flame structure and thus it underpredicts 
the temperature rise in the flame zone. Therefore, flame temperature T
f
 = 1400 K, height 
0.74 m of zero fuel mole fraction position from FDS calculation, and emission of H
2
O, 
CO
2
, and CO at flame were boundary condition.  Since methanol produces little soot in 
its combustion, zero soot volume fraction was assumed in radiation calculation.  
Radiation intensity I
species
, which is area under the curve in Figure 5-1, is 12,400 W/m
2
-sr 
 
 112
at fuel surface, and this value is quite similar to Klassen?s measurement (12,200 W/m
2
-sr) 
[8].  Figure 5-2 shows the integrated radiation intensity by all species, the intensity by 
methanol, and the ratio of methanol to all species intensity as a function of height.  As the 
height decreases, the contribution of methanol for radiation transport increases up to 
about 40% at the pool surface.  Figure 5-3 shows radiation intensity, mole fraction of 
each species, and temperature as a function of height.  From Figure 5-3, H
2
O and CO
2
 are 
seen to be major contributors to radiation transport near the flame, but the fuel mole 
fraction X
f
 increased above 0.3 (Z < 5 cm from the fuel surface).  Thus, in this region fuel 
became the major contributor to radiative absorption. The mole fraction of CO is very 
low (ppm level) compared to Hamins? experiment (3 %) [76], but the contribution of CO 
on total radiation intensity is very small since the total number of carbon doesn?t change 
at all and the carbon is shared by CO and CO
2
.  Radiation intensity gains from the flame 
to 10 cm above the fuel surface (emission > absorption), then slightly decreases toward 
the fuel surface (absorption > emission).  The temperature along the flame centerline is 
very high ranging from 900 K to 1400 K.  Since radiation absorption at high temperature 
becomes small and emission becomes larger, the temperature profile also supports the 
radiation intensity profile.  Figure 5-4 shows the spectral radiation intensity of C-H 
stretching of methanol about 3.4 ?m (3000 cm
-1
) as a function of height.  From the 
spectral intensity, methanol emission is stronger than absorption from flame to 6 cm 
above fuel surface, then absorption is more significant than emission toward to fuel 
surface.  Since the radiation transport equation calculates both absorption and emission, 
this result shows that emission by methanol is higher than absorption almost within the 
methanol fire, and absorption is only higher than emission near the fuel surface.  Figure 
 
 113
5-5 shows comparison of radiation intensity of 0.3 m methanol pool fire calculated by 
temperature dependent and independent (ambient temperature) methanol and temperature 
dependent methane absorption coefficients. Since calculation only changes fuel 
absorption coefficient, difference in radiation intensity is due to fuel absorption. Ambient 
absorption coefficient as an alternative absorption coefficient for all temperatures was set 
to see if temperature dependent absorption coefficient has significant impact on the 
radiation calculation. As the comparison of effect on the fuel species, radiation intensity 
at methanol fuel surface calculated the transport equation using methanol absorption 
coefficient is higher than the intensity by methane (error +17%).  This is because 
emission by methanol is higher than methane at high temperature. Intensity decay (dI/dz 
< 0) near the fuel surface also shows methanol absorbs more radiation than methane. 
Since methanol has higher absorption coefficient relative to methane.  As a comparison 
of temperature dependency of methanol absorption coefficient on radiation intensity, the 
radiation intensity during emission has maximum +17% error, but the error decreased 
toward to fuel surface and finally ? 3% at fuel surface. The position, where the sign of 
dI/dz changed from + to -, shifted higher if the temperature independent (ambient) 
methanol absorption coefficient was set.  Although there was an effect temperature 
dependency of absorption coefficient while a molecule was emitting and absorbing, there 
was small impact on radiation intensity at fuel surface.   
 
 
 
 
 114
11010
0
2000
4000
6000
8000
10000
Methanol 0.3 m pool fire
Intensity
 (W/m
2
-sr
)
Wavelength (?m)
 
Figure 5-1: Spectral directional radiation intensity along the flame centerline from flame 
to fuel surface for 0.3 m methanol pool fire. 
 
