NIST Technical Note 1440

Characteristics and Identification of SuperEffective Thermal Fire-Extinguishing Agents: 

Final Report, NGP Project 4C/1/890 

William M. Pitts

 Jiann C. Yang

Rodney A. Bryant

Linda G. Blevins

Marcia L. Huber

NIST Technical Note 1440

Characteristics and Identification of SuperEffective Thermal Fire-Extinguishing 

Agents: Final Report, NGP Project 4C/1/890

William M. Pitts

 Jiann C. Yang

 Rodney A. Bryant

Linda G. Blevins

Building and Fire Research Laboratory

Marcia L. Huber

Chemical Science and Technology Laboratory

June 2001

Issued July 2006

U.S. Department of Commerce

Donald L. Evans, Secretary

National Institute of Standards and Technology

Dr. Karen H. Brown, Acting Director
Certain commercial entities, equipment, or materials may be identified in this

document in order to describe an experimental procedure or concept adequately. Such

identification is not intended to imply recommendation or endorsement by the

National Institute of Standards and Technology, nor is it intended to imply that the

entities, materials, or equipment are necessarily the best available for the purpose.

National Institute of Standards and Technology Technical Note 1440

Natl. Inst. Stand. Technol. Tech. Note 1440, 138 pages (July 2006)

CODEN: NSPUE2
i

TABLE OF CONTENTS 

LIST OF TABLES............................................................................................................................................ iii 

LISTS OF FIGURES ......................................................................................................................................... v 

EXECUTIVE SUMMARY .............................................................................................................................. xi 

I. INTRODUCTION................................................................................................................................... 1

II. IDENTIFICATION AND TESTING OF POTENTIAL HIGHLY EFFECTIVE THERMAL 

AGENTS ................................................................................................................................................. 2

A. Screening Based on Thermophysical Properties............................................................................... 2

B. Experimental Testing of Lactic Acid and HFE7100....................................................................... 11

1. Lactic Acid ............................................................................................................................... 11

a) Estimation of the latent heat of vaporization for lactic acid/water mixtures ..................... 11

b) Experimental system.......................................................................................................... 13

c) Experimental results for lactic acid/water mixture fire suppression effectiveness ............ 14

2. HFE7100 .................................................................................................................................. 16

a) Testing of HFE7100 using the Dispersed Liquid Agent Fire Suppression Screen 

facility ................................................................................................................................ 16

b) Testing of HFE7100 using the Transient Application Recirculating Pool Fire facility..... 16

III. DETAILED CHEMICAL-KINETIC MODELING AND EXPERIMENTAL INVESTIGATIONS 

OF THEMAL AGENT FLAME EXTINGUISHMENT....................................................................... 19

A. Introduction..................................................................................................................................... 19

B. Introduction to Detailed Chemical-Kinetic Modeling of Diffusion Flames ................................... 22

C. Modeling Approach ........................................................................................................................ 27

1. CHEMKIN III and OPPDIF..................................................................................................... 27

2. Detailed Chemical-Kinetic Mechanism for Methane............................................................... 27

3. Detailed Chemical-Kinetic Mechanism for Propane................................................................ 27

4. Modeling Details ...................................................................................................................... 28

D. Model Results for Methane and Propane Flames Burning in Air................................................... 29

E. Extinction and Extinguishment of Methane and Propane Diffusion Flames by Nitrogen.............. 38

1. Experimental Systems for Measuring Extinguishing Concentrations of Gaseous Thermal 

Agents....................................................................................................................................... 40

a) Modified Dispersed Liquid Agent Fire Suppression Screen System (Tsuji Burner)......... 40

b) NIST Coflow Diffusion Flame Burner (Santoro Burner) .................................................. 41

2. Results for Thermal Agent Extinction of Methane and Propane Diffusion Flames Burning 

on Tsuji and Santoro Burners ................................................................................................... 43

a) Tsuji Burner ....................................................................................................................... 43

b) Santoro Burner................................................................................................................... 44

3. Modeling of Extinction and Extinguishment of Methane and Propane Flames by Nitrogen... 51

F. Effects of Argon Addition on Extinction and Extinguishment of Methane Diffusion Flames 

Burning in Argon “Air” .................................................................................................................. 56

G. Extinguishment of Methane and Propane Diffusion Flames by Carbon Dioxide, Argon, Helium 

and Water Vapor............................................................................................................................. 57

H. Effects of Dilution and Heat Extraction Location Relative to the Flame Front on Extinction and 

Extinguishment of Diffusion Flames .............................................................................................. 70

I. Prediction of Extinguishing Concentration for HFE7100............................................................... 80

IV. SURFACE COOLING .......................................................................................................................... 81

A. Introduction..................................................................................................................................... 81
ii

B. Evaporation of Liquid Droplets ...................................................................................................... 83

C. Spray Cooling ................................................................................................................................. 86

D. Convective Regime......................................................................................................................... 87

E. Nucleate Boiling Regime................................................................................................................ 87

F. Critical Heat Flux............................................................................................................................ 88

G. Transition and Film Boiling Regimes............................................................................................. 89

H. Summary......................................................................................................................................... 90

V. DISCUSSION........................................................................................................................................ 91

A. Liquid HFE7100 As a Potential Fire-Fighting Agent and Liquid Agent Effectiveness ................. 91

B. Conclusions from Detailed Chemical-Kinetic Modeling of Thermal Agent Effects...................... 93

VI. RECOMMENDATIONS FOR ADDITIONAL STUDY...................................................................... 96

VII. ACKNOWLEDGEMENTS .................................................................................................................. 96

VIII. APPENDIX A--DETAILED CHEMICAL-KINETIC MECHANISM FOR PROPANE 

COMBUSITON..................................................................................................................................... 97

IX. APPENDIX B—ADDITIONAL DETAILS CONCERNING THE COFLOW DIFFUSION 

FLAME EXPERIMENT ..................................................................................................................... 109

A. Mass-Flow Controllers and Their Calibration .............................................................................. 109

B. Detailed Description of Gas Flow Calculations............................................................................ 109

C. Uncertainty Analysis..................................................................................................................... 113

X. REFERENCES.................................................................................................................................... 115
iii

LIST OF TABLES 

Table 1. Family Types in the DIPPR Database...................................................................................................2 

Table 2. Results of Search for Compounds with High Heat of Vaporization at the Normal Boiling Point ........4 

Table 3. References for Property Data (Critical Point, Normal Boiling Point, Heat of Vaporization, 

Liquid Heat Capacity) ...........................................................................................................................5 

Table 4. Results of Search for Compounds with High Liquid Phase Heat Capacities at the Normal 

Boiling Point .........................................................................................................................................6 

Table 5. Results of Search for Compounds with High ΔHTotal (Molar Basis) .....................................................7 

Table 6. Results of Search for Compounds with High ΔHTotal (Mass Basis) ......................................................8 

Table 7. Some Properties of Lactic Acid Taken From Reference [9] ...............................................................11 

Table 8. Calculated Equivalent Mass and Mole Fraction Values for the Reference Blow-Off Velocity..........16 

Table 9. Some Parameters Used in Most OPPDIF Calculations of Methane and Propane Flames ..................30 

Table 10. Various Measures of Strain Rate Calculated for Methane/Air Diffusion Flames at Extinction.......34 

Table 11. Extinguishment Results Using the DLAFSS....................................................................................44 

Table 12. Measured Agent Volume Fractions at Onset of Flame-Base Instability (Osc) and for Flame 

Extinguishment (Ext) of Baseline Methane and Propane Coflow Diffusion Flames .......................48 

Table 13. Effects of Fuel and Oxidizer Velocity on Agent Concentrations at Onset of Flame Base 

Oscillation (Osc) and Flame Extinguishment (Ext) for the Methane Coflow Flame .......................48 

Table 14. Effects of Fuel and Oxidizer Velocity on Agent Concentrations at Onset of Flame Base 

Oscillation (Osc) and Flame Extinguishment (Ext) for the Propane Coflow Flame ........................48 

Table 15. Extinguishing Nitrogen Volume Fractions For Various Diffusion Flames Burning Methane 

and Propane ......................................................................................................................................51 

Table 16. Extinguishing Volume Fractions of Thermal Agents Calculated For Opposed-Flow Methane 

Flames and Measured For Heptane Flames in Cup Burner Experiments.........................................60 

Table 17. Calculated Extinguishing Volume Fractions for Methane and Propane Opposed-Flow 

Diffusion Flames for the Indicated Thermal Agents ........................................................................67 

Table 18. Adiabatic Flame Temperatures Calculated for Methane and Propane Premixed Flames 

Burning in Air Diluted with Extinguishing Volume Fractions of Thermal Agents..........................68 

Table 19. Mass-Flow Controller Specifications .............................................................................................110 

Table 20. Calibration Coefficients for the Air and Fuel Mass-Flow Controllers ...........................................110 
iv

Table 21. Calibration Coefficients for Path 1 Agent Mass-Flow Controller..................................................110 

Table 22. Calibration Coefficients for Path 2 Agent Mass-Flow Controller..................................................110 

Table 23. Agent Extinguishing Concentration Measurement Standard Deviation.........................................114 

Table 24. Uncertainty Budget – Agent Extinguishing Volume Fraction........................................................114 
v

LIST OF FIGURES 

Figure 1. The relative contributions of liquid heating, vaporization, and gas heating to 1400 K to the total 

heat absorbed by various thermal agents on a per mole basis are shown as bar graphs..................... 9 

Figure 2. The relative contributions of liquid heating, vaporization, and gas heating to 1400 K to the total 

heat absorbed by various thermal agents on a per mass basis are shown as bar graphs................... 10 

Figure 3. An equilibrium T-x,y diagram for lactic acid/water mixtures is shown for a pressure of 101 kPa. 

The symbols refer to the liquid ( ) and gaseous () phases. ........................................................ 12 

Figure 4. Enthalpies for the saturated vapor at the dew point ( ) and saturated liquid at the bubble point 

() are plotted as a function of water mole fraction for lactic acid/water mixtures........................ 12 

Figure 5. The enthalpy of vaporization for lactic acid/water mixtures for a pressure of 101 kPa is plotted 

as a function of the water mole fraction. .......................................................................................... 13 

Figure 6. A schematic of the dispersed liquid agent fire suppression screen (DLAFSS) apparatus is 

shown. .............................................................................................................................................. 14 

Figure 7. Velocities of the air at extinguishment (indicated by blow off of the opposed-jet diffusion 

flame) are plotted as a function of liquid application rate for the indicated lactic acid/water 

mixtures............................................................................................................................................ 15 

Figure 8. Velocities of the air at extinguishment (indicated by blow off of the opposed-jet diffusion 

flame) are plotted as a function of liquid application rate for HFE7100.......................................... 17 

Figure 9. A schematic is shown for the TARPF facility [37,38] as modified for the investigation of the 

effectiveness of liquid fire suppression agents................................................................................. 18 

Figure 10. Maximum flame temperatures are plotted as a function of the equal fuel and air velocity 

magnitudes for a methane/air opposed-flow diffusion flame. ....................................................... 30 

Figure 11. Calculated strain rates, a, are plotted as a function of distance from the fuel exit for low exit 

velocity magnitudes (25 cm/s for fuel and air) and for a condition very close to extinction 

(320.1 cm/s). .................................................................................................................................. 31 

Figure 12. The maximum flame temperature is plotted against a characteristic local strain rate, |ao|, 

defined to be equal to the highest absolute value of a on the air side observed outside of the 

boundary layer associated with the methane/air flame.................................................................. 32 

Figure 13. Mixture fraction is plotted as a function of distance from the fuel exit for low exit velocity 

magnitudes (25 cm/s for fuel and air) and for a condition very close to extinction (320.1 cm/s) 

for a methane/air diffusion flame. ................................................................................................. 32 

Figure 14. Calculated scalar dissipation rates, χ, are plotted as a function of distance from the fuel exit for 

low exit velocity magnitudes (25 cm/s for fuel and air) and for a condition very close to 

extinction (320.1 cm/s) for a methane/air diffusion flame. ........................................................... 33 
vi

Figure 15. Values of maximum flame temperature for opposed-flow methane/air diffusion flames are 

plotted as a function of χs that is varied by changing the velocities of the fuel and air. 

Extinction is calculated to occur for χs = 20.7 s-1........................................................................... 33 

Figure 16. Maximum flame temperatures are plotted as a function of the equal fuel and air velocity 

magnitudes for a methane/air opposed-flow diffusion flame. Results are compared for 

calculations using Versions 1.2, 2.11, and 3.0 of the GRIMech mechanism. [106]...................... 35 

Figure 17. Maximum flame temperatures are plotted as a function of the equal fuel and air velocity 

magnitudes for a propane/air opposed-flow diffusion flame......................................................... 36 

Figure 18. The maximum flame temperature is plotted as a function of the global stain rate ag for a 

propane/air opposed-flow diffusion flame..................................................................................... 36

Figure 19. The maximum flame temperature is plotted against a characteristic local strain rate, |ao|, 

defined to be equal to the highest absolute value of a on the air side observed outside of the 

boundary layer associated with the combustion zone for the propane/air flame. .......................... 37 

Figure 20. Values of maximum flame temperature for opposed-flow propane/air diffusion flames are 

plotted as a function of χs that is varied by changing the velocities of the fuel and air. 

Extinction is calculated to occur for χs = 26.3 s-1........................................................................... 38 

Figure 21. A schematic of the modified Santoro burner is shown.................................................................. 41 

Figure 22. A schematic and photo of the Santoro burner and flow control system are shown....................... 42 

Figure 23. Sketch of a methane flame showing the attached flame oscillation and subsequent stabilized 

lifted flame that result from the addition of nitrogen to the air coflow. ........................................ 45 

Figure 24. The evolution of the methane diffusion flame structure as additional N2 is added to the coflow 

air stream is shown. ....................................................................................................................... 45 

Figure 25. A sketch of the time evolution of a nearly extinguished propane flame is shown for the case of 

nitrogen dilution of the coflow air, t1 < t3. ..................................................................................... 46 

Figure 26. A time-resolved photograph taken by a digital camera shows the oscillating propane flame 

burning in air diluted with nitrogen. The complex azimuthal structure of the flame base, 

which has a much larger area than the burner tube, is clear. ......................................................... 49 

Figure 27. The cartoon shows the time evolution of the pulsing instability in the large flow-velocity 

propane diffusion flame observed when a concentration of a thermal fire-extinguishing agent 

near that required for extinguishment is added to the air coflow. The arrows indicate the 

direction of flame base propagation. The view is from an angle above the flame. ...................... 50 

Figure 28. Maximum calculated flame temperatures are plotted against methane and oxidizer exit 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

nitrogen. Symbols correspond to the volume fraction of added nitrogen..................................... 52 

Figure 29. Maximum calculated flame temperatures are plotted against propane and oxidizer exit velocity 

magnitudes for a series of propane/air opposed-flow diffusion flames diluted with nitrogen. 

Symbols correspond to the volume fraction of added nitrogen. .................................................... 52 
vii

Figure 30. Values of the maximum calculated flame temperature at extinction are plotted as a function of 

the fuel and oxidizer flow velocities for methane and propane flames burning in air diluted by 

various volume fractions of nitrogen............................................................................................. 53 

Figure 31. Values of maximum flame temperatures calculated using OPPDIF are plotted as a function of 

added nitrogen volume fraction for methane and propane opposed-flow flames. These values 

are compared with the corresponding adiabatic flame temperatures assuming stoichiometric 

combustion..................................................................................................................................... 54 

Figure 32. Ratios for the indicated measures of conditions at flame extinction are plotted as a function of 

nitrogen volume fraction added to the air for methane/air flames................................................. 55 

Figure 33. Maximum calculated flame temperatures are plotted against methane and oxidizer flow 

velocity magnitudes for a series of methane/argon “air” opposed-flow diffusion flames diluted 

with argon. Symbols correspond to the volume fraction of added argon. .................................... 57 

Figure 34. Maximum calculated flame temperatures are plotted against methane and oxidizer flow 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

argon. Symbols correspond to the volume fraction of added argon. ............................................ 58 

Figure 35. Maximum calculated flame temperatures are plotted against methane and oxidizer flow 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

helium. Symbols correspond to the volume fraction of added helium. ........................................ 58 

Figure 36. Maximum calculated flame temperatures are plotted against methane and oxidizer flow 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

carbon dioxide. Symbols correspond to the volume fraction of added carbon dioxide................ 59 

Figure 37. Maximum calculated flame temperatures are plotted against methane and oxidizer flow 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

water vapor. Symbols correspond to the volume fraction of added water vapor.......................... 59 

 Figure 38. Detailed chemical-kinetic modeling predictions for extinguishing volume fractions of 

nitrogen, carbon dioxide, argon, and helium for methane flames are compared with various 

experimental cup burner measurements using n-heptane. Model values for helium and 

nitrogen overlap and open symbols are used to identify the helium results. References for the 

cup burner measurements are Hamins et al. [33], Hirst and Booth [47], Sheinson et al. [49], 

Moore et al. [54], Saito et al. [55], and Babb et al. [56] ................................................................ 61 

Figure 39. Values of maximum flame temperatures (solid symbols) calculated using OPPDIF and the 

corresponding adiabatic flame temperatures (open symbols) calculated using EQUIL for 

methane flames are plotted as a function of added agent volume fraction in air for five thermal 

agents. Note that the adiabatic flame temperatures for argon and helium overlap and that the 

maximum calculated flame temperatures for helium and nitrogen fall very close together.......... 62 

Figure 40. Values of maximum flame temperature at extinction are plotted as a function of the 

corresponding fuel and oxidizer velocity magnitudes for a range of volume fractions of the 

various thermal agents. .................................................................................................................. 62 
viii

Figure 41. Values of maximum flame temperature at extinction are plotted as a function of the 

corresponding global strain rates, ag, for a range of volume fractions of the various thermal 

agents............................................................................................................................................. 63 

Figure 42. Values of maximum flame temperature at extinction are plotted against the corresponding 

characteristic local strain rates, |ao|, defined as the highest absolute value of strain rate 

observed outside of the boundary layer on the oxidizer side of the flame, for a range of volume 

fractions of the various thermal agents.......................................................................................... 64 

Figure 43. Maximum flame temperatures at extinction for N2, Ar, He, and CO2 as a function of the 

corresponding fuel and oxidizer velocity magnitudes are fit by two piecewise fourth-order 

polynomials (solid line). ................................................................................................................ 65 

Figure 44. The maximum temperature at extinction for opposed-flow methane flames is plotted as a 

function of the volume fraction of a thermal agent added to air divided by the volume fraction 

calculated to be required for flame extinguishment....................................................................... 65 

Figure 45. Calculated maximum flame temperatures are plotted as a function of velocity for a propane 

flame burning in air diluted with the indicated volume fractions of carbon dioxide. The 

extinguishing volume fraction is defined to be that (28.4 %) which yields an extinction 

temperature of 1433 K................................................................................................................... 66 

Figure 46. Calculated maximum flame temperatures are plotted as a function of velocity for a propane 

flame burning in air diluted with the indicated volume fractions of argon. The extinguishing 

volume fraction is defined to be that (50.2 %) which yields an extinction temperature of 

1433 K. .......................................................................................................................................... 66 

Figure 47. Calculated maximum flame temperatures are plotted as a function of velocity for a propane 

flame burning in air diluted with the indicated volume fractions of helium. The extinguishing 

volume fraction is defined to be that (39 %) which yields an extinction temperature of 1433 K. 67 

Figure 48. Experimental values of extinguishing volume fractions for N2, CO2, Ar, and He for 

counterflow porous (circles), opposed-jet (squares) and coflow (triangles) burners are plotted 

against the corresponding OPPDIF predictions (dotted line) for methane-air diffusion flames. 

Experimental values are taken from the present work as well from the following references: 

Ishizuka and Tsuji [48], Simmons and Wolfard [41], Puri and Seshadri [114], Hamins [121], 

and Ural [57]. Current results for helium are indicated by open symbols.................................... 68 

 Figure 49. Experimental values of extinguishing concentrations for N2, CO2, Ar, and He for counterflow 

porous (circles), opposed-jet (squares) and coflow (triangles) burners are plotted against the 

corresponding OPPDIF predictions (dotted line) for propane-air diffusion flames. 

Experimental values are taken from the present work as well from the following references: 

Simmons and Wolfhard [41], Puri and Seshadri [114], Hamins [121], Ural [57], Babb et al. 

[56], Moore et al. [54], and Hamins et al. [33]. ............................................................................ 69

Figure 50. Maximum calculated flame temperatures are plotted against methane and oxidizer exit 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with a 

surrogate agent similar to argon, but with Cp = 0. Symbols correspond to the volume fraction 

of surrogate agent added to the air................................................................................................. 70 
ix

Figure 51. Values of maximum flame temperature at extinction are plotted as a function of fuel and 

oxidizer extinction velocity magnitudes for a range of concentrations of argon and a similar 

surrogate agent having Cp = 0. The solid line is the result of the regression fits shown in 

Figure 43........................................................................................................................................ 71 

Figure 52. Temperature is plotted as a function of distance from the fuel exit for methane flames burning 

in air and air mixed with 60 % of a diluent having similar properties to Ar, but with zero heat 

capacity. Fuel and air exit velocity magnitudes are 25 cm/s for both flames. .............................. 72 

Figure 53. Calculated methane and oxygen volume fractions are shown on a semi-log plot as a function 

of distance from the fuel exit for methane flames burning in air (open symbols) and air mixed 

with 60 % of a diluent having similar properties to Ar, but with zero heat capacity. Fuel and 

air exit velocity magnitudes are 25 cm/s for both flames. ............................................................. 72 

 

Figure 54. Calculated flame temperature is plotted as a function of distance from the fuel exit for 

methane/air diffusion flames where the oxidizer is diluted with 5 % of either argon or the 

hypothetical agent X which reacts to form Y with Ea = 25.1 kJ/mol and ΔHX→Y = 96.1 kJ/mol. 

Methane and oxidizer exit velocity magnitudes are 25 cm/s......................................................... 74 

Figure 55. The volume fractions of X and Y are plotted as a function of distance from the fuel exit for a 

methane flame burning in air with 5 % added X. X reacts to form Y with Ea = 25.1 kJ/mol 

and ΔHX→Y = 96.1 kJ/mol. The spatial variation of temperature is also shown as the solid line. 

Methane and oxidizer exit velocity magnitudes are 25 cm/s......................................................... 74 

Figure 56. The volume fractions of X and Y are plotted as a function of distance from the fuel exit for a 

methane flame burning in air with 5 % added X. X reacts to form Y with Ea = 58.6 kJ/mol 

and ΔHX→Y = 96.1 kJ/mol. The spatial variation of temperature is also shown as the solid line. 

Methane and oxidizer exit velocity magnitudes are 25 cm/s......................................................... 75 

Figure 57. The volume fractions of X and Y are plotted as a function of distance from the fuel exit for a 

methane flame burning in air with 5 % added X. X reacts to form Y with Ea = 83.7 kJ/mol 

and ΔHX→Y = 96.1 kJ/mol. The spatial variation of temperature is also shown as the solid line. 

Methane and oxidizer exit velocity magnitudes are 25 cm/s......................................................... 76 

 

Figure 58. Values of maximum flame temperature for methane flames burning in air diluted with 5 % X 

are plotted as a function of the energy of activation for the conversion of X to Y. Methane and 

oxidizer exit velocity magnitudes are 25 cm/s............................................................................... 77 

Figure 59. Maximum calculated flame temperatures are plotted against methane and oxidizer exit 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

agent X that reacts to form Y with Ea = 41.8 kJ/mol and ΔHX→Y = 96.1 kJ/mol. Symbols 

correspond to the volume fractions of added X............................................................................. 77 

Figure 60. Maximum calculated flame temperatures are plotted against methane and oxidizer exit flow 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

argon and agent X (Ea = 41.8 kJ/mol and ΔHX→Y = 96.1 kJ/mol )................................................ 78 

Figure 61. Maximum calculated flame temperatures are plotted against methane and oxidizer exit flow 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

agent X which reacts to form Y with Ea = 41.8 kJ/mol and ΔHX→Y = 192.1 kJ/mol. Symbols 

correspond to the volume fractions of added X............................................................................. 79 
x

Figure 62. Values of maximum flame temperature at extinction are plotted as a function of fuel and 

oxidizer exit velocity magnitudes for air diluted with a range of volume fractions of argon and 

surrogate agent X having ΔHX→Y = 96.1 kJ/mol or 192.1 kJ/mol. The solid line is the result of 

the regression fits shown in Figure 43........................................................................................... 79 

Figure 63. Maximum calculated flame temperatures are plotted against methane and oxidizer exit velocity 

magnitudes for a series of methane/air opposed-flow diffusion flames diluted with C4F9OCH3. 

Symbols correspond to the volume fractions of added C4F9OCH3................................................ 80 

Figure 64. The droplet evaporation time is shown as a function of initial droplet diameter for the five 

fluids indicated. ............................................................................................................................. 85 

Figure 65. An illustration of a typical boiling curve associated with quenching of a hot surface by liquid 

droplets is shown. .......................................................................................................................... 86 

Figure 66. Calculated boiling curves in the convective regime are shown for the five indicated liquids....... 88 

Figure 67. Calculated boiling curves for the five liquids are shown for the transition and film boiling 

regimes........................................................................................................................................... 90 
xi

EXECUTIVE SUMMARY 

The use of halon 1301 for fire fighting is being phased out due to its deleterious effects on stratospheric 

ozone. This report summarizes the findings of a three-year study designed to characterize and identify 

super-effective thermal fire-fighting agents as possible replacements for these widely used compounds. 

Four distinct aspects related to the effectiveness of potential thermal agents have been considered. First, 

existing thermodynamic databases maintained by NIST have been searched in order to identify chemical 

compounds which are predicted to extract large amounts of heat from a combustion zone. Second, two 

liquids that were identified as being particularly interesting during the database search were tested 

experimentally for their extinguishing effectiveness. Third, detailed chemical-kinetic modeling and 

experimental studies of extinguishing volume fractions in simple flame systems were employed to 

improve the understanding of the effects of thermal agents on diffusion flames. Fourth, empirical heat 

transfer correlations for spray cooling of a surface were used to estimate the efficiencies of surface 

cooling by thermal agents. 

The database searches used two primary sources—the Design Institute for Physical Properties database 

containing 1458 compounds from 83 family types and a smaller database, REFPROP, containing 43 

compounds which is tailored to refrigerant applications. Additional substances were included that are not 

well represented in these databases. Compounds having high 1) heats of vaporization, 2) liquid-phase 

heat capacities, and 3) total heat absorption due to phase changes (if applicable), heating of a liquid (if 

applicable), and the heating of the gas phase to combustion temperatures were identified. The results are 

reported in tables of compounds ordered in terms of their ability to extract heat. 

Two compounds, methoxy-nonaflurobutane (HFE7100) and lactic acid, were identified during the data 

base searches as being especially interesting. HFE7100 was predicted to be particularly effective as a 

thermal agent and is available commercially. Lactic acid is capable of absorbing large quantities of heat 

even though it is very caustic and is flammable at certain volume fractions when mixed with air. Both 

agents were tested in the Dispersed Liquid Agent Fire Suppression Screen (DLAFSS) apparatus available 

at NIST. The effective extinguishing volume fraction of HFE7100 when released as a liquid was 1.5 %. 

Lactic acid was tested in mixtures with water at various concentrations. The acid mixtures were found to 

be less effective than water alone, indicating that the lactic acid was reacting and releasing heat that more 

than compensated for the heat extraction. 

HFE7100 was also tested in a screening apparatus known as the Transient Application Recirculating Pool 

Fire (TARPF) that incorporates a flame stabilized behind a bluff body in a turbulent oxidizer flow. The 

agent failed to extinguish a propane flame when it was released at nominal volume fractions in air twice 

as high as the extinguishing volume fraction measured in the DLAFSS. This observation is attributed to 

ineffective mixing. 

Even though the effects of thermal agents on diffusion flames have been widely studied, there are 

relatively few experimental or modeling investigations of the flame extinguishment process. As a result, 

flame extinguishment by thermal agents is incompletely understood. A combined experimental and 

modeling study was used to address this concern. Careful experimental measurements of extinguishing 

volume fractions by gaseous thermal agents added to air were made for two types of diffusion flames 

available at NIST. The first was a coflow laminar flame that has a similar configuration as the cup 

burner, which is widely used to test fire-fighting agents, and the second was the modified DLAFSS 

apparatus that incorporates a cylindrical porous burner with the fuel released in the opposite direction of 

the oxidizer flow (i.e., an opposed flow burner). Measurements were made for two fuels: methane and 

propane, and four thermal agents: nitrogen, carbon dioxide, argon, and helium. The results showed that 

the counterlfow flame was more difficult to extinguish than the coflow flame and that propane flames 
xii

required higher volume fractions of an agent for extinguishment than methane flames. The relative 

effectiveness of the agents in volume fraction terms was argon < nitrogen ≅ helium < carbon dioxide. 

Detailed chemical-kinetic modeling of opposed-flow diffusion flames was used to obtain insights into the 

effectiveness of thermal agents and their mechanisms of flame extinction. This approach is based on the 

hypothesis that the maximum flame temperature at extinguishment for a given fuel is a unique value as 

long as the agent is nonreactive in the flame. This hypothesis was tested by using experimental values for 

the volume fractions of nitrogen required to extinguish porous burner counterflow flames as the basis for 

the determination of the maximum flame temperature at extinguishment. This temperature was then used 

to determine the predicted extinguishing volume fractions for other agents. The calculations were 

performed for nitrogen, carbon dioxide, argon, helium, and water vapor added to the air and for methane 

and propane flames. For the methane flame the maximum flame temperature at extinguishment was 

calculated to be 1550 K and for the propane flame it was 1433 K. 

Comparisons of the predicted extinguishing volume fractions with the experimental measurements 

indicated that the chemical-kinetic modeling was capable of accurately predicting extinguishing 

conditions. The results for the methane flame were also found to be in good agreement with numerous 

published measurements of thermal agent extinguishing volume fractions for heptane pool fires recorded 

in cup burner experiments by a number of researchers. In particular, the calculations reproduced the 

experimental observation that similar volume fractions of nitrogen and helium are required to extinguish a 

flame, despite the fact that the heat capacity for nitrogen is considerably greater. The calculations also 

reproduced the experimental finding that propane flames are more difficult to extinguish than methane 

flames. 

A series of calculations were performed for gaseous HFE7100. An extinguishing concentration of 5.5 % 

was predicted, which is in good agreement with two unpublished experimental values of 6.1 %. Note that 

these values are nearly four times greater than the experimental value recorded when HFE7100 was 

released as a liquid. Measurements by other workers have indicated that water released as a liquid is also 

more effective than is predicted by simply considering the effects of heat removal. At present, these 

observations are not fully understood, but they do suggest that liquid agents may gain effectiveness from 

additional mechanisms. 

An advantage of detailed chemical-kinetic modeling studies is that surrogate agents having properties that 

are not physically realizable can be used to investigate specific details concerning extinguishment. A 

surrogate agent was specified which reacted over different temperature ranges to extract a predetermined 

amount of heat. The calculations showed that the effectiveness of this agent was independent of the 

location of heat extraction relative to the flame zone. In a second series of calculations a surrogate agent 

was used to isolate the role of dilution on extinguishment. When the agent, which was incapable of 

extracting heat, was added to the air, much higher concentrations were required to extinguish the flame 

than when heat was extracted. Details of the calculations revealed that extinguishment ultimately 

occurred due to oxygen passing through the flame zone as a result of the decreased overall reaction rate. 

Calculations of droplet evaporation times using the classical d2

-law for the five fluids (water, lactic acid, 

C3F5H3O, HFE7100, and R338mccq) identified as having the highest latent heat of vaporization (per unit 

mass) by the database searches were performed as part of the surface cooling studies. Empirical heat 

transfer correlations from the spray surface quenching literature were used to assess the surface cooling 

characteristics of these fluids for various heat transfer regimes. Based on these calculations, water and 

lactic acid appear to be more effective than the other three fluids for surface cooling applications. 
xiii

The following recommendations are made based on the findings of the study: 

1. The effectiveness of HFE7100 as a fire-extinguishing agent should be tested on full-scale 

simulations of aircraft fires. 

2. Additional studies of the effectiveness of fire extinguishing agents released as liquids should 

be performed with a focus on confirming and understanding their enhanced performance 

relative to that expected based on simple heat extraction. 

3. Experiments should be designed and performed with a goal of better understanding the 

interactions of liquid agent droplets with heated and reacting surfaces. Such an 

understanding is needed to better predict the effectiveness of liquid agents and could lead to 

improved approaches for delivering such agents to a fire. 
1

I. INTRODUCTION 

The use of halon 1301 for fire fighting is being phased out due to its deleterious effects on stratospheric 

ozone. This report summarizes the findings of a three-year study designed to characterize and identify 

super-effective thermal fire-fighting agents as possible replacements for these effective compounds. 

“Thermal” agents refer to compounds that act simply by extracting heat from a flame zone and lowering 

the temperature to a point where combustion can no longer be sustained. These types of agents should be 

contrasted with “chemical” agents that generate active chemical species (e.g., the bromine atoms 

generated by halons) that interfere with the radical chain branching mechanisms required to sustain 

combustion. 

There are a number of endothermic physical processes that can extract heat from a gaseous flame zone, 

thus lowering the temperature and ultimately leading to flame extinguishment. These include simple 

heating (i.e., heat capacity) of an agent, phase changes such as vaporization of a liquid or sublimation of a 

solid, endothermic molecular decomposition (note that this process is classed as a physical process as 

long as the initial agent and its products do not participate in the combustion chemistry), and simple 

dilution which can modify flame temperatures by spreading the heat released by combustion over larger 

volumes and by slowing three-body reactions due to lower species collision rates. The flame temperature 

is also expected to be a function of the thermal diffusivity of an agent. 

Another potentially effective way for thermal agents to extinguish a flame fueled by liquids or solids is to 

interact with the fuel surface to lower the temperature to a point where the fuel generation rate is 

insufficient to maintain combustion. This mechanism for fire extinguishment has not been extensively 

studied, and the physical properties that determine the effectiveness of an agent operating in this mode are 

not known. 

During this investigation several aspects related to the effectiveness of potential thermal agents have been 

considered. One part of the study focused on identifying and testing chemicals likely to be particularly 

effective as thermal fire extinguishing agents. Existing thermodynamic data bases maintained by NIST 

were searched to select compounds predicted to absorb large amounts of heat as the temperature is raised. 

Two chemicals—lactic acid and methoxynonafluorobutane—were identified as being particularly 

interesting. The effectiveness of these chemicals were characterized using screening tests developed as 

part of the Next Generation Fire Suppression Technology Program (NGP) of the Strategic Environmental 

Research and Development Program (SERDP) of the U. S. Department of Defense. A combined 

modeling and experimental effort was aimed at improving the understanding of the effects of thermal 

agents on fires. This effort was motivated in part by the realization that different types of experiments 

yield significantly different estimates for extinguishing concentrations. The effectiveness of the wellknown thermal agents nitrogen, carbon dioxide, argon, helium, and water were emphasized. Fuel effects 

were also considered. Lastly, empirical heat transfer correlations for spray cooling of a surface have been 

used to estimate the efficiencies of surface cooling by thermal agents that are expected to be very efficient 

at extracting heat from combustion regions. 

Separate major sections summarize the findings of the three major parts of the study. A fourth section 

summarizes the major findings and provides additional discussion, and the final section provides 

recommendations for additional research and development. This report incorporates material that is 

included in an earlier National Institute of Standards and Technology Internal Report that summarized the 

findings of the first year of the effort. [1] Selected aspects have been presented during a number of 

technical meetings. [2,3,4,5,6,7,8] 
2

Table 1. Family Types in the DIPPR Database 

1 n-Alkanes 29 Cycloaliphatic alcohols 57 Other amines, imines 

2 Methylalkanes 30 Aromatic alcohols 58 Nitriles 

3 Dimethylalkanes 31 Polyols 59 C,H,NO2 compounds 

4 Other alkanes 32 n-Aliphatic acids 60 Isocyanates/diisocyanates 

5 Cycloalkanes 33 Other aliphatic acids 61 Mercaptans 

6 Alkylcyclopentanes 34 Dicarboxylic acids 62 Sulfides/theophenes 

7 Alkylcyclohexanes 35 Aromatic carboxylic acids 63 Polyfunctional acids 

8 Multi-ring cycloalkanes 36 Anhydrides 64 Polyfunctional esters 

9 1-Alkynes 37 Formates 65 Other polyfunctional C,H,O 

10 2,3,4-Alkenes 38 Acetates 66 Polyfunctional nitriles 

11 Methylalkenes 39 Propionates & Butyrates 67 Nitroamines 

12 Ethyl and higher alkenes 40 Other saturated aliphatic esters 68 Polyfunc. amides/amines 

13 Cycloalkenes 41 Unsaturated aliphatic esters 69 Polyfunctional C,H,O,N 

14 Dialkenes 42 Aromatic esters 70 Polyfunctional C,H,O,S 

15 Alkynes 43 Aliphatic ethers 71 Polyfunc. C,H,O,halides 

16 n-Alkylbenzenes 44 Other ethers and diethers 72 Polyfunc. C,H,N,halides 

17 Other alkylbenzenes 45 Epoxides 73 Other polyfunc. organics 

18 Other monoaromatics 46 Peroxides 74 Elements 

19 Napthalenes 47 C1/C2 Aliphatic chlorides 75 Silanes/siloxanes 

20 Other condensed rings 48 C3 & higher aliph. chlorides 76 Organic-inorganic 

21 Diphenyl/polyaromatics 49 Aromatic chlorides 77 Inorganic acids 

22 Terpenes 50 C,H,Br compounds 78 Inorganic bases 

23 Other hydrocarbon rings 51 C,H,I compounds 79 Organic salts 

24 Inorganic gases 52 C,H,F compounds 80 Sodium salts 

25 Aldehydes 53 C,H multihalogen compounds 81 Other inorganic salts 

26 Ketones 54 n-Aliphatic primary amines 82 Inorganic halides 

27 n-Alcohols 55 Other aliphatic amines 83 Other inorganics 

28 Other alcohols (aliphatic) 56 Aromatic amines

II. IDENTIFICATION AND TESTING OF POTENTIAL HIGHLY EFFECTIVE THERMAL 

AGENTS 

The objective of this sub-task was to identify and test chemical compounds that were particularly 

promising as thermal agents. The first step in this process was to search thermophysical property 

databases and identify substances that had the potential to be particularly effective fire extinguishing 

agents based on thermophysical properties. Two compounds were subsequently tested experimentally 

using fire suppression screens developed as part of the SERDP effort. 

A. Screening Based on Thermophysical Properties 

We identified two thermophysical property databases to search. The first was the DIPPR (Design Institute 

for Physical Properties) Database, version 9.02 [9] which contained 1458 substances from 83 family 

types. The families are listed in Table 1. The second database, REFPROP, Version 5, [10] is a much 

smaller database tailored to alternative refrigerants. It contains 43 refrigerants including many candidates 

for replacing HCFCs. Some are fluorinated ethers (E134, E245) that are not present in the DIPPR 

database. 
3

In addition, we wanted to include representative substances from some families of chemicals not well 

represented in existing thermophysical property databases, such as fluorinated ethers, alcohols and 

amines. The fluorinated ethers are especially interesting since their atmospheric lifetimes may be 

significantly lower than those of chlorofluorocarbons. [11] Some of these have been identified as 

possible replacements for blowing agents, refrigerants, fire suppression agents, and as solvents. 

[12,13,14,15,16,17] We selected several cyclic fluorinated ether compounds [fluorinated oxiranes, 

oxetanes, and furans], some non-cyclic methyl ethers [HFE116, HFE125], fluorinated methyl ethyl ethers 

with two or fewer hydrogen atoms [HFE227me, HFE236me], and some larger fluorinated ethers 

[perfluorodimethoxymethane (CF3OCF2OCF3), perfluoropropyltrifluoromethyl ether (CF3OCF2CF2CF3), 

heptafluoropropyl-1,2,2,2-tetrafluoroethyl ether (CF3CHFOCF2CF2CF3), and methoxy-nonafluorobutane 

(C4F9OCH3, HFE7100)]. In addition to the fluorinated ethers, we added two fluorinated amines to the list 

of substances to search and also the alternative refrigerant HFC-338mccq (CH2FCF2CF2CF3) and the 

fluorinated alcohol 2,2,3,3,3-pentafluoropropanol (CF3CF2CH2OH). 

