Current Kinetic Modeling Techniques for Continuous Flow Combustors

  • A. M. Mellor


Analytical models existing in the open literature for gas turbine continuous flow combustors are reviewed and discussed from the point of view of predictions of pollutant emissions. Particular emphasis is placed on the kinetic aspects of the models involving liquid fuel droplet evaporation and/or combustion and homogeneous chemical kinetics for hydrocarbon/air combustion. A brief summary of the various flow models is also included. Comparisons with data obtained from experimental or practical combustors are made where appropriate, and suggestions for further research are listed.


Equivalence Ratio Recirculation Zone Partial Equilibrium Droplet Evaporation Fuel Vapor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



transfer number for droplet evaporation (i=e) or combustion (i=c)


gaseous specific heat at constant pressure, cal/g °K


instantaneous droplet diameter, cm


initial droplet diameter, cm


equivalence ratio distribution function


stoichiometric gravimetric oxidizer/fuel ratio


gaseous thermal conductivity, cal/cm sec °K


sensible enthalpy of liquid fuel from 15° C to temperature T and latent heat of evaporation at T, cal/g

mass flow rate, g/sec


pressure, atm


Prandtl number


heat of combustion, cal/g


universal gas constant, cal/mole


recirculating flowrate ratio


Reynolds number


Schmidt number


mixing parameter of Fletcher and Heywood (11)


time, sec


temperature of ambient gas, °K


boiling point temperature of liquid fuel at pressure p, °K


initial unburned mixture temperature, °K


droplet velocity relative to gas, m/sec


volume, cm3


ambient oxidizer mass fraction


evaporation coefficient in forced convection for droplet evaporation (i=e) or combustion (i=c), cm2/sec


evaporation coefficient in stagnant ambient for droplet evaporation (i=e) or combustion (i=c), cm2/sec