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
2000
4000
6000
8000
10000
12000
14000
Methanol 0.3 m pool fire 
 I
 I
fuel
Z (m)
I
n
ten
s
ity (W/m
2
-sr
)
0
10
20
30
40
50
 I
fuel
/I
I
fu
el
/I (
%
)
 
Figure 5-2: Integrated directional radiation intensity by all species and methanol, and the 
ratio of methanol to all species intensity as a function of height for 0.3 m methanol pool 
fire. 
Methanol Absorption 
Fuel Surface 
 
 115
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
2000
4000
6000
8000
10000
12000
14000
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0
200
400
600
800
1000
1200
1400
In
ten
s
it
y (
W
/m
2
-s
r)
Z (m)
Temperature
Methanol 0.3 m pool fire
Intensity
X
CO
X
CO
2
X
H
2
O
X
Fuel
 X
i
 
Tem
p
erature (K)
 
Figure 5-3: Integrated directional radiation intensity, mole fraction of each species (X
i
), 
and temperature as a function of height for 0.3 m methanol pool fire. 
 
34
0
2000
4000
6000
8000
10000
Inte
nsity (W/m
2
-sr)
Wavelength (?m)
 0.68 m
 0.42 m
 0.30 m
 0.22 m
 0.18 m
 0.10 m
 0.08 m
 0.04 m (Fuel)
 
Figure 5-4: Spectral radiation intensity of C-H stretching of methanol about 3.4 mm 
(3000 cm
-1
) as a function of height 
Fuel Surface 
 
 116
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0
2000
4000
6000
8000
10000
12000
14000
16000
Methanol 0.3 m pool fire
In
te
n
s
i
t
y (W/m
2
-s
r)
Z (m)
 ?
methanol, T dependent
 ?
methanol, T ambient
 ?
methane, T dependent
 
Figure 5-5: Comparison of radiation intensity of 0.3 m methanol pool fire calculated by 
temperature dependent and independent methanol absorption coefficient and temperature 
dependent methane absorption coefficient. 
 
 
5.3.3  Heptane pool fire analysis 
 
Figure 5-6 shows the solution of the spectral radiative transport equation along the 
fire centerline from the flame to fuel surface for a 0.3 m heptane pool fire. The grid is far 
too big to capture flame structure and thus it underpredicts the temperature rise in the 
flame zone. Emission of soot, H
2
O, CO
2
, and CO from a flame temperature T
f
 = 1400 K 
at a height 0.86 m, the highest temperature position in a flame region from FDS 
calculation, was the boundary condition. Radiation intensity I
species
, the area under the 
curve at the fuel surface, was 3,500 W/m
2
-sr.  The spectrum result was qualitatively good, 
but the integrated intensity was very low relative to Klassen?s measurement (23,500 
W/m
2
-sr) [8].  Figure 5-7 shows comparison of the integrated directional radiation 
intensities by all species and heptane, and the ratio of heptane to all species intensity as a 
Fuel Surface 
 
 117
function of height for 0.3 m heptane pool fire. Average radiation contribution of heptane 
is about 20% entire heptane fire, but slightly decreased about 13 % at fuel surface. 
In reality, the moderate sooty heptane flame is optically thick and emission is 
assumed as the blackbody emission. In order to compare previous results of weak species 
emission to blackbody radiation, the boundary condition to solve transport equation was 
changed to blackbody emission at 1400 K, and the transport equation was recalculated. 
Figure 5-8 shows the result of 1400 K blackbody emission as an alternative boundary 
condition.  Total directional radiation intensity I
BB
, the area under the curve for each 
flame sheet and fuel surface, at a flame position was 69,300 W/m
2
-sr and 25,700 W/m
2
-sr 
at fuel surface. This result was very close to Klassen?s measurement (23,500 W/m
2
-sr). 
This result implies that species emissions from the flame were likely issuing from much 
higher temperatures than predicted by the FDS simulation and that the temperature was 
not far from 1400 K.  As stated earlier, the underprediction of flame temperatures by FDS 
is expected because it fails to resolve flame structure properly. From Figure 5-8, 
combustion products (H
2
O, CO
2
, CO, and soot) and heptane attenuated about 60 % of 
flame radiation, 43,600 W/m
2
-sr, during radiation attenuation from flame to fuel surface. 
Heptane absorption was approximately 5,800 W/m
2
-sr, and occupied about 13 % of total 
energy absorption.  Soot was the most absorbed specie with 27,000 W/m
2
-sr, and 
occupied about 62 % of total absorption. Other specie (H
2
O, CO
2
, and CO) were 10,800 
W/m
2
-sr and 25 % of total absorption.   
Temperatures within the heptane fire decreased toward the fuel surface, and the 
temperature within the entire flame was lower than with methanol shown in Figure 5-9. 
Also the temperature near the heptane fuel surface was much lower (about 450 K) than 
 