The physical properties that are important for thermal agents are high latent heats of vaporization and 

high liquid and vapor heat capacities. We first searched the databases and the additional fluids mentioned 

above for high latent heats of vaporization. For fluids where data were unavailable, we estimated the 

critical properties using the NIST Structures and Properties program [18] and then estimated the latent 

heats using the approach of Fishtine [19]. We then eliminated substances on the list that either were 

identified as flammable, toxic, or had known ozone depletion problems. However, we did not have 

complete information on toxicity, so some substances that appear on our final list will need to be 

investigated further to determine if there are potential deleterious health effects. We also did not use 

global warming potential or electrical conductivity as screening parameters. If one considers global 

warming potential, then the fully fluorinated (perfluorinated) alkanes such as R218 and decafluorobutane 

would probably have to be ruled out. We used information in the DIPPR database on flash points and 

upper and lower flammability limits. The DIPPR database does not contain any information on toxicity 

or other health effects. For this information we used manufacturers safety data sheets and Hawley. [20] 

We also used the web site at http://chemfinder.camsoft.com/ that gives information on ozone depletion 

and global warming. 

Table 2 lists the compounds that remained, in order of decreasing heat of vaporization at the normal 

boiling point, and includes R13B1 and water for reference. Table 3 identifies the sources of property data 

for critical points, normal boiling points, latent heat of vaporization, and liquid heat capacity. The general 

trend shown in Table 2 is quite predictable--the larger molecules have higher boiling points and higher 

heats of vaporization. Lactic acid is the only unusual fluid that appears is Table 2--all other fluids are 

basically {C, F, H}, {C, F} or {C, F, O} compounds. Lactic acid, CH3CH(OH)COOH, is a strong irritant 

to the skin and corrosive in concentrated form and would not be a suitable agent. However, it may be at 

least partially soluble in fluorinated ethers such as HFE134 or in alternative refrigerants such as R227ea. 

The second property we searched on was liquid heat capacity at the normal boiling point. When data were 

unavailable, the liquid heat capacity was estimated using the Chueh-Swanson method. [21] This method 

provides the liquid heat capacity at 20 ΕC based on the structure of a compound. The results are shown in 

Table 4 in order of decreasing liquid-phase heat capacity at the normal boiling point and include R13B1 

and water for reference. Again, any compounds that were known to be flammable or toxic or to have 

known ozone depletion problems were eliminated. Table 4 indicates the same trend that was seen in 

Table 2, i.e., that larger compounds have higher boiling points and higher heats of vaporization and heat 

capacities. Also, in general, the ethers have higher boiling points and higher heats of vaporization at their 

normal boiling points than their alkane analogs. The fluorinated alcohol has a high boiling point due to 

the hydrogen bonding that occurs in alcohols. 
4

Table 2. Results of Search for Compounds with High Heat of Vaporization at the Normal Boiling 

Point

In addition to looking at the latent heat of vaporization and the liquid heat capacity at the normal boiling 

point, one may also look at the total heat absorbed in going from the fluid at room temperature up to a 

temperature of 1400 K, which was selected as a representative combustion temperature. Other choices 

are possible including the calculated maximum flame temperatures of 1550 K and 1433 K identified 

below during the detailed chemical-kinetic modeling of methane and propane flames, respectively. The 

actual value used is unlikely to affect the relative ordering of agents. The total heat absorbed consists of 

three contributions, 

, l v g

Total ΔH =ΔH +ΔH +ΔH ( 1 )

Compound Tb(K) ΔHvap (kJ/mol) 

lactic acid, C3H6O3 455 59.2 

water 373.1 40.0 

2,2,3,3,3-pentafluoropropanol, C3F5H3O 353.15 37.6 

perfluoro-2-butyltetrahydrofuran, C8F16O 375.15 35.4 

methoxy-nonafluorobutane, HFE7100 334.0 30.3 

heptafluoropropyl-1,2,2,2-tetrafluoroethyl ether 315.2 29.0 

difluoromethyl-1,2,2,2-tetrafluoroethyl ether, E236me 296.5 26.9 

1,1,1,2,2,3,3,4-octafluorobutane, R338mccq 301 26.8 

tris(difluoromethyl)amine, C3H3F6N 275 25.8 

1,1,2,2-tetrafluorodimethylether, E134 279.4 25.4 

1,1,1,2,3,3-hexafluoropropane, R236ea 279.7 25.1 

perfluorotrimethylamine, C3F9N 264 23.9 

trifluoromethyl-1,2,2,2-tetrafluoroethyl ether, E227me 263.6 23.7 

octafluorocyclobutane, C4F8 267 23.2 

decafluorobutane, C4F10 271 23.2 

perfluorodimethoxymethane, CF3OCF2OCF3 263 23.1 

perfluoropropylmethyl ether, C3F7OCF3 279.9 22.8 

bis(trifluoromethyl)ether, E116 257 22.8 

octafluorofuran, C4F8O 272.42 22.7 

1,1,2,2-tetrafluoroethane, R134 250 22.5 

1,1,1,2-tetrafluoroethane, R134a 247 22.3 

perfluoroisobutane, C4F10 252.45 22.0 

octafluoro-2-butene 270.4 21.7 

1,1,1,2,3,3,3-heptafluoropropane, R227ea 257.5 21.4 

perfluorooxetane, C3F6O 244.0 20.9 

pentafluorodimethylether, E125 235 20.0 

octafluoropropane, R218 236.4 19.7 

hexafluoropropylene 243.5 19.4 

pentafluoroethane, R125 225.2 19.1 

bromotrifluoromethane, R13B1 215.26 17.4 

hexafluoroethane, R116 194.95 16.1 
5

Table 3. References for Property Data (Critical Point, Normal Boiling Point, Heat of Vaporization, 

Liquid Heat Capacity)

where the first contribtion, ΔH1, is the heat involved in taking the liquid from room temperature up to the 

normal boiling point, Tb, 

Δ =∫

Tb

K

liquid H Cp T 1 298 d . ( 2 )

Since the heat capacity of a liquid does not change significantly over a small temperature range, we used 

the value of liquid heat capacity at the normal boiling point. If this was unavailable, we estimated the 

liquid phase heat capacity at 20 ΕC using the method of Chueh and Swanson. [21] The second term, ΔHv, 

is the latent heat of vaporization at the normal boiling point. The third contribution, ΔHg, is found by 

integrating the gas-phase heat capacity from the normal boiling point to 1400 K, 

Compound References 

perfluoro-2-butyltetrahydrofuran, C8F16O 22, 21, 19 

methoxy-nonafluorobutane, HFE7100 23, 21, 19 

lactic acid, C3H6O3 9 

heptafluoropropyl-1,2,2,2-tetrafluoroethyl ether 18, 21, 19 

decafluorobutane, C4F10 9 

perfluoropropylmethyl ether, C3F7OCF3 24, 21, 19 

perfluorodimethoxymethane, CF3OCF2OCF3 25, 21, 19 

octafluoro-2-butene 9 

octafluorofuran, C4F8O 24, 21, 19 

octafluorocyclobutane, C4F8 9 

perfluorotrimethylamine, C3F9N 18, 21, 19 

1,1,1,2,3,3,3-heptafluoropropane, R227ea 10 

perfluoroisobutane, C4F10 12, 21, 19 

tris(difluoromethyl)amine, C3H3F6N 18, 21, 19 

trifluoromethyl-1,2,2,2-tetrafluoroethyl ether, E227me 26, 21, 19 

1,1,1,2,2,3,3,4-octafluorobutane, R338mccq 27, 21, 19 

1,1,1,2,3,3-hexafluoropropane, R236ea 10 

difluoromethyl-1,2,2,2-tetrafluoroethyl ether, E236me 26, 21, 19 

octafluoropropane, R218 10 

2,2,3,3,3-pentafluoropropanol, C3F5H3O 28, 21, 19 

perfluorooxetane, C3F6O 25, 21, 19 

1,1,2,2-tetrafluorodimethylether, E134 29 

bis(trifluoromethyl)ether, E116 18, 21, 19 

hexafluoropropylene 9 

pentafluorodimethylether, E125 24, 21, 19 

pentafluoroethane, R125 10 

1,1,2,2-tetrafluoroethane, R134 10 

hexafluoroethane, R116 10 

1,1,1,2-tetrafluoroethane, R134a 10 

bromotrifluoromethane, R13B1 1 

water 9 
6

Table 4. Results of Search for Compounds with High Liquid Phase Heat Capacities at the Normal 

Boiling Point 

Δ =∫ K

T

gas

g p b

H C T 1400 d . ( 3 ) 

We estimated the gas phase heat capacities using the method of Rihani and Doraiswamy [30], which is 

based on structural contributions. For agents with boiling points below 298 K, the total heat involved is 

just the contribution ΔHv. Table 5 summarizes the results of this computation, with compounds listed in 

order of their ΔHTotal expressed on a molar basis (kJ/mol). Table 6 gives the same quantity, but expressed 

on a mass basis (kJ/kg). We have also included some common agents such as nitrogen, argon, water and 

carbon dioxide for comparison. 

The results of Table 5 indicate that the top candidates for streaming agents (defined here as having boiling 

points higher than 293 K), on a molar basis, are perfluoro-2-butyltetrahydrofuran, methoxynonafluorobutane, heptafluoropropyl-1,2,2,2-tetrafluoroethyl ether, and 1,1,1,2,2,3,3,4-octafluorobutane. 

Compound Tb (K) Cp (J/mol K) 

perfluoro-2-butyltetrahydrofuran, C8F16O 375.15 364.2 

methoxy-nonafluorobutane, HFE7100 334.0 292.8 

lactic acid, C3H6O3 455 290.1 

heptafluoropropyl-1,2,2,2-tetrafluoroethyl ether 315.2 269.6 

decafluorobutane, C4F10 271 241.4 

perfluoropropylmethyl ether, C3F7OCF3 279.9 231.9 

perfluorodimethoxymethane, CF3OCF2OCF3 263 226.0 

octafluoro-2-butene 270 218.1 

octafluorofuran, C4F8O 272.42 217.6 

octafluorocyclobutane, C4F8 267 208.1 

perfluorotrimethylamine, C3F9N 264 204.0 

1,1,1,2,3,3,3-heptafluoropropane, R227ea 257.5 200.1 

perfluoroisobutane, C4F10 252.45 196.8 

tris(difluoromethyl)amine, C3H3F6N 275 194.6 

trifluoromethyl-1,2,2,2-tetrafluoroethyl ether, E227me 263.6 187.9 

1,1,1,2,2,3,3,4-octafluorobutane, R338mccq 301 186.4 

1,1,1,2,3,3-hexafluoropropane, R236ea 279.7 185.4 

difluoromethyl-1,2,2,2-tetrafluoroethyl ether, E236me 296.5 184.9 

octafluoropropane, R218 236.4 183.8 

2,2,3,3,3-pentafluoropropanol, C3F5H3O 353.15 173.5 

perfluorooxetane, C3F6O 244.0 171.9 

1,1,2,2-tetrafluorodimethylether, E134 279.4 150.8 

bis(trifluoromethyl)ether, E116 257 150.3 

hexafluoropropylene 243.5 148.2 

pentafluorodimethylether, E125 235 147.1 

pentafluoroethane, R125 225.2 134.2 

1,1,2,2-tetrafluoroethane, R134 250 133.3 

hexafluoroethane, R116 194.95 130.6 

1,1,1,2-tetrafluoroethane, R134a 247 129.4 

bromotrifluoromethane, R13B1 215.26 100.3 

water 373.1 76.0 
7

Table 5. Results of Search for Compounds with High ΔHTotal (Molar Basis) 

Table 6 indicates that methoxy-nonafluorobutane (HFE7100) is high on the list when expressed on a mass 

basis. Methoxy-nonafluorobutane is available commercially [23], the others are not available 

commercially but have been synthesized and used for research [24,25,26]. The top total-flooding 

candidates (defined as having boiling points lower than 293 K) are perfluoropropyltrifluromethyl ether, 

perfluoroisobutane, decafluorobutane, and octafluorocyclobutane. Of these, decafluorobutane and 

octafluorocyclobutane are available commercially. [31] All of these compounds contain only C, H, F, 

and O. 

As noted above, HFE7100 is ranked near the top of the compounds ordered in terms of their predicted 

ability to extract heat upon heating from room temperature to a typical combustion temperature. This 

Compound Tb(K) ΔHTotal (kJ/mol) 

perfluoro-2-butyltetrahydrofuran, C8F16O 375.2 608.4 

heptafluoropropyl-1,2,2,2-tetrafluoroethyl ether 315.2 421.9 

methoxy-nonafluorobutane, HFE7100 334 407.6 

perfluoropropyltrifluoromethyl ether,CF3OCF2CF2CF3 279.9 336.3 

perfluoroisobutane, C4F10 252.5 321.2 

1,1,1,2,2,3,3,4-octafluorobutane, R338mccq 301 321.0 

decafluorobutane, C4F10 271 318.5 

octafluorocyclobutane, C4F8 267 303.2 

perfluorotrimethylamine, C3F9N 264 293.8 

lactic acid, C3H6O3 455 292.9 

perfluorodimethoxymethane, CF3OCF2OCF3 263 286.8 

octafluorofuran, C4F8O 272.4 289.8 

2,2,3,3,3-pentafluoropropanol, C3F5H3O 353.15 280.8 

octafluoro-2-butene 270 261.9 

tris(difluoromethyl)amine, C3H3F6N 275 256.5 

trifluoromethyl-1,2,2,2-tetrafluoroethyl ether, E227me 263.6 255.3 

perfluorooxetane, C3F6O 244.0 252.9 

octafluoropropane, R218 236.4 250.8 

difluoromethyl-1,2,2,2-tetrafluoroethyl ether, E236me 296.5 239.4 

1,1,1,2,3,3,3-heptafluoropropane, R227ea 257.5 236.5 

1,1,1,2,3,3-hexafluoropropane, R236ea 279.7 222.2 

bis(trifluoromethyl)ether, E116 257 196.2 

hexafluoropropylene 243.5 192.9 

pentafluorodimethylether, E125 235 183.8 

hexafluoroethane, R116 194.95 181.1 

1,1,2,2-tetrafluorodimethylether, E134 279.4 170.2 

pentafluoroethane, R125 225.2 166.8 

1,1,1,2-tetrafluoroethane, R134a 247 156.8 

1,1,2,2-tetrafluoroethane, R134 250 152.8 

bromotrifluoromethane, R13B1 215.26 110.9 

water 373.1 87.5 

carbon dioxide N/a 56.2 

nitrogen 77.4 34.7 

argon 87.3 22.9 
8

Table 6. Results of Search for Compounds with High ΔHTotal (Mass Basis) 

particular compound was developed as a replacement for ozone-depleting chemicals used in a variety of 

applications. It has been estimated to have a zero ozone depletion potential, a relatively low global 

warming potential, favorable toxicological properties, and good materials compatibility properties. [23] It 

has been approved under the Significant New Alternatives Policy (SNAP) of the United States 

Environmental Protection Agency. There is an existing patent dealing with use of HFE7100 as a fireextinguishing agent. [32] Based on these favorable properties, it was decided to experimentally 

characterize the extinguishing capability of HFE7100. 

The data included in Table 6 indicate that lactic acid is predicted to be highly effective as a thermal agent. 

Clearly, this compound is not a potential candidate as a fire suppression agent due to its high boiling and 

Compound Tb(K) ΔHtotal (kJ/kg) 

water 373.1 4855.7 

lactic acid, C3H6O3 455 3251.6 

2,2,3,3,3-pentafluoropropanol, C3F5H3O 353.15 1872.0 

methoxy-nonafluorobutane, HFE7100 334 1630.4 

1,1,1,2,2,3,3,4-octafluorobutane, R338mccq 301 1588.7 

1,1,1,2-tetrafluoroethane, R134a 247 1536.8 

tris(difluoromethyl)amine, C3H3F6N 275 1535.5 

perfluorooxetane, C3F6O 244.0 1523.2 

octafluorocyclobutane, C4F8 267 1515.8 

1,1,2,2-tetrafluoroethane, R134 250 1497.6 

heptafluoropropyl-1,2,2,2-tetrafluoroethyl ether 315.2 1475.0 

perfluoro-2-butyltetrahydrofuran, C8F16O 375.2 1462.3 

1,1,1,2,3,3-hexafluoropropane, R236ea 279.7 1461.4 

1,1,2,2-tetrafluorodimethylether, E134 279.4 1442.0 

difluoromethyl-1,2,2,2-tetrafluoroethyl ether, E236me 296.5 1424.7 

1,1,1,2,3,3,3-heptafluoropropane, R227ea 257.5 1390.9 

pentafluoroethane, R125 225.2 1389.8 

trifluoromethyl-1,2,2,2-tetrafluoroethyl ether, E227me 263.6 1372.4 

pentafluorodimethylether, E125 235 1351.3 

perfluoroisobutane, C4F10 252.5 1349.6 

octafluorofuran, C4F8O 272.4 1341.5 

decafluorobutane, C4F10 271 1338.2 

octafluoropropane, R218 236.4 1333.8 

perfluorotrimethylamine, C3F9N 264 1329.3 

perfluoropropyltrifluoromethyl ether, CF3OCF2CF2CF3 279.9 1323.9 

hexafluoroethane, R116 194.95 1312.2 

octafluoro-2-butene 270 1309.2 

perfluorodimethoxymethane, CF3OCF2OCF3 263 1303.5 

hexafluoropropylene 243.5 1285.8 

carbon dioxide, CO2 n/a 1276 

bis(trifluoromethyl)ether, E116 257 1273.9 

nitrogen, N2 77.4 1238.3 

bromotrifluoromethane, R13B1 215.26 744.7 

argon 87.3 573.2 
9

Figure 1. The relative contributions of liquid heating, vaporization, and gas heating to 1400 K to the total 

heat absorbed by various thermal agents on a per mole basis are shown as bar graphs. 

melting points and caustic nature. It is also an organic compound and may be combustible. However, 

based solely on its ability to extract heat, it is predicted to be nearly twice as effective on a mass basis as 

any of the other potential thermal agents considered, except water. Its ability to extract heat is predicted 

to be roughly 2/3 of that of water on a mass basis and 3.5 times greater on a molar basis. Since lactic acid 

is soluble in water, it was deemed worthwhile to investigate the suppression characteristics of mixtures of 

these two polar liquids. As described below, the extinguishing effectiveness of water/lactic acid mixtures 

was experimentally investigated. 

In order to better understand the effectiveness of thermal agents, experimental and modeling 

investigations of flame extinguishment by the widely recognized and investigated gaseous thermal agents 

nitrogen, carbon dioxide, argon, helium, and water were also carried out. It is of interest to compare the 

relative contributions of the various heat extraction mechanisms included in Eq. (1). Figure 1 shows a bar 

plot of the three heat extraction processes for the four gaseous agents, the two liquid agents identified for 

further investigation, and water in terms of heat extraction per mole of agent. On a molar basis HFE 7100 

is predicted to be the most effective, with lactic acid a close second. The contribution of liquid processes 

to the total heat extraction is relatively small for HFE7100. Liquid water is predicted to be the next most 

effective due primarily to the relatively high heat absorbed during evaporation. The four gaseous agents 

are predicted to be relatively ineffective and are ordered CO2 > N2 > Ar = He. 

Estimated Total Heat Extraction (kJ/mol)

ΔHTotal (kJ/mol)

0 100 200 300 400

ΔHl

ΔHv

ΔHg

N2

Ar

CO2 HFE7100 (C5F9H3O)

Lactic Acid (C3H6O3)

H2O

He
10

Figure 2. The relative contributions of liquid heating, vaporization, and gas heating to 1400 K to the total 

heat absorbed by various thermal agents on a per mass basis are shown as bar graphs. 

The results included in Figure 1 have been replotted in Figure 2 on a per mass basis. The plot now has a 

very different appearance. The most effective agent in these terms is helium followed by water and lactic 

acid. On this plot the role of heat extraction by heating and vaporization of the liquid agents is clear. It 

can be seen that for water over half of the heat extraction arises from the liquid processes. For lactic acid 

the contribution of liquid vaporization to the total heat extraction is significant, but greatly reduced as 

compared to water. The large differences between the HFE7100 and lactic acid and water are due to 

hydrogen bonding that exists in water and lactic acid. This bonding significantly increases the amount of 

heat energy required to vaporize liquids when it is present. 

Note that nitrogen and carbon dioxide are predicted to extract roughly the same amount of heat per kg, 

while the amount extracted by gaseous HFE7100 is only slightly higher. In fact, it has been found that for 

a number of gaseous species expected to act primarily as thermal agents the mass required to extinguish a 

fire is roughly constant. [33] However, it is clear from the results shown in Figure 2 that this criterion 

should only be used to provide guidance and that it is not generally applicable to a wide range of 

molecular species. 

Estimated Total Heat Extraction (kJ/kg)

ΔHTotal (kJ/kg)

0 1000 2000 3000 4000 5000

ΔHl

ΔHv

ΔHg

N2

Ar

CO2

HFE7100 (C5F9H3O)

Lactic Acid (C3H6O3)

H2O

He
11

Table 7. Some Properties of Lactic Acid Taken From Reference [9] 

Property 

Molecular weight (kg/kmol) 90.097 

Normal boiling point (K) 490.0 

Critical temperature (K) 675.0 

Latent heat of vaporization at normal boiling point (J/kmol) 5.92 × 107

Standard heat of combustion (J/kmol) − 1.228 × 109

Flash point (K) 410.0 

Lower flammability limits (vol %) 3.1 

Upper flammability limits (vol %) 18.0 

B. Experimental Testing of Lactic Acid and HFE7100 

Two chemicals—lactic acid and HFE7100—were identified in the last section as being particularly 

interesting as potential highly effective thermal agents. In this section the effectiveness of these agents 

are tested using experimental screens developed as part of the NGP. 

1. Lactic Acid 

Table 7 summarizes some of the thermophysical properties of lactic acid. Despite its expected ability to 

withdraw significant levels of heat from a flame zone, lactic acid is flammable. There will be competitive 

effects between the heat release and heat extraction in the suppression processes. One approach for 

mitigating the effect of the heat release is to mix lactic acid with a good thermal agent like water, which is 

miscible with lactic acid. The mixing of lactic acid with water may also offer potential synergistic effects 

for fire suppression effectiveness. For these reason, our main focus is the fire suppression performance of 

various lactic acid and water mixtures delivered to the flame in the form of droplets. 

a) Estimation of the latent heat of vaporization for lactic acid/water 

mixtures 

In order to explore the effectiveness of a lactic acid/water mixture as a potential thermal agent, it is 

necessary to know the latent heat of vaporization for the mixture. The estimation of the latent heat of 

vaporization for this case is more complicated than for a pure fluid. At constant pressure, the liquid 

begins to boil once it is heated to the bubble-point temperature for the mixture. At this time, the 

composition begins to change (unless it is an azeotrope). As the vaporization continues at constant 

pressure, the more volatile substance (water in this case) concentrates in the vapor phase, while the liquid 

phase becomes more concentrated in lactic acid. The temperature gradually increases from the bubble 

point temperature to the dew point temperature. Equilibrium phase diagrams have been constructed for 

the gaseous and liquid lactic acid/water mixtures. Figure 3 shows a T-x,y diagram (x and y refer to the 

mole fractions of the liquid and vapor phase, respectively, at a given temperature T) for lactic acid/water 

mixtures at a constant pressure of 101 kPa (1 atmosphere). The absence of a temperature where the two 

lines meet indicates that lactic acid and water do not form an azeotropic mixture. The T-x,y diagram was 

constructed using the Peng-Robinson equation of state with a binary interaction parameter of 0.88 [34]. 

If one assumes that the entire sample is vaporized, then the integral heat of vaporization at constant 

pressure can be found using ΔHv = Hd − Hb, where Hd is the enthalpy of the saturated vapor at the dew 
12

Figure 3. An equilibrium T-x,y diagram for lactic acid/water mixtures is shown for a pressure of 101 kPa. 

The symbols refer to the liquid ( ) and gaseous () phases. 

Figure 4. Enthalpies for the saturated vapor at the dew point ( ) and saturated liquid at the bubble point 

() are plotted as a function of water mole fraction for lactic acid/water mixtures. 

point and Hb is the enthalpy of the saturated liquid at the bubble point. Figure 4 shows the enthalpies of 

the saturated vapor at the dew point and the saturated liquid at the bubble point. 

The latent heat of vaporization (kJ/mol) was calculated and fit to a polynomial of the following form, 

62.35 51.71 130.1 57.92 , 2 3 H x x x Δ v = + − + ( 4 )

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

mole fraction water

370

380

390

400

410

420

430

440

450

460

T(K)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

mole fraction water

-300

-200

-100

0

100

Enthalpy (kJ/mol)
13

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

mole fraction water

40

45

50

55

60

65

70

Enthalpy of Vaporization (kJ/mol)

62.35 + 51.71*x - 130.1*x2 + 57.92*x3

Figure 5. The enthalpy of vaporization for lactic acid/water mixtures for a pressure of 101 kPa is plotted 

as a function of the water mole fraction. 

where x is the mole fraction of water. This relationship is illustrated in Figure 5. Compared to neat 

water, there is more than a one and a half fold increase in the latent heat of vaporization at a water mole 

fraction of 0.2.

b) Experimental system 

The fire suppression effectiveness of lactic acid/water mixtures was examined using the NIST Dispersed 

Liquid Agent Fire Suppression Screen (DLAFSS) Apparatus. The apparatus was built under the auspices 

of the NGP, and it is described in a published report. [35] A more detailed description of the apparatus 

and the experimental procedure is available in a NISTIR [36]. Figure 6 shows a schematic for the 

DLAFSS. 

Briefly described, the apparatus consists of a small vertical wind tunnel, a porous cylindrical burner 

located at the test section, and a small nebulizer located in the settling chamber of the tunnel. The open 

circuit wind tunnel incorporates a diffuser followed by a flow conditioning section consisting of 

honeycomb, screens, and a settling chamber. The settling chamber is connected to the 10 cm × 10 cm 

square cross section, 20 cm long test section by a contraction. Air is supplied to the tunnel via a 

frequency-controlled blower. 

The burner was located near the base of the test section and was constructed from a 3.18 cm long sintered 

stainless-steel threaded cup filter with a 1.58 cm outer diameter. Fuel was piped to the inside of the filter 

and exited through the porous surface. Water cooling was used to limit preheating of the fuel. A thin 

coat of high-temperature black paint was applied to the end of the filter and one half of the cylindrical 

surface to limit the fuel flow to a 180Ε section of the cylinder face. The burner was aligned in the test 

section with the open side facing downwards. In this way fuel, was released as a counter flow to the 

oxidizer flow over an area of 7.9 cm2

. This type of burner configuration is often referred to as a “Tsuji 

burner”. The fuel for the burner was propane with a volume flow rate of 2 L/min, corresponding to a 

nominal velocity of 4.2 cm/s. 
14

Figure 6. A schematic of the dispersed liquid agent fire suppression screen (DLAFSS) apparatus is 

shown. 

The nebulizer, located in the settling chamber, is used to generate a small poly-dispersed spray of liquid 

droplets. The droplet Sauter mean diameters (measured using a phase Doppler interferometer) at the 

burner location without the flame, varied between 25 μm and 35 μm under the test conditions. The 

experiments were conducted by increasing the airflow through the tunnel with a fixed liquid delivery rate 

to the nebulizer. The droplets were entrained by the airflow and were transported to the test section. The 

air velocity at which the flame at the forward stagnation region of the burner was blown-off was used as 

an indicator for comparing fire suppression efficiencies of various lactic acid/water mixtures. 

c) Experimental results for lactic acid/water mixture fire suppression 

effectiveness

Figure 7 shows the test results for three lactic acid/water mixtures. These mixtures were made by diluting 

a commercial stock solution of lactic acid in water with a lactic acid mass fraction of 88.5 %. Dilutions of 

the stock solution with water by one-third, a half, and two-thirds yielded lactic acid mass fractions of 

22.1 %, 44.3 %, and 59 %, respectively. The undiluted stock solution was not tested because it was so 

viscous it caused the syringe pump, used to deliver the liquid to the nebulizer, to stall. Each data point in 

Test section

Thermal insulation

Contraction section

Transition flange

Settling chamber

Screen + holder

Honeycomb + holder

Diffuser

Transition duct

X-Y traverse

Flexible

aluminum ductwork

Screw

jack

Aluminum plate

Aluminum plate

T-slotted aluminum

structural extrusion

Burner

Droplet generation

device

From blower

Gaseous agent

(optional)
15

Liquid application rate (mL/min)

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8

Blow-off velocity (cm/s)

60

80

100

120

140

160

180

200

220

240

260

5.4 % lactic acid

Linear regression line

13.7 % lactic acid

Linear regression line

22.4 % lactic acid 

Linear regression line

Water

Linear regression line

Figure 7. Velocities of the air at extinguishment (indicated by blow off of the opposed-jet diffusion 

flame) are plotted as a function of liquid application rate for the indicated lactic acid/water 

mixtures. Error bars represent one standard deviation. 

Figure 7 represents an average of 5 or more runs. The error bars represent one standard deviation. The 

blow-off velocity decreases with increasing liquid application rate. In other words, as more of the acid 

mixture is delivered to the flame, less airflow is required to induce extinction. Equivalently, the opposedflow diffusion flame is blown off at lower strain rates. 

The slopes of the lines in Figure 7 are a measure for the effectiveness of a liquid in suppressing a flame. 

The steeper the slope the more effective is the liquid. It can be seen that the three lactic acid/water 

mixtures show no improvement of fire suppression effectiveness over neat water. In fact, the fire 

suppression effectiveness decreases as the lactic acid mass fraction increases. Given that no chemical 

effects are to be expected for fire suppression with lactic acid, it can be concluded that the increased heat 

extraction due to lactic acid is being overwhelmed by heat release due to the combustion of this organic 

acid. 

Since there are many liquid delivery rates that one can use in the screening procedure, a reference 

delivery rate is needed to compare and interpret the fire suppression effectiveness of various liquid agents 

in a consistent way. The following protocol, which is based on the conditions commensurate with cupburner results for nitrogen, is used. 

The average propane cup burner value for nitrogen is 32 % (mass fraction) [33]. An examination of the 

nitrogen results indicates that the nitrogen mass fraction at blow-off equivalent to the cup burner value 

corresponds to a reference blow-off velocity of ~ 30 cm/s. [36] Similar reference blow-off velocities 

were obtained when the cup-burner results for other gases (argon, helium) were used. [36] For this 

reference velocity, there are some operational issues associated with the burner and the nebulizer [36]. 
16

Table 8. Calculated Equivalent Mass and Mole Fraction Values for the Reference Blow-Off 

Velocity 

Agent Equivalent mass percent (%) Equivalent mole percent (%) 

Water 2.3 3.7 

22.1 % lactic acid 2.5 2.1§

44.3 % lactic acid 3.8 3.9§

59 % lactic acid 5.1 6.7§

HFE7100 11.7 1.5 

§

Mole-fraction averaged molecular weight of lactic acid /water mixture is used in the calculation. 

Therefore, in order to compare the results obtained from the cylindrical burner to conditions 

commensurate with cup-burner results, extrapolation to the reference velocity is required. Table 8 

compares the results at the reference velocity for water and the three lactic acid/water mixtures in both 

mass and mole fraction terms. The result for HFE 7100 (see below) is also included in Table 8 for 

comparison purposes. 

The results in Table 8 provide further confirmation of the conclusion above that the heat release 

associated with combustion of lactic acid overwhelms the heat extracted by heating the compound. The 

amount of lactic acid/water mixture in molar terms required to cause extinction for the reference 

condition actually increases with increasing mole fraction of lactic acid. 

2. HFE7100 

HFE7100 has been identified as a particularly promising thermal agent for halon replacement based both 

on its predicted ability to extract heat and its commercial availability. Two screening tests for 

extinguishing agents developed as part of the NGP have been used to characterize the effectiveness of 

HFE7100. 

a) Testing of HFE7100 using the Dispersed Liquid Agent Fire Suppression 

Screen facility 

The relative effectiveness of HFE7100 was tested in the DLAFSS using the same experimental 

procedures described above for the lactic acid/water mixtures. Figure 8 shows a plot of the measured 

blow off velocity versus the liquid application rate for the HFE7100. Extrapolating to the reference 

velocity yields effective molar and mass fraction extinguishing concentrations of 1.5 % and 11.7 %, 

respectively. These values have been included in Table 8. 

b) Testing of HFE7100 using the Transient Application Recirculating Pool 

Fire facility 

To further evaluate the fire suppression effectiveness of HFE7100, the agent was introduced as a mist into 

the Transient Application Recirculating Pool Fire (TARPF) facility. The TARPF was developed 

originally to assess the effectiveness of gaseous agents for suppressing flames attached behind a bluff 

body in a turbulent air flow. The facility was designed to generate flow conditions typical of those 

present in aircraft engine nacelles. This facility was selected as a test bed because this flame 

configuration is believed to be particularly challenging for liquid agents. 
17

Figure 8. Velocities of the air at extinguishment (indicated by blow off of the opposed-jet diffusion 

flame) are plotted as a function of liquid application rate for HFE7100. Error bars represent 

one standard deviation. 

Briefly described, the TARPF is a horizontal, open-circuit wind-tunnel with a flat porous burner located 

behind a baffle or a backward-facing step where a propane flame simulating a pool fire can be stabilized. 

A gaseous agent is transiently or impulsively introduced upstream into the air stream for a short duration. 

Suppression effectiveness is assessed based on the amount of agent required to extinguish the flame as a 

function of the application duration and the air flow rate within the tunnel. Detailed descriptions of the 

TARPF facility have been provided by Grosshandler et al. [37,38,39]. 

For this project the TARPF facility was modified to accommodate the application of a liquid agent. 

Figure 9 shows a schematic of the modified TARPF used to assess the fire suppression effectiveness of 

HFE7100. The liquid dispensing system consisted of a liquid reservoir, a compressed air cylinder, two 

computer-controlled solenoids, and a mist-jet hollow-cone nozzle. The nozzle was positioned 65.5 cm 

upstream of the porous burner in the horizontal center and at a height corresponding to the midway point 

between the top of the ramp and the top of the wind tunnel. According to the manufacturer’s 

specifications, the nozzle has a nominal spray angle of 70° when operated at 1.03 MPa with a flow rate of 

1.9 mL/s. In order to generate a mist for a fixed duration, the computer activated the solenoid connected 

to the reservoir. At the end of the discharge, this solenoid was deactivated to terminate the flow to the 

nozzle, and the second solenoid leading to drain was simultaneously activated to prevent any residual 

flow to and/or dripping from the nozzle. 

For these tests the airflow in the tunnel was fixed at 6.67 × 10-3 m3

/s. The porous burner was operated 

with a propane flow rate of 33 mL/s. The mist nozzle had a flow rate of 1.9 mL/s at 1.03 MPa. The mist 

discharge duration was varied from 1 s to 10 s. The hot surface used to investigate re-ignition was not 

activated in this test sequence. The only heating of this surface came from the impinging flame. Based 

Liquid Application Rate (mL/min)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Blow-Off Velocity (cm/s)

180

190

200

210

220

230

240

HFE7100

Linear regression line
18

Figure 9. A schematic is shown for the TARPF facility [37,38] as modified for the investigation of the 

effectiveness of liquid fire suppression agents. 

on these conditions, the mass flow rate of the liquid agent, magent & , can be calculated using the liquid 

density of HFE7100 (1520 kg/m3

 at 25 °C). The mass fraction of the liquid agent in the air stream, Yagent, 

is then given by 

,

agent air

agent

agent m m

m

Y & &

&

+ = ( 5 )

where mair & is the calculated mass flow rate of air. Note that in deriving the equation, it is implicitly 

assumed that the mist droplets are homogeneously dispersed in the carrier phase (air). For the test 

conditions, the mass fraction of agent was calculated to be 0.30.

For these operating conditions, it was found that the pool fire stabilized behind the backward-facing step 

could not be completely suppressed by the HFE7100 mist. Observations concerning the suppression 

process can be summarized as follows. Before the mist application, the flame was luminous and yellow. 

During the mist application, the yellow flame was nearly extinguished with pockets of persistent, blue 

flames anchored along the flame attachment points at the outer edges of the bluff body. The duration of 

the small blue flames coincided with the mist application. Once the mist application was over, the flames 

resumed their original burning intensity and yellow luminosity. 

It was somewhat surprising to find that it was not possible to extinguish the propane flames for these test 

conditions. The nominal effective mass fraction of the HFE7100 for the current experiments is more than 

twice as high as that required to extinguish a propane flame in the DLAFSS (11.7 %). A similar behavior 

was observed when water was tested. [39] Possible explanations for these observations are discussed in 

Section V.A. 

Liquid reservoir

to drain

Ramp

Hot surface for re-ignition

Solenoids

from compressed air cylinder

70 cm

Porous burner

(Propane 33 mL/s)

65.5 cm

Mist nozzle

Air 

Wind tunnel
19

III. DETAILED CHEMICAL-KINETIC MODELING AND EXPERIMENTAL 

INVESTIGATIONS OF THEMAL AGENT FLAME EXTINGUISHMENT 

A. Introduction

The extinction of flames by the addition of thermal agents has been the focus of considerable research 

effort for decades. Much of this effort has been guided by the intuitively reasonable assumption that the 

addition of nonreactive gases to either the fuel or oxidizer side of a diffusion flame or the fuel/oxidizer 

mixture for a premixed flame results in extinguishment when the added molecules absorb sufficient heat 

to lower the temperature in the flame zone to a point at which the combustion reactions are no longer fast 

enough to generate sufficient heat to overcome local heat losses. For the case of premixed flame 

propagation, this concept was discussed at least as early as 1925. [40] There has also been considerable 

work on diffusion flames that are of more direct interest to the current investigation. 

Some of the earliest work for diffusion flames was associated with the development of the concept of the 

limiting oxygen index (LOI) that is often used to characterize the flammability of a fuel. The LOI is 

defined to be the minimum concentration of oxygen in a mixture of air and nitrogen that is just sufficient 

to sustain combustion. Simmons and Wolfhard recorded LOI for a wide range of gaseous and liquid fuels 

using a slow flow of fuel from a hemispherical porous burner into an opposed flow of air diluted with 

nitrogen. [41] These authors also introduced the concept of a limit flame temperature, which they defined 

as the adiabatic flame temperature calculated for a stoichiometric mixture of fuel and air at the 

extinguishing condition. 

Simmons and Wolfhard found that the limit flame temperature varied with fuel. [41] For the C1 to C10 

normal alkanes the range was 1636 K to 1791 K. Interestingly, the values for methane and the fuels 

having more than five carbons were all within 20 K of 1791 K. Starting with pentane, the limit flame 

temperatures fell rapidly as the number of carbons in the fuel was reduced, reaching a minimun value at 

ethane, before increasing sharply once again for methane. One interpretation of these results is that the 

smaller multi carbon hydrocarbons, particularly ethane, are more flammable than methane and their 

longer chain analogs. In 1979 Maĉek considered these results and provided a convincing argument that, 

in general, the flammability of the smaller straight-chain hydrocarbons, including methane, should 

increase with decreasing carbon number. [42] This conclusion was based on the behavior of premixed 

flames and consideration of LOIs for the corresponding normal alcohols. On this basis, Maĉek concluded 

that when methane is burned as a diffusion flame it has an unexpectedly low flammability. 

In the early 1970s the concept of a limit flame temperature was applied in a slightly different way. 

Huggett [43] and McHale [44] reported that an atmosphere would not support combustion when the 

available thermal capacity per mole of available oxygen was on the order of or greater than 167 J/K to 

209 J/K. Since the heat release per mole of oxygen consumed is roughly constant for most fuels, this 

finding is equivalent to assuming a common limit temperature. 

Tucker et al. explicitly combined the ideas of a constant heat release per mole of oxygen consumed and a 

limit flame temperature to develop a model for the extinction of diffusion flames by thermal agents. [45] 

They made the following assumptions in their model: 

1. Burke-Shumann diffusion flame model is applicable. 

2. Chemical kinetics are identical for premixed and diffusion flames 

3. Lower limit of flammability is a thermal limit with a well defined limit temperature 

4. In absence of chemical effects, additives do not change the limit temperature. 
20

Experimental extinguishment measurements were made in an apparatus similar to the cup burner [46,47] 

used for investigating flame extinguishment. Results for four agents, nitrogen, carbon dioxide, helium, 

and carbon tetrafluoride, which were expected to act as thermal agents, as well as the chemical agent 

halon 1301, were reported. Three fuels, n-heptane, methanol, and LPG, were used. Oxidizer mixtures 

having variable amounts of oxygen were prepared. The extinguishing concentrations for each of the 

thermal agents displayed the dependence on oxygen concentration predicted by the simple model. By 

assuming a single limit temperature of 1600 K, it was possible to estimate the magnitude of the enthalpy 

change necessary for extinguishment by each of the agents. These estimates were then compared with 

actual values calculated from the known heat capacities. It was found that the two results were close, but 

that the deduced values for carbon dioxide and helium were 11 % and 40 % to 50 % higher, respectively, 

than the values obtained by direct integration. The authors attributed these differences to chemical effect 

for the carbon dioxide and the high thermal diffusivity for the helium. 

Ishizuka and Tsuji investigated the extinguishment of methane flames burning in mixtures of oxygen with 

either added nitrogen, argon, or helium. [48] Their flames were stabilized on a porous cylindrical burner 

in a counterflow of oxidizer. The equivalent of LOIs were reported for each of their special “airs”. 