gaseous viscosity, g/cm sec


gaseous density, g/cm3


density of liquid fuel at T, g/cm3


lifetime of droplet in evaporation (i=e) or with combustion (i=c), sec


equivalence ratio


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  1. 1.
    Anon., “Nature and Control of Aircraft Engine Exhaust Emissions,” Northern Research Eng. Corp. Report No. 1134–1 (PB 187–711), 1968.Google Scholar
  2. 2.
    K. H. Homann and H. G. Wagner, “Chemistry of Carbon Formation in Flames,” Proc. Roy. Soc, Vol. 307A, 1968, pp. 141–152.Google Scholar
  3. 3.
    B. B. Chakraborty and R. Long, “The Formation of Soot and Polycyclic Aromatic Hydrocarbons in Diffusion Flames. III. Effect of Additions of Oxygen to Ethylene and Ethane Respectively as Fuels”, Comb. Flame, Vol. 12, 1968, pp. 469–476.CrossRefGoogle Scholar
  4. 4.
    J. B. Howard, “On the Mechanism of Carbon Formation in Flames,” Twelfth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1969, pp. 877–887.Google Scholar
  5. 5.
    T. Durrani, “The Control of Atmospheric Pollution from Gas Turbine Engines,” SAE Paper 680347, 1968.CrossRefGoogle Scholar
  6. 6.
    J. J. Faitani, “Smoke Reduction in Jet Engines through Burner Design,” SAE Paper 680348, 1968.CrossRefGoogle Scholar
  7. 7.
    K. Gradon and S. C. Miller, “Combustion Development on the Rolls-Royce Spey Engine,” Combustion in Advanced Gas Turbine Systems, Pergamon, Oxford, 1968, pp. 45–76.Google Scholar
  8. 8.
    A. H. Lefebvre, “Design Considerations in Advanced Gas Turbine Combustion Chambers,” Combustion in Advanced Gas Turbine Systems, Pergamon, Oxford, 1968, pp. 3–19.Google Scholar
  9. 9.
    B. Toone, “A Review of Aero Engine Smoke Emission,” Combustion in Advanced Gas Turbine Systems, Pergamon, Oxford, 1968, pp. 271–296.Google Scholar
  10. 10.
    L. H. Linden and J. B. Heywood, “Smoke Emission from Jet Engines,” Comb. Sci. Tech., Vol. 2, 1971, pp. 401–411.CrossRefGoogle Scholar
  11. 11.
    R. S. Fletcher and J. B. Heywood, “A Model for Nitric Oxide Emissions from Aircraft Gas Turbine Engines,” AIAA Paper No. 71–123, 1971.Google Scholar
  12. 12.
    R. Roberts, L. D. Aceto, R. Kollrack, J. M. Bonnell, and D. P. Teixeira, “An Analytical Model for Nitric Oxide Formation in a Gas Turbine Combustion Chamber,” AIAA Paper No. 71–715, 1971.Google Scholar
  13. 13.
    D. C. Hammond, Jr. and A. M. Mellor, “A Preliminary Investigation of Gas Turbine Combustor Modelling,” Comb. Sci. Tech., Vol. 2, 1970, pp. 67–80.CrossRefGoogle Scholar
  14. 14.
    D. C. Hammond, Jr. and A. M. Mellor, “Analytical Calculations for the Performance and Pollutant Emissions of Gas Turbine Combustors,” Revised Version of AIAA Paper No. 71–711, 1971, Vol.4, 1971, pp. 101–112.Google Scholar
  15. 15.
    D. T. Pratt, B. R. Bowman, C. T. Crowe, and T. C. Sonnichsen, “Prediction of Nitric Oxide Formation in Turbojet Engines by PSR Analysis,” AIAA Paper No. 71–713, 1971.Google Scholar
  16. 16.
    R. Edelman and C. Economos, “A Mathematical Model for Jet Engine Combustor Pollutant Emissions,” AIAA Paper No. 71–714, 1971.Google Scholar
  17. 17.
    J. B. Heywood, J. A. Fay, and L. H. Linden, “Jet Aircraft Air Pollutant Production and Disperson,” AIAA Paper No. 70–115, 1970.Google Scholar
  18. 18.
    J. B. Heywood, “Gas Turbine Combustor Modeling for Calculating Nitric Oxide Emissions,” AIAA Paper No. 71–712, 1971.Google Scholar
  19. 19.
    D. B. Spalding, “Mathematical Models of Continuous Combustion,” Emissions from Continuous Combustion Systems, Plenum, New York, 1972.Google Scholar
  20. 20.
    Anon, “Computer Program for the Analysis of Annular Combustors. Vol. I: Calculational Procedures,” Northern Research Eng. Corp. Report No. 1111–1 (NASA Cr 72374), 1968.Google Scholar
  21. 21.
    R. R. Tacina and J. Grobman, “An Analysis of Total Pressure Loss and Airflow Distribution for Annular Gas Turbine Combustors,” NASA TN D-5385, 1969.Google Scholar