 118
methanol fire (about 900 K), and the slope of radiation intensity (dI/dz) was negative. 
Therefore, the contribution of radiation absorption was larger than that of emission for 
radiation transfer process in a heptane fire. The difference of radiation intensity by 
heptane and methane absorption is also compared in Figure 5-10.  As for methanol, the 
difference of radiation intensity was due to these two fuels absorption coefficient.  For 
species emission boundary condition, radiation intensity by heptane was higher than 
methane due to more emission by heptane molecules, but the difference decreased toward 
the fuel surface and finally the intensity became lower than for methane (error ? 8%). For 
1400 K blackbody boundary condition, radiation intensity by heptane was always lower 
than methane (error -9 %).  This difference of radiation characteristic is due to the 
boundary radiation source intensity.  For comparison of radiation intensity calculated by 
temperature dependent and ambient absorption coefficient as an alternative of all 
temperature absorption coefficients, the radiation intensity by temperature dependent 
absorption coefficient was 6 % lower value than the ambient absorption coefficient.  
Figure 5-11 shows the comparison spectral radiation intensity of C-H stretching peak 
about 3.4 ?m (3000 cm
-1
) at the pool surface between heptane and methane absorption 
coefficient. Since heptane has a higher absorption coefficient than methane due to the 
increased number of C-H bonds, the radiation intensity with the heptane coefficient was 
lower than that of methane.  
 
 
 119
1 10 100
-200
0
200
400
600
800
1000
1200
1400
Heptane 0.3 m pool fire
In
te
n
s
ity (W/m
2
-sr)
Wavelength (?m)
 
Figure 5-6: Spectral directional radiation intensity along the flame centerline from flame 
to fuel surface for 0.3 m heptane pool fire. 
0.0 0.2 0.4 0.6 0.8 1.0
1000
2000
3000
4000
5000
6000
Heptane 0.3 m pool fire
 
 I
 I
fuel
Z (m)
Intensity (W/
m
2
-s
r)
0
5
10
15
20
25
30
 I
fuel
/I
 
 
I
f
uel
/I
 
Figure 5-7: Integrated directional radiation intensity by all species and heptane, and the 
ratio of heptane to all species intensity as a function of height for 0.3 m heptane pool fire. 
Heptane Absorption 
Fuel Surface 
 
 120
1 10 100
0
5000
10000
15000
20000
25000
 
Heptane 0.3 m T
f
 = 1400 K
Inte
nsity (W/m
2
-sr)
Wavelength (?m)
 Flame
 Fuel Surface
 
Figure 5-8: Spectral directional radiation intensity along the flame centerline from flame 
to fuel surface for 0.3 m heptane pool fire with blackbody intensity as an initial condition. 
400
600
800
1000
1200
1400
0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Soot
X
CO
X
CO
2
X
H
2
O
X
Fuel
Heptane 0.3 m pool fire
Z (m)
X
i
0.30
0.35
0.40
0.45
0.50
0.55
0.60
0.65
0.70
 S
o
o
t
 vol
u
me fra
c
tio
n (
p
p
m
)
Temperature
Te
mp
er
a
t
ur
e (
K
)
 
Figure 5-9: Mole fraction of species (X
i
) and soot volume fraction (ppm), and 
temperature as a function of flame height for 0.3 m heptane pool fire. 
 Heptane Absorption 
Fuel Surface 
 
 121
 
20000
30000
40000
50000
60000
70000
0.0 0.2 0.4 0.6 0.8 1.0
3500
4000
4500
5000
5500
6000
6500
 
Heptane 0.3 m pool fire
 ?
heptane
 ?
methane
Z (m)
In
te
nsi
t
y
 (W/m
2
-s
r)
 
Inte
n
s
ity
 (
W
/m
2
-s
r
)
Specie emission I.C.
Blackbody I.C.
  
 
Figure 5-10: Comparison of radiation intensity of 0.3 m heptane pool fire calculated by 
heptane and methane absorption coefficients, and by species and blackbody emission at 
1400 K as boundary conditions. 
 