Thermocouples were used to record flame temperatures just prior to extinguishment. For the methane 

flames, values ranged from 1443 K to 1623 K for the three inert agents. 

Sheinson et al. also considered the effects of thermal agents on flames as part of a larger effort to 

understand the role of chemical agents on flame extinguishment. [49] They based their analysis on the 

amount of enthalpy change associated with heating nitrogen and an agent gas from room temperature to 

1600 K. The upper value is the assumed maximum flame temperature below which a diffusion flame can 

no longer be sustained. It is based upon an estimate provided by Roberts and Quince [50] who, in turn, 

cited an estimate provided by Dodding et al. [51]. No additional references for this choice are cited by 

Dodding et al. Sheinson et al. recorded cup burner extinguishing concentrations for a number of thermal 

agents and concluded that the mixture heating of enthalpy was on the order of 250 kJ per mole of oxygen 

consumed. Consideration of heating effects then allowed the contribution of chemical effects to be 

estimated. 

Zegers et al. have recently performed an extensive test of the approach outlined above. [52] These 

authors have reported extinction measurements for methane and propane counterflow diffusion flames 

and cup burner extinguishment measurements for heptane and methanol for a large number of fluorinated 

hydrocarbons, halon 1301, carbon tetrafluoride, sulfur hexafluoride, and nitrogen. The last three are 

expected to act primarily as thermal agents. The measurements were compared with concentrations 

calculated based on the amount of an agent required to absorb an empirically determined amount of heat 

on going from 298 K to 1600 K. The amount of heat extraction required varied with fuel and was 

estimated from experimental results for either CF4 or SF6 assuming these agents act only thermally. The 

results were 267 kJ/mol O2, 267 kJ/mol O2, 254 kJ/mol O2, and 258 kJ/mol O2 for methanol, heptane, 

methane, and propane, respectively. 

The approach provided close estimates for the heavier thermal agents as well as for a number of the 

fluorinated compounds where chemical effects were small. Interestingly, it overpredicted the amount of 

nitrogen required for each fuel. The overestimate was largest for methane. 

Several other investigations have been reported in which thermal agents have been used to extinguish cup 

burner flames. In most cases the fuel was heptane. [33,53,54,55,56] Recently, Ural has reported 

measurements using a cup burner in which methane and propane were burned. [57] The findings of these 

studies will be discussed more fully below. 
21

A group of researchers have proposed a very different viewpoint with regard to thermal effects on 

extinguishment of flames and the role of limit temperature. [58,59,60,61] A major conclusion of their 

analysis is that the vast majority of flame extinguishing agents, including halons, operate primarily by 

heat extraction, i.e., interference with the flame chemistry is not a dominant mechanism. An early paper 

by Larsen considered the effects of inert gas agents on flames. [58] He concluded that the effects of 

thermal agents could be understood entirely based on their heat capacity. He also concluded that the 

relatively high thermal conductivity of helium did not play a primary role in its extinguishing capability. 

In later work Larsen extended his analysis to halons and reached the somewhat surprising conclusion that 

their extinguishing effectiveness could also be understood based entirely on their heat absorption ability. 

[59] 

Ewing et al. also concluded that the effectiveness of many agents recognized as being chemical in nature 

could be understood based purely on their ability to extract heat. [60] A major difference from earlier 

work was that while these authors based their analysis on adiabatic flame temperatures, they explicitly 

assumed that the required limit temperature depended on the suppressant and type of flame system. For 

nonreactive agents they presented data that indicated that the limit temperature increased with decreasing 

molecular weight of the agent. It was also argued that the limit temperature varied depending on the type 

of agent used. Four classes of materials, each with a separate limit temperature, were defined: A) nondecrepitating solids and liquids (2165 K), B) gases and volatile liquids which are fully dissociated in 

flames (2015 K), C) gases and liquids which are partially dissociated (2015 K), and D) thermally stable 

gases (variable). 

A follow up paper from Ewing et al. developed the idea of variable adiabatic flame temperature limits for 

extinguishment in much greater detail. [61] Instead of simply defining limit temperatures for different 

classes of compounds, an approach for estimating the temperature based on the location where heat 

extraction occurred was used. In fact, it was hypothesized that each agent and flame system has a unique 

limit temperature and extinguishing effectiveness that depends on the agent’s thermal properties. Heat 

extraction was viewed as either occurring in unburned reaction gases (< 1400 K) or in the combustion 

zone. The limit temperature was fixed by the relative sizes of the heat removal in the preheat and 

combustion zones. By assuming certain compounds form predictable secondary products, the authors 

were able to estimate the heat absorbed by an agent and its dissociation products and estimate the amount 

required to extinguish the flame as the amount needed to lower the adiabatic flame temperature to the 

limit temperature. This approach was able to correlate the findings for a wide variety of agents. Despite, 

the success of this correlation, it has not been widely employed for predictions of agent effectiveness. 

It should be clear from this short review that the current understanding of flame extinguishment is based 

on integral views of diffusion flames, and models for the process utilize the concept of a limit flame 

temperature that was originally conceived nearly eighty years ago. Meanwhile, within the last two 

decades the abilities of researchers to calculate simple flame structures using detailed chemical-kinetic 

models have been developing rapidly and have now reached the point where it is feasible to study flame 

extinguishment. There have been a number of investigations that have used detailed chemical-kinetic 

modeling to study flame inhibition and extinction processes. Most of these have involved the reduction 

of premixed flame speed due to the introduction of various inhibitors. Examples include the early studies 

of Westbrook [62,63,64] as well as a number of more recent works. [52,65,66,67,68,69,70] Very 

recently, inhibited flames studies have been extended to laminar opposed-flow diffusion flames. 

[69,71,72,73,74] 

Despite the large number of detailed chemical-kinetic modeling studies dealing with inhibition and 

extinction of flames by various agents, we have identified only one study which systematically considered 

the effects of inert thermal agents on a combustion system. Tuovinen calculated the structure of 

methane/air premixed flames in a well-stirred reactor with added CO2, H2O, N2, and He. [75] This author 
22

found that the extinguishing capability of these compounds was proportional to the heat capacity of the 

gases. The temperatures at extinguishment using the various agents were within 50 K for a given 

stoichiometric ratio, φ (a range of φ = 0.7 to 1.2 was studied). 

An investigation of the extinguishment of diffusion flames by thermal agents using detailed chemicalkinetic modeling approaches is described in the following section. During the project it became clear that 

insufficient experimental results for the two fuels considered, propane and methane, were available to 

fully validate the modeling results. For this reason, extinguishment experiments using two different 

burners were carried out concurrently and are also summarized. 

B. Introduction to Detailed Chemical-Kinetic Modeling of Diffusion Flames 

Combustion is a complicated physical process involving the interaction of fluid flow and chemical 

reaction accompanied by heat release. It is now recognized that combustion involves a large number of 

chemical species and reactions. The most important reactions are those involving radical species such as 

OH, HO2, and the atomic species O and H. The most dominant reaction (see [70] for a recent discussion) 

is usually recognized as the H atom chain branching reaction leading to breaking of the oxygen bond, i.e., 

H O OH O. + 2 → + ( 6 ) 

Subsequent reactions involving the product free radicals release heat and ultimately maintain the 

combustion. Reaction (6) is strongly temperature dependent, and extinguishment of a flame is expected 

to occur when the temperature is lowered to a point where the rate of generation of free radicals becomes 

so slow that the overall reactions cannot generate sufficient heat release to overcome the heat losses from 

the reaction zone (primarily by thermal diffusion, radiation, and incomplete combustion). 

During the past two decades the understanding of the chemical kinetics involved in combustion has 

reached the level where realistic detailed mechanisms including large numbers of reactants and reactions 

can be written for simple combustion systems, and mathematical techniques have been developed for 

simultaneously solving the large number of differential equations that result. While still involving 

significant approximations (some of which are discussed below), such modeling has developed to the 

point where it can be used to gain useful insights into the behavior of practically relevant flames. 

A number of different types of combustion systems have been modeled including plug flow reactors, 

perfectly stirred reactors, premixed flames, and opposed-flow laminar diffusion flames. For studies of 

fire extinguishment, we have chosen to use an opposed-flow laminar diffusion flame model because, for 

the vast majority of fires, the fuel and air are initially separated and therefore burn as diffusion flames. 

Most fires are large enough to be turbulent, so a laminar flame model is not strictly correct. However, the 

most widely used model for turbulent combustion incorporating detailed chemistry is the laminar flamelet 

model which treats the combustion as laminar flame sheets that are subjected to the local strain rate field 

associated with the motions of the fluid. [76,77] Thus, the opposed-flow laminar diffusion flame should 

be the most appropriate flame system available for detailed chemical-kinetic modeling of fire behavior. 

There are three configurations of opposed-flow diffusion flames that have been described in the 

literature—opposed jet, flow over a porous cylinder, and flow over a porous sphere. For the porous 

bodies, fuel typically flows from the surface, and the surrounding flow is the oxidizer. The three 

configurations are related in that a diffusion flame is stabilized in the region near the stagnation point in 

the flow. Numerous papers in the literature discuss these types of flames. Two excellent reviews have 

been provided by Tsuji [78] and Dixon-Lewis [79]. The review by Tsuji includes a discussion of the use 

of such burners to experimentally characterize flame inhibition. Examples of early studies include 
23

references [80], [81], [82], [83], and [84]. All three configurations are represented. Recently, opposedjet experiments have been used to investigate potential replacement agents for halons. [35,36,52,85,86] 

The most common of the three configurations used in the recent past is the opposed-jet laminar diffusion 

flame. This configuration has also been the choice for most of the available modeling investigations of 

opposed-flow flames. For these reasons, we have chosen this configuration for this modeling 

investigation. 

The review of Dixon-Lewis focuses on detailed chemical-kinetic modeling of opposed-flow diffusion 

flames. [79] Detailed chemical-kinetic models were initially developed in a series of steps. The earliest 

were designed to describe reactions between H2 and O2. The next step was to include CO with the H2 and 

O2. After these mechanisms were sufficiently developed, they were used as the basis for extended 

mechanisms describing the oxidation of methane. By the early 1980s researchers had begun to calculate 

the structure of opposed-flow laminar methane/air diffusion flames. The earliest such calculation we 

have identified is that of Hahn and Wendt that was published in 1981. [87] This was followed by the 

work of Dixon-Lewis et al. [88], Smooke et al. [89], Dixon-Lewis et al. [90], Puri et al. [91], and 

Chelliah et al. [92]. 

Before discussing the findings of these studies, it is important to introduce and clarify some ideas 

concerning the parameters used to characterize the flow field and its potential interactions with 

combustion reactions. Much of what follows is based on a review paper by Law. [93] 

The degree of interaction between combustion and a flow field is often treated using the concept of flame 

stretch. This is particularly true for laminar premixed flames. Flame stretch, K, is defined as 

, d

1 d

t

A

A

K = ( 7 )

where A is the infinitesimal area of an arbitrary flame surface lying within the flame structure, e.g., an 

isotherm or isopleth, and t represents time. In the general case, flame stretch can be broken into three 

individual contributions due to aerodynamic strain, flame curvature, and flame motion. For a planar, 

axisymmetric diffusion flame, however, the latter two effects are absent, and K is simply equal to the 

strain rate within the planar surface, b, with 

,

r

v b

∂

∂ = ( 8 )

where cylindrical coordinates have been introduced with z and r the directions perpendicular and parallel 

to the flame sheet, respectively, and u and v are the velocities in these directions. For the planar flame u

is assumed to be only a function of z. The velocities u and v are dependent on each other through the 

continuity equation, which for a cylindrical coordinate system is written as 

0, ( ) ( ) = ∂

∂ ρ +

∂

∂ ρ

r

r v

z

r u ( 9 )

with ρ equal to the local density. 

Law discusses the effects of flame stretch on flame behavior in terms of the different roles of velocity 

gradient elements tangent to and normal to the flame surface. He notes that there has been a great deal of 

confusion in the literature in distinguishing between the roles for each element. He argues that it is the 
24

normal element of the axial velocity gradient which determines the residence time within the flame and 

that the Damkohler number, Da, defined as the ratio of the characteristic flow time to a characteristic 

reaction time, should be based on this velocity gradient element. As we shall see shortly, Da is a 

dominant parameter for describing flame extinction. For now, it is important to note that for planar 

diffusion flames the most important characteristic flow parameter is the element of the axial velocity 

gradient in the axial direction, 

.

z

u

a

∂

∂ = ( 10 ) 

Returning now to the discussion of early detailed chemical-kinetic investigations of methane/air diffusion 

flames, the paper by Dixon-Lewis et al. is particularly interesting because it involved an intercomparison 

of calculated results for an opposed-flow methane/air diffusion flame by five different research groups. 

[88] Calculated flame structures were compared with the experimental measurements of Tsuji and 

Yamaoka [94,95] for the configuration of flow over a porous cylinder. All of the researchers used the 

same model for the velocity field. A similarity transform was used to convert the two-dimensional flow 

field to a pseudo one-dimensional flow, thus greatly reducing the amount of computation required. The 

coordinate system employed for these calculations was actually rectilinear, but the following discussion 

will be in terms of cylindrical coordinates. The opposed flows for ambient locations outside of the 

reacting boundary layer were assumed to be potential flows generated from point sources located at 

infinity. One appealing aspect of such a flow is that the characteristic strain rate, usually defined as the 

radial velocity gradient element in the radial direction, 

,

r

v bp ∂

∂

= ( 11 ) 

is constant in the isothermal region. The continuity equation allows the following relationship between ap

and bp to be derived, 

. 2

1

p p b

z

u

a = − ∂

∂ = ( 12 )

Dixon et al. concluded that the models described the qualitative flame structure quite well, but that the 

quantitative agreement was not perfect. [88] In particular, they argued that the assumption of potential 

flow was inadequate to describe the actual flow field. The results from the different investigators within 

the intercomparison also differed somewhat, and additional study was suggested to identify the sources of 

these variations. 

While the strain rate dictated by the potential flow provided a natural variable to characterize the velocity 

field, the authors also noted that the scalar dissipation rate at the stoichiometric surface of the flame, χs, is 

more commonly used to describe the effect of strain on diffusion flames in turbulent models. [76,77] The 

scalar dissipation rate is defined as 

2 ,

2

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

χ= x

Z D ( 13 )

where D is a molecular diffusion coefficient and Z is the fuel mixture fraction, a conserved scalar. An 

expression was provided which allowed χs to be calculated from the flow parameters. Most of the 
25

calculations were performed for strain rates of 100 s-1, but one set was carried to higher velocities where 

flame extinction occurred. The calculated value of ap at extinction was 410 s-1

, and the corresponding 

value of χs was 16.7 s-1

. [88] 

The limitations with regard to the use of potential flow conditions in opposed-flow flame calculations 

continued to worry early workers in the area. It was recognized that most experimental opposed-jet 

configurations were designed to generate plug flows either through the use of nozzles or active flow 

straighteners. In other words, the radial velocities at the burner exits were set to be zero, with both a and 

b also equal to zero at these locations. Furthermore, the nozzles had finite diameters as opposed to the 

infinite diameters assumed in the model. In 1988 Kee et al. demonstrated that it was possible to derive a 

pseudo one-dimensional similarity transform for problems that relaxed the conditions imposed by the 

assumption of potential flow that required bp and ap to be constant throughout the isothermal region of the 

flow. [96] In their formulation, it is only required that the radial velocity profile vary linearly with radial 

position for a given axial position, as opposed to having a constant value. Thus b is allowed to vary along 

the primary flow direction. This approach allows the case of initial plug flows, i.e., ∂v / ∂r = ∂u / ∂r = 0 at 

the burner exits, to be evaluated. The price paid for relaxing the potential flow boundary conditions was 

that the strain rate element normal to the flame surface, a, was no longer a constant for regions outside of 

the reacting boundary layer, but now varied with the similarity coordinate. Thus there was no longer a 

unique strain rate that could be used to characterize the flow field. Kee et al. used the approach to 

calculate the structure of opposed-flow premixed methane/air flames. 

The formulation used by Kee et al. [96] is related to earlier work by Seshadri and Williams [97] who 

considered flow in a two-dimensional channel. Their results can be used to derive a characteristic global 

strain rate, ag, for the pseudo one-dimensional flow, which is written for axisymmetric flow as 

, ( )1

2

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

ρ

ρ

− + − =

o

f

o

o f

g u

u

L

u

a ( 14 )

where L is the separation distance of the two burners, uf and uo are the fuel and oxidizer velocities, which 

have opposite signs for the opposed flow, and ρf and ρo are the fuel and oxidizer densities. This 

corresponds to the strain rate that would exist at the stagnation point for opposed flows if the boundary 

layer were infinitely thin. Flow fields with comparable values of ag are expected to have similar spatial 

variations of velocity. It should be mentioned that Eq. (14) is occasionally found in the literature without 

the factor of 2. The form of Eq. (14) is correct for axisymmetric opposed flows. A good discussion of 

this point is provided by DeCroix and Roberts. [98] 

Chelliah et al. [92] extended the formulation provided by Kee et al. [96] to treat opposed-flow 

methane/air diffusion flames. Calculations were made for two different boundary conditions 

corresponding to either potential flow with a characteristic strain rate of ap for the boundaries located at x

= 0 and x = L or plug flow conditions with strain rate a(x = 0, x = L) = 0 s-1 at the burner exits. An 

important feature of this work was comparison of the calculational results with detailed experimental 

measurements of the velocity field. The flows were generated by nozzles and were expected to be closely 

top hat in shape. Therefore, plug flow conditions at the burner exits would be expected to provide better 

agreement with experiments. This was indeed found to be the case, although small disagreements were 

still observed. 

Recall that plug flow conditions at the burner exits require that a varies with axial location. The global 

strain rate given by Eq. (14) is one means for quantification. However, the reacting boundary layer is 

known to have a finite thickness, and the volume expansion associated with the heat release causes a to 
26

vary rapidly through the combustion region. As a result, the value of a at the stagnation plane does not 

actually correspond to ag. For this reason, the measured value a on the oxidizer side of the flow just 

outside of the boundary layer, ao, has been suggested for use as the characteristic strain rate for opposedflow diffusion flames formed by plug flows. Chelliah et al. found that the values of ag and ao differed 

significantly. [92] 

The calculations of Chelliah et al. were carried to high enough velocities to cause extinction of the flame. 

[92] For plug flow conditions the corresponding values of ag and ao at extinction were 610 s-1 and 391 

s

-1, respectively, while the experimental value of ao was 380 s-1. Values of χs at extinction were also 

determined from the calculations. Interestingly, these values were nearly independent of the exit flow 

conditions, being roughly 14.7 s-1 in both cases. The experimental value was reported as 19.9 s-1. 

The existence of the various definitions of characteristic strain rates, i.e., ap, ag, and ao have resulted in 

some confusion in the literature when different experiments and calculations are considered. Fisher et al. 

have compared values of ao measured in a propane/air counterflow diffusion flame with the 

corresponding oxidizer air flow rates and values of ag. [52,99] In each case, a linear relationship was 

found. This suggests that for a given flow configuration, values of ag and ao should be related by a 

constant. 

Early calculations involving opposed-flow diffusion flames assumed the combustion occurred 

adiabatically and did not allow for the possibility of radiative heat loss. Recently, however, detailed 

chemical-kinetic calculations for methane/air diffusion flames have begun to appear in which the effects 

of radiation from combustion gases have been included. [100,101,102,103] The study by Maruta et al. 

considered laminar diffusion flames in the opposed-jet configuration burning nitrogen-diluted methane. 

[100] Both detailed chemical-kinetic modeling and experiments were reported. The experiments were 

performed in microgravity so that buoyancy effects on the flame were minimal. Their results showed that 

at high strain rates flame extinction was due primarily to strain effects. However, as the strain rate was 

lowered, the percentage of heat loss by radiation increased rapidly, lowering the flame temperature and 

ultimately extinguishing the flame. As a result of these competing effects, plots of maximum flame 

temperature versus strain rate showed a maximum, and plots of strain rate at extinction as a function of 

methane concentration in the fuel were double valued. 

For their investigation, Chan et al. used a different modeling approach. [101] Their calculation is based 

on a steady-state laminar flamelet model which is solved in mixture fraction coordinates. The effects of 

strain were incorporated indirectly by varying χs. Both detailed chemical kinetics and radiation losses 

were included. These authors considered a methane/air diffusion flame. Their findings are consistent 

with those of Maruta et al. [100] The effects of radiation were minimal at high strain rates and extinction 

occurred due to the well known strain-rate mechanism. Extinction was calculated to take place at χs = 

18.4 s-1, and the maximum flame temperature at extinction was 1773 K (1771 K with radiation losses 

included). However, as the strain rate was lowered, the percentage of the total heat release rate loss due 

to radiation increased dramatically. Calculations without radiation indicated a continual increase in 

maximum temperature with decreasing χs, while the inclusion of radiation resulted in maximum 

temperatures that first increased, but then began to fall for values of χs < 2.5 s-1. The falling temperature 

ultimately led to a second extinction at χs = 0.029 s-1. 

Gore et al. also found that radiation effects become more important at low strain rates. [102] Their 

calculations showed that there is a substantial range of strain rate for which the effects of strain rate and 

radiation losses nearly cancel, resulting in maximum flame temperatures that are roughly independent of 

strain rate. The recent study of Bai et al., which includes laminar flame calculations for hydrogen, 

methane, and propane flames, also showed that radiation could extinguish a flame at low strain rate. [103] 
27

C. Modeling Approach 

1. CHEMKIN III and OPPDIF 

The current investigation seeks to calculate the effects of adding thermal agents to the air side of laminar 

opposed-flow diffusion flames. There are a number of codes described in the literature for making such 

calculations. We desired to use a code that was easily accessible to researchers. The code OPPDIF [104] 

developed by Sandia National Laboratories was chosen. This code is now available commercially from 

Reaction Design*

 of San Diego, CA. OPPDIF is built on a number of general purpose subroutines, 

collectively known as CHEMKIN-III [105], which handle many of the tasks associated with the 

calculation. Data describing the reaction mechanism and thermodynamic and transport properties are 

either incorporated in OPPDIF or accessed as databases. 

OPPDIF solves the psuedo-one-dimensional equations describing an axisymmetric opposed-flow laminar 

diffusion flame. The equations are those originally reported by Kee et al. [96] for premixed flames to 

solve problems in which b is constant at the boundaries and were later extended to diffusion flames by 

Chelliah et al. [92] This includes the case of plug flows, i.e., b = a = 0 s-1 at the burner exits, which was 

used for all of the calculations that follow. 

2. Detailed Chemical-Kinetic Mechanism for Methane 

A detailed chemical-kinetic mechanism is required to model a flame. After reviewing the literature, we 

chose the widely used methane/air mechanism developed with the support of the Gas Research Institute. 

The version used was GRI-Mech 1.2. [106] At the time this investigation was initiated there was a later 

version of the mechanism, GRI-Mech 2.11, in which nitrogen chemistry was added. The earlier version 

was chosen for use since NOX formation is not of interest for the current investigation. Subsequent to the 

start of the project, GRI-Mech 3.0 was released. It incorporates new reaction data and updated 

optimization. A comparison of extinction calculations using the three GRI-Mech versions (described 

below) suggests that the choice of version has a minimal effect on the calculated results. 

GRI-Mech 1.2 consists of 32 chemical species undergoing 177 reactions. One- and two-carbon species 

are included. Thermodynamic and transport data are provided as separate files. The mechanism was 

created by starting with appropriate estimates for the rate constants and then optimizing to provide the 

best agreement with experimental measurements in such systems as premixed flames, shock tubes, and 

flow reactors. [106] Note that the mechanism was not optimized using diffusion flame results. 

3. Detailed Chemical-Kinetic Mechanism for Propane 

Detailed reaction mechanisms for propane combustion have not been as extensively developed as for 

methane, and no widely accepted version comparable to GRI-Mech is available. A mechanism assembled 

at NIST by Babushok and Tsang was used. [70] This mechanism was created by adding a block of 

reactions for C3-C4 compounds taken from Marinov et al. [107,108] to a C1 and C2 mechanism 

previously developed at NIST [67]. It consists of 83 species undergoing 509 reactions. Since this 

 

*

Certain commercial equipment, instruments, or material are identified in this paper in order to adequately 

specify the experimental procedure. Such identification does not imply recommendation or endorsement 

by the National Institute of Standards and Technology, nor does it imply that the materials or equipment 

are necessarily the best available for the purpose. 
28

mechanism has not been published in detail, it is included here as Appendix A. Thermodynamic and 

transport data are included with the mechanism as separate files. 

4. Modeling Details 

OPPDIF was mounted on a Silicon Graphics Incorporated Origin 200 workstation. An initial test for a 

laminar hydrogen/air opposed-flow diffusion flame yielded good agreement with the solution provided in 

the documentation. By simply replacing the mechanism provided for the hydrogen/air flame with GRIMech 1.2, we were able to obtain an initial solution for a methane/air diffusion flame. 

Calculations for the propane flame proved to be much more difficult. Considerable effort was required to 

identify an initial set of input conditions that would result in a converged solution for the diffusion flame. 

Appropriate conditions were eventually identified by a trial-and-error procedure. 

The purpose of our calculations is to determine extinction behavior for the flame as functions of flow 

conditions and agent concentration and to use this information to better understand the effectiveness of 

thermal agents for extinction of diffusion flames. Extinction of diffusion flames can be understood in 

terms of the “S” curve that was originally described by Fendell [109] and Liñán [110]. The name refers 

to the shape of a plot of maximum flame temperature versus Damkohler number, Da, where Da is the 

ratio of a characteristic flow mixing time and a characteristic combustion reaction time. The unique shape 

results from the highly nonlinear temperature dependence of combustion reactions. These authors 

showed that there were two possible solutions for mixtures of fuel and air—combustion and very slow 

reaction regimes. These two branches are connected by an unstable third branch that forms the central 

part of the “S”, but is not physically observable. Starting well up on the burning branch, it is found that 

the maximum flame temperature decreases with decreasing Da. As the Da is decreased still further, the 

temperature begins to drop faster and is ultimately predicted to curve onto the middle branch and continue 

to fall off with increasing Da. Such a dependence on Da is physically unrealistic, and, as a result, the real 

flame system drops to the lower branch at the turning point. This is interpreted as flame extinction. A 

similar behavior applies to ignition. Starting on the lower branch, as the temperature is increased the 

reaction rate increases very slowly at first. However, a temperature is eventually reached where the rate 

begins to increase quickly and ultimately begins to increase with falling Da, passing onto the middle 

branch. However, due to the instability of this branch, the system actually jumps rapidly up to the 

burning branch. This is the process of spontaneous ignition. 

The goal is to identify the flow conditions just sufficient to cause extinction of a flame formed by fuel and 

either air or air with added agent. Thus the problem becomes one of identifying the turning point for a 

plot of temperature versus Da. Either the velocity, appropriate characteristic strain rate, or stoichiometric 

scalar dissipation rate can be used as the independent variable, and since the mixing times associated with 

these parameters are inversely related to their values, the curve is reversed from that for a Da plot, with 

the maximum flame temperature decreasing with increasing velocity, characteristic strain rate, or scalar 

dissipation rate. 

Early calculations of flame extinction simply increased the controlling parameter for burning solutions 

until further increases resulted in a nonburning solution (e.g., see [88]). Due to the rapid changes in 

temperature with flow parameters near the extinction point, solutions of opposed-flow diffusion flames 

can become unstable, and there may be some uncertainty associated with the extinction value. As a 

result, so-called continuation methods have been implemented which allow calculations to be extended 

onto the unstable solution branch. [111,112] In this way it is possible to determine the turning point 

corresponding to extinction unambiguously. 
29

Unfortunately, continuation approaches are not implemented in OPPDIF. For this reason, we chose to 

employ the direct approach in which higher and higher flow velocities were used until either a nonburning 

solution was found or the differential solver was unable to find a solution. In order to minimize the 

associated uncertainties, very small incremental increases in velocity were utilized near the extinction 

point (the solver is more efficient when an earlier solution for similar conditions is used as the starting 

point). An arbitrary, but stringent, criterion was adopted which defined the extinction velocity as that for 

which a burning solution was still obtained, but for which an increase of only 0.01 cm/s in the fuel and air 

initial velocities either resulted in a failure to find a solution or a nonburning solution. Additional small 

increases in velocity always resulted in nonburning solutions. As we shall show, plots of maximum flame 

temperature versus the controlling parameters (e.g., velocity) indicate that the flames were indeed near the 

extinction point as reflected by large temperature drops for small changes in the control parameter. It is 

believed that this approach results in small errors for estimates of the calculated extinction condition. 

A number of parameters are relevant to OPPDIF calculations. [104] Many of these are summarized in 

Table 9 for the methane/air and propane/air cases. The general procedure was to find a solution for a 

given type of diffusion flame by first solving an isothermal case and using the solution as the input for a 

calculation in which the energy equation was added. Once a solution was available, it could be used as 

the starting point for calculations in which such parameters as the oxidizer and flow velocities were 

changed. Only the formulation including the energy equation was solved for the “restarted” cases. The 

new solution then became the starting point for cases involving further changes in the controlling 

parameters. OPPDIF allows the grid for the calculations to be adapted to best match the latest solution. 

This feature was used frequently for these calculations. Normally, between 130 and 150 grids points were 

used for a final solution for the methane flames, while 95 grid points would be typical for a propane 

flame. For simplicity, the opposed (i.e., opposite signs for velocity) fuel and oxidizer exit velocity 

magnitudes were always set equal to each other. The exit temperatures were 300 K. 

In general, it was found that calculations for the methane flames required considerably less time and were 

much more computationally stable than those for propane flames. For these reasons, the largest number 

of calculations was performed for the methane flames. A number of aspects of flame extinguishment 

were investigated using surrogate agents. These were done primarily using the methane flame. 

The final solutions for a particular problem were saved in binary files. A program named POSTOPP was 

supplied by Reaction Design [104] which reads these files and generates ASCII files containing such 

parameters as temperature, density, fuel mixture fraction, axial and radial velocities, and axial and normal 

strain rate elements a and b as functions of distance from the fuel nozzle (z = 0 cm). This program was 

modified to also output the largest absolute value a on the oxidizer side, ao, the stoichiometric mixture 

fraction, and the scalar dissipation rate at the location corresponding to a stoichiometric mixture fraction. 

The derivatives required in Eq. (13) were calculated by simple forward differencing, and values of D were 

corrected for variations in the local temperature using the expression recommended by Norton et al. [113] 

D. Model Results for Methane and Propane Flames Burning in Air 

Figure 10 shows a plot of maximum temperature, Tmax, versus flow velocity (equal magnitudes for the 

fuel and oxidizer opposed velocities) calculated for a laminar opposed-flow methane/air diffusion flame. 

The fuel is 100 % methane, and air is assumed to be composed of 78.1 % N2, 21.0 % O2, and 0.9 % Ar. 

As expected, Tmax decreases with increasing velocity. Extinction occurs for a velocity of 320.12 cm/s for 

a maximum flame temperature of 1785 K. A global strain rate, ag, of 558 s-1 is calculated for the 

extinction condition using Eq. (14). Experimental values in the literature include those of Puri and 

Seshadri [114] (ag =of 542 s-1), Chelliah et al. [92] (ag = 610 s-1) and DeCroix and Roberts [98] (ag = 590 

s

-1) The calculated value is in reasonable agreement with these results. 
30

Table 9. Some Parameters Used in Most OPPDIF Calculations of Methane and Propane Flames 

Keyword Methane Propane 

ENRG Energy Equation Included 

NOFT Skip the Fixed Temperature Problem 

RSTR Restart From Earlier Solution 

GRAD 0.3 0.5 

CURV 0.3 0.5 

IRET (retirement period) 20 

RTOL (relative convergence for Newton’s method) 1.E-3 

ATOL (absolute convergence for Newton’s method) 1.E-6 

ATIM (absolute convergence for timestepping) 1.E-6 

RTIM (relative convergence for timestepping) 1.E-3 

XEND (physical length) 2 cm 

TFUE , TOXI (fuel and oxidizer initial temperatures) 300 K 

PRES 1 atmosphere 

AFUE, AOXI (radial gradient at inlet) 0 s-1

MIX Mixture-Averaged Formula for Diffusion Velocities

Figure 10. Maximum flame temperatures are plotted as a function of the equal fuel and air velocity 

magnitudes for a methane/air opposed-flow diffusion flame. 

Figure 11 shows two examples, one for relatively low fuel and air velocity magnitudes and one for the 

methane flame very close to extinction, of the variation of the local characteristic strain rate, a, with 

position. Several interesting behaviors can be seen. First, as expected, absolute values of a are higher for 

the case with higher initial velocities. For regions outside of the boundary layer, a values increase or 

decrease roughly linearly with increasing position, but large intense variations are evident in the vicinity 

Methane/Air Diffusion Flame

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Flame Temperature (K)

1800

1850

1900

1950

2000

2050
31

Figure 11. Calculated strain rates, a, are plotted as a function of distance from the fuel exit for low exit 

velocity magnitudes (25 cm/s for fuel and air) and for a condition very close to extinction 

(320.1 cm/s). 

of the flame front. These large fluctuations within the flame zone result from the volume expansion due 

to heat release. It is clear that the boundary layer width for the low velocity case is considerably broader 

than for the higher flow velocity. This is expected since higher absolute velocities should more 

effectively overcome the effects of molecular diffusion and result in a narrower mixing layer. 

The first maximum in the absolute value of a on the oxidizer side, denoted as |ao|, (see Figure 11) can be 

taken as representative of the strain rate just outside of the boundary layer. Figure 12 shows a plot of 

maximum flame temperature versus |ao| for the various flow velocities. As expected, the maximum flame 

temperature decreases with increasing |ao|. Extinction is calculated to occur when |ao| is increased to 509 

s

-1. At least seven experimental measurements of |ao| at extinction are available in the literature for 

methane/air diffusion flames (if listed, uncertainties are ± 1 σ): Papas et al., |ao| = (405 ± 25) s-1 [85], 

Chelliah et al., |ao| = 380 s-1 [92], Du et al., |ao| = (380 ± 20 s-1) [115], Yang and Kennedy, |ao| = 340 s-1

[116], Du and Axelbaum, |ao| = (375 ± 10) s-1 [117], Pellett et al., |ao| = 384 s-1 and 396 s-1 for two 

different burners [118], and Zegers et al., |ao| = (415 ± 32) s-1. [52] These values are equal within 

experimental uncertainty. The value calculated here is roughly 30 % higher. Two possible reasons for 

this are different boundary conditions in the experiments and model and the possible dependence of the 

results on chemical mechanism. Reasons for the difference are discussed further below. 

Figure 13 shows the mixture fraction, i.e., the fraction of the mass of the combustion mixture derived 

from fuel, plotted as a function of distance from the fuel source for the two same conditions used for 

Figure 11. The narrowing of the boundary layer due to increased strain rate is clearly evident. The shape 

of the curve becomes more asymmetric as the velocity decreases. Since values of the mixture fraction are 

now available, it is possible to calculate the scalar dissipation rate, χ, as a function of x using Eq. (13). 

Figure 14 shows the results, which demonstrate the strong dependence of χ on the flow velocities. The 

value of χ at the stoichiometric surface, χs, can now be determined by interpolating the results to find the 

value of χ for a mixture fraction of 0.055, the stoichiometric value. The results are χs = 1.70 s-1 and χs = 

20.7 s-1 for fuel and air exit velocity magnitudes of 25 cm/s and 320.1 cm/s, respectively. 

Methane/Air Diffusion Flame

Distance From Fuel Exit (cm)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Local Strain Rate, a (s-1) -1500

-1000

-500

0

500

1000

1500

25 cm/s

320.1 cm/s

ao

ao
32

Figure 12. The maximum flame temperature is plotted against a characteristic local strain rate, |ao|, 

defined to be equal to the highest absolute value of a on the air side observed outside of the 

boundary layer associated with the methane/air flame. 

Figure 13. Mixture fraction is plotted as a function of distance from the fuel exit for low exit velocity 

magnitudes (25 cm/s for fuel and air) and for a condition very close to extinction (320.1 cm/s) 

for a methane/air diffusion flame. 

Maximum calculated flame temperatures are plotted as a function of χs for a series of methane/air flames 

in which the fuel and air velocities were varied in Figure 15. The temperature drops with increasing χs, 

and extinction is calculated to occur for χs = 20.7 s-1. No experimental measurements of χs were

Methane/Air Diffusion Flame

Distance From Fuel Exit (cm)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Mixture Fraction

0.0

0.2

0.4

0.6

0.8

1.0

25 cm/s

320.1 cm/s

Methane/Air Diffusion Flame

Characteristic Strain Rate on Oxidizer Side, |ao| (s-1)

0 100 200 300 400 500

Maximum Flame Temperature (K)

1800

1850

1900

1950

2000

2050
33

Figure 14. Calculated scalar dissipation rates, χ, are plotted as a function of distance from the fuel exit for 

low exit velocity magnitudes (25 cm/s for fuel and air) and for a condition very close to 

extinction (320.1 cm/s) for a methane/air diffusion flame. 

Figure 15. Values of maximum flame temperature for opposed-flow methane/air diffusion flames are 

plotted as a function of χs that is varied by changing the velocities of the fuel and air. 

Extinction is calculated to occur for χs = 20.7 s-1. 

Methane/Air Diffusion Flame

Distance From Fuel Exit (cm)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Scalar Dissipation, (s-1)

0

50

100

150

200

250

300

25 cm/s

320.1 cm/s

χ

χ

Methane/Air Diffusion Flame

Stocihiometric Scalar Dissipation Rate, χs

 (s-1)

0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0

Maximum Flame Temperature (K)

1800

1850

1900

1950

2000

2050
34

Table 10. Various Measures of Strain Rate Calculated for Methane/Air Diffusion Flames at 

Extinction 

Source L (cm) uf (cm/s) uo (cm/s) ag (s-1) |ao| (s-1) χs (s-1) Tmax (K) 

This Work 

(GRIMech 1.2) 1.0 157 -157 547 500 19.9 1792 

This Work 

(GRIMech 1.2) 2.0 320 -320 558 509 20.7 1785 

This Work 

(GRIMech 2.11) 2.0 312 -313 544 492 21.3 1793 

This Work 

(GRIMech 3.0) 2.0 313 -313 546 500 21.7 1805 

Dixon-Lewis et al. [88] 1.0 - - - - 16.7 1769 

Chelliah et al. [92] 1.0 185 -135 610 391 14.7 1758 

Du and Axelbaum [117] 0.8 - - - 494 - 1770 

Tanoff et al. [72] - - - 350 - 1808 

Tanoff et al. [72] - - - - 490 - - 

Tanoff et al. [72] 585 - - 

Chan et al. [101] - - - - - 19.4 1773 

Lentati and Chelliah [73] 1.0 - - - 425 - 1790 

identified for methane/air diffusion flames. However, Yang and Kennedy have reported measurements of 

χs for a methane flame near inhibited by trichloroethylene near extinction. [116] These authors found that 

the extinction strain rate varied linearly with trichloroethylene volume fraction. Assuming that values of 

χs have the same dependence, it is possible to estimate a value of χs =18.6 s-1 from their result for χs with 

16.1 % trichloroethylene added to the methane fuel. Given the various approximations, this represents 

reasonable agreement with the current calculated value. 

In order to obtain insights into the effect of the separation of the fuel and oxidizer sources, calculations 

were also performed for L = 1.0 cm. Table 10 compares the various measures used to quantify extinction 

for the two sets of calculations and includes the maximum flame temperature at extinction. While the 

initial flow velocities required for extinguishment depend strongly on L, the various measures for the 

effects of strain vary only slightly for the two cases. These minor differences are most likely due to the 

variations in the grids used for the calculations. These limited results suggest that for the assumed initial 

conditions, i.e., no radial gradients at the fuel and air exits, the velocities of fuel and air required for 

extinction are roughly proportional to L, while the various measures used to describe the role of strain are 

roughly independent of L. 

It is of interest to compare the results of the current calculations with comparable modeling results found 

in the literature. Parameters used to characterize methane/air diffusion flames near extinction are 

included in Table 10 for a number of studies. Substantial variations are evident for calculated extinction 

parameters in terms of ag, |ao|, and χs. As discussed earlier, the GRIMech version used for the current 

study (Version 1.2) has been superseded by two later versions. A series of calculations was performed for 

methane/air flames using GRIMech 2.11 and 3.0 in order to assess whether substantial differences in 

calculated extinction behavior can be attributed to the GRIMech version used. Figure 16 compares the 

results for the three versions. Calculated values for uo, |ao|, and Tmax for GRIMech Versions 1.2, 2.11, and 

3.0 have been included in Table 10. The results for each mechanism fall close together, indicating that 

differences between the various GRIMech versions will have little effect on the findings discussed here. 
35

Figure 16. Maximum flame temperatures are plotted as a function of the equal fuel and air velocity 

magnitudes for a methane/air opposed-flow diffusion flame. Results are compared for 

calculations using Versions 1.2, 2.11, and 3.0 of the GRIMech mechanism. [106] 

The three sets of results for Tanoff et al. included in Table 10 provide a strong clue as to the reason for 

these variations. [72] The only change in their calculations was that different detailed chemical-kinetic 

mechanisms were used for each. Values of |ao| vary by nearly a factor of two. One of the mechanisms 

used by Tanoff et al. was GRI-Mech 2.11 (|ao| = 585 s-1) that would be expected to provide similar results 

to the calculations reported here. The actual difference is roughly 15 %. We are not able to provide an 

explanation for the discrepancy, but do note that the calculations of Tanoff et al. included the effects of 

thermal diffusion and radiative heat losses that are not treated by the current calculations. The only other 

study which used GRI-Mech 2.11 was that of Chan et al. [101] Their value of χs = 19.4 s-1 is in 

reasonable agreement with the current result of 21.3 s-1. 