  22. 22.
    D. C. Hammond, Jr. and A. M. Mellor, “An Investigation of Gas Turbine Combustors with High Inlet Air Temperatures. Part I: Combustor Modelling,” U.S. Army Tank-Automotive Command Tech. Rep. 11321, 1971.Google Scholar
  23. 23.
    O. Levenspiel, “Chemical Reaction Engineering,” Wiley, New York, 1962.Google Scholar
  24. 24.
    H. C. Hottel, G. C. Williams, and A. H. Bonnell, “Application of Stirred Reactor Theory to the Prediction of Combustor Performance,” Comb. Flame, Vol. 2, 1958, pp. 13–34.CrossRefGoogle Scholar
  25. 25.
    A. H. Lefebvre, “Theoretical Aspects of Gas Turbine Combustion Performance,” Note Aero. No. 163, College of Aeronautics, Cranfield, 1966.Google Scholar
  26. 26.
    P. G. Parikh, R. F. Sawyer, and A. L. London, “Pollutants from Methane Fueled Gas Turbine Combustion,” College of Eng. Rep. No. TS-70–15, U. Cal. Berkeley, 1971.Google Scholar
  27. 27.
    J. P. Longwell, “Combustion of Liquid Fuels,” Combustion Processes, Princeton Univ. Press, Princeton, 1956, pp. 407–443.Google Scholar
  28. 28.
    B. V. Raushenbakh, S. A. Belyy, I. V. Bespalov, V. Ya. Borodachev, M. S. Volynskiy, and A. G. Prudnikov, “Physical Principles of the Working Process in Combustion Chambers of Jet Engines,” English Translation, Wright-Patterson Air Force Base FTD-MT-65–78, 1964.Google Scholar
  29. 29.
    D. B. Spalding, “The Combustion of Liquid Fuels,” Fourth Symposium (International) on Combustion, Williams and Wilkins, Baltimore, 1953, pp. 847–864.Google Scholar
  30. 30.
    D. B. Spalding, “Some Fundamentals of Combustion,” Butterworths, London, 1955.Google Scholar
  31. 31.
    H. Wise, J. Lorell, and B. J. Wood, “The Effects of Chemical and Physical Parameters on the Burning Rate of a Liquid Droplet,” Fifth Symposium (International) on Combustion, Reinhold, New York, 1955, pp. 132–141.Google Scholar
  32. 32.
    B. J. Wood, W. A. Rosser, Jr., and H. Wise, “Combustion of Fuel Droplets,” AIAA J., Vol. 1, 1963, pp. 1076–1081.CrossRefGoogle Scholar
  33. 33.
    F. A. Williams, “Combustion Theory,” Addison-Wesley, Reading, 1965.Google Scholar
  34. 34.
    W. E. Ranz and W. R. Marshall, Jr., “Evaporation from Drops, ”Chem. Eng. Prog., Vol. 48, 1952, pp. 141–146 (Part I) andGoogle Scholar
  35. 34a.
    W. E. Ranz and W. R. Marshall, Jr., “Evaporation from Drops, ”Chem. Eng. Prog., Vol. 48, 1952, 173–180 (Part II).Google Scholar
  36. 35.
    P. Eisenklam, S. A. Arunachalam, and J. A. Weston, “Evaporation Rates and Drag Resistance of Burning Drops,” Eleventh Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1967, pp. 715–728.Google Scholar
  37. 36.
    A. H. Lefebvre, “Factors Controlling Gas Turbine Combustor Performance at High Pressure, ” Combustion in Advanced Gas Turbine Systems, Pergamon, Oxford, 1968, pp. 211–226.Google Scholar
  38. 37.
    H. C. Barnett and R. R. Hibbard, “Properties of Aircraft Fuels, “NACA TN 3276, 1956.Google Scholar
  39. 38.
    D. R. Stull, Editor, “JANAF Thermochemical Tables,” PB 168 370, 1965.Google Scholar
  40. 39.
    W. M. Kays, “Convective Heat and Mass Transfer, ” McGraw-Hill, New York, 1966.Google Scholar
  41. 40.
    D. S. Smith, R. F. Sawyer, and E. S. Starkman, “Oxides of Nitrogen from Gas Turbines,” Air Poll. Control Assn. J., Vol. 18, 1968, pp. 30–35.CrossRefGoogle Scholar
  42. 41.
    R. F. Sawyer and E. S. Starkman, “Gas Turbine Exhaust Emissions, ” SAE Paper 680462, 1968.CrossRefGoogle Scholar
  43. 42.
    R. F. Sawyer, D. P. Teixeira, and E. S. Starkman, “Air Pollution Characteristics of Gas Turbine Engines,”ASME Trans., J. Eng. Power, Vol. 91, 1969, pp. 290–296.CrossRefGoogle Scholar
  44. 43.
    E. S. Starkman, Y. Mizutani, R. F. Sawyer, and D. P. Teixeira, “The Role of Chemistry in Gas Turbine Emissions,” ASME Paper 70-GT-81, 1970.Google Scholar
  45. 44.