34
-200
0
200
400
600
800
1000
1200
1400
Heptane 0.3 m pool fire
In
te
n
s
it
y
 (W/m
2
-sr)
Wavelength (?m)
 ?
heptane
 
 ?
methane
 
Figure 5-11: Comparison of spectral radiation intensity of C-H stretching peak about 3.4 
?m (3000 cm
-1
) at heptane pool surface between heptane and methane absorption 
coefficient (Specie emission boundary condition). 
Fuel Surface 
Blackbody B.C. 
Specie emission 
B.C. 
 
 122
 
 
 
5.3.4  Toluene pool fire analysis 
 
Since toluene pool fires are sootier than heptane fires, the radiation intensity 
calculation of toluene was more difficult than previous heptane analysis. Figure 5-12 
shows the solution of the spectral radiative transport equation along the fire centerline 
from the flame to fuel surface for a 0.3 m toluene pool fire.  As for methanol and heptane 
fire analysis, emission of soot, H
2
O, CO
2
, and CO of flame temperature T
f
 = 1400 K at 
height 0.86 m of the highest temperature position in a flame region from FDS calculation, 
was the first boundary condition.   Radiation intensity at the fuel surface I
species
, which is 
area under the curve in Figure 5-12, was 4,100 W/m
2
-sr.    Figure 5-13 shows a 
comparison of integrated directional radiation intensities by all species and toluene, and 
the ratio of toluene to all species intensity as a function of height for 0.3 m toluene pool 
fire, when species emission at 1400 K was set as a second boundary condition. The 
radiation contribution of toluene increased toward the fuel surface up to 40 %. 
Combustion products (mainly soot) absorbed the radiation. Figure 5-14 shows the mole 
fraction of each species and soot volume fraction (ppm), and temperature as a function of 
height.  Compared to heptane analysis, toluene had 5.6 times higher soot volume fraction.  
Since soot strongly absorbed radiation in the toluene fire, water vapor and carbon dioxide 
were minor contribution relative to soot on radiation transport. Although fuel absorption 
dramatically increased from 0.05 m above the fuel surface and reached a maximum near 
the fuel surface, contribution of fuel on radiation transport was small relative to soot.  
Figure 5-15 shows the difference of radiation intensity calculated by temperature 
 
 123
dependent and independent (ambient temperature) toluene and temperature dependent 
methane absorption.  As for methanol and heptane, the difference of radiation intensity 
was also due to these two fuels absorption coefficient.  The difference decreased toward 
the fuel surface, and finally the intensity became lower than for methane.  Figure 5-16 
shows the comparison spectral radiation intensity from 3 to 11 ?m at the pool surface by 
heptane and methane absorption coefficient.  Since toluene has more bands coefficient 
than methane, the radiation intensity at pool surface by toluene absorption coefficient was 
lower than that of methane.  Radiation intensity by toluene was slightly higher than 
methane, but total radiation intensity at fuel surface was not so different. The little effect 
of temperature dependency absorption coefficient on radiation intensity could be seen in 
the same figure.  Temperature within the toluene fire dropped near the fuel surface, and 
the temperature within the entire flame was lower than methanol as well as heptane. This 
could be due to mainly soot absorption. The temperature near fuel surface was much 
lower (about 490 K) than methanol fire (about 900 K) as well as heptane.  
Blackbody radiation at 1400 K as an alternative boundary condition was set and 
recalculated as well as heptane fire, in order to compare the result of previous boundary 
condition.  Radiation intensity I
BB
, which is the area under the curve for each flame and 
fuel surface shown in Figure 5-17, was 69,300 W/m
2
-sr at the flame position and 6,400 
W/m
2
-sr at the fuel surface. This value was still lower than Klassen?s measurement 
(20,200 W/m
2
-sr).  Combustion products (H
2
O, CO
2
, CO, and soot) and toluene absorbed 
about 91% of flame radiation, 63,000 W/m
2
-sr, as a result of radiation attenuation from 
the flame to fuel surface. Soot was the most absorbed specie with 58,400 W/m
2
-sr, and 
 