Bai et al. [103] have also reported flame structure calculations for methane/air diffusion flame using a 

reduced chemical-kinetic mechanism taken from Peters. [119] Unlike most earlier studies, they used the 

scalar dissipation rate at the peak temperature, χp, as their characteristic parameter. For a methane/air 

flame near extinction they calculated χp = 26.7 s-1. The corresponding result from the current calculations 

is χp = 27 s-1. While the agreement between these two modeling studies is very good, it must be kept in 

mind that the current calculations do overestimate the experimental value for ao by roughly 20 %. 

Based on the above discussion, we conclude that the current calculations for methane/air flames are 

consistent with existing literature results, but that there is a relatively large variation in the quantitative 

results due to the dependence of the results on the particular detailed chemical-kinetic mechanism used. 

The extinction behavior for a propane/air flame has also been calculated using the mechanism of 

Babushok and Tsang. [70] Figure 17 shows a plot of maximum flame temperature versus the propane and 

air velocity magnitudes. Comparison with Figure 10 shows that while the flow velocities at extinction for 

the methane (320 cm/s) and propane (329 cm/s) flames are roughly the same, the maximum flame 

temperatures (1785 K and 1695 K, respectively) differ substantially. Differences of comparable 

magnitude exist over the full range of flow velocities considered. 

Methane/Air Diffusion Flame

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Flame Temperature (K)

1750

1800

1850

1900

1950

2000

2050

2100

GRIMech 1.2

GRIMech 2.11

GRIMech 3.0
36

Figure 17. Maximum flame temperatures are plotted as a function of the equal fuel and air velocity 

magnitudes for a propane/air opposed-flow diffusion flame. 

Figure 18. The maximum flame temperature is plotted as a function of the global stain rate ag for a 

propane/air opposed-flow diffusion flame. 

It is also of interest to compare the propane flame extinction behavior in terms of the global strain rate, 

local strain rate behavior on the oxidizer side, and the scalar dissipation rate at the stoichiometric point. 

Figure 18 shows a plot of the maximum flame temperature versus the global strain rate, ag. Extinction is 

calculated to take place for ag = 735 s-1. Experimental values reported in the literature include those of 

Puri and Seshadri [114] (ag = 610 s-1), Lin and Faeth [120] (ag = 590 s-1), DeCroix and Roberts [98] 

Propane/Air Diffusion Flame

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Flame Temperature (K)

1700

1750

1800

1850

1900

1950

2000

Propane/Air Diffusion Flame

Gobal Strain Rate (s-1)

0 100 200 300 400 500 600 700

Maximum Flame Temperature (K)

1700

1750

1800

1850

1900

1950

2000
37

Figure 19. The maximum flame temperature is plotted against a characteristic local strain rate, |ao|, 

defined to be equal to the highest absolute value of a on the air side observed outside of the 

boundary layer associated with the combustion zone for the propane/air flame. 

(ag = 700 s-1) and Zegers et al. [52] (ag = 381 s-1). These values cover a wide range, with all of the 

experimental results falling below the calculated value. The reason for the wide variation in experimental 

results is not clear, but it may be associated with the different initial velocity profiles used in the various 

studies. 

Figure 19 shows the calculated temperature data replotted in terms of the local strain rate |ao|. Extinction 

is calculated to occur for |ao| = 621 s-1. This result can be compared with experimental values available in 

the literature: Du et al. [115] (|ao| = 510 s-1 ± 10 s-1), DeCroix and Roberts [98] (|ao| = 721 s-1) and Zegers 

et al. [52] (|ao| = 583 s-1 ± 53 s-1). As was found for ag, there is a great deal of variation in the 

experimental results for |ao| that is greater than was found for methane flames. It is difficult to understand 

these variations since the local strain rate is supposed to compensate for differences in initial velocity 

profiles for the fuel and oxidizer. DeCroix and Roberts discuss experimental difficulties that arise when 

using propane for opposed-flow flame measurements. It is possible that these difficulties are responsible 

for the observed variations. Even though the experimental value is not well defined, it is encouraging that 

the calculated value falls in the general range provided by the experiments. 

The calculated temperature data for a propane/air flame are replotted as a function of the mixture fraction 

scalar dissipation rate at the stoichiometric location, χs, in Figure 20. Flame extinction is calculated to 

occur when χs, is increased to 26.3 s-1. No other experimental or modeling values of this parameter have 

been identified for propane/air flames. However, Bai et al. have reported a calculated value of 66.0 s-1 for 

χp, the value of χ at the location of the peak flame temperature. [103] The value obtained from the current 

calculations is 44.9 s-1, which must be considered poor agreement. Recall that the corresponding values 

were quite close for the methane/air flame. 

The calculations and experiments suggest that propane burns more robustly than methane. Propane 

extinction requires a higher strain rate (calculated |ao| = 621 s-1 for propane versus |ao| = 509 s-1 for 

Propane/Air Diffusion Flame

Characteristic Strain Rate on Oxidizer Side |ao| (s-1)

0 100 200 300 400 500 600

Maximum Flame Temperature (K)

1700

1750

1800

1850

1900

1950
38

Figure 20. Values of maximum flame temperature for opposed-flow propane/air diffusion flames are 

plotted as a function of χs that is varied by changing the velocities of the fuel and air. 

Extinction is calculated to occur for χs = 26.3 s-1. 

methane) and the calculated maximum flame temperature is lower for propane (1695 K for propane 

versus 1784 K for methane). With regard to strain rate, the difference is likely larger than indicated here 

since the value calculated for methane seems to be overestimated by roughly 30 %. The differences 

between methane and propane are consistent with the discussion of Maĉek. [42] 

E. Extinction and Extinguishment of Methane and Propane Diffusion Flames by 

Nitrogen 

The purpose of the detailed chemical-kinetic modeling calculations is to investigate the effects of thermal 

agents on the structure of opposed-flow diffusion flames and to use the findings to gain insights into 

flame extinguishment by these agents. Note that we are purposefully distinguishing between the 

meanings of flame “extinction” and “extinguishment”. Flame extinction is used to describe a flame that 

goes out due to the local strain rate or other conditions causing the flame to become unstable. Flame 

extinguishment refers to the more specific conditions necessary to put out buoyancy-dominated flames 

that are expected to be characteristic of most fires. The cup burner test is an example of an experimental 

technique designed to characterize extinguishment. [46,47] Thus flame extinguishment can be considered 

to be a particular case of flame extinction.

In order to evaluate the effectiveness of the calculations, it is necessary to compare with experimental 

findings. Since the focus of this investigation is extinguishment of fires, the most appropriate measure to 

consider for characterizing diffusion flame extinction is the amount of thermal agent required to 

extinguish a buoyancy-dominated flame burning at standard gravity. This concentration is related to the 

concept of a limiting oxygen index (LOI), which is defined to be the lowest oxygen concentration in air 

diluted with nitrogen that can support a flame burning under these conditions. The minimum agent 

volume fraction required to meet this condition is sometimes referred to as the inerting concentration. 

Propane/Air Diffusion Flame

Stocihiometric Scalar Dissipation Rate, χs

 (s-1)

0 5 10 15 20 25

Maximum Flame Temperature (K)

1700

1750

1800

1850

1900

1950
39

In order to define an extinguishing condition for the addition of thermal agents to the oxidizer it is 

necessary to relate the calculations to an experimental result. For the methane/air and propane flames of 

interest here we wished to use the LOI for this purpose. Somewhat surprisingly, only a limited number of 

LOI values have been published for these flames. 

For methane, Simmons and Wolfhard reported a LOI value of 0.139 using a hemispherical burner located 

in a slow oxidizer counter flow. [41] This corresponds to an added N2 volume fraction of 33.8 %. 

Measurements by Ishizuka and Tsuji in a similar burner yielded a value of 31.9 %. [48] Puri and Seshadri 

reported that a 28.6 % N2 volume fraction was sufficient to extinguish an opposed-jet methane/air 

diffusion flame. [114] In a recent, as yet unpublished, study, researchers at NIST made measurements in 

a similar low strain-rate flame and measured a value of 30.0 % for the maximum N2 volume fraction at 

extinguishment. [121] At the 1999 HOTWC meeting, Ural reported a study of extinguishment of a 

methane flame in a cup burner apparatus. [57] The extinguishing volume fraction of N2 over a relatively 

wide range of fuel and oxidizer velocities was 27.1 %. 

As for methane, there are only a limited number of LOI values reported for propane/air diffusion flames. 

Simmons and Wolfhard measured a LOI of 0.127 using their porous hemispherical burner, corresponding 

to a nitrogen volume fraction for extinguishment of 39.5 %. [41] Note that that the measured 

extinguishing concentration is roughly 17 % greater than observed for a methane flame. For an opposedflow diffusion flame, Puri and Seshadri recorded an extinguishing volume fraction of 34.8 % nitrogen. 

[114] This value is nearly 22 % higher than found for methane by the same authors. Note that for a given 

fuel, the nitrogen extinguishing volume fraction is significantly lower for the opposed-flow burner. 

Several values of nitrogen extinguishing concentration are available for propane flames burning in a cup 

burner configuration. Hamins et al. reported an extinguishing volume fraction of 32.5 %. [33] Babb et 

al. measured a value of 33 %. [56] The results of Ural also yield a value of roughly 33 %. [57] These 

results are all very close together, suggesting that lab-to-lab variations are not responsible for the 

differences observed between different burners. Comparison of the results of Babb et al. for methane and 

propane indicates that a propane flame again requires a higher concentration for extinguishment (roughly 

22 %). 

The range of extinguishing concentrations for methane and propane flames burning in air for different 

types of burners reported in the various investigations cited above is much larger than can be explained by 

uncertainty in the measurements and suggests that different types of diffusion flames yield different 

results. This raises the important question of what type of burner is appropriate for determining a 

characteristic extinguishing nitrogen volume fraction (or LOI) for buoyancy-dominated diffusion flames. 

Due to the limited data available and the wide range of values reported, it was decided to carry out 

additional measurements of nitrogen extinguishing concentration using two diffusion flame burners 

available at NIST. The first was a modified version of the DLAFSS system described earlier that 

incorporates a Tsuji-type opposed-flow cylindrical diffusion flame burner, and the second was a Santorotype burner (a coflow diffusion flame) previously used at NIST for investigations of diffusion flame 

structure. Descriptions of these burners are provided in the following section. 
40

1. Experimental Systems for Measuring Extinguishing Concentrations of Gaseous 

Thermal Agents 

a) Modified Dispersed Liquid Agent Fire Suppression Screen System (Tsuji 

Burner) 

The DLAFSS described in Section (II.B.1.b) was used to investigate the extinguishment of Tsuji-type 

methane and propane diffusion flames by gaseous thermal agents. Even though designed primarily for 

evaluating liquid fire suppression agents, the system can also be used for gaseous agents. [35,36] The 

injection point for gases is at the bottom of the system as can be seen in Figure 6. 

The goal of these measurements was to identify extinction conditions for thermal agents added to the 

oxidizer flow for porous-burner-stabilized opposed-flow diffusion flames under the relatively low strain 

rates characteristic of buoyancy-dominated flames. Typically, the Tsuji burner is operated at 

considerably higher oxidizer flow velocities than required here, and the resulting strain rates are much 

greater than found in buoyancy-dominated flames. In order to generate the required low oxidizer 

velocities, the fan used to induce the flow in the DLAFSS was operated at the lowest setting possible. 

The thermal agents were then added to the induced air flow. Note that the oxidizer flow velocity is 

expected to vary as the agent volume fraction increases. 

The flow rate of agent was controlled using a needle valve, and the volume flow rate was measured using 

a rotameter (Fischer Porter, Model 10A1755). Even though the agent volume flow rate was known, it 

was discovered that it was not possible to predict the agent volume fraction using only the assumed airflow rate. This observation was attributed to variations in the oxidizer total volume flow rate due to 

changes in the fan efficiency as agent was added. An alternate approach was adopted to estimate the 

oxidizer total flow rate and thus the local flow velocity at the flame. The agent concentration was 

determined by measuring the oxygen volume fraction in the oxidizer stream at the center of the settling 

chamber of the wind tunnel (see Figure 6) using a paramagnetic oxygen meter (Servomex Oxygen 

Analyzer Model 570A) in conjunction with a small sampling pump (Gilian Hi Flow Sampler, Model HFS 

513A). The oxygen analyzer was zeroed and spanned using nitrogen and room air. Since the volume 

flow rate for the agent was known, knowledge of the degree of air dilution allowed the total flow rate to 

be calculated assuming complete mixing. 

In a typical DLAFSS experiment, extinction is defined to occur when the flame on the upstream side of 

the burner blows out. For high strain-rate conditions, it is generally found that a flame stabilized in the 

wake of the cylinder continues to burn following blow out of the upstream flame. During the current 

experiments, it was observed that when sufficient agent was added to the air flow to induce extinction of 

the stretched flame on the upstream side of the cylinder, the downstream flame was either extinguished at 

the same time, or disappeared when the agent concentration was increased only slightly. Since the 

stabilized flame is essentially a buoyancy-dominated flame, this is taken as evidence that the 

measurements are actually recording flame extinguishment values. 

Extinguishment tests were performed by gradually adding the gaseous inhibitor to the oxidizer (air) 

stream until blow-off occurred (abrupt transition from envelope to wake flame or blow out). The 

volumetric flow rates of the suppressant at blow-off were recorded. The oxygen concentration was then 

noted for the same flow conditions. 
41

Figure 21. A schematic of the modified Santoro burner is shown. 

b) NIST Coflow Diffusion Flame Burner (Santoro Burner) 

An existing coflow burner and computer-controlled gas mixing system were modified to allow 

extinguishing concentrations of thermal agents to be determined for buoyancy-dominated laminar 

diffusion flames formed by a flow of gaseous fuel from a circular tube into a slow surrounding coflow of 

an air/agent mixture. The burner is based on a design originally developed by Santoro et al. that is 

commonly referred to as a “Santoro burner”. [122] This type of burner has been employed for numerous 

flame studies at NIST. In a particularly relevant study, Smyth and Everest reported volume fractions of 

CF3Br and CF3I in air required to extinguish a propane flame on the Santoro burner. [123] 

The actual burner used in this investigation is a modified Santoro burner that was originally employed to 

investigate acoustically forced, time-varying diffusion flames. [124] A drawing of the burner is shown in 

Figure 21. It consists of an open 13.7 cm length of tubing with a 1.27 cm outer diameter that serves as the 

central fuel tube. The tube lip thickness is 0.065 cm, yielding an inner diameter of 1.14 cm. One end of 

the tube is attached to a plenum containing a loud speaker. The speaker, used to acoustically force the 

fuel flow, was not employed during this study. The open end of the fuel tube extends 0.4 cm above a 

surrounding 10.2 cm diameter ceramic honeycomb formed from 0.15 cm square cells and having an 

overall length of 2.5 cm. After passing through a chamber filled with glass beads and several screens, a 

flow of air and agent enters the honeycomb to form the surrounding coflow for the flame. 

The flow velocities for the fuel and coflow streams were low and resulted in small buoyancy-dominated 

flames that were highly susceptible to room drafts. Screens were placed around the burner to minimize 

these disturbances. Flame products were removed from the area by an exhaust cone connected to the 

room exhaust by a flexible hose. The effect of the exhaust cone on the flames was judged to be negligible 

due to its low rate of suction and its location well above the burner. 

Fuel and the air/agent mixture were delivered to the burner using a system of thermal mass flow 

controllers (MFC’s). The flow-control system, shown in Figure 22, is a modification of a system 

developed at NIST for a previous investigation as described in detail by Pitts et al. [125] The flow system 

was software controlled by a desktop 486-DX personal computer. The volume flow rates required to 

Air & Agent Air & Agent

Fuel

1.14 cm

1.27 cm

10.2 cm
42

Figure 22. A schematic and photo of the Santoro burner and flow control system are shown. 

generate precise mixtures of air and agent were specified by the software. The air and agent streams were 

combined upstream of the burner in a mixing chamber designed to ensure a homogenous mixture. 

Pneumatic shut-off valves prevented unwanted backflow of gases and allowed for easy calibration of each 

MFC. Modifications for the current study included the addition of a 30 SLMN (standard liters of nitrogen 

per minute) mass-flow controller for the air flow and moving the 10 SLMN and 2 SLMN mass-flow 

controllers to the agent and fuel streams, respectively. Appendix B includes additional details concerning 

the MFCs and their calibration. Gas supplies for the fuel and agents were bottled gases with nominal 

purities of 99.0 %. Air was supplied from an in-house high-pressure line, and its relative humidity was a 

consistent 4.5 %. 

The system performed automated experimental control and data acquisition using a Flash-12 Model 1 

data acquisition card and an ACAO-12-2 analog and digital output board, both from Strawberry Tree, to 

provide interfaces with the experiment. The mass flow controllers were connected to a MKS Instruments, 

Inc. Type 247C 4-channel readout, set point, and power supply that also served to interface the MFC’s 

with the data acquisition and output boards. 

Software control was provided by an icon-based worksheet, developed using WorkBench PC (from 

Strawberry Tree, Inc.). The worksheet, named AGFCTL.WBB (Automatic Gas Flow Control), was a 

modification of a similar program used in the study described by Pitts et al. [125] The modified 

worksheet provides the necessary calculations and controls for operation of the mass-flow controllers, 

on/off control of the electro-pnuematic valves and indicator lights, series step changes in agent 

concentrations, and display and data logging of key parameters. Another worksheet, MFCCAL.WBB 

(Mass Flow Controller Calibration), was developed for the calibration of the individual mass flow 

controllers. 

Most experimental systems designed to study the effects of a fire-fighting agent on coflow diffusion 

flames, e.g., the cup burner, create agent/air mixtures by holding the air volume flow rate constant and 

adding the agent. As a result, the velocity of the oxidizer flow increases as the agent is added. This 

increases the local strain rates in the vicinity of the flame and is therefore a potential source of variation in 

the measurement. An advantage of the computer-controlled system used here is that it is possible to 

maintain the total volume flow rate for the agent/air mixture constant as the agent concentration increases. 

For a majority of the methane flame measurements reported here, the nominal exit flow velocities for the 

fuel and oxidizer coflow were matched at 7 cm/s. Similar velocities were employed in earlier studies with 

this burner. The required volume flow rates of fuel and oxidizer were calculated using the general 

equation, 

0 - 10 SLMN

0 - 10 SLMN

0 - 30 SLMN

0 - 2 SLMN

Mass

Flow

Controllers Pneumatic

Valves

Mixing Chamber

Air

Agent

Fuel

Burner

Screens

P1

P2

0 - 10 SLMN

0 - 10 SLMN

0 - 30 SLMN

0 - 2 SLMN

Mass

Flow

Controllers Pneumatic

Valves

Mixing Chamber

Air

Agent

Fuel

Burner

Screens

0 - 10 SLMN

0 - 10 SLMN

0 - 30 SLMN

0 - 2 SLMN

Mass

Flow

Controllers Pneumatic

Valves

Mixing Chamber

Air

Agent

Fuel

Burner

Screens

P1

P2
43

, Qexit = Uexit Aexit ( 15 ) 

where Uexit is the desired velocity and Aexit is the flow area and equals 1.02 cm2

 and 79.8 cm2 for the fuel 

and air, respectively. Other combinations of fuel and coflow velocities were employed during the study 

as discussed below. 

An experiment consisted of: 

1) Entering the desired volume flow rates for fuel and oxidizer in SLM into the appropriate 

worksheet locations. 

2) Setting the initial volume fraction for the desired thermal agent at the computer control panel 

window. The starting volume fraction was typically 0.010 to 0.020 less than the expected 

extinguishment concentration. (Preliminary survey experiments were run to determine 

approximate extinguishing concentrations) 

3) Starting the program at the computer-control panel. The program automatically increased the 

agent concentration in the agent/air mixture by increments of 0.001 in volume fraction. The 

agent concentration was held for 40 s in order allow any effects of transients associated with the 

volume fraction change to decay. 

4) Monitoring the flame and recording the agent concentration at which the flame extinguished. 

Once the flame was extinguished, the program was immediately manually aborted, which in turn 

interrupted the gas flows. 

Additional details concerning the calculation of the appropriate gas volume flow rates are included in 

Appendix B. A discussion of the analysis employed to estimate uncertainties for the volume fraction of 

agent in air is also included in Appendix B. 

2. Results for Thermal Agent Extinction of Methane and Propane Diffusion Flames 

Burning on Tsuji and Santoro Burners 

The extinguishment behavior of flames stabilized on the Tsuji and Santoro burners were investigated 

using the gaseous thermal agents nitrogen, carbon dioxide, argon, and helium. The following two 

sections summarize the general observations and the results of extinguishment volume fraction 

measurements. 

a) Tsuji Burner 

Multiple extinguishment tests were run for each agent. Table 11 summarizes measured values of 

extinguishing volume fraction for the four thermal agents. The repeatability of the measurements is 

indicated by the magnitude of the standard deviation. The actual number of repeated tests is denoted by 

the symbol n. The table also includes values of the stagnation velocity gradient, aT, defined as 2Vo/R, 

where Vo is the velocity based on the total volumetric flow rate of air and gaseous agent at blow-off and R

is the burner radius. aT represents the characteristic stagnation strain rate that is often used for Tsuji burners 

and has units of s-1. aT is similar to the global strain rate, ag (see Eq. (14)), used to characterize the strain 

rate for axisymmetric opposed-flow diffusion flames. Note that a one-to-one correspondence should not be 

expected for ag and aT, and direct comparisons are inappropriate. 

As already discussed, measurements of extinguishing volume fractions in the literature are limited for 

opposed-flow porous burners. Simmons and Wolfhard [41] reported values of 34 % and 39.5 % for the 

extinguishing concentrations of methane and propane flames on a hemispherical porous burner, while 
44

Table 11. Extinguishment Results Using the DLAFSS 

Agent 

Methane Propane 

 Agent volume fraction 

at blow-off 

aT = 2Vo/R 

(s-1) 

Agent volume fraction 

at blow-off 

aT = 2Vo/R

(s-1)

Carbon Dioxide 0.240 ± 0.003* (n = 4) 39 ± 1 0.257 ± 0.008 (n = 3) 45 ± 2 

Nitrogen 0.332 ± 0.004 (n = 5) 52 0.390 ± 0.004 (n = 5) 56 

Helium 0.207 ± 0.003 (n = 5) 94 0.224 ± 0.003 (n = 5) 95 ± 1 

Argon 0.468 ± 0.002 (n = 4) 44 ± 1 0.550 ± 0.005 (n = 5) 44 

Ishizuka and Tsuji [48] found a value of 31.9 % for a methane flame stabilized on a cylindrical porous 

burner. These values agree very well with those included in Table 11, (33.2 ± 0.4) % and (39.0 ± 0.4) % for 

methane and propane, respectively. This agreement is found even though two different types of porous 

burners were used. Recall that the extinguishing nitrogen volume fractions of Simmons and Wolfhard were 

the highest observed for the various types of diffusion flames discussed earlier. It must be concluded that a 

flame for a given fuel is more stable on an opposed-flow porous burner than for the corresponding flames 

burning between two axisymmetric opposed-jet flows or in a coflow configuration. The reasons for these 

observations are currently unclear. 

Note that in the case of helium included in Table 11, the values for aT = 2Vo/R are almost a factor of two 

higher than those obtained using nitrogen, carbon dioxide, and argon. Recall that the fan in the DLAFSS is 

set to operate at the lowest possible revolution rate. Even though the fan speed is nominally constant, when 

the density downstream of the fan is significantly reduced, the fan generates a higher volume flow rate. The 

net result is that the characteristic strain rate, aT, at the flame is roughly a factor of two higher for the helium 

case than for the other agents, and it is to be expected that the observed extinguishing concentration will be 

somewhat lower than would be measured for a purely buoyancy-dominated flame. The variation of 

extinguishing volume fractions with different agents will be discussed in more detail below. 

b) Santoro Burner 

The coflow gas burner is a deceptively simple flame configuration. During the extinguishment studies 

summarized here a number of complex behaviors were observed that complicated what should have been, 

in principle, a simple measurement of extinguishing concentration. The behaviors are also shown to be 

fuel dependent, being different for methane and propane flames. 

Consider first the methane base flame (i.e., fuel and oxidizer nominal velocities equal to 7 cm/s) burning 

in air diluted with N2. With only air present, a blue flame was evident slightly below the exit and very 

close to the fuel tube. Further downstream the flame was yellow indicating the presence of soot. As the 

N2 concentration in the oxidizer was increased, the base of the flame gradually moved downstream and 

away from the burner tube, but the flame still appeared to be attached. At the same time, the fraction of 

the flame that appeared yellow decreased. When the N2 volume fraction reached 20.2 %, an up and down 

oscillation of the flame base suddenly appeared as indicated in Figure 23. This flame was entirely blue. 

The oscillating flame only existed over a narrow range of N2 volume fraction. Similar oscillations for 

flames near extinction have been reported previously in the literature. [126,127] 

* mean ± standard deviation 

n = number of samples
45

Figure 23. Sketch of a methane flame showing the attached flame oscillation and subsequent stabilized 

lifted flame that result from the addition of nitrogen to the air coflow. 

Figure 24. The evolution of the methane diffusion flame structure as additional N2 is added to the coflow 

air stream is shown. 

When the N2 volume fraction was increased to 20.5 %, the flame detached from the burner and moved 

downstream, where it became stable and floated lazily up and down 15 mm to 20 mm above the burner. 

With further increases in N2 concentration, the flame moved further downstream, while becoming shorter 

and broader. These changes in appearance are shown in cartoon form in Figure 24. Similar lifted-flame 

structures have been observed in investigations with different fuels and burner configurations and are 

attributed to the presence of triple flames. [128,129,130,131] The presence of lifted flames has also been 

reported during cup burner experiments using gaseous fuels. [33,56,57] When the N2 volume fraction 

reached 21.8 %, the lifted flame could no longer be stabilized, and it simply floated away, i.e., it was 

blown off. 

~ 5 mm

~ 15 mm

Attached flame instability

0.202 < XN2 < 0.205

Lifted flame

XN2 > 0.205

~ 5 mm

~ 15 mm

Attached flame instability

0.202 < XN2 < 0.205

Lifted flame

XN2 > 0.205

h

w

l h

w

l

XN2 ~ 0.210 XN2 = 0.218

Blow off

h

w

l h

w

l

XN2 ~ 0.210 XN2 = 0.218

Blow off
46

Increasing N2 dilution of the air resulted in three distinct behaviors—attached flame instability, lift off, 

and blow off. The N2 volume fraction range where these processes occurred was narrow, ranging from 

20.5 % to 21.8 %. It is difficult to define any of these processes as a true extinguishment, though blow 

off would seem to be the most appropriate. For reasons that will be clear shortly, the onset of the 

fluctuation behavior was used for the characteristic extinguishing concentration for methane flames 

burning in air diluted with thermal agents. 

When CO2, Ar, and He were used as diluents, the response of the baseline methane flame changed from 

that observed for N2. Initial changes in flame structure with increasing inert agent volume fraction were 

similar to those observed with nitrogen. For all three agents, an agent volume fraction was reached for 

which the attached flame instability appeared. Similar to the results for N2, additional small increases in 

the volume fractions of CO2 and Ar resulted in detachment of the flame from the burner, with 

stabilization further downstream. At first, these flames moved further downstream with additional 

increases in diluent concentration, but eventually the flames reached lift-off heights where further 

increases appeared to have little effect. The most likely reason for this observation is that the flames 

reached a downstream location where surrounding room air was able to diffuse through the oxidizer 

coflow and provide sufficient O2 to sustain combustion. For these cases it is impossible to define the 

agent volume fraction required for flame blow off. The behavior of the flame burning in air diluted with 

He was quite different. After a few oscillations following the onset of the attached flame instability, the 

flame was extinguished without further increases in helium concentration. Apparently, the onset of the 

attached flame instability was sufficient to extinguish the methane flame burning in the He/air mixture. 

Since the appearance of the attached flame instability was the only common characteristic for all four of 

the agents, its onset was selected as the condition determining extinguishment of methane flames. 

When the baseline fuel and oxidizer volume flow rates for the methane case were used for propane, the 

resulting flame length was much greater than observed for methane. This observation is easily 

understood by considering the flame stoichiometries for the two fuels, 

Methane: CH4 + 2O2 → 2H2O + CO2

 Propane: C3H8 + 5O2 → 4H2O + 3CO2 , 

which indicate that combustion of a given volume of propane requires 2.5 times more oxidizer than the 

same volume of methane. Since the entrainment rate of oxidizer into laminar diffusion flames is roughly 

independent of the fuel flow rate, a longer flame length is required for the complete combustion of 

propane than for methane when the volume flow rates are equal. 

In order to have roughly comparable flame lengths for the two fuels, the nominal fuel velocity for propane 

was reduced to 40 % of that used for methane (i.e., a nominal velocity of 2.8 cm/s, volume flow rate of 

0.171 L/min). With the oxidizer nominal velocity maintained at 7 cm/s, the propane flame length was 

comparable to that for the baseline methane flame. These flow velocities were adopted as the baseline 

conditions for the propane flame. 

Similar to the baseline methane flame, the propane flame was attached to the fuel tube prior to the 

addition of nitrogen to the coflow. As the nitrogen volume flow rate was increased, the blue region at the 

base of the flame occupied a larger volume, as was also observed for the methane flame. However, 

unlike the methane flame, the base of the propane flame broadened substantially as it moved away from 

the burner tube with increasing nitrogen addition. By the time the nitrogen volume fraction was increased 

to 26.5 %, the flame base was stabilized approximately 5 mm downstream of the fuel exit. When the 

nitrogen volume fraction was increased to 27.4 %, the flame base was approximately 10 mm above the 
47

Figure 25. A sketch of the time evolution of a nearly extinguished propane flame is shown for the case of 

nitrogen dilution of the coflow air, t1 < t3. 

fuel tube and began to oscillate with a combined vertical and radial motion. Further downstream the 

flame formed a necked-down region. With only an additional increase of 0.1 % nitrogen volume fraction, 

the flame suddenly extinguished by collapsing at the necked-down region. A cartoon of the nearly 

extinguished flame is shown in Figure 25. The extinguishment of the propane flame following stands in 

sharp contrast to the methane flame, which formed a stable lifted flame following detachment from the 

burner. 

Unlike the baseline methane flame, the general response of the propane flame to dilution of the coflow air 

by CO2, Ar, and He was the same as described above for nitrogen dilution. Since an easily characterized 

extinguishment was observed for each agent using propane, this event was designated as the characteristic 

flame extinguishment behavior. 

The results of extinguishment studies for baseline methane and propane diffusion flames on a Santoro 

burner are summarized in Table 12. Agent volume fractions corresponding to the onset of flame 

fluctuation and flame extinguishment (if observed) are included. Expanded uncertainties, U, calculated as 

described in Appendix B are included in the table. Extinguishment was not observed for the methane 

flame with CO2 and Ar. The volume fraction of agent required to induce oscillation is taken as the 

characteristic extinguishing concentration for the methane flame, while the actual concentration at flame 

extinguishment is used for the propane flame. Note that the small differences observed between the two 

values for given agent and fuel suggests that small differences will be introduced by the use of different 

definitions for extinguishment. 

The extinguishing concentrations for a given agent listed in Table 12 for the Santoro burner are much 

lower than for the corresponding agent included in Table 11 for the Tsuji burner. A potential explanation 

for this observation is a dependence of the Santoro burner results on the fuel and/or flow velocities. In 

order to check this possibility, measurements were made using both methane and propane in which the 

velocities were varied from the baseline cases. These results are summarized in Table 13 and Table 14, 

which list results for flames where the fuel and oxidizer volume flow rates were varied independently. 

Recall that baseline values for the methane and propane flames are Qfuel = 0.429 L/min and Qcoflow = 

Necked down region

& extinguishment point

Direction of flame

base propagation

a) t=t1 b) t=t2 c) t=t3
48

Table 12. Measured Agent Volume Fractions at Onset of Flame-Base Instability (Osc) and for 

Flame Extinguishment (Ext) of Baseline Methane and Propane Coflow Diffusion Flames 

Methane Propane 

Osc Ext Osc Ext 

Carbon Dioxide 0.120 

(U = ± 0.001) - 0.169 

(U = ± 0.009)

0.176 

(U = ± 0.004) 

Nitrogen 0.202 

(U = ± 0.006) 

0.218 

(U = ± 0.006)

0.276 

(U = ± 0.010)

0.280 

(U = ± 0.016) 

Helium 0.200 

(U = ± 0.004) 

0.200 

(U = ± 0.004)

0.271 

(U = ± 0.007)

0.273 

(U = ± 0.006) 

Argon 0.290 

(U = ± 0.004) - 0.356 

(U = ± 0.006)

0.368 

(U = ± 0.007) 

U = Expanded Uncertainty with K = 2 

Table 13. Effects of Fuel and Oxidizer Velocity on Agent Concentrations at Onset of Flame Base 

Oscillation (Osc) and Flame Extinguishment (Ext) for the Methane Coflow Flame 

Qfuel Qcoflow CO2 N2 He Ar 

L/min L/min Osc Ext Osc Ext Osc Ext Osc Ext 

0.429 33.52 0.120 - 0.202 0.218 0.200 0.200 0.290 - 

0.215 33.52 0.121 0.128 0.198 0.198 0.291 - 

0.107 33.52 0.123 0.131 0.204 0.233 0.199 0.199 0.296 0.309 

 

0.429 16.76 0.124 - 0.205 0.206 0.294 - 

0.429 8.38 0.127 - 0.206 - 0.232 - 0.301 - 

Table 14. Effects of Fuel and Oxidizer Velocity on Agent Concentrations at Onset of Flame Base 

Oscillation (Osc) and Flame Extinguishment (Ext) for the Propane Coflow Flame 

Qfuel Qcoflow CO2 N2 He Ar 

L/min L/min Osc Ext Osc Ext Osc Ext Osc Ext 

0.171 33.52 0.169 0.176 0.276 0.280 0.271 0.273 0.356 0.368 

0.086 33.52 0.171 0.174 0.270 0.274 0.280 0.280 0.365 0.370 

 

0.086 16.76 0.172 0.176 0.296 0.297 0.362 0.363 

0.429 33.52 0.149 0.178 0.228 0.280 

33.5 L/min and Qfuel = 0.171 L/min and Qcoflow = 33.5 L/min, respectively. Blank spots indicate 

measurements that were not recorded for a particular agent, while dashes indicate cases where blow off of 

the methane flame was not observed. 

In general, the volume fractions of added agent where flame oscillation and extinction occur are nearly 

insensitive to the fuel and oxidizer velocities for the ranges considered. The only exceptions are the 

flames for which helium was added to the air. For the methane flame, the effect of the velocities on the 

helium results is only evident for changes in the oxidizer velocity, with the extinguishing volume fraction 

increasing by 15 % as the velocity is decreased by a factor of four. In the case of propane, the 

dependence of the helium extinguishing volume fraction on flow velocity is evident for both the fuel and 
49

Figure 26. A time-resolved photograph taken by a digital camera shows the oscillating propane flame 

burning in air diluted with nitrogen. The complex azimuthal structure of the flame base, 

which has a much larger area than the burner tube, is clear. 

oxidizer. A reduction of the oxidizer velocity by a factor two resulted in a 10 % increase in the volume 

fraction of helium required to induce flame oscillation or extinguishment. Based on the relative 

insensitivity to the fuel and oxidizer velocities, we conclude that the experimental results provide good 

estimates for the agent extinguishing conditions using the Santoro burner. 

Generally, the variations in fuel and oxidizer velocities from the baseline cases are reductions. This is 

appropriate because the net effect should be a reduction in strain rate at the flame surfaces due to the 

initial flow velocities. The low insensitivity of the agent extinguishing volume fractions to these changes 

indicates that these strain rates are small relative to those resulting from the buoyancy-induced flows 

associated with the heated combustion gases. 

The only case where the nominal fuel velocity was increased from the baseline value was for the propane 

flame, where it was set to the value for the methane baseline flame, i.e., a volume flow rate of 0.429 

L/min. Recall that the resulting flame length is much longer than for the corresponding methane flame. 

The primary effect of this increase was a dramatic decrease in the volume fractions of CO2 and N2

required to induce flame oscillations. The extinguishing concentrations were nearly unchanged. 

Not only did the propane flame oscillations begin at much lower concentrations for the higher fuel-flow 

velocity, but the flames present during the oscillation also displayed unique instability behaviors over the 

agent concentration range where the oscillation occurred. Similar to the smaller propane flames, a 

combined vertical and radial oscillation with a necked down region above the flame base appeared at the 

first occurrence of the oscillation. However, as the agent concentration was increased toward the 

extinguishment value, the vertical and radial displacements grew in intensity, while the frequency of 

oscillation decreased. The flame base became distorted, losing its axisymmetric symmetry, and 

developed lobes or flower-like petals, which increased in number with increasing agent concentration. 

Figure 26 shows a digital photograph recorded for a propane flame as it approached extinction due to the 

addition of nitrogen to the air coflow. Near flame extinction, as many as six lobes or petals were 
50

Figure 27. The cartoon shows the time evolution of the pulsing instability in the large flow-velocity 

propane diffusion flame observed when a concentration of a thermal fire-extinguishing agent 

near that required for extinguishment is added to the air coflow. The arrows indicate the 

direction of flame base propagation. The view is from an angle above the flame. 

observed. At times the ends appeared to detach from the main flame and form small isolated flame tips. 

A cartoon of the various flame instability behaviors observed with increasing agent concentration is 

shown in Figure 27. 

The physical mechanisms responsible for these interesting flame instability behaviors are not currently 

known and are not legitimately part of the current investigation. However, it is worthwhile to point out 

the similarities between these flame structures and the structures formed by vortices in the near fields of 

axisymmetric jets and flames subject to strong forcing or absolute instability. [132,133,134] 

The relative insensitivity of the measured characteristic extinction concentrations for thermal agents to the 

flow velocities used in the Santoro burner indicates that they are indeed extinguishment volume fractions. 

The results have the same dependence on fuel as already discussed, with characteristic agent volume 

fractions required for extinguishment varying from 25 % to 46 % greater for the propane flames. 

Table 15 provides a summary of nitrogen extinguishing volume fractions reported in the literature for 

various methane and propane diffusion flames, along with results from the current investigation. Values 

for different types of diffusion flame burners are grouped together. The dependencies of extinguishing 

concentration on both fuel and burner type are evident. 

It is clear from the results in Table 15 that N2 extinguishing volume fractions for the Santoro burner are 

considerably lower than have been reported for cup burner studies. This is, at first, somewhat surprising 

since both burners generate coflow diffusion flames, and the flow velocities of fuel and oxidizer are 

comparable in each, with the results for both types of flame shown experimentally to be nearly 

independent of the initial flow velocities. There are three major differences between the cup and Santoro 

burners. First, cup burners typically have a glass “cup” which serves as the fuel port, while the Santoro 

burner uses a straight stainless steel tube. Second, the inside diameters of the fuel tube (2.2 cm to 2.8 cm) 

for the cup burners included in Table 15 are on the order of a factor of two greater than for the fuel tube 

(1.14 cm) in the Santoro burner. Third, the coflow in the cup burner is enclosed within a tube (open at the 

top) while the Santoro burner coflow is exposed to the ambient surroundings. 

