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Current Kinetic Modeling Techniques for Continuous Flow Combustors

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Emissions from Continuous Combustion Systems

Abstract

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.

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Abbreviations

Bi :

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

Cp :

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

d:

instantaneous droplet diameter, cm

do :

initial droplet diameter, cm

f(ø) :

equivalence ratio distribution function

i:

stoichiometric gravimetric oxidizer/fuel ratio

k:

gaseous thermal conductivity, cal/cm sec °K

L:

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

ṁ:

mass flow rate, g/sec

p:

pressure, atm

Pr:

Prandtl number

Q:

heat of combustion, cal/g

R:

universal gas constant, cal/mole

°K:

recirculating flowrate ratio

Re:

Reynolds number

Sc:

Schmidt number

so :

mixing parameter of Fletcher and Heywood (11)

t:

time, sec

T:

temperature of ambient gas, °K

Tℓ :

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

To :

initial unburned mixture temperature, °K

u:

droplet velocity relative to gas, m/sec

V:

volume, cm3

yox :

ambient oxidizer mass fraction

λi :

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

λoi :

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

μ:

gaseous viscosity, g/cm sec

ρ:

gaseous density, g/cm3

ρ ℓ :

density of liquid fuel at Tℓ, g/cm3

τ i :

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

ϕ:

equivalence ratio

References

  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. 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. 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.

    Article  CAS  Google Scholar 

  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. T. Durrani, “The Control of Atmospheric Pollution from Gas Turbine Engines,” SAE Paper 680347, 1968.

    Book  Google Scholar 

  6. J. J. Faitani, “Smoke Reduction in Jet Engines through Burner Design,” SAE Paper 680348, 1968.

    Book  Google Scholar 

  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. 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. B. Toone, “A Review of Aero Engine Smoke Emission,” Combustion in Advanced Gas Turbine Systems, Pergamon, Oxford, 1968, pp. 271–296.

    Google Scholar 

  10. L. H. Linden and J. B. Heywood, “Smoke Emission from Jet Engines,” Comb. Sci. Tech., Vol. 2, 1971, pp. 401–411.

    Article  CAS  Google Scholar 

  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. 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. 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.

    Article  CAS  Google Scholar 

  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.

    CAS  Google Scholar 

  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. R. Edelman and C. Economos, “A Mathematical Model for Jet Engine Combustor Pollutant Emissions,” AIAA Paper No. 71–714, 1971.

    Google Scholar 

  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. J. B. Heywood, “Gas Turbine Combustor Modeling for Calculating Nitric Oxide Emissions,” AIAA Paper No. 71–712, 1971.

    Google Scholar 

  19. D. B. Spalding, “Mathematical Models of Continuous Combustion,” Emissions from Continuous Combustion Systems, Plenum, New York, 1972.

    Google Scholar 

  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. 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. 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. O. Levenspiel, “Chemical Reaction Engineering,” Wiley, New York, 1962.

    Google Scholar 

  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.

    Article  CAS  Google Scholar 

  25. A. H. Lefebvre, “Theoretical Aspects of Gas Turbine Combustion Performance,” Note Aero. No. 163, College of Aeronautics, Cranfield, 1966.

    Google Scholar 

  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. J. P. Longwell, “Combustion of Liquid Fuels,” Combustion Processes, Princeton Univ. Press, Princeton, 1956, pp. 407–443.

    Google Scholar 

  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. D. B. Spalding, “The Combustion of Liquid Fuels,” Fourth Symposium (International) on Combustion, Williams and Wilkins, Baltimore, 1953, pp. 847–864.

    Google Scholar 

  30. D. B. Spalding, “Some Fundamentals of Combustion,” Butterworths, London, 1955.

    Google Scholar 

  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. B. J. Wood, W. A. Rosser, Jr., and H. Wise, “Combustion of Fuel Droplets,” AIAA J., Vol. 1, 1963, pp. 1076–1081.

    Article  Google Scholar 

  33. F. A. Williams, “Combustion Theory,” Addison-Wesley, Reading, 1965.

    Google Scholar 

  34. W. E. Ranz and W. R. Marshall, Jr., “Evaporation from Drops, ”Chem. Eng. Prog., Vol. 48, 1952, pp. 141–146 (Part I) and

    CAS  Google Scholar 

  35. W. E. Ranz and W. R. Marshall, Jr., “Evaporation from Drops, ”Chem. Eng. Prog., Vol. 48, 1952, 173–180 (Part II).

    CAS  Google Scholar 

  36. 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. 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. H. C. Barnett and R. R. Hibbard, “Properties of Aircraft Fuels, “NACA TN 3276, 1956.

    Google Scholar 

  39. D. R. Stull, Editor, “JANAF Thermochemical Tables,” PB 168 370, 1965.

    Google Scholar 

  40. W. M. Kays, “Convective Heat and Mass Transfer, ” McGraw-Hill, New York, 1966.

    Google Scholar 

  41. 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.

    Article  CAS  Google Scholar 

  42. R. F. Sawyer and E. S. Starkman, “Gas Turbine Exhaust Emissions, ” SAE Paper 680462, 1968.

    Book  Google Scholar 

  43. 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.

    Article  CAS  Google Scholar 

  44. 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. 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. 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.

    Article  CAS  Google Scholar 

  47. P. J. Marteney, “Analytical Study of the Kinetics of Nitrogen Oxide in Hydrocarbon-Air Combustion,” Comb. Sci. Tech., Vol. 1, 1970, pp. 461–469.

    Article  CAS  Google Scholar 

  48. D. C. Hammond, Jr. and A. M. Mellor, Unpublished Data.

    Google Scholar 

  49. 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. 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.

    Article  CAS  Google Scholar 

  51. W. Cornelius and W. R. Wade, “The Formation and Control of Nitric Oxide in a Regenerative Gas Turbine Burner,” SAE Paper 700708, 1970.

    Book  Google Scholar 

  52. G. A. Lavoie, “Spectroscopic Measurements of Nitric Oxide in Spark Ignition Engines,” Comb. Flame, Vol. 15, 1970, pp. 97–108.

    Article  CAS  Google Scholar 

  53. 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.

    Book  Google Scholar 

  54. 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. 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. 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. R. B. Edelman, General Applied Science Laboratories, Personal Communication, July 15, 1971.

    Google Scholar 

  58. 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.

    Article  Google Scholar 

  59. K. W. Porter and L. H. Williams, “Gas Turbines for Emergency Vehicles,” SAE Paper 650460, 1965.

    Book  Google Scholar 

  60. 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.

    Book  Google Scholar 

  61. M. W. Korth and A. H. Rose, Jr. “Emissions from a Gas Turbine Automobile,” SAE Paper 680402, 1968.

    Google Scholar 

  62. 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. 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. 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 

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Authors and Affiliations

  1. Purdue University, Lafayette, Indiana

    A. M. Mellor

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Editors and Affiliations

  1. General Motors Research Laboratories, USA

    Walter Cornelius  & William G. Agnew  & 

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Mellor, A.M. (1972). Current Kinetic Modeling Techniques for Continuous Flow Combustors. In: Cornelius, W., Agnew, W.G. (eds) Emissions from Continuous Combustion Systems. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1998-6_2

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  • DOI: https://doi.org/10.1007/978-1-4684-1998-6_2

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-2000-5

  • Online ISBN: 978-1-4684-1998-6

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