 124
occupied about 93% of total absorption. Combustion products (H
2
O, CO
2
, and CO) and 
toluene were 2% and 5% of total absorption, respectively.   
Although the highest temperature position in the flame along the flame centerline, 
and accurate absorption coefficients for all species were set, solution of the radiation 
transport equation of line of sight was underestimated at the toluene pool surface.   
Although the radiation intensity of methanol pool fire was predicted well relative to 
experimental result, the result of heptane and toluene were not.  Most of the radiation for 
moderate sooty and heavy soot fires (heptane and toluene fires) was attenuated before the 
intensity reached to the fuel surface.  In order to obtain more radiation at fuel surface, the 
emission intensity must be stronger (a higher flame temperature), or the position of the 
emission source within the pool fire could be lower.   
Since radiation transport of sooty fires depends on soot concentration, the location 
of emission origin of heptane might be higher than toluene.  If the radiation transport 
equation is solved reversibly from fuel surface with fuel radiation intensity as an initial 
condition until the intensity goes to maximum, the emission source (say virtual emission 
source) can be determined. More details of the radiation transport mechanism within the 
fire can be obtained if accurate species and temperature distribution are used.   
 
 125
 
11010
0
200
400
600
800
1000
Toluene 0.3 m pool fire
Intensity
 (W/m
2
-sr
)
Wavelength (?m)
 
Figure 5-12: Spectral directional radiation intensity along the flame centerline from flame 
to fuel surface for 0.3 m toluene pool fire. 
 
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0
2000
4000
6000
8000
10000
12000
14000
16000
 I
 I
fuel
Z (m)
In
te
n
s
i
t
y (
W
/m
2
-sr)
5
10
15
20
25
30
35
40
45
Toluene 0.3 m pool fire
 I
fuel
/I
I
fuel
/I
 (%)
 
Figure 5-13: Integrated directional radiation intensity by all species and toluene, and the 
ratio of toluene to all species intensity as a function of height for 0.3 m toluene pool fire. 
Toluene Absorption 
Fuel Surface 
 
 126
400
600
800
1000
1200
1400
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Toluene 0.3 m pool fire
Z (m)
X
i
2.0
2.2
2.4
2.6
2.8
3.0
3.2
3.4
Temperature
 
Soo
t
 vo
lum
e
 fractio
n
 (pp
m
)
X
CO
X
CO
2
X
H
2
O
Soot
X
Fuel
 
Te
mp
era
t
ure
 (K
)
 
Figure 5-14: Mole fraction of species (X
i
) and soot volume fraction (ppm), and 
temperature as a function of flame height for 0.3 m toluene pool fire. 
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
4000
6000
8000
10000
12000
14000
16000
Toluene 0.3 m pool fire
 ?
toluene, T dependent
 ?
toluene, T ambient
 ?
methane, T dependent
Z (m)
Intensit
y (W
/m
2
-s
r)
  
Figure 5-15: Comparison of radiation intensity of 0.3 m toluene pool fire calculated by 
toluene and methane absorption coefficients, and by specie emission as a boundary 
condition. 
Fuel Surface 
Fuel Surface 
 
 127
310
0
200
400
600
800
1000
Toluene 0.3 m pool fire
Int
e
nsit
y
 (W/m
2
-sr)
Wavelength (?m)
 ?
toluene
 ?
methane
 
Figure 5-16: Comparison of spectral radiation intensity from 3 to 11 ?m at toluene pool 
surface by toluene and methane absorption coefficient. 
11010
0
5000
10000
15000
20000
25000
Toluene 0.3 m pool fire 
Int
e
n
s
ity (W
/m
2
-sr
)
Wavelength (?m)
 Flame
 Fuel Surface
 
Figure 5-17: Spectral directional radiation intensity along the flame centerline from flame 
to fuel surface for 0.3 m toluene pool fire with blackbody boundary condition. 
Toluene Absorption 
 
 128
 
 
5.3.5 Radiation transport between gas phase and condensed phase 
Spectral directional radiative intensity at the fuel surface for each fuel pool fire 
shows that the characteristic band region for each fuel is very small relative to the entire 
infrared region.  Since the fuel molecule can only absorb the radiation at the 
characteristic wavelength, the radiation at other bands is transmitted. Figure 5-18 through 
Figure 5-20 show the condensed and gas phase infrared spectrum for methanol, heptane, 
and toluene, respectively.  From these figures, condensed phase spectra are broad and 
many additional peaks due to association and dense population of the molecules are seen.  
Once the radiation by gas phase strikes the fuel surface, the absorption characteristic of 
fuel molecule changes to a condensed phase one. Therefore, a wider range of radiation 
can be absorbed by condensed fuel.  Also, combustion products effect should be 
considered at the phase interface.  For methanol, water vapor can be associated with 
methanol molecule. Since temperature on the interface of methanol can be assumed as 
methanol boiling point, water condensation is considered.  Therefore, liquid water and 
liquid methanol absorption should be considered for radiation transport within the 
condensed phase.  For heptane and toluene, it can be assumed that large concentrations of 
soot floating on the fuel surface absorbs radiation in addition to condensed fuel 
absorption, as a result of soot distribution within heptane and toluene pool fires. Hamins 
[77] observed much soot on the pool surface and a black liquid color after the heptane 
and toluene experiments.  Condensed water is minor effect relative to soot absorption.    
 