Exterior flames

d) t=t4 b) t=t2 a) t=t1

Lobes/petals

c) t=t3

Necked down

region
51

Table 15. Extinguishing Nitrogen Volume Fractions For Various Diffusion Flames Burning 

Methane and Propane 

Burner Type 

Methane Propane 

(Porous Hemisphere/Opposed Flow) [41] 33.8 % 39.5 % 

Tsuji (Porous Cylinder/Opposed Flow) [48] 31.9 % -- 

Tsuji (Porous Cylinder/Opposed Flow) (This Work) 32.2 % 39.0 % 

 

Opposed-Flow Gas Jets [114] 28.6 % 34.8 % 

Opposed-Flow Gas Jets [121] 30.0 % -- 

 

Cup Burner (Coflow) [33] -- 32.5 % 

Cup Burner (Coflow) [56] -- 33.0 % 

Cup Burner (Coflow) [57] 27.1 % 33.0 % 

Santoro (Coflow) (This Work) 20.2 % 28.0 % 

Previous studies have suggested that extinguishing concentrations for cup burners depend on the fuel flow 

cross-sectional area. Tucker et al. reported a slight dependence on diameter when cup burner 

measurements were made for two burners with different diameters (2.1 cm and 0.9 cm), with the smaller 

diameter flame requiring lower volume fractions of extinguishing agents. [45] They attributed their 

observations to the smaller diameter flame having proportionally higher heat losses to the burner. Saso et 

al. studied the effects of burner size on cup burner measurements with liquid fuels. [135] For a n-heptane 

flame they found that the extinguishing volume fraction of halon 1301 decreased by roughly 30 % when 

the cup diameter was reduced from 3 cm to 1 cm. This dependence on burner diameter is roughly the 

same as suggested by the results included in Table 15. If heat losses are indeed the source of the 

difference, the higher conductivity of the metal fuel tube in the Santoro burner as compared to the glass 

cup in the cup burner will also play a role. 

Smyth and Everest have reported an extinguishing volume fraction of CF3Br of 4.1 % for propane 

burning on a Santoro burner. [123] They note that this value is close to the corresponding value of 4.3 % 

CF3Br observed by Hamins et al for a propane flame on a cup burner. [33] The small difference between 

these two values is somewhat less than would be expected based on the current results for thermal agents. 

3. Modeling of Extinction and Extinguishment of Methane and Propane Flames by 

Nitrogen 

OPPDIF was used to calculate flame structures for methane and propane opposed-flow diffusion flames 

reacting with air containing various percentages of added nitrogen. Figure 28 and Figure 29 show the 

results. Several points are immediately obvious. As the percentage of added nitrogen increases, the fuel 

and oxidizer velocity magnitudes sufficient to cause flame extinction decrease. The maximum flame 

temperature at extinction also decreases with increasing nitrogen concentration. The negative slopes of 

the plots for Tmax versus velocity increase in absolute value as the concentration of nitrogen increases. 

Even though the results for methane and propane have similar appearances, there are quantitative 

differences. In Section III.D it was noted that propane flames burning in air required higher velocities, 

strain rates, and scalar dissipation rates to extinguish than methane flames. The maximum flame 

temperature at extinction was also lower for the propane flame. These trends continue as the flames are 

diluted with nitrogen. This can be seen in Figure 30, where values of the calculated maximum flame 
52

Figure 28. Maximum calculated flame temperatures are plotted against methane and oxidizer exit 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

nitrogen. Symbols correspond to the volume fraction of added nitrogen. 

Figure 29. Maximum calculated flame temperatures are plotted against propane and oxidizer exit velocity 

magnitudes for a series of propane/air opposed-flow diffusion flames diluted with nitrogen. 

Symbols correspond to the volume fraction of added nitrogen. 

Nitrogen Dilution of CH4/Air Diffusion Flames

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Flame Temperature (K)

1500

1600

1700

1800

1900

2000

0 %

5 %

10 %

15 %

20 %

25 %

30 %

33 %

Nitrogen Dilution of C3H8/Air Diffusion Flames

Flow Velocities (cm/s)

0 50 100 150 200 250 300 350

Maximum Flame Temperature (K)

1400

1500

1600

1700

1800

1900

2000

0 %

5 %

10 %

15 %

20 %

25 %

30 %

35 %

39.5 %
53

Figure 30. Values of the maximum calculated flame temperature at extinction are plotted as a function of 

the fuel and oxidizer flow velocities for methane and propane flames burning in air diluted by 

various volume fractions of nitrogen. 

temperature at extinction for the two flames are plotted as a function of the fuel and oxidizer flow 

velocities. For lower flow velocities the differences between the maximum flame temperatures at 

extinction become smaller, but the values for methane remain higher for a given velocity. In Figure 31 

the maximum flame temperatures have been replotted as a function of the nitrogen volume fraction. For 

later comparison purposes, this plot also contains adiabatic flame temperatures at stoichiometric 

conditions for methane and propane calculated using the program EQUIL supplied by Reaction Design. 

It is particularly interesting that the order of the temperatures for methane and propane is reversed when 

comparing the two cases. This demonstrates that either transport properties or chemical-kinetic effects 

play an important role in determining the flame structure. Note also that both types of temperature fall 

with increasing nitrogen volume fraction, but that the adiabatic flame temperature drops more quickly. 

As a result, the two temperatures approach each other at higher nitrogen concentrations. 

The discussion thus far has been in terms of the general extinction behavior for the two flames. Now we 

will turn our attention to extinguishment. As discussed earlier, it is first necessary to define a 

characteristic extinguishing nitrogen volume fraction for the diffusion flames. As shown by the results in 

Table 15, experimental values depend on the diffusion flame burner configuration. It seems reasonable to 

use the highest experimental values, which are found for the opposed-flow porous burners. This choice is 

also consistent with the widespread use of this type of burner for LOI measurements. Based on the results 

included in Table 15, characteristic extinguishing volume fractions of 33 % and 39.5 % were chosen for 

methane and propane flames, respectively. 

Calculated maximum flame temperatures for the two characteristic extinguishing concentrations are 

included in Figure 28 and Figure 29. From these, the corresponding extinguishment maximum flame 

temperatures can be obtained as 1545 K for methane and 1433 K for propane. These values can be 

compared with temperatures reported in the literature for diffusion flames near extinguishment. For 

methane flames experimental values of 1483 K (Tsuji burner) and 1595 K (opposed-flow burner) have 

 Extinction Results for Methane and

Propane Flames Diluted with Nitrogen

Flow Velocities (cm/s)

0 50 100 150 200 250 300 350

Maximum Flame Temperature (K)

1400

1500

1600

1700

1800

Propane

Methane
54

Figure 31. Values of maximum flame temperatures calculated using OPPDIF are plotted as a function of 

added nitrogen volume fraction for methane and propane opposed-flow flames. These values 

are compared with the corresponding adiabatic flame temperatures assuming stoichiometric 

combustion. 

been reported by Ishizuka and Tsuji [48] and Puri and Seshadri [114], respectively. The agreement 

between the two studies is probably better than a simple comparison indicates since the thermocouple 

measurements of Ishizuka and Tsuji were not corrected for radiative heat losses, which would be expected 

to decrease the measured temperature below the actual temperature. The thermocouple measurements of 

Puri and Seshadri were corrected for radiative heat losses. The calculated temperature is expected to be a 

slight overestimate due to neglect of radiative heat losses from flame gases. 

Puri and Seshadri reported that the maximum flame temperature for a propane flame at the limit condition 

with added nitrogen was 1656 K. This value is 77 K higher than they measured for methane. These 

results are in disagreement with the current calculations that predict that the propane flame will have the 

lower temperature for extinguishing conditions. We cannot provide an explanation for this difference. 

Babb et al. have reported a maximum flame temperature of 1600 K for a nitrogen-inhibited propane flame 

near extinction. [56] Similar measurements in a heptane flame yielded a value of 1500 K. 

Based on the above discussion, we conclude that the experimental data currently available for 

temperatures in diffusion flames near extinction is too limited to allow a meaningful assessment of the 

effectiveness of the calculations in predicting flame temperatures. More careful experiments are required 

for such a validation. 

As discussed earlier, Sheinson et al. [49] and Zegers et al. [52] have argued that hydrocarbon combustion, 

in general, is not sustainable when the maximum flame temperature drops below roughly 1600 K. This 

estimate is in reasonable agreement with the maximum flame temperatures at extinguishiment estimated 

by the current study, but it should be noted that it does not allow for any fuel-to-fuel variations such as 

those reported here. 

 Extinction Results for Methane and

Propane Flames Diluted with Nitrogen

Nitrogen Volume Fraction (%)

0 10 20 30 40

Maximum Flame Temperature (K)

1200

1400

1600

1800

2000

2200

Propane, Oppdif

Propane, Adiabatic

Methane, Oppdif

Methane, Adiabatic
55

Figure 32. Ratios for the indicated measures of conditions at flame extinction are plotted as a function of 

nitrogen volume fraction added to the air for methane/air flames. 

For the conditions corresponding to the assumed extinguishing volume fraction of nitrogen, the velocities 

of the fuel and air at extinction are calculated to be 21.42 cm/s for the methane flame. Corresponding 

values for the various measures used to characterize the flow condition at extinction are ag = 37.5 s-1, |ao| 

= 27.0 s-1, and χs = 0.80 s-1. It is interesting to see how the various measures vary relative to each other 

with added nitrogen concentration. Figure 32 shows plots of ag/|ao|, ag/χs, and |ao|/χs versus the percentage 

of added nitrogen. It is clear that the three measures have different dependencies on the amount of 

thermal agent added. The reason for this is the variation in the thickness of the boundary layer as the flow 

velocities are changed. The dependence on agent concentration requires that great care be exercised when 

comparing results in terms of different measures of strain rate. 

The extinguishing condition for the calculated propane flame corresponds to uf = uo = 13.4 cm/s, ag = 29.8 

s

-1, |ao| = 15.3 s-1, and χs = 2.2 s-1. The values for propane and methane have similar magnitudes, but are 

not identical. These differences are likely associated with differences in the stoichiometries and 

flammability for the two fuels. 

An important question is: what strain rate is appropriate to use when determining the minimum value of 

an added thermal agent required to extinguish a buoyancy-dominated diffusion flames at normal gravity? 

Only limited discussions of this point are available in the literature. In their early work, Puri and Seshadri 

reported that extinguishment by nitrogen added to air occurred when ag was decreased to approximately 

30 s-1 and 35 s-1 for methane and propane, respectively. [114] Hamins et al. compared cup burner 

measurements (heptane fuel) of extinguishing concentrations for a variety of agents with corresponding 

measurements made in a counter-flow flame. [53] The measurements were made over a range of flow 

velocities characterized in terms of a global strain rate, agl, defined as 

, 2

ol

ol

gl L

u

a = ( 16 )

Nitrogen-Diluted Methane/Air Diffusion Flames

Nitrogen Volume Fraction (%)

0 5 10 15 20 25 30 35

Ratios of Measures for Extinction Conditions

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

ag/|ao|

ag/χs

|ao|/χs
56

which is appropriate for an oxidizer flow impinging on a liquid surface. Lol and uol are the distance 

between the oxidizer exit and the liquid surface and the nominal oxidizer exit velocity, respectively. In 

agreement with the current calculations, the strain rates necessary to induce extinction of the counterflow 

flame decreased with increasing concentration of added agent. When the concentrations of added agents 

for the opposed-flow flame were comparable to those observed in the cup burner test, the values of agl

required for extinction were on the order of 50 s-1. Saso et al. have reported a similar comparison. [136] 

For nitrogen, carbon dioxide, and a number of fluorinated hydrocarbons they found that extinction 

volume fractions for their opposed-flow burner agreed very well with their cup burner results when agl

was equal to 60 s-1. Note that Saso et al.’s definition for the global strain rate did not include the factor of 

2 that appears in Eq. (16). For this reason, their results have been multiplied by this factor to allow 

comparison with the results of Hamins et al. They agree to within 20 %. Due to the different boundary 

conditions and fuels used between the current investigation and those of Hamins et al. and Saso et al., as 

well as slightly different definitions for the global strain rates, direct quantitative comparisons are not 

appropriate. However, it is clear that the strain rates have comparable magnitudes in each case. It is 

important to note that the strain rates appropriate for characterizing the LOI are much lower than typically 

used for experimental and modeling investigations of opposed-flow laminar diffusion flames. 

The calculations indicate that extinguishment of diffusion flames not only occurs at a well-defined 

maximum flame temperature, but also with a well-defined strain rate. It is interesting to speculate as to 

why lower and lower strain rates are not sustained for such flames. The most likely reason is that 

buoyancy induced velocity results in a lower limit for the strain rate perpendicular to the flame surface. 

The results of Hamins et al. and the current findings suggest this minimum strain rate is on the order of a 

few tens of inverse seconds. [53] 

F. Effects of Argon Addition on Extinction and Extinguishment of Methane Diffusion 

Flames Burning in Argon “Air” 

As already pointed out, we have identified no additional literature measurements of LOI for thermal 

agents added to methane/air diffusion flames. However, Ishizuka and Tsuji did make measurements for 

methane burning in an artificial “air”, consisting of 21 % oxygen and 79 % argon. [48] This “air” was 

diluted with argon until a LOI was found. The result corresponded to an added argon concentration of 

54.3 %. The measured maximum flame temperature for the LOI flame was 1443 K, or roughly 40 K less 

than for standard air diluted with nitrogen. In order to test the ability to predict LOI concentrations of 

added thermal agents, a series of calculations for argon “air” diluted with argon were made. 

Figure 33 shows a plot of the maximum calculated flame temperature as a function of the percentage of 

argon added to the argon “air” and the equal fuel and oxidizer velocity magnitudes. Comparison with 

Figure 28 shows that replacing nitrogen with argon has a dramatic effect on the flame behavior. First, 

flame temperatures are considerably higher for given diluent concentration and fuel and oxidizer 

velocities for the argon “air”. This is due to the lower heat capacity of argon as compared to nitrogen. As 

a result of the increase in temperature, much higher flow velocities are required to generate the 

characteristic strain rate necessary to result in extinction of the methane flame. For the same reason, 

higher concentrations of argon must be added to achieve the LOI than in the nitrogen case. 

The flame formed by oxidizer diluted with 50 % argon is calculated to undergo extinction with a 

maximum temperature of 1610 K and methane and oxidizer velocity magnitudes of 37.8 cm/s. The 

results for 54 % argon, corresponding to the experimental LOI, are 1473 K and 15.9 cm/s. These values 

are both slightly smaller than found for the methane/air flame diluted with nitrogen, 1545 K and 21.4 

cm/s, respectively. However, they are remarkably close when one recalls that the use of argon instead of 

nitrogen should result in a significantly different flame structure due to changes in heat capacity and 

thermal diffusivity on going from nitrogen to argon. In fact, if one simply assumes that the LOI occurs 
57

Figure 33. Maximum calculated flame temperatures are plotted against methane and oxidizer flow 

velocity magnitudes for a series of methane/argon “air” opposed-flow diffusion flames diluted 

with argon. Symbols correspond to the volume fraction of added argon. 

for the same maximum flame temperature, i.e., roughly 1550 K, as for the nitrogen-diluted air flame, it is 

possible to estimate the required argon concentration as 52 % from Figure 33. This is only 4 % less than 

the experimental value. Thus, assuming that the LOI corresponds to the added concentration necessary to 

reduce the maximum flame temperature at extinction to 1550 K should provide excellent estimates for the 

amount of an arbitrary thermal agent required to extinguish a methane flame. The approach of using a 

limit flame temperature as the basis for estimating extinguishing concentrations extends the ideas of such 

researchers as Simmons and Wolfhard [41], Maĉek [42], Tucker et al. [45], Sheinson et al. [49] and 

Zegers et al. [52] The major difference from these earlier studies is that the effects of detailed chemical 

kinetics and transport properties are accounted for in estimating the extinguishing concentrations of 

thermal agents. In the following section this approach is used to predict extinguishing concentrations for 

CO2, Ar, He, and water vapor. 

G. Extinguishment of Methane and Propane Diffusion Flames by Carbon Dioxide, 

Argon, Helium and Water Vapor 

Opposed-flow diffusion flame calculations have been used to estimate the required extinguishing 

concentrations, i.e., the added concentration corresponding to the LOI for nitrogen, for a number of gases 

that are expected to act primarily as thermal agents. Figure 34 to Figure 37 show plots of the maximum 

calculated flame temperature as a function of the fuel and oxidizer velocity magnitudes, where air has 

been diluted by the indicated percentages of argon, helium, carbon dioxide, and water vapor, respectively. 

It should be noted that both water and carbon dioxide are products of methane combustion and could 

conceivably modify the combustion chemistry slightly. However, both are believed to act primarily as 

thermal agents. Calculations using surrogate agents whose physical properties are identical to those for 

CO2 and H2O, but which did not participate in the flame chemistry, gave similar results, indicating that 

the chemical effects are indeed small. 

Argon Dilution of CH4/Ar "Air" Diffusion Flame

Flow Velocities (cm/s)

0 200 400 600 800 1000 1200

Maximum Flame Temperature (K)

1500

1600

1700

1800

1900

2000

2100

2200

2300

0 %

10 %

20 %

30 %

40 %

50 %

54 %
58

Figure 34. Maximum calculated flame temperatures are plotted against methane and oxidizer flow 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

argon. Symbols correspond to the volume fraction of added argon. 

Figure 35. Maximum calculated flame temperatures are plotted against methane and oxidizer flow 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

helium. Symbols correspond to the volume fraction of added helium. 

Argon Dilution of CH4/Air Diffusion Flames

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Flame Temperature (K)

1500

1600

1700

1800

1900

2000

0 %

5 %

10 %

15 %

20 %

25 %

30 %

35 %

40 %

45 %

Helium Dilution of CH4/Air Diffusion Flames

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Flame Temperature (K)

1500

1600

1700

1800

1900

2000

0 %

5 %

10 %

15 %

20 %

25 %

30 %

33 %

35 %
59

Figure 36. Maximum calculated flame temperatures are plotted against methane and oxidizer flow 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

carbon dioxide. Symbols correspond to the volume fraction of added carbon dioxide. 

Figure 37. Maximum calculated flame temperatures are plotted against methane and oxidizer flow 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

water vapor. Symbols correspond to the volume fraction of added water vapor. 

Carbon Dioxide Dilution of CH4/Air Diffusion Flames

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Flame Temperature (K)

1500

1600

1700

1800

1900

2000

0 %

4 %

8 %

12 %

16 %

20 %

22 %

Water Dilution of CH4/Air Diffusion Flames

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Flame Temperature (K)

1500

1600

1700

1800

1900

2000

0 %

1 %

4 %

8 %

12 %

16 %

20 %

24 %

26 %
60

Table 16. Extinguishing Volume Fractions of Thermal Agents Calculated For Opposed-Flow 

Methane Flames and Measured For Heptane Flames in Cup Burner Experiments 

Thermal 

Agent 

Current 

Work 

Cup 

Burner 

[47] 

Cup 

Burner 

[49] 

Cup 

Burner 

[56] 

Cup 

Burner 

[33] 

Cup 

Burner 

[54] 

Cup 

Burner 

[55] 

Nitrogen 0.33 0.302 0.30 0.33 0.32 0.30 0.336 

Argon 0.43 - 0.41 - 0.41 0.38 0.433 

Helium 0.33 - 0.32 - 0.31 - - 

Carbon 

Dioxide 0.22 0.205 0.21 0.20 0.23 0.20 0.220 

Water 0.28 - - - - - - 

For water, the vapor pressure at the lower temperatures is less than required to generate the concentrations 

assumed in the calculations. As an example, at 300 K the water vapor pressure is 3.57 kPa, which 

corresponds to a volume fraction of 0.035 in atmospheric air. Therefore, for temperatures near 300 K, the 

higher water vapor concentrations are assumed to be supersaturated. 

By assuming the limit temperature for methane flames is 1550 K, it is possible to estimate the 

extinguishing concentrations for each of these thermal agents. These estimates are tabulated in Table 16. 

As already discussed, the only experimental values for opposed-flow methane diffusion flames we have 

identified in the literature are for nitrogen dilution. Cup burner determinations of extinguishing 

concentrations using heptane as fuel have been reported for some of these thermal agents by Hirtst and 

Booth [47], Sheinson et al. [49], Babb et [56], Hamins et al. [33], Moore et al. [54], and Saito et al. [55]. 

These values are included in Table 9 for comparison purposes and are shown graphically in Figure 38. 

Some variation, roughly ± 10 %, is evident in the experimental results. In general, the agreement between 

the experimental cup burner values for heptane and the calculated values for the methane opposed-flow 

diffusion flame is good. The maximum difference between values calculated for methane and the 

experimental values for heptane is 12 %, with the vast majority being less than 10 %. The degree of 

agreement between the current results and the measurements of Saito et al. is particularly good. [55] With 

the exception of carbon dioxide, the cup burner results are somewhat lower than predicted for the 

opposed-flow flame. The differences between the cup burner and opposed-flow flame results could be 

due to the use of different fuels or to differences in burner configuration. The heptane fires are burning 

just above a liquid fuel in a coflow of oxidizer, and it may be easier to blow out this type of flame than the 

opposed-flow diffusion flame that is stabilized away from surfaces. It has also been shown that 

extinguishing concentrations for coflow flames depend on the burner diameter. The close tracking of the 

calculated results and the experimental findings suggests that detailed chemical-kinetic modeling can 

accurately predict the amount of a thermal agent required to extinguish opposed-flow diffusion and cup 

burner flames. 

The differences in the extinguishing concentrations of helium and argon are interesting since these agents 

are both monatomic gases and have the same heat capacities. The difference is clear in both the 

calculations and the experimental values. The fact that helium is a more efficient extinguishing agent 

means that at least one other parameter, in addition to heat capacity, is important in determining 

extinguishing efficiency. A related observation was reported by Coward and Hartwell for the inerting of 

premixed flames and was attributed to the much higher thermal conductivity of helium, which distributes 

the heat of combustion over a larger region of space and therefore weakens the flame. [137] The same 

explanation is most likely valid for diffusion flames. Sheinson et al. reached the same conclusion. [49]
61

 Figure 38. Detailed chemical-kinetic modeling predictions for extinguishing volume fractions of 

nitrogen, carbon dioxide, argon, and helium for methane flames are compared with various 

experimental cup burner measurements using n-heptane. Model values for helium and 

nitrogen overlap and open symbols are used to identify the helium results. References for the 

cup burner measurements are Hamins et al. [33], Hirst and Booth [47], Sheinson et al. [49], 

Moore et al. [54], Saito et al. [55], and Babb et al. [56] 

. 

In Figure 39 values of the calculated maximum flame temperature at extinction are plotted as a function 

of agent volume fraction for the five thermal agents. For each case extinguishment is assumed to occur 

when the calculated maximum flame temperature drops to 1550 K. Corresponding values for the 

adiabatic flame temperature are also included in the figure. It can be seen that the adiabatic flame 

temperatures for N2, CO2, Ar, and H2O in air at the extinguishing concentration fall relatively close 

together (roughly 1800 K), with that for CO2 being somewhat higher. For helium the calculated adiabatic 

flame temperature at the extinguishing condition is more than 100 K higher (note that the adiabatic flame 

temperatures for given added volume fractions of helium and argon are the same since these two gases 

have identical heat capacities). The calculated maximum flame temperatures for helium and nitrogen for 

a given volume fraction fall very close together, even though nitrogen has a higher heat capacity. These 

points emphasize the enhanced effectiveness of helium as compared to the other thermal agents. 

Inspection of the various curves for the dependence of calculated maximum flame temperature on the fuel 

and oxidizer velocity magnitudes in Figure 28 and Figure 34 - Figure 37 shows that for given velocities 

and extinction temperatures, they have very similar shapes. This is true despite the fact that the amount of 

added agent and, therefore, the oxygen concentration and stoichiometric ratio vary dramatically with 

agent. This is confirmed by the results plotted in Figure 40, which show the maximum flame temperature 

at extinction as a function of the exit velocity magnitudes for the five thermal agents added to air as well 

as the results for argon added to argon “air”. The data fall within a narrow band on either side of a welldefined curve. 

Closer inspection of Figure 40 shows that the data for argon “air” tend to fall at higher temperatures by 

amounts that decrease with dilution, while the water vapor data tend to lie near the top of the band by 

Methane Predictions/Cup Burner with Heptane

OPPDIF-Calculated Extinguishing Volume Fraction

0.20 0.25 0.30 0.35 0.40 0.45

Cup Burner Extinguishing Volume Fraction

0.20

0.25

0.30

0.35

0.40

0.45

OPPDIF-Prediction

Hamins et al.

Hirst and Booth

Sheinson et al.

Moore et al.

Saito et al.

Babb et al.

CO2

N2/He

Ar
62

Figure 39. Values of maximum flame temperatures (solid symbols) calculated using OPPDIF and the 

corresponding adiabatic flame temperatures (open symbols) calculated using EQUIL for 

methane flames are plotted as a function of added agent volume fraction in air for five thermal 

agents. Note that the adiabatic flame temperatures for argon and helium overlap and that the 

maximum calculated flame temperatures for helium and nitrogen fall very close together. 

Figure 40. Values of maximum flame temperature at extinction are plotted as a function of the 

corresponding fuel and oxidizer velocity magnitudes for a range of volume fractions of the 

various thermal agents. 

Methane/Air Diffusion Flame

Agent Volume Fraction (%)

0 10 20 30 40

Temperature (K)

1500

1600

1700

1800

1900

2000

2100

2200

Maximum

Flame

Temperature

Adiabatic

Flame

Temperature

N2

CO2

Ar

He

H2

O

Inert-Diluted Methane Flames

Extinction Flow Velocity (cm/s)

0 50 100 150 200 250 300

Maximum Temperature (K) at Extinction

1500

1550

1600

1650

1700

1750

1800

No Added Agent

Nitrogen

Argon

Argon "Air"

Helium

Carbon Dioxide

Water
63

Figure 41. Values of maximum flame temperature at extinction are plotted as a function of the 

corresponding global strain rates, ag, for a range of volume fractions of the various thermal 

agents. 

amounts that increase with dilution. The difference between adding argon to air and argon “air” is most 

likely due to the different physical properties of argon and nitrogen. Apparently, these differences are 

most important for high strain rates and are relatively minor at the lower strain rates typical of buoyancydominated diffusion flames. Recall that the estimated value of the extinguishing concentration for argon 

added to argon “air” was in good agreement with the experimental value of Ishizuka and Tsuji. [48] The 

increasing differences with decreasing strain rate for water may be due to two possible effects. The first 

is the higher thermal diffusivity expected for the relatively small water molecule. However, the results 

for helium, which has a much higher thermal diffusivity, fall close to the results for nitrogen, argon, and 

carbon dioxide. The second possibility is that the water vapor slightly modifies the chemical structure of 

the flame and seems the more likely of the two. Increases in water concentration can interact with the 

flame chemistry through a number of reactions including the well-known water-gas shift reaction, 

H O CO CO H . 2 + ⇔ 2 + 2 ( 17 )

The addition of water to the oxidizer is expected to drive this equilibrium towards the right, resulting in 

additional heat release and a slightly higher temperature, as observed. The findings of Lentati and 

Chelliah indicate that water does display a small chemical effect. [74] Dilution with carbon dioxide 

would be expected to drive the equilibrium in Reaction 17 in the opposite direction, however, this effect 

on extinguishment must be smaller since the carbon dioxide results lie very close to those for nitrogen, 

argon, and helium. 

Simply plotting the results in terms of the exit velocity magnitudes of methane and oxidizer at extinction 

leads to a collapse of the results for different thermal agents to a well-defined curve. It is of interest to see 

if the collapse is improved by plotting the data in terms of the global strain rate given by Eq. (14), ag, or 

the maximum absolute value of the characteristic strain rate element on the oxidizer side lying outside of 

the boundary layer, |ao|. Figure 41 and Figure 42 show the data plotted in terms of these two 

Inert-Diluted Methane Flames

Global Strain Rate, ag (s-1)

0 100 200 300 400 500 600

Maximum Temperature (K) at Extinction

1500

1550

1600

1650

1700

1750

1800

No Added Agent

Nitrogen

Argon

Ar "air"

Helium

Carbon Dioxide

Water
64

Figure 42. Values of maximum flame temperature at extinction are plotted against the corresponding 

characteristic local strain rates, |ao|, defined as the highest absolute value of strain rate 

observed outside of the boundary layer on the oxidizer side of the flame, for a range of volume 

fractions of the various thermal agents. 

characteristic strain rates. The overall appearances of the two plots are very similar to Figure 40, which is 

simply in terms of the exit velocities. For this reason, further discussion is based only on the flow 

velocity magnitudes for methane and oxidizer. 

A more quantitative idea of the degree of correlation between the maximum calculated flame 

temperatures at extinction and the fuel and oxidizer flow velocity magnitudes is obtained from Figure 43 

where the results for N2, Ar, He, and CO2 addition have been consolidated and fit to two piecewise fourthorder polynomials on either side of 105 cm/s. The resulting fits are drawn as a solid line. The 

coefficients of determination for the nonlinear curve fits were 0.97 and 0.98, which indicate a high degree 

of confidence in the fits. The polynomials can be used to predict values of maximum temperature for 

given exit velocities. 

To determine if there is a relationship between added agent volume fraction and the calculated maximum 

temperature at extinction, the temperatures were plotted versus the ratio of the volume fraction of added 

agent and that required for extinguishment as shown in Figure 44. The results for argon added to argon 

“air” lie well away from the remaining data. The trend of less effectiveness of water vapor at low 

velocities is also evident. While the data partially collapse for the remaining agents, the spread indicates 

that simply calculating a single extinction condition for a single agent volume fraction will not suffice for 

predicting the extinguishing volume fraction for that agent. 

Due to the long run times required for calculating opposed-flow propane diffusion flames, extinction 

curves for a wide range of thermal agent concentrations were not performed. Instead, more limited 

calculations designed to determine the extinguishing concentration, defined as the volume fraction having 

a maximum flame temperature of 1433 K at extinction, were performed. Figure 45 to Figure 47 show the 

results with CO2, Ar, and He added to the air. The corresponding extinguishing volume fractions are 

Inert-Diluted Methane Flames

Local Strain Rate, |ao| (s-1)

0 100 200 300 400 500

Maximum Temperature (K) at Extinction

1500

1550

1600

1650

1700

1750

1800

No Added Agent

Nitrogen

Argon

Argon "air"

Helium

Carbon Dioxide

Water
65

Figure 43. Maximum flame temperatures at extinction for N2, Ar, He, and CO2 as a function of the 

corresponding fuel and oxidizer velocity magnitudes are fit by two piecewise fourth-order 

polynomials (solid line). 

Figure 44. The maximum temperature at extinction for opposed-flow methane flames is plotted as a 

function of the volume fraction of a thermal agent added to air divided by the volume fraction 

calculated to be required for flame extinguishment. 

Results of Regression Fit

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Temperature (K) at Extinction

1500

1550

1600

1650

1700

1750

1800

Inert-Diluted Methane Flames

Fraction of Extinguishing Concentration

0.0 0.2 0.4 0.6 0.8 1.0 1.2

Maximum Temperature (K) at Extinction

1500

1550

1600

1650

1700

1750

1800

No Added Agent

Nitrogen

Argon

Argon "Air"

Helium

Carbon Dioxide

Water
66

Figure 45. Calculated maximum flame temperatures are plotted as a function of velocity for a propane 

flame burning in air diluted with the indicated volume fractions of carbon dioxide. The 

extinguishing volume fraction is defined to be that (28.4 %) which yields an extinction 

temperature of 1433 K. 

Figure 46. Calculated maximum flame temperatures are plotted as a function of velocity for a propane 

flame burning in air diluted with the indicated volume fractions of argon. The extinguishing 

volume fraction is defined to be that (50.2 %) which yields an extinction temperature of 

1433 K. 

Propane, Air Diluted with CO2

Velocity (cm/s)

12.5 13.0 13.5 14.0 14.5

Maximum Temperature (K)

1420

1430

1440

1450

1460

1470

1480

29.25 % CO2

29.2 % CO2

29 % CO2

28.8 % CO2

28.4 % CO2

Propane, Air Diluted with Argon

Velocity (cm/s)

12.50 12.75 13.00 13.25 13.50

Maximum Temperature (K)

1430

1440

1450

1460

1470

1480

48.8 % Ar

50.05 % Ar

50.2 % Ar

50.3 % Ar
67

Figure 47. Calculated maximum flame temperatures are plotted as a function of velocity for a propane 

flame burning in air diluted with the indicated volume fractions of helium. The extinguishing 

volume fraction is defined to be that (39 %) which yields an extinction temperature of 1433 K. 

Table 17. Calculated Extinguishing Volume Fractions for Methane and Propane Opposed-Flow 

Diffusion Flames for the Indicated Thermal Agents 

Thermal Agent Methane Flame Propane Flame 

Nitrogen 33 % 39.5 % 

Carbon Dioxide 22 % 28.4 % 

Argon 43 % 50.2 % 

Helium 33 % 39.0 % 

28.4 %, 50.2 %, and 39 %, respectively. These values are summarized in Table 17 along with the 

corresponding results for the methane diffusion flame. The relative effectiveness of the agents is the 

same for both fuels even though a considerably higher volume fraction of a given agent is required to 

extinguish the propane flame than the methane flame. It is particularly noteworthy that the required 

concentrations of nitrogen and helium are nearly identical for both flames. This suggests that while fuel 

effects influence the volume fraction of an agent required for extinguishment, such effects do not have a 

large influence on the relative effectiveness of different thermal agents. 

Premixed adiabatic flame temperatures have been calculated for stoichiometric mixtures of propane and 

air diluted with extinguishing volume fractions of the thermal agents. The results are summarized in 

Table 18 along with the corresponding results for methane flames. The results for air diluted with N2, 

CO2, and Ar are remarkably close. As found for methane, the calculated adiabatic flame temperature for 

air diluted with helium is much higher than for the other thermal agents. The differences between 

methane and propane flame indicated by the results in Table 18 follow the same trend as identified in 

Figure 31, calculated adiabatic flame temperatures for extinguishing volume fractions of a given agent are 

lower for propane flames than for methane flames. This is true even though, for a given amount of air 

Propane, Air Diluted with Helium

Velocity (cm/s)

12.5 13.0 13.5 14.0 14.5 15.0

Maximum Temperature (K)

1430

1440

1450

1460

1470

1480

1490

39 % He

38.5 % He

38 % He
68

Table 18. Adiabatic Flame Temperatures Calculated for Methane and Propane Premixed Flames 

Burning in Air Diluted with Extinguishing Volume Fractions of Thermal Agents

Thermal Agent Methane Flame Propane Flame 

Nitrogen 1796 K 1719 K 

Carbon Dioxide 1815 K 1722 K 

Argon 1805 K 1724 K 

Helium 1928 K 1903 K 

Figure 48. Experimental values of extinguishing volume fractions for N2, CO2, Ar, and He for 

counterflow porous (circles), opposed-jet (squares) and coflow (triangles) burners are plotted 

against the corresponding OPPDIF predictions (dotted line) for methane-air diffusion flames. 

Experimental values are taken from the present work as well from the following references: 

Ishizuka and Tsuji [48], Simmons and Wolfard [41], Puri and Seshadri [114], Hamins [121], 

and Ural [57]. Current results for helium are indicated by open symbols. 

dilution, propane flames have higher adiabatic flame temperatures. These results support the conclusion 

that propane flames are more difficult to extinguish. 

It is of interest to compare the predictions of the calculated extinguishing concentrations with 

experimental data for extinguishment of diffusion flames. Figure 48 and Figure 49 show plots of 

experimental values of extinguishing volume fractions for N2, CO2, Ar, and He versus the values 

calculated using OPPDIF. The dotted lines on the graphs correspond to the predicted results, which are 

also included on the plot. 

The strong dependence of the experimental results on burner type discussed earlier is evident in both 

plots. In particular, the values for the Santoro burner measured during the current investigation are 

considerably lower for both fuels. These results do fall on a straight line indicating that the calculations 

have adequately captured the qualitative dependence on extinguishment for this flame type. Close 

inspection shows that the slopes of lines that would fit the Santoro-burner results are slightly less than that 

obtained from the OPPDIF predictions. It is particularly noteworthy that both calculations and 

Methane Predicted and Experimental Results

OPPDIF-Calculated Extinguishing Volume Fraction

0.20 0.25 0.30 0.35 0.40 0.45

Experimental Extinguishing Volume Fraction

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45 Tsuji, This work

Tsuji, Ishizuka

Hemishperical, Simmons

Opposed Jet, Puri

Opposed Jet, Hamins

Cup Burner, Ural

Santoro, This work

OPPDIF Prediction

Col 3 vs Col 13 

Col 3 vs Col 14 

CO2

N2/He

Ar
69

Figure 49. Experimental values of extinguishing concentrations for N2, CO2, Ar, and He for counterflow 

porous (circles), opposed-jet (squares) and coflow (triangles) burners are plotted against the 

corresponding OPPDIF predictions (dotted line) for propane-air diffusion flames. 

Experimental values are taken from the present work as well from the following references: 

Simmons and Wolfhard [41], Puri and Seshadri [114], Hamins [121], Ural [57], Babb et al. 

[56], Moore et al. [54], and Hamins et al. [33]. 

experiments indicate that nitrogen and helium have very similar extinguishing concentrations. The same 

was shown to be true for cup burner measurements with heptane fuel (see Figure 38 and Table 16). 

Inspection of Figure 48 and Figure 49 shows that experimental extinguishing volume fractions for argon 

and carbon dioxide measured using the DLAFSS are in reasonable agreement with the model predictions. 

Recall that the extinguishing concentrations for nitrogen are tied to experimental values for porous 

burners in opposed-flow configurations, so this is agreement is to be expected. Unfortunately, the 

experimental results for helium lie well below the predicted extinguishing volume fractions for both fuels. 

As discussed earlier, it is likely that the strain rates present during the helium measurements were higher 

than required for buoyancy-dominated burning due to limitations of the flow system. These higher strain 

rates are expected to reduce the amount of thermal agent required for extinguishment as observed. 

Experimental values from the literature are limited. Only two cases are available where measurements for 

the same burner have been reported for more than one agent. For methane, Hamins has reported 

extinguishing concentrations for nitrogen and carbon dioxide in an opposed-jet burner. [121] The two 

results fall on a line that lies below, but parallels the calculated values. Similar comments apply to the 

cup burner measurements of Babb et al. for a propane flame. [56] 

Even though the available experimental data for comparison are limited, extinguishing concentrations for 

diffusion flames vary with burner type, and there are some inconsistent data, the results summarized here 

suggest detailed chemical-kinetic modeling combined with the concept of a limit temperature does a good 

job of capturing the relative effectiveness of thermal agents for extinguishing diffusion flames as well as 

the effects of using different fuels. 

Propane Predicted and Experimental Results

OPPDIF-Calculated Extinguishing Volume Fraction

0.25 0.30 0.35 0.40 0.45 0.50 0.55

Experimental Extinguishing Volume Fraction

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0.55

Tsuji, This work

Hemispherical, Simmons

Opposed Jet, Puri

Opposed Jet, Hamins

Cup Burner, Ural

Cup Burner, Babb

Cup Burner, Moore

Cup Burner, Hamins

Santoro, This work

OPPDIF Predictions

CO2

N2

He

Ar
70

Figure 50. Maximum calculated flame temperatures are plotted against methane and oxidizer exit 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with a 

surrogate agent similar to argon, but with Cp = 0. Symbols correspond to the volume fraction 

of surrogate agent added to the air. 

H. Effects of Dilution and Heat Extraction Location Relative to the Flame Front on 

Extinction and Extinguishment of Diffusion Flames 

An important advantage of modeling investigations is the ability to perform calculations for conditions 

that are not physically possible in order to learn details concerning the role of various system parameters. 

In this section this approach is applied to methane opposed-flow diffusion flames. One question that has 

been the subject of speculation is the relative importance of heat extraction and dilution on the 

effectiveness of a thermal agent. Here dilution effects refer to any role of a thermal agent that is not 

simply due its ability to physically lower the flame-zone temperature. In order to obtain insights into this 

behavior, an artificial agent was created starting with argon and setting its heat capacity to zero. Direct 

comparison with the results for added argon allows the relative roles of heat removal and dilution to be 

characterized. Sheinson et al. have discussed the effects of dilution on extinguishment. [49] They 

concluded that they are relatively small compared to direct heat removal due to heat capacity for the 

thermal agents CF4 and SF6. Zegers et al. have suggested that dilution effects play a role for relatively 

inefficient thermal agents such as nitrogen. [52] 

Figure 50 is a plot of calculated maximum flame temperature versus fuel and oxidizer velocity 

magnitudes for the zero-heat-capacity argon added to air. It is obvious that this species does decrease the 

strength of the flame, but that its effect is much smaller than for the argon results shown in Figure 34. 

Based on an extinguishment temperature of 1550 K, the extinguishing concentration is estimated as 73 %, 

or roughly 1.7 times greater than required for argon. This corresponds to an oxygen concentration of 5.7 

% at the LOI. Interestingly, the dependence of the maximum flame temperature at extinction on the fuel 

and oxidizer velocities is very similar for both sets of calculations as can be seen in Figure 51, where they 

are compared. The solid line is that shown in Figure 43, which was derived by fitting to the methane 

results for N2, Ar, He, and CO2. The data for the zero-heat-capacity argon fall slightly below those for 

Dilution by Argon Having No Heat Capacity

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Flame Temperature (K)

1500

1600

1700

1800

1900

2000

0 %

20 %

40 %

60 %

70 %

80 %
71

Figure 51. Values of maximum flame temperature at extinction are plotted as a function of fuel and 

oxidizer extinction velocity magnitudes for a range of concentrations of argon and a similar 

surrogate agent having Cp = 0. The solid line is the result of the regression fits shown in 

Figure 43. 

argon, but it is clear that simple dilution of air has a similar effect on the flame as heat absorption by an 

inert. Assuming that the effects of heating an inert and dilution are additive, as suggested by this close 

correspondence, the effectiveness of Ar as a thermal agent is estimated to be 41 % due to dilution and 59 

% due to heat extraction. 