    R. B. Edelman and O. F. Fortune, “A Quasi-Global Chemical Kinetic Model for the Finite Rate Combustion of Hydrocarbon Fuels, with Application to Turbulent Burning and Mixing in Hypersonic Engines and Nozzle,” AIAA Paper No. 69–86, 1969.Google Scholar
  46. 45.
    D. J. Seery and C. T. Bowman, “An Experimental and Analytical Study of Methane Oxidation behind Shock Waves,” Comb. Flame, Vol. 14, 1970, pp. 37–48.CrossRefGoogle Scholar
  47. 46.
    P. J. Marteney, “Analytical Study of the Kinetics of Nitrogen Oxide in Hydrocarbon-Air Combustion,” Comb. Sci. Tech., Vol. 1, 1970, pp. 461–469.CrossRefGoogle Scholar
  48. 47.
    D. C. Hammond, Jr. and A. M. Mellor, Unpublished Data.Google Scholar
  49. 48.
    Ya. B. Zeldovich, P. Ya. Sadovnikov, and D. A. Frank-Kamenetskii, “Oxides of Nitrogen in Combustion,” Acad, Sci. USSR, Inst. Chem. Phys., Moscow-Leningrad (M. Shelef, Translator), 1947.Google Scholar
  50. 49.
    C. T. Bowman, “Investigation of Nitric Oxide Formation Kinetics in Combustion Processes: the Hydrogen-Oxygen-Nitrogen Reaction,” Comb. Sci. Tech., Vol. 3, 1971, pp. 37–45.CrossRefGoogle Scholar
  51. 50.
    W. Cornelius and W. R. Wade, “The Formation and Control of Nitric Oxide in a Regenerative Gas Turbine Burner,” SAE Paper 700708, 1970.CrossRefGoogle Scholar
  52. 51.
    G. A. Lavoie, “Spectroscopic Measurements of Nitric Oxide in Spark Ignition Engines,” Comb. Flame, Vol. 15, 1970, pp. 97–108.CrossRefGoogle Scholar
  53. 52.
    J. B. Heywood, S. M. Mathews, and B. Owen, “Predictions of Nitric Oxide Concentrations in a Spark-Ignition Engine Compared with Exhaust Measurements,” SAE paper 710011, 1971.CrossRefGoogle Scholar
  54. 53.
    H. K. Newhall and S. M. Shahed, “Kinetics of Nitric Oxide Formation in High Pressure Flames,” Thirteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1971, pp. 381–389.Google Scholar
  55. 54.
    C. T. Bowman and D. J. Seery, “Investigation of NO Formation Kinetics in Combustion Processes; the Methane-Oxygen-Nitrogen Reaction,” Emissions from Continuous Combustion Systems, Plenum, New York, 1972.Google Scholar
  56. 55.
    C. P. Fenimore, “Formation of Nitric Oxide in Premixed Hydrocarbon Flames,” Thirteenth Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, 1971, pp. 373–380.Google Scholar
  57. 56.
    R. B. Edelman, General Applied Science Laboratories, Personal Communication, July 15, 1971.Google Scholar
  58. 57.
    R. E. George, J. A. Verssen, and R. L. Chass, “Jet Aircraft: a Growing Pollution Source,” Air Poll. Control Assn. J., Vol. 19, 1969, pp. 847–855.CrossRefGoogle Scholar
  59. 58.
    K. W. Porter and L. H. Williams, “Gas Turbines for Emergency Vehicles,” SAE Paper 650460, 1965.CrossRefGoogle Scholar
  60. 59.
    W. Cornelius, D. L. Stivender, and R. E. Sullivan, “A Combustion System for a Vehicular Regenerative Gas Turbine Featuring Low Air Pollutant Emissions,” SAE Paper 670936, 1967.CrossRefGoogle Scholar
  61. 60.
    M. W. Korth and A. H. Rose, Jr. “Emissions from a Gas Turbine Automobile,” SAE Paper 680402, 1968.Google Scholar
  62. 61.
    F. V. Bracco, “A Model for the Diesel Engine Combustion and NO Formation,” Paper Presented at the 1971 Meeting, Central States Section/The Combustion Institute, 1971.Google Scholar
  63. 62.
    J. A. Nicholls, “Aerodynamic Shattering and Combustion of Fuel Drops and Films in I. C. Engines,” Paper Presented at the 1971 Meeting, Central States Section/The Combustion Institute, 1971.Google Scholar
  64. 63.
    D. L. Baulch, D. D. Drysdale, D. G. Horne, and A. C. Lloyd, “Critical Evaluation of Rate Data for Homogeneous, Gas Phase Reactions of Interest in High-Temperature Systems. Parts 1 through 4,” Dept. of Phys. Chem., The University, Leeds, May 1968 — Dec. 1969.Google Scholar

Copyright information

© Springer Science+Business Media New York 1972

Authors and Affiliations

  • A. M. Mellor
    • 1
  1. 1.Purdue UniversityLafayetteIndiana

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