 
 129
 
Figure 5-18: Transmissivity of methanol infrared spectrum; (a) gas phase and (b) 
condensed phase from NIST Webbook [58]. 
 
Figure 5-19: Transmissivity of heptane infrared spectrum; (a) gas phase and (b) 
condensed phase from NIST Webbook [58]. 
 
 
Figure 5-20: Transmissivity of toluene infrared spectrum; (a) gas phase and (b) 
condensed phase from NIST Webbook [58]. 
 
 
 
 
 
 
(a) (b) 
(a) (b) 
(a) (b) 
 
 130
5.4 Conclusion 
The radiation intensity at the pool surface of 0.3 m methanol, heptane, and toluene 
pool fire was calculated using one dimensional radiative transport equation with species 
concentration and temperature profile calculated by FDS.  Emission of combustion 
species was set as a boundary condition to solve the transport equation for all pool fires.  
Solution of methanol pool fire had small error (2%) relative to previous experimental 
data, but heptane and toluene errors were large (> 100%).  When the blackbody emission 
at 1400 K was set as an alternative initial condition of heptane and toluene fire because of 
the optically thick flame, heptane agreed well with previous experimental data, but 
toluene did not.  From this analysis, the radiation intensity of methanol fire can be solved 
by optically thin condition, and heptane can be solved using an optically thick blackbody 
boundary condition.  If the radiation intensity at the toluene fuel surface is assumed from 
previous experiment by Klassen, emission sources within the fire could be closer to fuel 
surface or the boundary intensity could be stronger since soot absorbed much of the 
radiation energy. Toluene fire needs more careful investigation since soot absorption and 
emission completely controls radiation heat transfer within the toluene fire relative to 
methanol and heptane. Since the grid is far too big for FDS to capture flame structure, 
underprediction of temperature rise in the flame zone led low radiation intensity at fuel 
surface for heptane and toluene.  
The effect of change of fuel absorption coefficient from each fuel to methane on the 
radiation intensity at fuel surface was analyzed and average 20 % for all fuels was 
observed.  Use of the correct fuel absorption coefficient significantly impacted the 
radiation intensity. The effect of temperature dependency absorption coefficient on the 
 
 131
radiation intensity at the fuel surface was also investigated by comparison between 
temperature dependent absorption coefficient and ambient absorption coefficient as an 
alternative for all temperature coefficients.  The average impact for all pool fires was 4 %.  
Although differences between radiation intensity due to temperature dependency on 
absorption coefficient within the characteristic bands of each fuel were large, the 
difference was small impact on the total intensity at entire infrared region.  The pool fires 
with cool fuel rich core don?t receive the impact of temperature dependency, since 
radiation absorption of fuel is conducted within the fuel core.  This analysis is only for 
small-scale (0.3 m diameter) fire, but medium scale (~1m) and large scale (~20 m) cases 
should be investigated since the flame structure changes.     
 
 132
CHAPTER 6 CONCLUSION 
6.1 Summary of Results 
An experimental apparatus was developed to obtain infrared measurements at high 
temperature.  This unique instrument with a nitrogen jet window cooling unit protected 
the ZnSe window from oxidation and thermal degradation and allowed good spectral 
transmissivity for long running times at high temperature.  Cooling effects on the infrared 
window were evaluated by temperature measurement inside and outside of the windows 
by thermocouples, and cooling velocity on the window was determined.  Gas fuels and 
vaporized liquid fuels, and nitrogen mixture were supplied by two mass flow controllers, 
one for fuel delivery and the other for fuel dilution, and supplied continuously to optical 
cell.   
Propane, heptane, methanol, toluene, propylene and methyl methacrylate (MMA) 
infrared absorption coefficients were obtained at five temperatures from 300 K to 1000 K. 
As temperature increased, absorption coefficients for each fuel decreased around the band 
peaks and became noisy since lower vibrational states become less probable with higher 
temperatures and the spectrum featured vibrational and rotational energy transition at 
higher energy levels.  At the band wings, absorption coefficient increased due to shifted 
and broadened rotational transition.  Simplified extrapolation techniques for absorption 
coefficients were developed and its capability was evaluated by HITEMP database and 
experimental data (propane). Fuel pyrolysis at high temperature was investigated by 
CHEMKIN AURORA, and the possibility of fuel pyrolysis during high temperature 
infrared measurement was evaluated.  All fuels except heptane were not expected to have 
 