The availability of detailed flame structure information from the calculations allows the effect of a zeroheat-capacity diluent to be understood. As a starting point, it is important to recognize that flames 

burning in air and air diluted with a zero-heat-capacity agent have identical adiabatic flame temperatures. 

This suggests that the observed decreases in maximum temperature must be due to redistribution of the 

heat generated by combustion over a larger region of space and/or a reduction in the amount of heat 

released. In order to investigate this point, results for a methane counterflow diffusion flame burning in 

air are compared with those for a flame burning in air diluted with 60 % of the zero-heat capacity diluent 

in Figure 52. It is evident that while the maximum flame temperature is significantly reduced by the 

addition of the agent, the spatial temperature distributions are very similar for the two flames. This 

suggests that the primary effect of dilution is to reduce the amount of heat released. 

Figure 53 shows CH4 and O2 volume fractions as a function of distance from the burner on a semi-log plot 

for both flames. It can be seen that while the primary fuel is completely reacted at the flame surface, 

some O2 “leaks” from the oxidizer side to the fuel side. O2 reaching the fuel side of the reaction layer 

eventually diffuses to a location where the temperature is low enough that reaction can no longer occur. 

At this point the O2 acts like a diluent having a heat capacity with the result that the maximum 

temperature in the flame zone is reduced. Close inspection of Figure 53 shows that a significantly larger 

fraction of the available O2 leaks through to the fuel side of the flame when the oxidizer is diluted air as 

opposed to air. This difference explains the lower maximum flame temperatures calculated for burning in 

air diluted by an agent having no heat capacity. 

Diluted Methane/Air Flames

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Temperature (K) at Extinction

1500

1550

1600

1650

1700

1750

1800

No Added Agent

Ar

Ar, Cp = 0

Curve from Fig. 43
72

Figure 52. Temperature is plotted as a function of distance from the fuel exit for methane flames burning 

in air and air mixed with 60 % of a diluent having similar properties to Ar, but with zero heat 

capacity. Fuel and air exit velocity magnitudes are 25 cm/s for both flames. 

Figure 53. Calculated methane and oxygen volume fractions are shown on a semi-log plot as a function 

of distance from the fuel exit for methane flames burning in air (open symbols) and air mixed 

with 60 % of a diluent having similar properties to Ar, but with zero heat capacity. Fuel and 

air exit velocity magnitudes are 25 cm/s for both flames. 

Methane/Oxidizer Diffusion Flame

Distance From Fuel Exit (cm)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Volume Fraction

0.0001

0.001

0.01

0.1

1

CH4, air

O2, air

CH4, diluted air

O2, diluted air

Methane/Oxidizer Diffusion Flames

Distance From Fuel Exit (cm)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Temperature (K)

400

600

800

1000

1200

1400

1600

1800

2000

60 % Ar, Cp = 0

air
73

The leakage of O2 through the flame front is due to the finite rates of reaction for oxidation reactions. 

Liñán and Williams provide a good introductory discussion of this behavior and the reasons for it. [138] 

Oxygen leakage was observed experimentally several decades ago [139] and was predicted by early 

calculations of counter-flow diffusion flames [88]. Du and Axelbaum discuss the effect of O2 leakage 

with respect to a series of methane flames where they systematically varied the stoichiometric mixture 

fraction while maintaining a constant adiabatic flame temperature. [117] These authors found that the 

flame strength increased with increasing stoichiometric mixture fraction and argued that this was due to 

the shift of the O2 profile into regions of higher temperature. Decreased O2 flame leakage was also 

evident in the calculations with higher stoichiometric mixture fraction. Lentati and Chelliah have also 

noted the importance of oxygen leakage for understanding flame extinction. [74] The increased O2

leakage and decreased maximum flame temperature observed with decreasing stoichiometric mixture 

fraction found for the current calculations are consistent with these trends.

One of the goals of the current work was to test the hypothesis that the effectiveness of a thermal agent 

depends on the location, relative to the high temperature flame zone, where heat extraction occurs. A 

surrogate thermal agent, X, was used for these calculations. The molecular weight, thermodynamic 

properties, and transport properties of X are identical to those of argon, but it is capable of undergoing a 

simple reaction in the presence of ambient bath gases to generate a new species, Y, i.e., 

X + M → Y + M. ( 18 )

Y is also very similar to argon, the only difference being that its heat of formation is assigned an 

arbitrary positive value instead of being zero. As a result, when Reaction (18) takes place it 

extracts heat and cools the local surroundings by an amount equal to the heat of reaction, 

ΔHX→Y. Since X and Y do not react with any other species, the reaction is effectively simply a 

heat sink, and X therefore meets the definition of a thermal agent. 

The rate constant for Reaction (18) is expressed as 

, /

X Y

Ea RT k AT eβ −

→ = ( 19 )

where A is the pre-exponential factor, β is the temperature exponent, Ea is the energy of activation, R is 

the gas constant, and T is temperature. By varying the parameters A, β, and Ea it is possible to change the 

temperature range over which the reaction occurs and hence the location relative to the flame zone for 

heat extraction. For the calculations which follow, initial values were chosen for A and β, and only the 

value of Ea was changed in order to vary kX→Y. One problem faced in such calculations is that due to the 

variations in the residence time, which depends on the velocities of the fuel and oxidizer, the 

completeness of reaction over a given temperature range can vary with initial conditions. For this reason, 

a set of calculations was performed for one value of fuel and oxidizer exit velocity magnitudes in which 

Ea was varied. A relatively low value of 25 cm/s was chosen because this condition is close to that for 

which flame extinguishment occurs. An initial calculation was run for which the parameters in Eq. (19) 

were set to A = 1×1010 cm3

/(mol≅s), β = 0, and Ea = 25.1 kJ/mol, and the heat of formation for Y was 

chosen to be 96.1 kJ/mol. The concentration of X added to the air was 5 %. Figure 54 compares the 

resulting temperature profile across the flame with that calculated for the case when 5 % argon is added. 

The heat extracted by agent X has lowered the temperature on the oxidizer side below ambient. The 

maximum flame temperature with X is reduced, and its position has been shifted towards the oxidizer side 

relative to the case with argon. 

It is clear from Figure 54 that the majority of the heat extraction is occurring at low temperatures for Ea = 

25.1 kJ/mol. This is evident in Figure 55 which shows X and Y volume fractions plotted as a function of 
74

Figure 54. Calculated flame temperature is plotted as a function of distance from the fuel exit for 

methane/air diffusion flames where the oxidizer is diluted with 5 % of either argon or the 

hypothetical agent X which reacts to form Y with Ea = 25.1 kJ/mol and ΔHX→Y = 96.1 kJ/mol. 

Methane and oxidizer exit velocity magnitudes are 25 cm/s. 

Figure 55. The volume fractions of X and Y are plotted as a function of distance from the fuel exit for a 

methane flame burning in air with 5 % added X. X reacts to form Y with Ea = 25.1 kJ/mol 

and ΔHX→Y = 96.1 kJ/mol. The spatial variation of temperature is also shown as the solid 

line. Methane and oxidizer exit velocity magnitudes are 25 cm/s. 

Ea = 25.1 kJ/mol

Distance From Fuel Exit (cm)

0.0 0.5 1.0 1.5 2.0

Volume Fraction

0.00

0.01

0.02

0.03

0.04

0.05

Temperature (K)

400

600

800

1000

1200

1400

1600

1800

2000

X

Y

Temperature

Inert-Diluted Methane/Air Flames

Distance From Fuel Exit (cm)

0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00

Temperature (K)

200

400

600

800

1000

1200

1400

1600

1800

2000

5 % X

5 % Ar
75

Figure 56. The volume fractions of X and Y are plotted as a function of distance from the fuel exit for a 

methane flame burning in air with 5 % added X. X reacts to form Y with Ea = 58.6 kJ/mol 

and ΔHX→Y = 96.1 kJ/mol. The spatial variation of temperature is also shown as the solid line. 

Methane and oxidizer exit velocity magnitudes are 25 cm/s. 

distance from the fuel exit. The corresponding temperature profile is included as the solid line. The 

conversion of X to Y is well advanced before the boundary layer is reached at roughly 1.3 cm from the 

fuel exit, and then rapidly accelerates. The concentration of X has become nearly zero by the time the 

location on the oxidizer side is reached where the temperature has increased to 1200 K. The maximum 

calculated temperature for this flame is 1928 K, which can be compared with a value of 2006 K when 5 % 

argon is used as the thermal agent. 

In order to change the location where heat extraction takes place, the calculation was repeated for a series 

of increasing Ea. Figure 56 is similar to Figure 55, but is for the case with Ea increased to 58.6 kJ/mol. 

The reaction behavior of X is very different than observed for the lower Ea. The concentration of X does 

not decrease appreciably until the temperature begins to increase at the boundary layer. As the 

temperature begins to rise on the oxidizer side, conversion of X to Y begins and accelerates with 

increasing temperature. A substantial fraction of the conversion takes place for temperatures greater than 

1600 K, but, even so, the amount of unreacted X reaching the rich side of the flame is minimal. A 

maximum temperature of 1934 K is calculated. This is very close to the value found for Ea = 25.1 kJ/mol. 

Figure 57 shows the results when the Ea is increased to 83.7 kJ/mol. For this large energy of activation, 

the conversion of X to Y has become so slow that a substantial fraction of X passes through the high 

temperature zone without conversion to Y. As the temperature falls on the rich side of the flame, the 

reaction slows down, and the remaining X becomes kinetically “frozen” and simply diffuses toward the 

fuel side. As a result, the amount of heat absorption is less than that occurring when X fully reacts. This 

is reflected in the maximum calculated flame temperature of 1963 K, which is intermediate between that 

found for X with lower Ea’s and that for a 5 % argon volume fraction added to air, which only has 

dilution and heat removal effects. 

Ea = 58.6 kJ/mol

Distance From Fuel Exit (cm)

0.0 0.5 1.0 1.5 2.0

Volume Fraction

0.00

0.01

0.02

0.03

0.04

0.05

Temperature (K)

400

600

800

1000

1200

1400

1600

1800

2000

X

Y

Temperature
76

Figure 57. The volume fractions of X and Y are plotted as a function of distance from the fuel exit for a 

methane flame burning in air with 5 % added X. X reacts to form Y with Ea = 83.7 kJ/mol 

and ΔHX→Y = 96.1 kJ/mol. The spatial variation of temperature is also shown as the solid line. 

Methane and oxidizer exit velocity magnitudes are 25 cm/s. 

Figure 58 shows the maximum calculated flame temperature as a function of assumed Ea for a series of 

calculations carried out for 5 % X added to the air. For Ea ≤ 50 kJ/mol the calculated temperature is 

constant within the variations expected for the different grids used for the calculations. As the Ea is 

increased further, the maximum temperature begins to increase. As we have seen, this is due to some 

fraction of X passing through the flame to the rich side without reacting to form Y. Since the temperature 

range over which the heat is absorbed by the reaction of X to Y varies widely as the Ea increases from 25 

kJ/mol to 50 kJ/mol, these findings show that the maximum flame temperature and, by extension, flame 

extinction only depend on the amount of heat extracted and not where it occurs relative to the flame zone. 

It is concluded that the original hypothesis concerning the role of heat absorption location by gaseous 

thermal agents on extinguishment is not valid. This conclusion should be contrasted with the recent 

results of Lentati and Chelliah, who report that the location where heat extraction occurs can be important 

for flame inhibition when evaporating water droplets are added to the oxidizer flow. [73,74] Their 

findings seem to be associated with the fact that larger water droplets do not follow the oxidizer flow 

streamlines, whereas gaseous agents do.

A complete set of calculations was carried out for species X having ΔHX→Y = 96.1 kJ/mol and Ea = 41.8 

kJ/mol. The results are plotted in Figure 59 as maximum calculated flame temperature versus exit 

velocity magnitudes for methane and oxidizer. Based on an extinction temperature of 1550 K, the 

extinguishing volume fraction for X in air is estimated to be 15.9 %. The corresponding value for argon 

was 43 %. Thus the heat extracted by the reaction of X to Y has reduced the amount of agent required by 

nearly 2/3. Figure 60 compares calculated values of maximum flame temperature as a function of 

velocity for 15 %, 30 %, and 45 % argon volume fraction with the corresponding results for 5 %, 10 %, 

and 15 % X. The two set of curves fall close together, but the agreement is not complete. At the lower 

concentrations the results for X fall slightly below those for Ar, while the opposite is true for the highest 

Ea = 83.7 kJ/mol

Distance From Fuel Exit (cm)

0.0 0.5 1.0 1.5 2.0

Volume Fraction

0.00

0.01

0.02

0.03

0.04

0.05

Temperature (K)

400

600

800

1000

1200

1400

1600

1800

2000

X

Y

Temperature
77

Figure 58. Values of maximum flame temperature for methane flames burning in air diluted with 5 % X 

are plotted as a function of the energy of activation for the conversion of X to Y. Methane and 

oxidizer exit velocity magnitudes are 25 cm/s. 

Figure 59. Maximum calculated flame temperatures are plotted against methane and oxidizer exit 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

agent X that reacts to form Y with Ea = 41.8 kJ/mol and ΔHX→Y = 96.1 kJ/mol. Symbols 

correspond to the volume fractions of added X. 

Methane/Air Flame Diluted with 5 % X

Ea (kJ/mole)

20 30 40 50 60 70 80 90

Maximum Flame Temperature (K)

1925

1930

1935

1940

1945

1950

1955

1960

1965

X (ΔHX Y = 96.1 kJ/mol, Ea = 41.8 kJ/mol) Dilution

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Flame Temperature (K)

1500

1600

1700

1800

1900

2000

0%

2.5%

5%

7.5%

10%

12.5%

15%
78

Figure 60. Maximum calculated flame temperatures are plotted against methane and oxidizer exit flow 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

argon and agent X (Ea = 41.8 kJ/mol and ΔHX→Y = 96.1 kJ/mol ). 

concentrations. This behavior is most likely associated with the nonlinear dependence of the maximum 

flame temperature on concentration evident in Figure 44 and the contribution of dilution to 

extinguishment. 

The effect of doubling the amount of heat absorbed by X was considered by running a series of 

calculations for ΔHX→Y = 192.1 kJ/mol. Calculated maximum flame temperatures are plotted as a 

function of the exit velocity magnitudes for methane and oxidizer in Figure 61. From these results the 

extinction volume fraction of X with the higher heat absorption can be estimated as 9.7 %. This value is 

roughly 60 % of that found with ΔHX→Y = 95.2 kJ/mol, or 20 % higher than would be expected if flame 

extinguishment was due solely to the heat extracted. The most likely source for the difference is the 

effect of dilution discussed earlier. The concentration of added agent required for flame extinguishment 

decreases as the amount of heat it can absorb increases, but the decreased concentration reduces the 

degree of dilution, with the result that the effectiveness of extracting additional heat is offset somewhat. 

The role of dilution has an important implication with regard to simple estimates of extinguishing 

efficiency for thermal agents that are often obtained by taking ratios of heat capacities for various agents. 

If the agents have a large heat capacity difference, and the volume fractions required for extinguishment 

therefore differ substantially, a simple linear dependence on heat capacity should not be observed. In 

fact, the agent having the largest heat capacity should be less effective than expected, as observed in the 

current calculations. 

Figure 62 shows a plot of maximum flame temperature at extinction versus exit flow velocity magnitudes 

for air diluted with various concentrations of argon and X with ΔHX→Y = 96.1 kJ/mol and 192.1 kJ/mol. 

The solid line is the result shown in Figure 43 based on a fit to data for known thermal agents. Despite 

the fact that the amount of agent required for extinction varies nonlinearly with ΔHX→Y, the data all fall 

very close together. This supports the conclusion that assuming a common extinction temperature should 

Ar and X (ΔHX Y=192 kJ/mol, Ea=41.8 kJ/mol) Dilution

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Flame Temperature (K)

1500

1600

1700

1800

1900

2000

0 %

15 % Ar

30 % Ar

45 % Ar

5 % X

10 % X

15 % X
79

Figure 61. Maximum calculated flame temperatures are plotted against methane and oxidizer exit flow 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

agent X which reacts to form Y with Ea = 41.8 kJ/mol and ΔHX→Y = 192.1 kJ/mol. Symbols 

correspond to the volume fractions of added X. 

Figure 62. Values of maximum flame temperature at extinction are plotted as a function of fuel and 

oxidizer exit velocity magnitudes for air diluted with a range of volume fractions of argon and 

surrogate agent X having ΔHX→Y = 96.1 kJ/mol or 192.1 kJ/mol. The solid line is the result of 

the regression fits shown in Figure 43. 

X (ΔHX Y = 192 kJ/mol, Ea = 41.8 kJ/mol) Dilution

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Flame Temperature (K)

1500

1600

1700

1800

1900

2000

0 %

1.25 %

2.5 %

3.75 %

5 %

6.25 %

7.5 %

8.5 %

9.25 %

Diluted Methane/Air Flames

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Temperature (K) at Extinction

1500

1550

1600

1650

1700

1750

1800

No Added Agent

Ar

X (ΔH=96.1 kJ/mol)

X (ΔH=192.1 kJ/mol)

Curve from Fig. 43
80

Figure 63. Maximum calculated flame temperatures are plotted against methane and oxidizer exit 

velocity magnitudes for a series of methane/air opposed-flow diffusion flames diluted with 

C4F9OCH3. Symbols correspond to the volume fractions of added C4F9OCH3. 

provide excellent estimates for flame extinguishing volume fractions of thermal agents. The slight 

variations present near the extinguishing volume fractions are likely due to dilution effects. 

I. Prediction of Extinguishing Concentration for HFE7100 

The first section of this report summarizes data base searches that yielded a list of thermal agents that are 

expected to be particularly effective. In order to obtain some idea of the concentrations that might be 

required for extinguishment by such agents, a series of calculations were carried out for a compound that 

is predicted to be one of the more effective, methoxy-nonafluorobutane (C4F9OCH3; HFE7100). It was 

assumed that the only mechanism for heat extraction was the heat capacity of the gaseous agent, even 

though significant heat could also be removed by evaporation if the agent were released as a liquid at 

room temperature. It is also true that this molecule is likely to decompose as it enters the high 

temperature region of the flame and will react to form final products. Reaction of the agent was not 

modeled. Due to the presence of a large number of fluorine atoms, it is also likely that the extinguishing 

efficiency will include a small chemical component. [65,67,68,85] On this basis it might be expected that 

the result of this calculation will be an upper limit for the required extinguishing concentration. 

Figure 63 shows the maximum flame temperature as a function of the methane and oxidizer exit velocity 

magnitudes. As now expected, the curves have similar appearances to those found for the other thermal 

agents. However, what is particularly noteworthy is the relatively small volume fraction of C4F9OCH3

required to lower the maximum flame temperature to the extinguishment temperature of 1550 K. The 

addition of only 5.5 % of C4F9OCH3 is calculated to be sufficient. The high heat capacity of this 

molecule due to its large number of atoms makes it a particularly effective thermal agent in molar terms. 

If liquid vaporization and chemical effects improve its effectiveness still further, this species may well 

approach the effectiveness of halon 1301, which has an extinguishing concentration of 2.9 % [54] on a 

C4F9OCH3 Dilution of CH4/Air Diffusion Flames

Flow Velocities (cm/s)

0 50 100 150 200 250 300

Maximum Flame Temperature (K)

1500

1600

1700

1800

1900

2000

0 %

1 %

2 %

3 %

4 %

4.5 %

5 %

5.5 %
81

molar basis. On a mass basis this fluorinated ether will be less effective, based on the molecular weights 

of 148.9 g/mol for halon 1301 and 250 g/mol for C4F9OCH3, but not dramatically so. It might be 

expected that the mass fraction of C4F9OCH3 that must be added would be similar to other agents, which 

do not have a strong component of chemical effectiveness. [33] 

Using the same assumptions as for the diffusion flame calculations, the adiabatic flame temperature for a 

premixed methane flame burning in air diluted by an extinguishing concentration of C4F9OCH3 was 

calculated to be 1696 K. This is considerably lower than the corresponding temperatures calculated for 

extinguishing concentrations of N2, CO2, Ar, and He (see Table 18). 

The vapor pressure for C4F9OCH3 as a function of temperature is given by [23] 

,

3627.2 10.839

C4F9OCH3

T P e −

= ( 20 ) 

where C4F9OCH3 P is the partial pressure of C4F9OCH3 in atmospheres and T is the temperature in K. For 

300 K and atmospheric pressure the saturation volume fractions of the ether in air is calculated to be 

29 %. Thus the saturation pressure at room temperature should be more than sufficient to extinguish a 

diffusion flame. 

Two experimental measurements of the volume fractions of methoxy-nonafluorobutane required to 

extinguish diffusion flames have been identified. Unpublished measurements from the New Mexico 

Engineering Institute using a standard cup burner with heptane fuel yielded an extinguishing volume 

fraction of 6.1 %. [140] In a patent disclosure, Flynn and Scott also reported that a volume fraction of 

6.1 % was sufficient to extinguish a butane flame in a “micro-cup burner”. [141] These values are 11 % 

higher than estimated using detailed chemical-kinetic modeling for the extinguishment of a methane 

flame. 

Earlier it was shown that cup burner measurements using heptane fuel for agents known to act only 

thermally yielded extinguishing concentrations that were roughly 90 % to 95 % of those estimated using 

detailed kinetic modeling. This would suggest that the expected difference between calculated and 

experimental values for C4F9OCH3 are actually somewhat greater than indicated above. A plausible 

explanation for this difference is the effect of chemical reactions. If this is the indeed the case, the results 

indicate that the net effect of reactions involving this agent is to decrease its effectiveness slightly from 

that expected if it acted simply as a nonreactive thermal agent. Other reaction effects must counteract the 

expected small chemical enhancement due to the fluorine atoms. 

IV. SURFACE COOLING

A. Introduction 

When liquid suppressant droplets released from a discharge port approach a fire, several things can 

happen. Droplets with sufficient momentum to penetrate the flame, depending on their sizes, can either 

be consumed in the flame (participate directly in the suppression processes through physical and/or 

chemical mechanisms) or reach the fuel surface. Droplets with little momentum (e.g., very small 

droplets) may not penetrate the fire and will be deflected away by the rising hot plume. [142] These 

deflected droplets will eventually evaporate or strike adjacent objects. For droplets landing outside the 

burning area, the cooling of the adjacent and surrounding surfaces could mitigate or contain the flame 
82

spread processes. Therefore, droplet interaction with surfaces is an integral part in the understanding of 

the overall suppression processes. 

One of the possible fire suppression mechanisms using a liquid fire suppressant (e.g., water) is fuel 

surface cooling. The relatively cool impacting droplets will interact with the relatively hot fuel surface. 

One of the droplet/surface interactions is the extraction of heat from the surface to vaporize the 

continuously deposited droplets, thereby reducing the surface temperature. The burning rate falls, which 

leads to a decrease in heat feedback to the fuel surface. Eventually, a critical burning rate is reached 

beyond which combustion can no longer be sustained. The other effect of the deposited droplets on the 

burning rate is the reduction of mass transfer area on the fuel surface, which also causes a reduction in 

burning rate. For solid fuels these processes are generally regarded as the dominant mechanism for 

extinguishment by water sprays. [143] 

In order to understand surface cooling without resorting to a detailed analysis of the coupling between the 

transient thermal response of the fuel bed as a result of the application of liquid agent and the heat 

feedback from the flame to the fuel, the transient coupling process is considered as a series of quasisteady steps. At any instant in time, a steady-state energy balance at the fuel surface can be written as: 

m H Q Q T T q fuel fuel cond conv flame flame s surf ′′ Δ = ′′ + ′′ + − − ′′ 4 4 & ε σ ε σ ( 21 ) 

where m fuel & ′′ is the fuel burning mass flux, ΔH fuel is the effective heat of gasification of the fuel, Qcond ′′ is 

the conductive heat flux to the fuel surface, Qconv

′′ is the convective heat flux to the fuel surface, flame ε is 

the flame emissivity, σ is the Stefan-Boltzmann constant, Tflame is the average flame temperature, εs is the 

surface emissivity, Tsurf is the fuel surface temperature, and q" is the heat flux removal from the fuel 

surface due to surface cooling. 

The surface cooling heat flux, q", depends on the interaction of the liquid droplets with the surface. There 

are many different scenarios of droplet impact on a surface. The impacting processes depend on the 

thermophyscial and geometrical properties of the drop and of the target surface and on the magnitude and 

direction of the impact velocity vector. In addition, for a flaming surface, the droplet will traverse 

through an environment different from that of a non-burning surface before impact. However, in the 

literature, droplet/surface interaction studies focus almost exclusively on non-burning surfaces. 

When relatively cool liquid droplets impact on a solid surface, cooling of the surface occurs as a result of 

heat transfer between the surface and the droplets. A liquid droplet impacting a solid surface has been 

extensively studied in the literature. [144,145,146,147,148,149,150,151,152] Maps that identify the 

various impact and heat transfer regimes over a wide range of experimental conditions have been 

constructed. Spray cooling or quenching of hot metallic surfaces has also been extensively studied. 

[153,154,155,156,157,158] Many empirical heat transfer correlations for spray cooling applications exist. 

For a liquid droplet interaction with a liquid surface, several scenarios need to be considered, and the 

impact dynamics are complicated by the ability of the liquid surface to deform and to displace in response 

to the impinging droplet and by the internal fluid motion of the liquid pool initiated by the impact 

processes. [159] If the droplet has a very high impact velocity, it can cause a crater in the liquid pool and 

a splash upon impact. For a burning liquid pool, the splash may result in a sudden increase in burning 

rate due to an increase in the liquid surface area caused by the splash droplets. If the droplet is soluble in 

the liquid, mass transfer between the penetrating droplet and the liquid will occur. Depending on droplet 

impact parameters, differences in miscibilities and physical properties (surface tension and viscosity) 

between the droplet and the target liquid, and the depth of the liquid layer, the droplet may float on the 
83

surface, may coalesce into the liquid pool with little or no splashing and produce a vortex ring, may 

rebound or splash, forming a crater and a small jet or column of liquid at the surface, or may dissolve into 

the liquid pool. Most work in the literature has examined the isothermal impact of a liquid droplet onto a 

surface of the same liquid (e.g., see the review article of Rein [159] and the references therein). In a fire 

suppression scenario, the impacting droplet encounters a different liquid target (suppression fluid versus 

fuel) with different physical properties. The temperature of the droplet can be much lower than that of the 

liquid surface (especially, in the case of burning), and the contact between a cold droplet with a hot liquid 

may sometimes results in vapor explosion [160], an unwanted situation. All of these complicated factors 

render the study of heat transfer processes between liquid droplets and a liquid surface an arduous and 

daunting task. To the best of our knowledge, appropriate heat transfer correlations do not exist in the 

literature; therefore, liquid surface cooling calculations, in spite of the importance of the process, will not 

be attempted here. 

In this section, we will discuss droplet evaporation and solid surface cooling by droplets. Droplet 

evaporation is considered because it is an integral part of the surface cooling problem. If the droplets 

evaporate completely before reaching the fuel surface, the heat removal from the surface will decrease 

significantly due to the fact that the liquid latent heat of vaporization does not play a role. Under this 

circumstance, the surface will only be cooled by a vapor jet, which is not an effective cooling mechanism. 

Another important aspect in surface cooling is the ability of the droplets to reduce the surface temperature 

of metallic components in the vicinity of a fire to prevent re-ignition, which is a potential problem in 

suppressing aircraft engine nacelle fires. If sufficient cooling of hot surfaces cannot be achieved after the 

release of fire suppressant, re-ignition of residual fuel vapor/air mixture by hot surfaces may occur. 

In the following discussion, the five fluids (water, lactic acid, C3F5H3O, HFE7100, and R338mccq) 

identified in Section II.A as having the highest total ΔH (mass basis) are considered to evaluate their 

droplet vaporization and surface cooling characteristics. Low boiling-point fluids will not be considered 

here because under typical operating conditions, these fluids can be easily flash-vaporized soon after they 

leave the discharge opening; thus they likely arrive at the surface in the form of a vapor. 

B. Evaporation of Liquid Droplets 

The estimation of liquid droplet evaporation is based on the classical d2-law, which gives the droplet 

diameter as a function of time as 

 , 2 2 D D Kt = o − ( 22 ) 

where D is the instantaneous droplet diameter, Do is the initial droplet diameter, t is the time, and K is the 

evaporation constant. The evaporation constant can be calculated by 

, ρ

8 ln(1 )

F pg

g

C

k B

K

+ = ( 23 ) 

where B is the transfer number, kg is the gas-phase thermal conductivity, Cpg is the gas-phase heat 

capacity, and ρF is the liquid density. The B number based on mass transfer considerations is given by 

, 1 FS

FS F

M Y

Y Y B −− = ∞ ( 24 ) 
84

where YFS and YF∞ are the vapor-phase mass fraction at the droplet surface and ambiance, respectively. 

The mass fraction, YFS, can be evaluated by 

, ( ) FS F FS A

FS F

FS P M P P M

P M Y

+ − = ( 25 ) 

where PFS is the liquid vapor pressure at the droplet surface, P is the ambient pressure, which is equal to 

the sum of the liquid vapor pressure and partial pressure of air at the droplet surface, and MF and MA are 

the molecular weights of liquid and air, respectively. 

The B number based on heat transfer considerations is given by 

, ( )

vap

pg s

T H

C T T

B

Δ

− = ∞ ( 26 ) 

where T∞, Ts, and ΔHvap are the ambient temperature, droplet surface (wet-bulb) temperature, and latent 

heat of vaporization of the liquid, respectively. Under steady-state conditions, BM = BT, and either Eq. 

(24) or Eq. (26) may be used to calculate the evaporation constant in Eq. (23). 

If Ts is known, the calculation of the evaporation constant is straightforward; however, under normal 

circumstances it is necessary to determine Ts in order to evaluate B and K. The calculation procedure can 

be found in references [161,162,163]. The basic idea is to find Ts such that BM = BT. Spalding [161] and 

Kanury [162] used a graphical approach. By plotting BM and BT against Ts, the intersection of these two 

curves defines the wet-bulb temperature and the corresponding B. An iterative method was used by Chin 

and Lefebvre. [163] The calculations presented here use the latter approach. 

To calculate K, the reference temperature (Tr) and mass fractions (YFr and YAir for the fluid and air, 

respectively), based on the one-third rule [163], were used to estimate the gas-phase thermophysical 

properties, 

3

s

r s

T T T T − = + ∞ ( 27 ) 

3

F FS

Fr FS

Y Y Y Y − = + ∞ ( 28 ) 

1 . YAir = −YFr ( 29 ) 

The equation for calculating the gas-phase heat capacity, Cpg, is given by 

( ) ( ) ( ) Cpg Tr =YAirCpA Tr +YFrCpF Tr ( 30 ) 

where CpA is the heat capacity of air and CpF is the gas-phase heat capacity of the fluid, all evaluated at Tr. 

The thermal conductivity of the gas phase is estimated by the following equation, 

( ) ( ) ( ), g r Air A r Fr F Tr k T =Y k T +Y k ( 31 ) 
85

Figure 64. The droplet evaporation time is shown as a function of initial droplet diameter for the five 

fluids indicated. 

where kA is the thermal conductivity of air and kF is the gas-phase thermal conductivity of the liquid, all 

evaluated at Tr. 

The conditions used in the calculations were: (1) T∞ = 1400 K (to simulate a flaming ambiance), (2) YF∞ = 

0, and (3) P = 0.101 MPa. 

The thermophysical properties of air, water, and lactic acid were obtained from the database of the Design 

Institute for Physical Properties. [9] The properties of C3F5H3O, HFE7100, and R338mccq were 

estimated by methods described in Reid et al. [164]; the modified Rackett technique was used for ρF, the 

method of Joback for CpF, the method of Lee and Kesler for PFS, the method of Pitzer’s acentric factor 

correlation for ΔHvap, and the method of Ely and Hanley for kF. 

Figure 64 shows droplet evaporation times, tb, as a function of initial droplet diameter. The droplet 

evaporation time can be easily obtained by assigning D = 0 in Eq. (22) once K is known, 

.

2

K

D

t o

b = ( 32 ) 

For a given initial droplet diameter under the same ambient conditions, the evaporation time for a water 

droplet is the longest and for a R338mccq droplet the shortest. For the five fluids examined, the ranking 

based on droplet evaporation times is 

. , 338 , 7100 , , , b R mccq b HFE b C3F5H3O b lacticacid b water t <t <t < t <t ( 33 ) 

Droplet Initial Diameter (μm)

0 10 20 30 40 50 60 70 80 90 100

Evaporation Time (s)

0.00

0.01

0.02

0.03

0.04

0.05

0.06

Water

Lactic acid

C3F5H3O 

HFE7100 

R338mccq 

Ambient temperature @ 1400 K
86

Figure 65. An illustration of a typical boiling curve associated with quenching of a hot surface by liquid 

droplets is shown. 

How fast a droplet evaporates determines whether it will still remain as a droplet upon reaching the 

surface. However, if flame cooling is the dominant fire suppression mechanism, then it would be better to 

have the droplet completely vaporized in the flame. 

C. Spray Cooling 

In order to assess surface cooling, we consider the literature on spray cooling and quenching of hot 

metallic surfaces. The application of spray-cooling correlations to fuel surface cooling is only appropriate 

when the fuel surface is solid (e.g., a PMMA or wood slab). Even in this case, care should be exercised 

because subtle differences in cooling mechanisms exist. A burning PMMA surface in reality is in a 

molten state, and wood forms a porous char layer. The interactions of droplets with molten and porous 

surfaces remain very difficult problems to tackle. Differences also arise between fuel surface cooling and 

quenching of metallic surfaces. In the latter, radiative heat transfer to the droplets only occurs from the 

heated surface; however, in the former, it also occurs from the flame. Strictly speaking, the following 

calculations are more applicable to the cooling of a hot surface to prevent re-ignition than to the cooling 

of a burning fuel surface. 

Depending on the surface temperature, when a hot surface is being quenched by a liquid spray, it will 

experience several distinct heat transfer regimes which can be followed along the “boiling curve”. Such a 

curve is a plot of surface heat flux versus surface temperature and represents the strong relationship 

between heat flux and surface temperature during quenching. The characteristics of the boiling curve are 

classified as (with increasing surface temperature): (1) convective, (2) nucleate boiling, (3) critical heat 

flux, (4) transition boiling, (5) Leidenfrost point, and (6) film boiling. Detailed descriptions are available. 

[153,154] Figure 65 is an illustration of a boiling curve associated with spray cooling of a hot surface. 

The general features of the curve are similar to those for a pool boiling curve. 

Since the boiling curve of one fluid may differ from that of other fluids, there are several important 

assumptions that have to be made in the following analysis. 

Surface Temperature

 Transition boiling

Convective regime

Film boiling

Nucleate boiling

Surface Heat Flux 

Critical heat flux (CHF)

Leidenfrost point

Onset of

nucleate boiling
87

When a comparison of surface heat fluxes is made, it is assumed that for the prevailing surface 

temperature, these fluids are in the same regime on the boiling curve. This assumption may not be valid 

because, for example, the surface temperatures at which the critical heat flux and Leidenfrost phenomena 

occur may be significantly different among the fluids studied; therefore, while one fluid may be at the 

critical heat flux, the other fluid may be in the nucleate boiling regime at the prevailing surface 

temperature. Unfortunately, in most cases, it is not possible a priori to determine the demarcation point 

(surface temperature) from one cooling regime to another without resorting to experimental observations. 

The second assumption is that the dimensionless heat transfer correlations obtained in the literature using 

water (in most cases) are applicable to the other fluids considered here. A third assumption is that the 

effect of surface roughness on surface heat flux is not considered. Furthermore, the spray parameters 

used in the following calculations were chosen to be within the range of applicability of the empirical 

correlations. These operating parameters, though encountered in spray quenching applications, may not 

be identical to those appropriate for fire fighting applications. In addition, since different droplet 

generation techniques (sprays vs. mono-dispersed droplet streams) have been used to obtain the heat 

transfer correlations in various regimes, it is imperative that a comparison among the calculated surface 

heat fluxes should be made with these fluids in the same regime. 

D. Convective Regime 

Mudawar and co-workers [153,154] have performed extensive studies on cooling of metal surface in this 

regime using water sprays. Their heat transfer data were correlated using the Nusselt number (Nu), the 

Reynolds number (Re), and the Prandtl number (Pr) by the following expression, 

2.512 2.512 , 0.76 0.56

0.76 0.56

32 32 Re Pr

k

Q D C

Nu

k

hD

f

pf f

f f

=

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡ μ

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

ν

′′ = = ( 34 ) 

where h is the heat transfer coefficient, kf is the thermal conductivity of the liquid, νf is the liquid 

kinematic viscosity, Cpf is the liquid heat capacity, and μf is the liquid viscosity. The Reynolds number is 

based on the volumetric spray flux, Q", and the Sauter mean diameter, D32, of the spray. All the liquid 

properties are evaluated at (Tsurf + Tf)/2 where Tf is the droplet temperature before impact. 

Figure 66 shows the calculated heat flux as a function of Tsurf - Tf. The calculations were performed using 

Q′′ = 0.005 m3

/m2-s, Tf = 295 K, and D32 = 0.5 mm. The thermophysical properties of water and lactic 

acid were obtained from the DIPPR. [9] The properties of C3F5H3O, HFE7100, and R338mccq were 

estimated by methods described in Reid et al. [164]; the boiling point method of Sato was used for kf, the 

corresponding states method of Rowlinson for Cpf, and the method of Brule and Starling for μf. In this 

regime, water removes heat from the surface more efficiently than the other four fluids. It should be 

noted that it may not be feasible in practice to maintain the same D32 with a fixed Q′′ (the conditions used 

in the calculations) for the five fluids because the atomization characteristics at the spray nozzle would be 

vastly different among the fluids owing to their thermophysical properties, thus resulting in different D32. 

[165] 

E. Nucleate Boiling Regime 

Compared to other regimes on the boiling curve, the nucleate boiling regime in spray cooling is probably 

the least studied. In this regime, the heat flux removal from the surface was found to scale only with 

Tsurf-Tf in the studies by Mudawar and co-workers [153,154] where a water spray was used. The heat 

flux, q", was correlated in the form of 
88

Figure 66. Calculated boiling curves in the convective regime are shown for the five indicated liquids. 

1.87 10 ( ) . 5 5.55 Tsurf Tf q′′= × − − ( 35 ) 

In the work of Qiao and Chandra [166] on nucleate boiling enhancement using a surfactant/water 

solution, the heat flux measurements could also be correlated well by scaling with Tsurf - Tf in a form 

similar to Eq. (35), 

0.56 10 ( ) . 5 6 Tsurf Tf q′′= × − − ( 36 ) 

If we assume that the proportionality constant and the power in the scaling law do not change 

significantly among the five chemical compounds and that the heat flux can be scaled with (Tsurf - Tf), then 

the heat flux removal from the surface in the nucleate boiling regime using these five liquids should be 

similar for a given Tsurf. 

F. Critical Heat Flux 

The dimensionless correlation developed by Mudawar and Valentine [153] for water spray cooling over a 

wide range of flow rates is used to estimate the critical heat flux (CHF), 

, ρ

σ

ρ

ρ ( )

ρ

ρ 122.4 1 0.0118

ρ

0.198

32

2

1/ 4

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

′′ ⎪⎭

⎪

⎬

⎫

⎪⎩

⎪

⎨

⎧

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

Δ

−

⎥

⎦

⎤ ⎢

⎣

⎡ = +

Δ ′′ H Q D

C T T

H Q

CHF

F

f

g vap

F pf sat f

F

g

g vap

 ( 37 ) 

where ρg is the vapor density of the fluid, Tsat is the saturation temperature of the fluid, and σf is the 

surface tension of the fluid. All the fluid properties are evaluated at the fluid saturation temperature. 

Using Q" = 0.005 m3

/m2-s, Tf = 295 K, and D32 = 0.5 mm, the resulting CHFs for water, lactic acid, 

C3F5H3O, HFE7100, and R338mccq are 0.63 × 107

 W/m2, 0.86 × 107 W/m2, 0.33 × 107 W/m2, 0.23 × 107

Tsurf - Tf (K)

0 20 40 60 80 100 12

q" (W/m2

) 104

105

106

107

Water

Lactic acid 

C3F5H3O

HFE7100 

R338mccq 
89

W/m2, and 0.21 × 107 W/m2, respectively. In the calculations, surface tensions of water and lactic acid 

were obtained from the DIPPR [9]; while those of C3F5H3O, HFE7100, and R338mccq were estimated 

using the method of Brock and Bird. [164] Although lactic acid and water have the highest and second 

highest CHFs, respectively, under the conditions used in the calculations, it should be noted that it is 

inappropriate to compare the CHFs unless they occur at the same surface temperature for the five fluids, a 

situation highly unlikely given the differences in the thermophysical properties of these fluids. 

G. Transition and Film Boiling Regimes 

Based on dimensional analysis, Deb and Yao [167] statistically derived an equation for heat transfer 

effectiveness (ε) in terms of droplet Weber number (We), dimensionless wall superheat (Bw) and vapor 

parameters (Kd), and surface factor (SF) for surface material effect, 

, 1

90 0.21 exp

60.5

1

35

0.08 ln

=0.027exp 1.5 ⎥

⎦

⎤ ⎢

⎣

⎡

+

+ −

⎥

⎥

⎥

⎥

⎥

⎦

⎤

⎢

⎢

⎢

⎢

⎢

⎣

⎡

⎟

⎠

⎞ ⎜

⎝

⎛ +

⎟

⎠

⎞ ⎜

⎝

⎛ +

ε

We

K B

SF B

We

d w

w

 ( 38 ) 

with 

f

F Vi Do We

σ

ρ

= , ( )

vap

pF surf sat

w H

C T T

B

Δ

− = , 

pF v

F

d C

k K

μ = , and 

( ) −1, ρ

ρ =

steel p

s s ps

k C

k C

SF

where Vi is the droplet impact velocity, Kd is the dimensionless vapor parameter, μv is vapor viscosity, and 

ks, ρs, and Cps are the thermal conductivity, density, and heat capacity of the surface material, respectively. 

All liquid and vapor properties are evaluated at Tsat. The heat transfer effectiveness is defined as the ratio 

of actual heat transfer from the hot surface to the total heat transfer required for complete evaporation of 

the droplets.; therefore, the heat flux from the surface is 

[ ( )], G Hvap Cpf Tsat Tf q′′=ε Δ + − ( 39 ) 

where G is the liquid mass flux. ε was obtained from Eq. (38) by fitting data mainly from experiments 

using a single stream of droplets. The experimental conditions covered the film boiling regime and to 

some extent the adjacent transition boiling regime and Leidenfrost point. 

Figure 67 shows the calculated heat fluxes for the five fluids as a function of the surface temperature. 

The calculations were performed using Tf = 295 K, Vi = 2.5 m/s, Do = 0.3 mm, and G = 0.5 kg/m2

-s. For 

illustration, a stainless steel, SS 304, was used as the target surface. Under the conditions used in the 

calculations, the resulting droplet We are 31, 97, 181, 297, and 339 for water, lactic acid, C3F5H3O, 

HFE7100, and R338mccq, respectively. The range of surface temperatures used in the calculations was 

chosen so that the calculated ε did not exceed 1. The three boiling regimes (transition boiling, 

Leidenfrost condition, and film boiling) are apparent in Figure 67. If we assume that at Tsurf ≥ 800 K, all 

five fluids exhibit film boiling, and lactic acid has the highest surface heat flux. 
90

Figure 67. Calculated boiling curves for the five liquids are shown for the transition and film boiling 

regimes. 

Figure 67 also demonstrates again the difficulty in comparing the heat fluxes at a given surface 

temperature. For example, at Tsurf = 550 K, C3F5H3O, HFE7100, and R338mccq are in the film boiling 

regime, whereas, water and lactic acid are in the transition boiling regime. As stated above, unless the 

surface temperature at which the onset of a particular boiling regime is known a priori, it is not possible 

to know which heat flux correlation pertaining to which boiling regime should be applied in the 

estimation. 

H. Summary 

Empirical heat transfer correlations from the literature have been used to assess surface cooling in various 

heat transfer regimes. Based on the above calculations, water and lactic acid generally appear to be 

superior to C3F5H3O, HFE7100, and R338mccq in surface cooling applications. Water and lactic acid 

evaporate much slower than C3F5H3O, HFE7100, and R338mccq; therefore, the likelihood for water and 

lactic acid droplets to reach the surface is higher. For the convective boiling regime, the calculations 

show that water is better than lactic acid, C3F5H3O, HFE7100, and R338mccq. Lactic acid has the highest 

calculated critical heat flux as well as the highest heat flux in the film boiling regime. In order to validate 

the calculated ranking of surface cooling effectiveness of these agents, experiments should be performed 

in various heat transfer regimes under conditions commensurate with those in actual applications. 

Surface cooling by liquid droplets is a very complicated heat transfer process because it depends on so 

many parameters which include the thermophysical properties (surface tension, density, viscosity, heat of 

vaporization, etc.) of the liquid, droplet size, droplet impact velocity, spray mass flux, and surface 

properties. Even for non-burning, smooth surfaces, calculations of surface heat fluxes from first 

principles are not possible without resorting to experimental observations. Empirical heat transfer 

correlations under conditions encountered in fires are lacking, and the quantification of surface cooling as 

a means to extinguish the burning fuel remains elusive, especially when the fuel is a liquid. 

Tsurf (K)

300 400 500 600 700 800 900 1000

q" (W/m2

) 103

104

105

106

Water

Lactic acid 

C3F5H3O 

HFE7100 

R338mccq 
91

V. DISCUSSION 

A. Liquid HFE7100 as a Potential Fire-Fighting Agent and Liquid Agent Effectiveness 

One of the major goals of this project was to identify highly effective thermal agents that might serve as 

replacements for halon 1301. Based on a thermodynamic analysis and practical considerations such as 

physical properties and commercial availability, HFE7100 was identified as being particularly promising. 

As a purely thermal agent it ranked near the top of the list of potential replacement agents on both molar 

and mass bases (see Table 5 and Table 6). Measurements in the Distributed Liquid Agent Fire 

Suppression Screen apparatus yielded effective extinguishing concentrations of 1.5 % and 11.7 % in 

volume fraction and mass fraction terms, respectively, for a propane flame burning on a Tsuji-type 

burner. Note that the HFE7100 was released as a liquid, while the extinguishing concentrations are those 

obtained by assuming the agent is totally vaporized. 

The results of the detailed chemical-kinetic modeling study suggested that the effectiveness of gaseous 

thermal agents does not depend on the location of heat extraction relative to the flame front as long as the 

heat extraction is complete and the gases are convected into the flame zone. If the same holds true for 

liquid agents, it should be possible to estimate the required effective liquid concentration assuming full 

vaporization of the agent and using a thermal analysis similar to that suggested by Eq. (1). Based on the 

data included in Table 2, Table 4, Table 5, and Table 6 and plotted in Figure 1 and Figure 2, it is apparent 

that the largest fraction of heat absorption by HFE7100 takes place due to gas-phase heating, with liquidphase processes contributing roughly 10 % of the overall heat extraction. The detailed chemical-kinetic 

modeling study of the extinction behavior of a methane counterflow flame by gas-phase HFE7100 yielded 

an estimated extinguishing volume fraction of 5.9 %, which was slightly less than suggested by 

unpublished experimental measurements. The modeling study also indicated that roughly 20 % more 

thermal agent was required to extinguish a propane flame as for a methane flame. On this basis, we 

estimate that the extinguishing volume fraction of gaseous HFE7100 required for a propane flame should 

be on the order of 7.1 %. Reducing this by 10 % to account for the heat absorbed by the liquid yields an 

estimate of 6.4 % for the effective volume fraction of liquid agent required to extinguish a propane flame. 

This value is more than four times larger than observed experimentally. 

Despite the wide spread use of fire-fighting agents released as liquids, note that liquid water remains the 

most frequently used means for fire fighting and that halon 1301 is generally released as a pressurized 

liquid, there are very few studies that have considered the direct interaction of a flame with liquid droplets 

such as reported here. This is particularly surprising given the importance of water for practical fire 

fighting. In a very early study, Seshadri investigated the extinguishment of heptane, methanol, and wood 

flames in counterflow configurations using water droplets. [168] The droplets were small enough that 

they were considered to have evaporated before reaching the flame surfaces. Ewing et al. cite 

unpublished values for water falling in the range of 5.5 % to 13.3 % for the effective volume fraction of 

water (assuming complete evaporation) for diffusion flames. [61] The only other studies of which we are 

aware have been carried out as part of the NGP and have investigated water. Similar to the current 

investigation, these studies were performed in counterflow flames using strain rates that were 

considerably higher than are characteristic of buoyancy-dominated flames. In order to estimate 

extinguishing concentrations it is necessary to extrapolate the findings to appropriate lower strain rates. 

 Zegers et al. have reported extinction results for a propane opposed-jet diffusion flame using various 

sized water droplets. [169]. The effectiveness of the water for inhibiting the flame varied with nominal 

droplet diameter. Simple extrapolation of the results to strain rates characteristic of buoyancy-dominated 

flames provides estimates of 1.3 %, 4.6 %, and 5.2 % in terms of mass fractions (2.1 %, 6.4 %, and 8.1 % 

in terms of volume fractions) for droplets having nominal diameters of 14 μm, 30 μm, and 42 μm, 
92

respectively. Similar measurements for a propane flame were made by Yang et al. using the DLAFSS. 

[35] Their result in mass fraction terms is 5.2 %, which corresponds to a volume fraction of 8.1 %, for 

nominally 30 μm-diameter water droplets. (Note that a factor of two has been incorporated into this result 

to reflect the coverage factor for the spray in the DLAFSS.) Lazzarini et al. have reported similar 

extinction measurements for a methane/air opposed-jet flame using droplets with a median diameter of 20 

μm. [170] Extrapolation of their results leads to estimated extinguishing concentrations of 3.3 % (mass 

fraction) and 5.2 % (volume fraction). Even though these estimates must be considered very crude and do 

not consider fuel effects, there is general agreement between the three investigations. 

From the detailed chemical-kinetic modeling the extinguishing volume fraction of water vapor in air for a 

methane flame has been estimated as 28 %. Using the data included in Table 2, Table 4, Table 5, and 

Table 6 and plotted in Figure 1 and Figure 2, it can be estimated that roughly one half of the heat 

extracted by heating water from room temperature to flame temperatures arises from heating of the liquid 

and vaporization. Based simply on thermal considerations, one would therefore predict nominal volume 

fractions of 14 % for extinguishment of methane flames and 1.2 times higher, or nearly 17 % for propane 

flames. Again, these simple arguments result in overestimates as compared to the extrapolated 

experimental values by factors that range from three to thirteen. 

Experimental extinguishment measurements using liquid agents are difficult and are subject to substantial 

uncertainties. Furthermore, it is necessary to extrapolate from relatively high strain rates to the lower 

strain rates characteristic of buoyancy-dominated flames. However, based on the existing data, it does 

appear that liquid agents are considerably more effective than would be predicted based simply on their 

ability to extract heat from a flame zone. Other physical processes may be playing a role. If such effects 

are actually present, it may be possible to tailor such effects to improve the effectiveness of liquid agents. 

Additional research is required to confirm the results discussed here and to provide an understanding for 

the mechanisms that lead to the observed improvements in liquid agent effectiveness. 

Even though liquid agents appear to be more effective than expected in extinguishing opposed-flow 

diffusion flames, the opposite was found to be the case for HFE7100 in the TARPF. Here a nominal 

volume fraction of 2.8 % HFE7100 was insufficient to extinguish the flame. This value is nearly a factor 

of two higher than required to extinguish the flame in the DLAFSS. The difference in the two 

experiments is almost certainly associated with agent distribution and entrainment in the TARPF. The 

volume fraction of HFE7100 cited is a nominal value, and it is unclear how evenly distributed the agent 

was in the wind tunnel. There may be regions in the cross section near the flame front that have actual 

HFE7100 concentrations below those required for flame extinguishment. It is also possible that efficient 

extinguishment requires entrainment of the agent into the recirculating zone located behind the bluff body 

used for flame attachment in the TARPF. It is likely that droplets of agent dispersed in the high-speed air 

flow have sufficient momentum to pass above the recirculating zone without being entrained. In this way, 

it would be possible to have an extinguishing concentration of liquid agent in the air above the flame, but 

a lower concentration in the actual location where the flame is stabilized. In either case, the results 

demonstrate the importance of agent distribution for effective flame extinguishment. 

Based on the thermodynamics analysis and experimental results reported in the current work it is 

concluded that HFE7100 warrants further consideration as a potential replacement for halon 1301. It 

should be noted that other compounds included in Table 5 and Table 6 also have the potential to be 

effective thermal fire extinguishing agents. Even though the search for chemicals was extensive, it is also 

possible that similar compounds might have been overlooked. We focused on HFE7100 because it 

appeared to be highly promising on both a mass and a volume fractions basis, was available 

commercially, and had already received SNAP approval from the EPA for another use. 
93

B. Conclusions from Detailed Chemical-Kinetic Modeling of Thermal Agent Effects 

Even though flame extinguishment has been extensively studied, the short review in Section III.A 

demonstrates that models for flame extinguishment by thermal agents are not well developed and that 

contradictory approaches have been discussed. Detailed chemical-kinetic modeling of counterflow 

diffusion flames has been shown to be an effective approach for improving the understanding of the 

effects of thermal agents and for predicting flame extinction and extinguishment behaviors. Important 

findings of the study are summarized here. 

Exit flow velocities, the various strain rates, and the stoichiometric scalar dissipation rates calculated for 

extinction of a given flame depend on the detailed chemical-kinetic mechanism used. This was clearly 

demonstrated for the methane flame. The mechanism employed here, GRI-Mech 1.2, predicts flames 

which are more robust than observed experimentally. On the other hand, the maximum flame 

temperatures for flames at extinction seem to be relatively independent of mechanism. This is relevant 

for the current work because a characteristic maximum flame temperature at extinction is used as the 

criteria for flame extinguishment. 

Flame radiation is expected to have a noticeable effect on flame structure for the conditions relevant to 

extinguishment of diffusion flames. Recent detailed chemical-kinetic modeling investigations that 

incorporate radiation indicate that the relative importance of radiation increases with decreasing strain 

rate. For the strain rates identified as being typical of extinguishment of buoyancy-dominated diffusion 

flames, the effects of radiation represent a relatively small fraction of the total heat release. The neglect 

of radiation does not appear to seriously limit predictions of extinguishing concentrations, even though its 

neglect would be expected to change such properties as the extinguishing limit temperature and strain 

rate. 

Assuming maximum flame temperatures at extinction of 1550 K for methane and 1433 K for propane as 

the extinguishing criteria provides good agreement between experimental results and the model 

predictions for the extinguishing volume fraction for nitrogen added to the air side of opposed-flow 

laminar diffusion flames stabilized on porous burners. Since the maximum flame temperatures at 

extinguishment seem to be relatively independent of mechanism, this finding suggests that there is a real 

difference between these two fuels. Predicted extinguishing concentrations are roughly 20 % greater for 

propane flames than for methane. This conclusion is consistent with the discussion of Maĉek who used 

experimental oxygen indices for various hydrocarbon fuels to predict that methane would have a higher 

extinguishing temperature and lower oxygen index than propane. [42] Interestingly, his analysis 

indicated that heptane flames should have flame temperatures very similar to those for methane and 

somewhat higher than for propane. This may explain why experimental cup burner measurements of 

extinguishment using thermal agents for heptane agree so closely with the detailed chemical-kinetic 

modeling results for the methane flame. A note of caution is required here since the amount of agent 

required to extinguish coflowing diffusion flames has been found to depend on burner diameter. The 

close agreement of the methane predictions and heptane measurements suggests that this effect is small 

for the cup burner. The current experimental results for the Santoro and Tsuji burners also indicate that 

propane flames require higher concentrations of a given thermal agent for extinguishment than the 

corresponding methane flames. 

By assuming that the same limit temperatures derived from the nitrogen results could be applied to other 

agents, it was possible to obtain predicted extinguishing volume fractions of other thermal agents for 

methane and propane flames. An assessment of the validity of this hypothesis is complicated by the 

dependence of extinguishing concentrations for diffusion flames on burner type and configuration, 

however, it is clear from the results that the approach provides the correct ordering and relative 

magnitudes for a number of thermal agents (see Figure 38, Figure 48, and Figure 49). It is particularly 
94

noteworthy that the calculations correctly predict the experimental observation that nitrogen and helium 

have nearly equal extinguishing concentrations for both fuels. Other estimation approaches based simply 

on the heat capacities of the agents or adiabatic flame temperatures fail to successfully predict this 

experimental observation. For the methane flame the approach also provides an estimate for the 

extinguishing concentration of HFE7100 that is in excellent agreement with experimental estimates. 

The calculations suggest that the relative effectiveness of thermal agents is the same for propane and 

methane flames despite the fact that the higher concentrations of a given agent are required to extinguish 

the propane flames. This conclusion is consistent with recent work of Babushok and Tsang, based on 

detailed chemical-kinetic modeling of premixed flames, that the relative effectiveness of agent does not 

vary with fuel. [70] Zegers et al. reached the same conclusion based on their experimental measurements 

using methanol, heptane, methane, and propane. [52] 

 

Various approaches that have been used to estimate extinguishing concentrations of thermal agents in the 

past were discussed in Section III.A. One of these approaches was to identify the adiabatic flame 

temperature for a mixture of air and the thermal agent and to assume that this value would be a constant 

for other thermal agents. Figure 39 compares values of the calculated maximum flame temperature and 

the corresponding adiabatic flame temperatures for methane flames burning in air diluted with N2, CO2, 

Ar, He, and H2O. The calculated maximum flame temperatures lie well below the corresponding 

adiabatic flame temperatures, but it is clear that, with the exception of helium, the adiabatic flame 

temperatures for extinguishing concentrations of the agents fall close together. 

Table 18 lists adiabatic flame temperatures for both methane and propane flames burning in air for 

calculated extinguishing concentrations of N2, CO2, Ar, and He. For the three heavier agents the adiabatic 

flame temperatures for the extinguishing concentrations fall close together for both fuels, but particularly 

so for propane. The average adiabatic flame temperatures for the three agents are 1805 K and 1722 K for 

methane and propane, respectively. Based on results for these three agents one would conclude that the 

use of representative adiabatic flame temperature (fuel dependent) provides an effective approach for 

predicting extinguishing concentrations for a given fuel. Since earlier experimental studies often 

considered these three thermal agents, this was a reasonable conclusion. However, it is also clear from 

the results in Table 18 that the corresponding values for He, 1928 K for methane and 1903 K for propane, 

are much higher, reflecting an apparent higher effectiveness for this agent. Also recall that the adiabatic 

flame temperature corresponding to an extinguishing concentration of HFE7100 for the methane flame 

was 1696 K. This latter value suggests that HFE7100 is less effective than N2, CO2, and Ar as a thermal 

agent. 

For a given adiabatic flame temperature, the amount of a thermal agent required should be directly 

proportional to its heat capacity. This is consistent with the early observation that extinguishing 

concentrations seemed to correlate inversely with heat capacity. However, as Larson [58] and Ewing et 

al. [60] have noted, this concept fails when extinguishing concentrations for the inert gases He (4.0 

g/mol), Ne (20.2 g/mol), and Ar (39.9 g/mol) are compared (values in parentheses are atomic masses). 

These three gases have the same heat capacity, but the volume fraction required for extinguishment is 

ordered as He < Ne < Ar. These effects have been attributed to variations in thermal diffusivity, which 

increases as the atomic weight decreases. 

The simple correlation of extinguishing concentration with heat capacity also disagrees with the finding 

reported here that simple dilution of the oxidizer by a species that does not absorb heat weakens the flame 

and can ultimately result in extinguishment. Since dilution effects increase as the agent concentration 

increases, an inverse relationship between the ability to extract heat and extinguishing concentration is not 

to be expected. The calculations run with surrogate agents designed to extract different known amounts 

of heat confirmed this expectation. Increasing the amount of heat extracted by a factor of two did not 
95

result in a factor of two decrease in the amount of agent required for extinguishment, but in a somewhat 

smaller change. 

Thus there are at least three processes at work when a thermal agent extinguishes a flame, namely, 

absorption of heat, dilution, and removal of heat from the flame zone by thermal diffusion. Since 

removal of heat from the flame zone is favored by lower molecular weights, one would expect the 

effectiveness of N2 to be somewhat increased relative to Ar and CO2. The fact that that extinguishing 

concentrations are found to be inversely proportional to the heat capacities suggests that the effects of 

thermal conductivity and dilution roughly cancel for these species. The extinguishing concentration of 

HFE7100 is much lower than for N2, CO2, and Ar, with the result that the role of dilution is greatly 

reduced and a higher agent volume fraction is required for extinguishment than would be predicted based 

simply on thermal grounds. This leads to the lower adiabatic flame temperature calculated for the 

extinguishing condition for HFE 7100. 

Zegers et al. have briefly discussed the relative roles of heat removal, dilution, and heat diffusion with 

regard to the effectiveness of thermal agents. [52] In particular, they argue that dilution and thermal 

conductivity effects are responsible for the fact that the effectiveness of high molecular weight thermal 

agents such as CF4 and SF6 are somewhat less than expected by comparison to such agents as N2, CO2, 

Ar, and He. 

Several papers summarized in Section III.A have suggested that extinguishment by nearly all species can 

be understood simply in terms of their ability to extract heat. [58,59,60,61] These models require that 

some measure of the flame temperature at extinguishment, such as the maximum temperature or adiabatic 

flame temperature, depend on the flame system and agent used. On the other hand, the success of the 

current calculations in predicting extinguishment by thermal agents indicates that while the limit 

temperature is somewhat fuel dependent, the use of a single limit temperature is appropriate for different 

thermal agents. Furthermore, it was found that the location of heat extraction relative to the flame zone 

had no effect on the effectiveness of the agent. This contradicts one of the assumptions used in the 

correlation approach developed by Ewing et al. [61] Contrary to the conclusions of these earlier workers, 

we contend that variations of the limit temperature when different agents are used are actually an 

indication of the presence of chemical effects that weaken (or enhance) the flame and result in higher (or 

lower) limit temperatures. Such an effect can be observed in a recent detailed chemical-kinetic modeling 

study of flame inhibition by halon 1301. [72] 

One of the findings of this investigation is that there is a substantial variation in the amount of a thermal 

agent required to extinguish a diffusion flame with burner type and, in the case of coflow burners, 

diameter. These differences were identified for methane, propane, and heptane flames. In general, 

opposed-flow flames were somewhat more difficult to extinguish than coflow flames attached to a burner. 

For the opposed-flow types the most stable flames appear to be those formed by having the fuel pass 

through a porous surface, while opposed-jet flames were somewhat easier to extinguish. Despite the 

similarity of the flames and flow conditions, a flame burning on a Santoro burner was considerably easier 

to extinguish than the corresponding cup burner flame. The reasons for these variations are not known at 

the present time. It is worthwhile to point out a major difference between the opposed-flow and coflow 

flames. Opposed-flow flames are formed near the stagnation plane of the opposed flows and are therefore 

truly stationary diffusion flames, with fuel and air mixing by molecular diffusion. In contrast, coflow 

flames are stabilized in the wake resulting from the no-slip boundary conditions near the burner exit at a 

location subject to a flow field. At the attachment point the flame is not a pure diffusion flame, but must 

propagate into a fuel/air mixture. Downstream of the attachment point the flame resembles a classical 

diffusion flame more closely. The existence of the propagating "edge flame" is probably responsible for 

the unusual flame behaviors observed during the Santoro Burner investigation. The success of the 

diffusion flame modeling in predicting the relative effects of agents on this burner suggests that the 
96

inhibition of edge flames depends on thermal agent properties in much the same way as pure diffusion 

flames. 

For this investigation we chose the most stable diffusion flames, i.e., opposed-flow porous burner type, as 

the basis for modeling and experimental comparison. This seems reasonable from a fire safety 

standpoint. It is worthwhile to point out that it should be possible to use the same calculational approach 

to predict extinguishing concentrations for the other burners, but the required limit temperatures will vary 

from flame to flame. The collapse of the data for different agents when plotted in terms of the burner exit 

velocities (e.g., see Figure 43) supports this contention. 

VI. RECOMMENDATIONS FOR ADDITIONAL STUDY 

HFE 7100 has been identified as a potential thermal-agent replacement for halon 1301. However, 

experiments in the TARPF were inconclusive. Additional screening tests in which the distribution of the 

released agent is more carefully controlled should be performed. Full-scale tests in simulated aircraft 

applications designed to assess the effectiveness of this agent should also be performed. 

The tentative conclusion that agents released as liquids have higher than expected extinguishing 

efficiency than predicted based solely on their ability to extract heat and dilute the flame gases should be 

confirmed and investigated further to develop an understanding of the underlying mechanisms. It is 

possible that such an understanding would allow the design of more effective fire extinguishment 

systems. 

In order to obtain a better understanding of droplet cooling of solid surfaces during fires, experiments 

performed under the conditions (droplet size, momentum, application rate, etc.) encountered in fire 

fighting are needed in the various heat transfer regimes. These types of experiments are still lacking in 

the literature. Surface cooling experiments involving liquid droplets and liquid surfaces are non-existent 

because the complexity of droplet-surface interaction makes the characterization of the heat transfer 

processes very difficult. A significant experimental effort in this area will be necessary to develop the 

knowledge and engineering correlations required for fire-fighting applications 

VII. ACKNOWLEDGEMENTS 

This research is part of the Department of Defense’s Next Generation Program Fire Suppression 

Technology Program, funded in part by the DOD Strategic Environmental Research and Development 

Program under Contract W74RDV73243630.
97

VIII. APPENDIX A--DETAILED CHEMICAL-KINETIC MECHANISM FOR PROPANE 

COMBUSITON 

Reactions are listed along with the three Arrhenius coefficients, A, β, Ea required to calculate the 

temperature-dependent rate constant, k, from 

, RT

Ea

k AT e

−

= β

where units of A are in cgs units and vary with the order of reaction and Ea has units of cal/mol. 

 REACTION A β Ea

H + H + M = H2 + M 1.00E18 -1.00 0. 

H + H + H2 = 2H2 9.20E16 -0.60 0. 

H + H + H2O = H2 + H2O 6.00E19 -1.25 0. 

H + H + CO2 = H2 + CO2 5.49E20 -2.00 0. 

2O + M = O2 + M 1.200E+17 -1.000 0. 

H + OH + M = H2O + M 2.200E+22 -2.000 0. 

O + H + M = OH + M 5.000E+17 -1.000 0. 

O + OH = O2 + H 4.00E14 -0.50 0. 

O + H2 = OH + H 5.06E04 2.67 6290. 

2OH = O + H2O 1.50E09 1.14 99. 

H2 + O2 = 2OH 1.70E13 0.00 47780. 

OH + H2 = H2O + H 1.17E09 1.30 3626. 

H + O2 + M = HO2 + M 3.61E17 -0.72 0. 

H + HO2 = H2 + O2 1.25E13 0.00 0. 

O + HO2 = O2 + OH 1.40E13 0.00 1073. 

OH + HO2 = O2 + H2O 2.900E+13 0.000 -500. 

2OH (+M) = H2O2 (+M) 7.400E+13 -0.370 0. 

H + HO2 = 2OH 1.69E14 0.00 874. 

HO2 + H = H2O + O 3.01E13 0. 1721. 

2HO2 = O2 + H2O2 1.300E+11 0.000 -1630.00 

H2O2 + H = H2 + HO2 4.79E13 0. 7950. 

H2O2 + OH = H2O + HO2 1.00E13 0.00 1800. 

O + H2O2 = OH + HO2 9.63E+6 2.000 4000. 

CH4 + H = CH3 + H2 1.32E04 3.00 8040. 

CH4 + O = CH3 + OH 1.02E09 1.50 8604. 

CH4 + OH = CH3 + H2O 1.60E06 2.10 2460. 

CH4 + O2 = CH3 + HO2 7.90E13 0.00 56000. 

CH4 + HO2 = CH3 + H2O2 1.13E13 0.00 24641. 

CH3 + H (+M) = CH4 (+M) 6.00E16 -1.00 0. 

CH3 + H = CH2 + H2 9.00E13 0.00 15100. 

CH3 + O = CH2O + H 8.00E13 0.00 0. 

CH3 + OH = CH2 + H2O 7.50E06 2.00 5000. 

CH3 + OH = CH3O + H 5.74E12 -0.23 13931. 

CH3 + OH = CH2SING + H2O 8.90E19 -1.80 8067. 
98

CH3 + O2 = CH3O + O 2.05E18 -1.57 29229. 

CH3 + O2 = CH2O + OH 3.59E09 -0.14 10150. 

CH3 + HO2 = CH3O + OH 2.00E13 0.00 0. 

CH3 + CH3 = C2H4 + H2 1.00E16 0. 32005. 

CH3 + CH3 (+M) = C2H6 (+M) 9.03E16 -1.20 654. 

H + CH2 (+M) = CH3 (+M) 2.500E+16 -0.800 0.00 

CH2 + OH = CH2O + H 2.50E13 0.00 0. 

CH2 + O = CO + 2H 5.00E13 0.00 0. 

CH2 + CO2 = CH2O + CO 1.10E11 0.00 1000. 

CH2 + O = CO + H2 3.00E13 0.00 0. 

CH2 + O2 = CO2 + 2H 1.60E12 0.00 1000. 

CH2 + O2 = CH2O + O 2.00E14 0.00 10000. 

CH2 + O2 = CO2 + H2 6.90E11 0.00 500. 

CH2 + O2 = CO + H2O 1.90E10 0.00 -1000. 

CH2 + O2 = CO + OH + H 8.60E10 0.00 -500. 

CH2 + O2 = HCO + OH 4.30E10 0.00 -500. 

CH2 + CH3 = C2H4 + H 3.00E13 0.00 0. 

2CH2 = C2H2 + H2 4.00E13 0.00 0. 

CH2 + HO2 = CH2O + OH 3.01E13 0. 0. 

CH2 + H2O2 = CH3O + OH 3.01E13 0. 0. 

CH2 + CH2O = CH3 + HCO 1.20E12 0. 0. 

CH2 + HCO = CH3 + CO 1.81E13 0. 0. 

CH2SING + M = CH2 + M 1.00E13 0.00 0. 

CH2SING + H2O (+M) = CH3OH (+M) 2.000E+13 0.000 0.00 

CH2SING + H = CH2 + H 2.00E14 0.00 0. 

O + CH2SING = H2 + CO 1.500E+13 0.000 0.00 

O + CH2SING = H + HCO 1.500E+13 0.000 0.00 

OH + CH2SING = H + CH2O 3.000E+13 0.000 0.00 

CH2SING + CH3 = H + C2H4 1.80E13 0. 0. 

CH2SING + O2 = H + OH + CO 2.800E+13 0.000 0.00 

CH2SING + O2 = CO + H2O 1.200E+13 0.000 0.00 

CH2SING + H2 = CH3 + H 7.00E13 0.00 0. 

CH2SING + CH2O = CH3 + HCO 4.00E13 0. 0. 

CH2SING + CO2 = CO + CH2O 1.00E+13 0. 0. 

CH2SING + CH4 = 2CH3 4.00E13 0.00 0. 

CH2SING + C2H6 = CH3 + C2H5 1.20E14 0.00 0. 

CH2 + H = CH + H2 1.00E18 -1.56 0. 

CH2 + OH = CH + H2O 1.13E07 2.00 3000. 

CH + O2 = HCO + O 3.30E13 0.00 0. 

CH + O = CO + H 5.70E13 0.00 0. 

H + CH = C + H2 1.1E+14 0.00 0. 

CH + OH = HCO + H 3.00E13 0.00 0. 

CH + CO2 = HCO + CO 3.40E12 0.00 690. 

CH + H2O = CH2O + H 1.17E15 -0.75 0. 

CH + CH2O = CH2CO + H 9.46E13 0.00 -515. 

CH + CH2 = C2H2 + H 4.00E13 0.00 0. 
99

CH + CH3 = C2H3 + H 3.00E13 0.00 0. 

CH + CH4 = C2H4 + H 6.00E13 0.00 0. 

C2H3 + CH = CH2 + C2H2 5.00E13 0.00 0. 

HCCO + CH = C2H2 + CO 5.00E13 0.00 0. 

CH + CO (+M) = HCCO (+M) 5.000E+13 0.000 0.00 

OH + C = H + CO 5.000E+13 0.000 0.00 

C + O2 = O + CO 5.800E+13 0.000 576.00 

C + CH2 = H + C2H 5.000E+13 0.000 0.00 

C + CH3 = H + C2H2 5.000E+13 0.000 0.00 

CH3OH + H = CH3O + H2 4.24E06 2.11 4870. 

CH3OH + H = CH2OH + H2 1.7E07 2.11 4870. 

CH3OH + OH = CH3O + H2O 6.00E13 0.00 5500. 

CH3OH + OH = CH2OH + H2O 7.23E12 0.00 1610. 

CH3OH + HO2 = CH3O + H2O2 1.00E12 0.00 18400. 

CH3OH + CH3 = CH3O + CH4 1.45E+1 3.10 6935. 

CH3OH + O = CH2OH + OH 3.88E05 2.50 3080. 

O + CH3OH = OH + CH3O 1.300E+05 2.50 5000. 

CH3OH + HO2 = CH2OH + H2O2 1.0E12 0.00 10000. 

CH3OH + O2 = CH2OH + HO2 2.05E13 0.00 44910. 

CH3OH + CH3 = CH2OH + CH4 3.20E01 3.20 7170. 

CH3OH + CH3O = CH3OH + CH2OH 6.E11 0. 4070. 

CH3OH + C2H5 = C2H6 + CH2OH 31.9 3.2 9160. 

CH3OH + C2H5 = C2H6 + CH3O 14.4 3.1 8940. 

CH3OH + CH3CO = CH3HCO + CH2OH 4.85E3 3. 12340. 

CH3OH + C2H3 = C2H4 + CH2OH 31.9 3.2 7170. 

CH3OH + C2H3 = C2H4 + CH3O 14.4 3.1 6940. 

CH3OH + CH2 = CH3 + CH2OH 31.9 3.2 7170. 

CH3OH + CH2 = CH3 + CH3O 14.4 3.1 6940. 

CH3OH (+M) = CH3 + OH (+M) 1.90E16 0. 91780. 

CH3OH (+M) = CH2OH + H (+M) 1.54E16 0. 96844. 

CH3CO + M = CH3 + CO + M 1.20E15 0. 12516. 

CH3CO + H = CH3 + HCO 9.64E13 0. 0. 

CH3CO + O = CH3 + CO2 9.64E12 0. 0. 

CH3CO + OH = CH2CO + H2O 1.20E13 0. 0. 

CH3CO + OH = CH3 + CO + OH 3.01E13 0. 0. 

CH3CO + HO2 = CH3 + CO2 + OH 3.01E13 0. 0. 

CH3CO + HCO = CH3HCO + CO 9.03E12 0. 0. 

CH3CO + C2H6 = C2H5 + CH3HCO 1.81E04 2.75 17517. 

CH3CO + CH2O = CH3HCO + HCO 1.81E11 0. 12909. 

CH3O + M = CH2O + H + M 1.00E14 0.00 25000. 

CH3O + O2 = CH2O + HO2 6.30E10 0.00 2600. 

CH3O + H = CH2O + H2 2.00E13 0.00 0. 

H + CH3O = H + CH2OH 3.400E+06 1.600 0.00 

H + CH3O = CH2SING + H2O 1.600E+13 0.000 0.00 

H + CH3O (+M) = CH3OH (+M) 5.000E+13 0.000 0.00 

CH3O + O = CH2O + OH 1.00E13 0.00 0. 
100

CH3O + OH = CH2O + H2O 1.00E13 0.00 0. 

CH3O + HO2 = CH2O + H2O2 3.01E11 0. 0. 

CH3O + CO = CH3 + CO2 1.57E13 0. 11797. 

CH3O + C2H5 = CH2O + C2H6 2.41E13 0. 0. 

CH3O + C2H3 = CH2O + C2H4 2.41E13 0. 0. 

CH3O + C2H = CH2O + C2H2 2.41E13 0. 0. 

CH3O + CH3 = CH4 + CH2O 2.40E13 0. 0. 

CH2OH + M = CH2O + H + M 1.00E14 0.00 25000. 

CH2OH + O2 = CH2O + HO2 2.41E14 0.00 5000. 

CH2OH + H = CH3 + OH 9.64E13 0. 0. 

CH2OH + H = CH2O + H2 6.03E12 0. 0. 

CH2OH + HO2 = CH2O + H2O2 1.20E13 0. 0. 

CH2OH + HCO = CH3OH + CO 1.20E14 0. 0. 

CH2OH + HCO = CH2O + CH2O 1.81E14 0. 0. 

CH2OH + CH3 = C2H5 + OH 1.37E14 -.41 6589. 

CH2OH + CH2O = HCO + CH3OH 5.54E03 2.81 5862. 

CH2OH + CH2OH = CH3OH + CH2O 1.20E13 0. 0. 

CH2OH + O = CH2O + OH 2.40E13 0. 0. 

CH2O + M = HCO + H + M 3.31E16 0.00 81000. 

CH2O + H = HCO + H2 2.19E08 1.77 3000. 

CH2O + O = HCO + OH 1.80E13 0.00 3080. 

CH2O + OH = HCO + H2O 3.43E09 1.18 -447. 

CH2O + HO2 = HCO + H2O2 1.99E12 0.00 11665. 

CH2O + O2 = HCO + HO2 2.04E13 0.00 38900. 

CH2O + CH3 = HCO + CH4 4.09E12 0.00 8843. 

H2 + CO (+M) = CH2O (+M) 4.300E+07 1.500 79600.00 

HCO + M = CO + H + M 2.50E14 0.00 16802. 

HCO + H = CO + H2 1.19E13 0.25 0. 

HCO + O = CO + OH 3.00E13 0.00 0. 

HCO + O = CO2 + H 3.00E13 0.00 0. 

HCO + OH = CO + H2O 1.00E14 0.00 0. 

HCO + O2 = HO2 + CO 7.600E+12 0.000 400.00 

HCO + HO2 = CO2 + OH + H 3.00E13 0. 0. 

CH3 + HCO = CH4 + CO 1.20E14 0. 0. 

O + CO + M = CO2 + M 6.020E+14 0.00 3000. 

CO + OH = CO2 + H 1.51E07 1.30 -758. 

O2 + CO = O + CO2 2.500E+12 0.00 47800. 

CO + HO2 = CO2 + OH 5.80E13 0.00 22934. 

C2H6 + H = C2H5 + H2 5.40E02 3.50 5210. 

C2H6 + O = C2H5 + OH 3.00E07 2.00 5115. 

C2H6 + OH = C2H5 + H2O 8.70E09 1.05 1810. 

C2H6 + CH3 = C2H5 + CH4 5.50E-1 4.00 8300. 

C2H6 + O2 = C2H5 + HO2 4.03E13 0. 50842. 

C2H6 + HO2 = C2H5 + H2O2 2.95E11 0. 14935. 

H + C2H5 (+M) = C2H6 (+M) 5.21E+17 -0.990 1580. 

C2H5 + H = CH3+CH3 1.00E14 0.00 0. 
101

C2H5 + H = C2H4 + H2 1.81E12 0. 0. 

C2H5 + O = CH3HCO + H 5.50E13 0. 0. 

C2H5 + O = CH2O + CH3 1.10E13 0. 0. 

C2H5 + O2 = C2H4 + HO2 2.56E19 -2.77 1977. 

C2H5 + OH = C2H4 + H2O 2.41E13 0. 0. 

C2H5 + HO2 = CH3 + CH2O + OH 2.40E13 0. 0. 

C2H4 + M = C2H2 + H2 + M 1.50E15 0.00 55800. 

C2H4 + M = C2H3 + H + M 1.40E16 0.00 82360. 

H + C2H4 (+M) = C2H5 (+M) 1.080E+12 0.454 1820.00 

H + C2H4 = C2H3 + H2 1.325E+06 2.530 12240.00 

C2H4 + O = CH3 + HCO 1.60E09 1.20 746. 

C2H4 + OH = C2H3 + H2O 4.50E06 2.00 2850. 

CH3 + C2H4 = C2H3 + CH4 2.270E+05 2.000 9200. 

C2H4 + O2 = C2H3 + HO2 4.22E13 0. 57594. 

C2H4 + CO = C2H3 + HCO 1.51E14 0. 90562. 

C2H3 + H = C2H2 + H2 1.20E13 0.00 0. 

C2H3 + OH = C2H2 + H2O 5.00E12 0.00 0. 

C2H3 + CH2 = C2H2 + CH3 3.00E13 0.00 0. 

C2H3 + O2 = CH2O + HCO 1.05E38 -8.22 7030. 

C2H3 + O = CH2CO + H 3.00E13 0.00 0. 

C2H3 + O2 = C2H2 + HO2 1.20E11 0. 0. 

C2H3 + HO2 = CH2CO + OH + H 3.00E13 0. 0. 

C2H2 + H (+M) = C2H3 (+M) 5.54E12 0.00 2410. 

C2H2 + OH = HCCOH + H 5.04E05 2.30 13500. 

C2H2 + OH = CH2CO + H 2.18E-4 4.50 -1000. 