 133
fuel pyrolysis at 1000 K.  The extrapolation technique was verified to give great 
contribution to obtain an infrared spectrum at high temperature, up to 1000 K. 
A high-resolution infrared absorption coefficient database of fuels and combustion 
products (H
2
O, CO
2
, and CO from HITEMP database, and soot from modeling) was 
created.  Planck mean absorption coefficients of measured fuels and methane absorption 
coefficients calculated from the HITRAN database were fitted to 4
th
 order polynomial 
equations as a function of temperature and compared with each other.  Based on the 
characteristics of Planck mean absorption coefficient, it was clear that an accurate 
description of radiative transfer in fires requires temperature dependent absorption 
coefficients for all fuels. Hydrocarbon (alkanes) had similar trends in Planck mean 
absorption coefficients, but propylene (alkenes) showed a large contribution for 
absorption and emission at lower temperatures due to the bending motion of the C=C 
bond and the associated =C-H bond.  Other fuels such as toluene, methanol, and methyl 
methacrylate, which contain characteristic band groups that absorb at low wavenumber as 
well as propylene, had a large Planck mean absorption coefficient compared to 
hydrocarbons (alkanes). 
Radiation intensity at the fuel surface of 0.3 m methanol, heptane, and toluene pool 
fires was investigated using one dimensional radiative transport equation with species 
concentration and temperature profile obtained by FDS.  The grid for FDS was far too big 
to capture flame structure and thus it underpredicts the temperature rise in the flame zone 
for all pool fires. Emission of combustion species of flame temperature at 1400 K was set 
as a boundary condition, and the transport equation for all pool fires was solved.  
Methanol pool fires had good agreement with previous experimental data, but heptane 
 
 134
and toluene didn?t when emission by species was set as the boundary condition.  When 
blackbody emission at 1400 K was set as an alternative boundary condition of heptane 
and toluene fire because of their optically thick flame, heptane yielded good agreement 
with previous experimental data, but toluene did not.  As a result, radiation intensity of 
methanol fire can be solved by optically thin condition with species emission and heptane 
can be by optically thick blackbody condition.  From the analysis of heptane and toluene, 
emission source within the fire could be stronger or source position could be closer to 
fuel surface since soot absorbed much radiation. Toluene fires need to be further 
investigated since soot absorption and emission completely dominates radiation heat 
transfer within the toluene fire relative to methanol and heptane.  Underprediction of the 
temperature rise in the flame zone resulted in low radiation intensity. Using the exact fuel 
absorption coefficient has a significant impact on radiation intensity at the fuel surface, 
but temperature dependency on the absorption coefficient is small since the discrete 
characteristic band range for fuel is much smaller than the entire infrared region 
absorption by soot. 
6.2 Recommendation for Further Research 
This dissertation only focused on the radiation heat transfer in the gas phase.  
However, radiation heat transfer of the condensed phase cannot be ignored since a fuel 
can only absorb radiation at fuel?s several characteristic band groups.  An infrared 
spectrum in the condensed phase is also broadened and more absorption can be 
considered relative to gas phase spectrum due to the huge population and association of 
molecules.  Moreover, condensed combustion products such as water and soot near or 
floating on the fuel surface can also affect the infrared absorption.  These additional 
 
 135
conditions should be included to understand more deeply the radiation absorption at fuel 
surface. Radiation absorption coefficient measurement of condensed phase fuel should be 
the first step to understand radiation transport at interface between gas and condensed 
phase.  The absorption coefficient database in this thesis will be incorporated into current 
FDS and will make significant improvement of fuel burning rate calculation including 
accurate prediction of radiation feedback on fuel surface. Additional fuel information 
such as acetylene, ethylene, gasoline and LNG will be conducted by the unique FTIR and 
expand fuel database in the FDS. This future work is necessary to expand energy 
feedback study to control practical large scale fire such as an oil tank fire.  
 
 136
 
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