C2H2 + OH = CH3 + CO 4.83E-4 4.00 -2000. 

C2H2 + O = CH2 + CO 1.02E07 2.00 1900. 

C2H2 + O = HCCO + H 1.02E07 2.00 1900. 

O + C2H2 = OH + C2H 4.600E+19 -1.410 28950. 

C2H2 + O2 = HCCO + OH 2.00E08 1.50 30100. 

C2H2 = C2H + H 1.80E41 -7.76 137510. 

C2H2 + H = C2H + H2 6.02E13 0. 22243. 

C2H2 + OH = C2H + H2O 1.45E4 2.68 12035. 

C2H2 + O2 = C2H + HO2 1.20E13 0. 74475. 

C2H + O = CH + CO 1.81E13 0. 0. 

OH + C2H = H + HCCO 2.000E+13 0. 0. 

OH + C2H = CH2 + CO 2.00E13 0. 0. 

C2H + O2 = CO + HCO 2.41E12 0. 0. 

HCCOH + H = CH2CO + H 1.00E13 0.00 0. 

CH2CO + H = CH3 + CO 1.13E13 0.00 3428. 

CH2CO + H = HCCO + H2 5.00E13 0.00 8000. 

CH2CO + O = CO2 + CH2 1.75E12 0.00 1350. 

CH2CO + O = HCCO + OH 1.00E13 0.00 8000. 

CH2CO + OH = HCCO + H2O 7.50E12 0.00 2000. 

CH2CO (+M) = CH2 + CO (+M) 3.00E14 0.00 70980. 

CH2CO + O = HCO + HCO 2.00E13 0. 2293. 
102

CH2CO + O = CH2O + CO 2.00E13 0. 0. 

CH2CO + OH = CH2O + HCO 2.80E13 0. 0. 

HCCO + OH = HCO + CO + H 1.00E13 0. 0. 

HCCO + CH2 = C2H + CH2O 1.00E13 0. 2000. 

HCCO + H = CH2SING + CO 1.00E14 0.00 0. 

HCCO + O = H + 2CO 1.00E14 0.00 0. 

HCCO + O2 = 2CO + OH 1.60E12 0.00 854. 

2HCCO = C2H2 + 2CO 1.00E13 0.00 0. 

HCCO + CH2 = C2H3 + CO 3.00E13 0.00 0. 

CH2 + C2H2 = H2CCCH + H 1.20E+13 0.0 6600.0 

CH2SING + C2H2 = H2CCCH + H 1.50E+14 0.0 0.0 

CH2SING + C2H4 = aC3H5 + H 1.30E+14 0.0 0.0 

CH + C2H2 = C3H2 + H 1.00E+14 0.0 0.0 

CH3CH2O + M = CH3HCO + H + M 1.16E+35 -5.89 25274.0 

CH3CH2O + M = CH3 + CH2O + M 1.35E+38 -6.96 23800.0 

CH3CH2O + O2 = CH3HCO + HO2 4.68E+2 3.16 5380.0 

CH3CH2O + H = CH3 + CH2OH 1.00E+13 0.0 0.0 

CH3CH2O + H = CH3HCO + H2 1.00E+13 0.0 0.0 

CH3CH2O + OH = CH3HCO + H2O 1.00E+13 0.0 0.0 

CH3CHOH + O2 = CH3HCO + HO2 4.82E+14 0.0 5017.0 

CH3CHOH + CH3 = iC3H7 + OH 2.00E+13 0.0 0.0 

CH3CHOH + O = CH3HCO + OH 1.00E+14 0.0 0.0 

CH3CHOH + H = CH3HCO + H2 1.00E+13 0.0 0.0 

CH3CHOH + H = CH3 + CH2OH 1.00E+13 0.0 0.0 

CH3CHOH + HO2 = CH3HCO + OH + OH 4.00E+13 0.0 0.0 

CH3CHOH + OH = CH3HCO + H2O 5.00E+12 0.0 0.0 

CH3CHOH + M = CH3HCO + H + M 1.00E+14 0.0 25000.0 

CH3HCO + OH = CH3CO + H2O 9.24E+6 1.5 -962.0 

CH3HCO + OH = CH2HCO + H2O 1.72E+5 2.4 815.0 

CH3HCO + O = CH3CO + OH 1.77E+18 -1.9 2975.0 

CH3HCO + O = CH2HCO + OH 3.72E+13 -0.2 3556.0 

CH3HCO + H = CH3CO + H2 4.66E+13 -0.35 2988.0 

CH3HCO + H = CH2HCO + H2 1.85E+12 0.40 5359.0 

CH3HCO + CH3 = CH3CO + CH4 3.90E-7 5.8 2200.0 

CH3HCO + CH3 = CH2HCO + CH4 2.45E+1 3.15 5727.0 

CH3HCO + HO2 = CH3CO + H2O2 2.40E+19 -2.2 14030.0 

CH3HCO + HO2 = CH2HCO + H2O2 2.32E+11 0.40 14864.0 

CH3HCO + O2 = CH3CO + HO2 1.00E+14 0.00 42200.0 

C2H5 + HO2 = CH3CH2O + OH 3.00E+13 0.0 0.0 

C2H5 + O2 = CH3HCO + OH 4.90E+11 -0.48 8357.0 

C2H4 + OH = C2H4OH 1.29E+12 0.0 -817.0 

C2H4OH + O2 = HOC2H4O2 1.00E+12 0.0 -1100.0 

HOC2H4O2 = CH2O + CH2O + OH 6.00E+10 0.0 24500.0 

C2H4 + O = CH2HCO + H 3.39E+06 1.88 179.0 

C2H3 + O2 = CH2HCO + O 5.50E+14 -0.611 5260.0 

C2H3 + CH3 = aC3H5 + H 4.73E+02 3.7 5677. 
103

C2H3 + CH3 = C3H6 4.46E+56 -13.0 13865.0 

CH2HCO + H = CH3 + HCO 5.00E+13 0.0 0.0 

CH2HCO + H = CH2CO + H2 2.00E+13 0.0 0.0 

CH2HCO + O = CH2O + HCO 1.00E+14 0.0 0.0 

CH2HCO + OH = CH2CO + H2O 3.00E+13 0.0 0.0 

CH2HCO + O2 = CH2O + CO + OH 3.00E+10 0.0 0.0 

CH2HCO + CH3 = C2H5 + CO + H 4.90E+14 -0.50 0.0 

CH2HCO + HO2 = CH2O + HCO + OH 7.00E+12 0.0 0.0 

CH2HCO + HO2 = CH3HCO + O2 3.00E+12 0.0 0.0 

CH2HCO = CH3 + CO 1.17E+43 -9.83 43756.0 

CH2HCO = CH2CO + H 1.81E+43 -9.61 45868.0 

CHOCHO (+M) = CH2O + CO (+M) 4.27E+12 0.0 50600.0 

CHOCHO = CO + CO + H2 4.07E+42 -8.5 69278.0 

CHOCHO + OH = HCO + CO + H2O 1.00E+13 0.0 0.0 

CHOCHO + O = HCO + CO + OH 7.24E+12 0.0 1970.0 

CHOCHO + H = CH2O + HCO 1.00E+12 0.0 0.0 

CHOCHO + HO2 = HCO + CO + H2O2 1.70E+12 0.0 10700.0 

CHOCHO + CH3 = HCO + CO + CH4 1.74E+12 0.0 8440.0 

CHOCHO + O2 = HCO + CO + HO2 1.00E+14 0.0 37000.0 

HCCO + C2H2 = H2CCCH + CO 1.00E+11 0.0 3000.0 

HCCO + OH = C2O + H2O 3.00E+13 0.0 0.0 

C2O + H = CH + CO 1.00E+13 0.0 0.0 

C2O + O = CO + CO 5.00E+13 0.0 0.0 

C2O + OH = CO + CO + H 2.00E+13 0.0 0.0 

C2O + O2 = CO + CO + O 2.00E+13 0.0 0.0 

C3H8 (+M) = C2H5 + CH3 (+M) 7.90E+22 -1.8 88629.0 

C3H8 + O2 = iC3H7 + HO2 4.00E+13 0.0 48610.0 

C3H8 + O2 = nC3H7 + HO2 4.00E+13 0.0 51360.0 

C3H8 + HO2 = nC3H7 + H2O2 4.76E+04 2.55 16492.0 

C3H8 + HO2 = iC3H7 + H2O2 9.64E+03 2.6 13909.0 

C3H8 + OH = nC3H7 + H2O 3.16E+07 1.8 934.0 

C3H8 + OH = iC3H7 + H2O 7.08E+06 1.9 -159.0 

C3H8 + O = nC3H7 + OH 3.73E+06 2.4 5504.0 

C3H8 + O = iC3H7 + OH 5.48E+05 2.5 3139.0 

C3H8 + H = iC3H7 + H2 1.30E+06 2.4 4471.0 

C3H8 + H = nC3H7 + H2 1.33E+06 2.54 6756.0 

C3H8 + CH3 = nC3H7 + CH4 9.04E-01 3.65 7153.0 

C3H8 + CH3 = iC3H7 + CH4 1.51E+00 3.46 5480.0 

C3H8 + C2H3 = iC3H7 + C2H4 1.00E+03 3.1 8830.0 

C3H8 + C2H3 = nC3H7 + C2H4 6.00E+02 3.3 10500.0 

C3H8 + C2H5 = iC3H7 + C2H6 1.51E+00 3.46 7470.0 

C3H8 + C2H5 = nC3H7 + C2H6 9.03E-01 3.65 9140.0 

C3H8 + aC3H5 = C3H6 + nC3H7 2.35E+02 3.3 19842.0 

C3H8 + aC3H5 = C3H6 + iC3H7 7.83E+01 3.3 18169.0 

nC3H7 (+M) = C2H4 + CH3 (+M) 1.23E+13 -0.1 30202.0 

nC3H7 + O2 = C3H6 + HO2 3.58E+09 0.0 -3532.0 
104

iC3H7 + O2 = C3H6 + HO2 6.10E+20 -2.86 7910.0 

C3H6 + H (+M) = iC3H7 (+M) 5.70E+09 1.16 874.0 

iC3H7 + H = C2H5 + CH3 5.00E+13 0.0 0.0 

nC3H7 + H = C2H5 + CH3 1.00E+14 0.0 0.0 

pC3H5 + H = C3H6 7.0e13 0.0 0.0 

sC3H5 + H = C3H6 5.0e13 0.0 0.0 

C3H6 = C2H2 + CH4 2.50E+12 0.0 70000.0 

C3H6 = aC3H4 + H2 3.00E+13 0.0 80000.0 

C3H6 + HO2 = aC3H5 + H2O2 9.64E+03 2.6 13910.0 

C3H6 + OH + O2 = CH3HCO + CH2O + OH 3.00E+10 0.0 -8280.0 

C3H6 + OH = aC3H5 + H2O 3.12E+06 2.0 -298.0 

C3H6 + OH = sC3H5 + H2O 1.11E+06 2.0 1451.0 

C3H6 + OH = pC3H5 + H2O 2.11E+06 2.0 2778.0 

C3H6 + O = CH3CHCO + H + H 5.01E+07 1.76 76.0 

C3H6 + O = C2H5 + HCO 1.58E+07 1.76 -1216.0 

C3H6 + O = aC3H5 + OH 5.24E+11 0.7 5884.0 

C3H6 + O = pC3H5 + OH 1.20E+11 0.7 8959.0 

C3H6 + O = sC3H5 + OH 6.03E+10 0.7 7632.0 

C3H6 + H = C2H4 + CH3 7.23E+12 0.0 1302.0 

C3H6 + H = aC3H5 + H2 1.73E+05 2.5 2492.0 

C3H6 + H = sC3H5 + H2 4.09E+05 2.5 9794.0 

C3H6 + H = pC3H5 + H2 8.04E+05 2.5 12284.0 

aC3H5 + HO2 = C3H6 + O2 3.0e12 0.0 0.0 

C3H6 + CH3 = aC3H5 + CH4 2.22E+00 3.5 5675.0 

C3H6 + CH3 = sC3H5 + CH4 8.43E-01 3.5 11656.0 

C3H6 + CH3 = pC3H5 + CH4 1.35E+00 3.5 12848.0 

C3H6 + HCO = aC3H5 + CH2O 1.08E+07 1.9 17010.0 

CH3CHCO + OH = CH2CHCO + H2O 4.00E+06 2.0 0.0 

CH3CHCO + O = CH2CHCO + OH 7.60E+08 1.5 8500.0 

CH3CHCO + H = CH2CHCO + H2 2.00E+05 2.5 2500.0 

CH3CHCO + H = C2H5 + CO 2.00E+13 0.0 2000.0 

CH3CHCO + O = CH3 + HCO + CO 3.00E+07 2.0 0.0 

CH2CHCHO + OH = CH2CHCO + H2O 1.00E+13 0.0 0.0 

CH2CHCHO + O = CH2CHCO + OH 7.24E+12 0.0 1970.0 

CH2CHCHO + O = CH2CO + HCO + H 5.01E+07 1.76 76.0 

CH2CHCHO + H = CH2CHCO + H2 3.98E+13 0.0 4200.0 

CH2CHCHO + H = C2H4 + HCO 2.00E+13 0.0 3500.0 

CH2CHCHO + O2 = CH2CHCO + HO2 3.00E+13 0.0 36000.0 

CH2CHCO = C2H3 + CO 1.00E+14 0.0 34000.0 

CH2CHCO + O = C2H3 + CO2 1.00E+14 0.0 0.0 

aC3H5 + O2 = CH2CHCHO + OH 1.82E+13 -0.41 22859.0 

aC3H5 + O2 = aC3H4 + HO2 4.99E+15 -1.4 22428.0 

aC3H5 + O2 = CH2HCO + CH2O 1.06E+10 0.34 12838.0 

aC3H5 + O2 = C2H2 + CH2O + OH 2.78E+25 -4.8 15468.0 

aC3H5 + HO2 = CH2CHCHO + H + OH 1.00E+13 0.0 0.0 

aC3H5 + OH = aC3H4 + H2O 1.00E+13 0.0 0.0 
105

aC3H5 + H = aC3H4 + H2 5.00E+13 0.0 0.0 

aC3H5 + H = C3H6 1.88E+26 -3.6 5468.0 

aC3H5 + O = CH2CHCHO + H 1.81E+14 0.0 0.0 

aC3H5 + CH3 = aC3H4 + CH4 3.02E+12 -0.32 -131.0 

aC3H5 + CH3 = C4H8-1 1.76E+50 -11.0 18600.0 

pC3H5 + O2 = CH3HCO + HCO 1.09E+23 -3.29 3892.0 

pC3H5 + O2 = CH3CHCO + H + O 1.60E+15 -0.78 3135.0 

pC3H5 + O = CH3CHCO + H 1.00E+14 0.0 0.0 

pC3H5 + H = pC3H4 + H2 2.00E+13 0.0 0.0 

pC3H5 + OH = pC3H4 + H2O 1.00E+13 0.0 0.0 

pC3H5 + H = aC3H5 + H 1.00E+14 0.0 0.0 

sC3H5 + H = aC3H5 + H 1.00E+14 0.0 0.0 

sC3H5 + O2 = CH3CO + CH2O 1.09E+22 -3.29 3892.0 

sC3H5 + O = CH2CO + CH3 1.00E+14 0.0 0.0 

sC3H5 + H = pC3H4 + H2 4.00E+13 0.0 0.0 

sC3H5 + OH = pC3H4 + H2O 2.00E+13 0.0 0.0 

aC3H4 + H = H2CCCH + H2 2.0e7 2.0 5000. 

aC3H4 + O = C2H4 + CO 1.34E+07 1.88 179.0 

aC3H4 + OH = H2CCCH + H2O 1.00e7 2.0 1000.0 

aC3H4 + CH3 = H2CCCH + CH4 1.5e0 3.5 5600. 

aC3H4 = pC3H4 1.48e13 0.0 60401. 

pC3H4 + H = H2CCCH + H2 2.00e7 2.0 5000. 

pC3H4 + O = C2H4 + CO 1.50E+13 0.0 2102.0 

pC3H4 + OH = H2CCCH + H2O 1.00e7 2.0 1000.0 

pC3H4 + CH3 = H2CCCH + CH4 1.5e0 3.5 5600. 

pC3H4 + H = CH3 + C2H2 5.12e10 1.0 2060. 

pC3H4 + H (+M) = sC3H5 (+M) 6.50E+12 0.0 2000.0 

aC3H4 + H (+M) = aC3H5 (+M) 1.20E+11 0.69 3007.0 

aC3H4 + H (+M )= sC3H5 (+M) 8.49E+12 0.0 2000.0 

H2CCCH + O2 = CH2CO + HCO 3.00E+10 0.0 2868.0 

H2CCCH + O = CH2O + C2H 2.00E+13 0.0 0.0 

H2CCCH + H = C3H2 + H2 5.00E+13 0.0 3000.0 

H2CCCH + OH = C3H2 + H2O 2.00E+13 0.0 0.0 

H2CCCH + CH3 = CH3CHCCH2 5.00E+12 0.0 0.0 

H2CCCH + CH3 = CH3CH2CCH 5.00E+12 0.0 0.0 

H2CCCH + CH = HCCHCCH + H 7.00E+13 0.0 0.0 

H2CCCH + CH = H2CCCCH + H 7.00E+13 0.0 0.0 

H2CCCH + H (+M) = aC3H4 (+M) 1.66E+15 -0.37 0.0 

H2CCCH + H (+M) = pC3H4 (+M) 1.66E+15 -0.37 0.0 

C3H2 + O2 = HCCO + CO + H 5.00E+13 0.0 0.0 

C3H2 + OH = C2H2 + HCO 5.00E+13 0.0 0.0 

CHCHCHO + O2 = C2H2 + CO + HO 2 3.00E+12 0.0 0.0 

CHCHCHO = C2H2 + HCO 1.00E+14 0.0 33000.0 

CHCHCHO + H = CH2CHCO + H 1.00E+14 0.0 0.0 

CHCHCHO + OH = HCCCHO + H2O 1.00E+13 0.0 0.0 

CHCHCHO + H = HCCCHO + H2 2.00E+13 0.0 0.0 
106

HCCCHO + H = C2H2 + HCO 1.00E+14 0.0 3000.0 

HCCCHO + OH = HCCCO + H2O 1.00E+13 0.0 0.0 

HCCCHO + H = HCCCO + H2 4.00E+13 0.0 4200.0 

HCCCO + O2 = HCO + CO + CO 1.40E+09 1.0 0.0 

HCCCO + H = C2H2 + CO 1.00E+14 0.0 0.0 

C4H10 = C2H5 + C2H5 2.00E+16 0.0 81300.0 

C4H10 = nC3H7 + CH3 1.74E+17 0.0 85700.0 

C4H10 = pC4H9 + H 1.00E+14 0.0 100000.0 

C4H10 = sC4H9 + H 1.00E+14 0.0 100000.0 

C4H10 + O2 = pC4H9 + HO2 2.50E+13 0.0 49000.0 

C4H10 + O2 = sC4H9 + HO2 4.00E+13 0.0 47600.0 

C4H10 + aC3H5 = pC4H9 + C3H6 7.94E+11 0.0 20500.0 

C4H10 + aC3H5 = sC4H9 + C3H6 3.16E+11 0.0 16400.0 

C4H10 + CH3 = pC4H9 + CH4 5.0e11 0.0 13600.0 

C4H10 + CH3 = sC4H9 + CH4 4.3e11 0.0 10500.0 

C4H10 + H = pC4H9 + H2 2.84e5 2.54 6050. 

C4H10 + H = sC4H9 + H2 4.13E+07 1.73 753.0 

C4H10 + OH = sC4H9 + H2O 7.23E+07 1.64 -247.0 

C4H10 + O = pC4H9 + OH 1.13E+14 0.0 7850.0 

C4H10 + O = sC4H9 + OH 5.62E+13 0.0 5200.0 

C4H10 + HO2 = pC4H9 + H2O2 1.70E+13 0.0 20460.0 

C4H10 + HO2 = sC4H9 + H2O2 1.12E+13 0.0 17700.0 

sC4H9 (+M) = C3H6 + CH3 (+M) 2.14e12 0.65 30856. 

sC4H9 = C4H8-1 + H 2.00E+13 0.0 40400.0 

sC4H9 = C4H8-2 + H 5.01E+12 0.0 37900.0 

pC4H9 (+M) = C2H5 + C2H4 (+M) 1.06e13 0.0 27828.0 

pC4H9 = C4H8-1 + H 1.26E+13 0.0 38600.0 

C4H8-1 = C2H3 + C2H5 1.00E+19 -1.0 96770.0 

C4H8-1 = H + C4H7 4.11E+18 -1.0 97350.0 

C4H8-1 + CH3 = C4H7 + CH4 1.00E+11 0.0 7300.0 

C4H8-1 + H = C4H7 + H2 5.00E+13 0.0 3900.0 

C4H8-1 + O = nC3H7 + HCO 1.80E+05 2.5 -1029.0 

C4H8-1 + O = CH2CHCHO + CH3 + H 9.67E+04 2.5 -1029.0 

C4H8-1 + OH = C4H7 + H2O 2.25E+13 0.0 2217.0 

C4H8-1 + aC3H5 = C4H7 + C3H 6 7.90E+10 0.0 12400.0 

C4H8-1 + O2 = C4H7 + HO2 4.00E+12 0.0 33200.0 

C4H8-2 = H + C4H7 4.11E+18 -1.0 97350.0 

C4H8-2 + CH3 = C4H7 + CH4 1.00E+11 0.0 8200.0 

C4H8-2 + H = C4H7 + H2 5.00E+13 0.0 3800.0 

C4H8-2 + O = iC3H7 + HCO 2.79E+06 2.12 -1775.0 

C4H8-2 + OH = C4H7 + H2O 3.90E+13 0.0 2217.0 

C4H8-2 + O = CH3CO + C2H5 1.53E+07 1.87 -1476.0 

C4H8-2 + O = CH3 + CH3CHCO + H 8.22E+06 1.87 -1476.0 

C4H8-2 + O2 = C4H7 + HO2 8.00E+13 0.0 37400.0 

C4H7 = CH2CHCHCH2 + H 1.00E+14 0.0 55000.0 

C4H7 + OH = CH2CHCHCH2 + H2O 1.00E+13 0.0 0.0 
107

C4H7 + CH3 = CH2CHCHCH2 + CH4 8.00E+12 0.0 0.0 

C4H7 + aC3H5 = C3H6 + CH2CHCHCH2 6.31E+12 0.0 0.0 

C4H7 + O2 = CH2CHCHCH2 + HO2 1.00E+09 0.0 0.0 

C4H7 + H = CH2CHCHCH2 + H2 3.16E+13 0.0 0.0 

CH2CHCHCH2 + OH = CH2CHCHCH + H2O 2.00E+07 2.0 5000.0 

CH2CHCHCH2 + OH = CH2CHCCH2 + H2O 2.00E+07 2.0 2000.0 

CH2CHCHCH2 + O = HCO + aC3H5 6.02E+08 1.45 -858.0 

CH2CHCHCH2 + O = CH2HCO + C2H3 1.00E+12 0.0 0.0 

CH2CHCHCH2 + H = CH2CHCHCH + H2 3.00E+07 2.0 13000.0 

CH2CHCHCH2 + H = CH2CHCCH2 + H2 3.00E+07 2.0 6000.0 

CH3CH2CCH + OH = CH3CHCCH + H2O 1.00E+07 2.0 2000.0 

CH3CH2CCH + H = C2H5 + C2H2 1.00E+14 0.0 3000.0 

CH3CHCCH2 + OH = CH2CHCCH2 + H2O 2.00E+07 2.0 1000.0 

CH3CHCCH2 + OH = CH3CCCH2 + H2O 1.00E+07 2.0 2000.0 

CH3CHCCH2 + OH = CH3CHCCH + H2O 2.00E+07 2.0 2500.0 

CH3CHCCH2 + H = CH2CHCCH2 + H2 5.00E+07 2.0 5000.0 

CH3CHCCH2 + H = CH3CCCH2 + H2 1.50E+07 2.0 6000.0 

CH3CHCCH2 + H = CH3CHCCH + H2 3.00E+07 2.0 6500.0 

CH3CHCCH2 + H = CH3 + aC3H4 2.00E+13 0.0 2000.0 

CH3CHCCH + H = CH3 + H2CCCH 1.00E+14 0.0 0.0 

CH3CHCCH + O2 = CH3CHCO + HCO 4.16E+10 0.0 2510.0 

CH3CHCCH + OH = CH2CHCCH + H2O 3.00E+13 0.0 0.0 

CH2CHCCH2 + H = CH3 + H2CCCH 1.00E+14 0.0 0.0 

CH2CHCCH2 + H = CH3CCCH2 + H 3.00E+13 0.0 0.0 

CH3CCCH2 + H = CH3 + H2CCCH 1.00E+14 0.0 0.0 

CH3CCCH2 + O2 = CH3CO + CH2CO 4.16E+10 0.0 2510.0 

CH3CCCH2 + H = H2CCCCH2 + H2 1.00E+14 0.0 8000.0 

CH3CCCH2 + OH = H2CCCCH2 + H2O 1.00E+13 0.0 0.0 

CH2CHCHCH + H = CH2CHCCH2 + H 1.0E+14 0.0 0.0 

CH2CHCHCH + OH = CH2CHCCH + H2O 2.00E+07 2.0 1000.0 

CH2CHCHCH + H = CH2CHCCH + H2 3.00E+07 2.0 1000.0 

CH3CHCCH (+M) = CH2CHCCH + H (+M) 1.00E+13 0.0 49000.0 

CH3CCCH2 (+M) = H2CCCCH2 + H (+M) 1.00E+13 0.0 56000.0 

CH2CHCCH2 (+M) = CH2CHCCH + H (+M) 1.00E+14 0.0 50000.0 

CH2CHCHCH (+M) = CH2CHCCH + H (+M) 1.00E+14 0.0 37000.0 

CH2CHCHCH + O2 = CHCHCHO + CH2O 1.00E+12 0.0 0.0 

CH2CHCHCH + O2 = CH2CHCCH + HO2 1.00E+07 2.0 10000.0 

H2CCCCH2 + OH = H2CCCCH + H2O 2.00E+07 2.0 2000.0 

H2CCCCH2 + H = H2CCCCH + H2 3.00E+07 2.0 6000.0 

CH2CHCCH + OH = HCCHCCH + H2O 7.50E+06 2.0 5000.0 

CH2CHCCH + H = HCCHCCH + H2 2.00E+07 2.0 15000.0 

CH2CHCCH + OH = H2CCCCH + H2O 1.00E+07 2.0 2000.0 

CH2CHCCH + H = H2CCCCH + H2 3.00E+07 2.0 5000.0 

HCCHCCH + H = H2CCCCH + H 1.00E+14 0.0 0.0 

HCCHCCH + O2 = HCCCHO + HCO 3.00E+12 0.0 0.0 

H2CCCCH + O2 = CH2CO + HCCO 1.00E+12 0.0 0.0 
108

H2CCCCH + OH = C4H2 + H2O 3.00E+13 0.0 0.0 

H2CCCCH + O = CH2CO + C2H 2.00E+13 0.0 0.0 

H2CCCCH + O = H2C4O + H 2.00E+13 0.0 0.0 

H2CCCCH + H = C4H2 + H2 5.00E+13 0.0 0.0 

H2CCCCH + CH2 = aC3H4 + C2H 2.00E+13 0.0 0.0 

H2CCCCH (+M) = C4H2 + H (+M) 1.00e14 0.0 47000. 

HCCHCCH (+M) = C4H2 + H (+M) 1.00E+14 0.0 36000.0 

C4H2 + CH2 = C5H3 + H 1.30E+13 0.0 4326.0 

C4H2 + CH = C5H2 + H 1.00E+14 0.0 0.0 

C4H2 + CH2SING = C5H3 + H 3.00E+13 0.0 0.0 

C4H2 + C2H = C6H2 + H 9.60E+13 0.0 0.0 

C4H2 + OH = H2C4O + H 6.66E+12 0.0 -410.0 

C4H2 + O = C3H2 + CO 1.20E+12 0.0 0.0 

H2C4O + H = C2H2 + HCCO 5.00E+13 0.0 3000.0 

H2C4O + OH = CH2CO + HCCO 1.00E+07 2.0 2000.0 
109

IX. APPENDIX B—ADDITIONAL DETAILS CONCERNING THE COFLOW DIFFUSION 

FLAME EXPERIMENT 

 

A. Mass-Flow Controllers and Their Calibration 

The thermal mass-flow controllers (MFCs) were manufactured by MKS Instruments, Inc. Some 

performance and electrical specifications are listed in Table 19. Each MFC was calibrated for nitrogen by 

the manufacturer over its designed flow range. Each MFC was also calibrated at NIST/BFRL for the 

specific gases that it would control. 

NIST/BFRL calibrations were performed using an electronic soap-film flow meter, the Gilibrator-2. 

Using two LED/detectors, the instrument measures the transit time of a soap-film bubble of prescribed 

diameter over a prescribed distance. The instrument displays the volume flow rate based on the most 

recent bubble as well as an average over the previous n bubbles. An average over at least 10 bubbles was 

used for the current calibrations. 

Calibration curves were determined for the MFC set point dc voltage (0 V – 5 V) as a function of the 

volume flow rate. The units of volume flow rate required for input into the calibration curves are 

standard liters per minute (SLM), Q*

, with a standard condition of 101.3 kPa and 273.15 K. Equation 40 

was used to convert the actual desired volume flow rate, Q, to SLM, 

 

. 101325

* 273.15 amb

amb

P

T Q = Q ( 40 )

The units for the ambient temperature (Tamb) and pressure (Pamb) are Kelvins and Pascals, respectively. 

Calibration curves were determined for each MFC and for each gas that was controlled by a given MFC. 

The general calibration curve, described by the following equation, 

( ) ( ) ( ) , * 4 * 3 * 2 * V = A Q + B Q + C Q + DQ + E ( 41 )

is a fourth-order polynomial that is used to compute a set point voltage, V, for a desired standard volume 

flow rate. The coefficients for each MFC and its associated gas(es) are listed in Table 20 to Table 22. 

The relative expanded uncertainty of volume flow rate measurements using the Gilibrator-2 has been 

estimated by Mulholland and Fernandez [171] to be ±1.8 % at a confidence level of 95 % (i.e. a relative 

combined standard uncertainty of 0.9 %). 

B. Detailed Description of Gas Flow Calculations 

The gases were assumed to be ideal at constant pressure and temperature and therefore the partial volume 

flow rates were assumed to sum to the total volume flow rate as described by the Amagat Law. [172] 

Matching exit velocity conditions required the volume flow rate of the agent/air coflow mixture 

(Qexit,coflow) to remain constant, therefore the flow rate of air was decreased as the flow rate of agent 

increased. Equations 42 – 44 demonstrate the basis of the software calculations for combining the air 

(Qair) and agent (Qagent) volume flow rates in the proper proportions to achieve the desired agent volume 

fraction (Xagent) with the required nominal coflow velocity, 
110

Table 19. Mass-Flow Controller Specifications 

Specifications Model 1359C Model 1559A 

Full Scale Range 0-2, 0-10 (SLM, nitrogen) 0-30 (SLM, nitrogen) 

Accuracy ± 0.5 % of full scale ± 1.0 % of full scale 

Repeatability ± 0.2 % of reading ± 0.2 % of reading 

Resolution ± 0.1 % of full scale ± 0.1 % of full scale 

Settling Time < 2 s < 2 s 

Input/Command Signal 0 V - 5 V 0 V - 5 V 

Output Signal 0 V - 5 V 0 V - 5 V 

Table 20. Calibration Coefficients for the Air and Fuel Mass-Flow Controllers 

Coefficient MFC: Model 1559A, 

0 SLM - 30 SLM 

Gas: Air 

MFC: Model 1359C,

0 SLM - 2 SLM 

Gas: Methane 

MFC: Model 1359C, 

0 SLM - 2 SLM 

Gas: Propane 

A 1.0937e-6 0.10513 5.8104 

B -6.7825e-5 -0.47988 -8.6052 

C 0.0016515 0.62864 3.9647 

D 0.15187 3.0543 6.9005 

E 0.00099804 0.00093596 0.0010185 

Table 21. Calibration Coefficients for Path 1 Agent Mass-Flow Controller 

 MFC: Model 1359C, 0 SLM - 10 SLM, Path 1 

Gas 

Coefficient Carbon Dioxide Nitrogen Helium Argon 

A -0.0070237 -0.00010244 4.8531e-6 -4.3803e-5 

B 0.0091754 0.0022735 -6.8489e-5 0.00086595 

C -0.031546 -0.014304 -0.0041908 -0.00309 

D 0.72343 0.52598 0.36329 0.36215 

E -0.0024164 -0.001183 0.0017435 -0.00026244 

Table 22. Calibration Coefficients for Path 2 Agent Mass-Flow Controller

 MFC: Model 1359C, 0 SLM - 10 SLM, Path 2 

Gas 

Coefficient Carbon Dioxide Nitrogen Helium Argon 

A -0.00038376 -5.3406e-5 9.8721e-6 -2.656e-5 

B 0.0045127 0.0010618 -0.00033397 0.00044042 

C -0.0097097 -0.005722 0.0011492 8.3247e-5 

D 0.67999 0.50352 0.33335 0.34989 

E -0.0044515 -0.0040498 0.0031573 -0.0010613 
111

Qair + Qagent = Qexit,coflow ( 42 )

Qagent = XagentQexit,coflow ( 43 )

Qair X agent Qexit,coflow = (1− ) ( 44 )

Two mass-flow controllers were employed for the agent flow, as displayed in Figure 22. Therefore the 

Qagent was halved along two paths upstream of the MFC’s, Path 1 and Path 2, and then recombined 

downstream. The input for each agent MFC calibration curve was therefore one half of Qagent. 

2 , 1 , 2

agent

agent path agent path

Q Q = Q = ( 45 )

The ambient temperature and pressure were recorded for each test and were input into the control 

program as parameters. The following is an example calculation of the software algorithm used for 

controlling the fuel and oxidizer flows. The exit velocity for both the fuel and coflow is held constant at 

7.0 cm/s, while the coflow is diluted with nitrogen in volume fraction steps of 0.001 until the methane 

flame is extinguished. 

Experiment Constant Conditions

Fuel: Methane (CH4) 

Oxidizer: Air 

Agent: Nitrogen 

Uexit: 7.0 cm/s 

Xagent,o: 0.195 

Tamb: 295.4 K (22.2 o

C) 

Pamb: 100.0 kPa 

User Calculations

Actual volume flow rates: 

min

0.429 ,

L Qexit fuel =

min

33.52 ,

L Qexit coflow =

Standard volume flow rates: 

0.392 SLM

101325

100000

295.4

273.15 0.429 * ⎟ =

⎠

⎞ ⎜

⎝

⎛

⎟

⎠

⎞ ⎜

⎝

⎛ Qfuel =

30.6 SLM

101325

100000

295.4

273.15 33.52 * ⎟ =

⎠

⎞ ⎜

⎝

⎛

⎟

⎠

⎞ ⎜

⎝

⎛ Qcoflow =
112

Software Calculations:

Begin iterations 

For i = 0 to 30 

Fuel MFC set point voltage 

0.62864 (0.392) 3.0543 (0.392) 0.00093596 1.268 V

0.10513 (0.392) 0.47988 (0.392)

2

4 3

+ × + × + =

Vfuel = × − ×

Agent volume flow rate: 

0.195 30.6 5.97 SLM *

,

* Qagent = X agent i ×Qcoflow = × =

2.984 SLM

2

* 5.97 , 2* Qagent, path1 = Qagent path = =

Path 1 and 2 Agent MFC set point voltage 

0.014304 (2.984) 0.52598 2.984 0.001183 1.493 V

0.00010244 (2.984) 0.0022735 (2.984)

2

4 3

, 1

− × + × − =

Vagent path = − × + ×

0.005722 (2.984) 0.50352 2.984 0.0040498 1.471 V

5.3406 5 (2.984) 0.0010618 (2.984)

2

4 3

, 2

− × + × − =

Vagent path = − e − × + ×

Air volume flow rate: 

(1 ) (1 0.195) 30.607 24.64 SLM *

,

* Qair = − Xagent i ×Qcoflow = − × =

Air MFC set point voltage: 

0.0016515 (24.64) 0.15187 24.64 0.00099804 4.134 V

1.0937 6 (24.64) 6.7825 5 (24.64)

2

4 3

+ × + × + =

Vair = e − × − e − ×

Elapsed time of 40 seconds on software counter: 

Step increase of agent volume fraction: 

0.001 0.195 0.001 0.196 Xagent,i = Xagent,o + = + =

Return to Beginning of Software Calculations: 

Next i 

The algorithm continues to increment the agent volume fraction until the flame is extinguished, at which 

point the operator records the agent concentration and stops the program, or until 30 iterations has been 

executed and the program automatically shuts off. 
113

C. Uncertainty Analysis 

Goals were initially established to meter the flows sufficiently accurately to determine the agent volume 

fraction in air with an absolute uncertainty of ±0.01. Selection of mass-flow controllers having sufficient 

accuracy to meet this goal was therefore important. Volumes fractions were calculating using 

.

, 1 , 2

, 1 , 2

air agent path agent path

agent path agent path

agent Q Q Q

Q Q X

+ +

+ = ( 46 )

An uncertainty propagation analysis [173,174,175] was performed on the equation used to calculate the 

agent concentration. Equation 47 is a generalized form of the error propagation, where R is the calculated 

result that is a function of the independent variables z1, z2, ...., zn and the uncertainties of those 

independent variables are w1, w2, ....,w3, with wR being the uncertainty of the calculated result based on 

the uncertainties in the primary measurements. 

2

1

2 2

2

2

2

1

1 ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

+ + ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂

+ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

∂

∂ = n

n

R w

z

R

w

z

R

w

z

R

w K ( 47 )

Therefore, taking Xagent as the calculated result based on the independently measured volume flow rates, 

each with an associated uncertainty, the following equations are employed to estimate the uncertainty of 

the agent concentration. The result, Eq. 48, is the estimated uncertainty for the calculated agent 

concentration, 

( )2

, 1 , 2 air agent, path1 agent, path2

air

agent path

agent

agent path

agent

Q Q Q

Q

Q

X

Q

X

+ + = ∂

∂ = ∂∂

( )

( )2

, 1 , 2

, 1 , 2

air agent path agent path

agent path agent path

air

agent

Q Q Q

Q Q

Q

X

+ +

− + = ∂∂

( )

( ) . ( ) 2

1

4

, 1 , 2

2 2

, 1 , 2

2 2 2

, 1 , 2

⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

+ +

+ + + =

air agent path agent path

air Q Q agent path agent path Q

X Q Q Q

Q w w Q Q w

w agent path agent path air

agent ( 48 ) 

The MFC’s were calibrated within an uncertainty of ± 0.9 % (± 1 σ) for the volume flow rate 

measurement. This uncertainty is less than those reported by the manufacturer for the MFC. Therefore 

the standard uncertainty for MFC volume flow rate based on the NIST/BFRL calibration was applied in 

the uncertainty propagation to compute the agent concentration measurement uncertainty, Xagent w . 

Agent extinguishing concentrations were measured by recording the agent volume fraction at the moment 

the flame extinguished or at the onset of the lifting instability. Multiple measurements of the agent 

extinguishing concentration were made in order to provide a significant statistical sample. The 

measurements were conducted over multiple days and in two separate NIST/BFRL laboratories. The 

measured standard deviations included in Table 23 for the measurements, Xagent ext s , , capture the effects of 

a variable environment and contribute to the overall uncertainty of the agent extinguishing concentration 
114

Table 23. Agent Extinguishing Concentration Measurement Standard Deviation 

Methane Propane 

Agent Osc Ext Osc Ext 

Carbon Dioxide 0.001 - 0.004 0.001 

Nitrogen 0.002 0.002 0.005 0.008 

Helium 0.001 0.001 0.003 0.002 

Argon 0.001 - 0.002 0.003 

Number of samples ≥ 6 

Table 24. Uncertainty Budget – Agent Extinguishing Volume Fraction 

Source of Uncertainty Basis Standard 

Uncertainty 

Type A / B 

Evaluation [173]

Xagent w Uncertainty 

Propagation (Eq. 48) ±0.002 A 

Xagent ext s , Statistical Table 23 

(e.g.= 0.002) A 

Combined standard uncertainty: 2 2 2 2

, , , ( ) 0.002 Xagent Xagent ext Xagent ext c agent ext u X = w + s = + s

measurement. Therefore, both the agent concentration measurement uncertainty and the agent 

extinguishing concentration measurement standard deviation are combined to give the resultant combined 

standard uncertainties, uc, for the agent extinguishing volume fraction measurements. The overall 

uncertainty budget is summarized in Table 24. 

In order to obtain a confidence level of 95 %, the combined expanded uncertainty, U, is given by U = 2uc. 

Values of U have been calculated for the base flame measurements and are included in Table 12. 
115

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