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Results of a Study of Several Transport Algorithms for Premixed, Laminar Steady-State Flames

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Numerical Methods in Laminar Flame Propagation

Part of the book series: Notes on Numerical Fluid Mechanics ((NONUFM,volume 6))

Abstract

Our model /1/ of a premixed, steady-state flame includes detailed elementary chemical reactions and requires as input not only the kinetics information (of our immediate interest), but also thermodynamic and transport data. Fortunately for the types of chemical species we are interested in, the thermodynamics input is by and large well defined /2/, /3/. In addition, while some transport coefficients are only well defined through low temperature (< 1000 K) measurements /4/, the theory is sufficiently developed to allow reasonable estimates to be made at higher temperatures /5/. A theory has been developed for multi-component mixtures /5/ – /9/, but it is computationally cumbersome. To circumvent this, previous workers have generally employed some level of simplification /10/ – /20/.

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References

  1. J.M. Heimerl and T.P. Coffee, Combust. Flame 39 301–315 (1980).

    Google Scholar 

  2. G.S. Gordon and B.J. McBride, NASA-SP-273, 1971, Computer Program for Calculation of Complex Chemical Equilibrium Compositions, Rocket Performance, Incident and Reflected Shocks, and Chapman-Jouquet Detonations, (1976 program version).

    Google Scholar 

  3. D.R. Stull and H. Prophet, JANNAF Thermochemical Tables 2nd Edition, NSRDS-NBS-37, June 1971.

    Google Scholar 

  4. Y.S. Touloukian, P.E. Liley and S.C. Saxena, Thermophysi-cal Properties of Matter Vol. 3, Thermal Conductivity (Nonmetallic Liquids and Gases), IFI/Plenum, NY-Washington (1970).

    Google Scholar 

  5. J.0. Hirshfelder, C.F. Curtis and R.B. Bird, “Molecular Theory of Gases and Liquids”, 2nd printing, corrected, with notes, John Wiley and Sons, NY, 1960.

    Google Scholar 

  6. C.S. Wang Chang, G.E. Uhlenbeck and J. deBoer, Studies in Statistical Mechanics Vol. 2, John Wiley and Sons, NY, 1964.

    Google Scholar 

  7. L. Monchick, K.S. Yun and E.A. Mason, “Formal Kinetic Theory of Transport Phenomena in Polyatomic Gas Mixtures”, J. Chem. Phys. 32, 654–669 (1963).

    Google Scholar 

  8. L. Monchick, A.N.G. Pereira and E.A. Mason, “Heat Conduc-tivity in Polyatomic and Polar Gases and Gas Mixtures”, J. Chem Phys. 42, 3241–3256 (1965).

    Article  Google Scholar 

  9. L. Monchick, R.J. Munn and E.A. Mason, “Thermal Diffusion in Polyatomic Gases: A Generalized Stefan-Maxwell Diffu-sion Equation”, J. Chem. Phys. 45, 3051–3058 (1966).

    Article  Google Scholar 

  10. J. Warnatz, Ber. Bunsenges. Phys. Chem. 1978, 82, 193200, Calculation of the Structure of Laminar Flat Flames I: Flame Velocity of Freely Propagating Ozone Decomposition Flames.

    Google Scholar 

  11. G. Dixon-Lewis, et al., “Flame Structure and Flame Reac-tion Kinetics”, Proc. R. Soc., London A 317, 235–263 (1970); A 331, 571–584 (1973); and A 346, 261–278 (1975).

    Article  Google Scholar 

  12. G. Dixon-Lewis, “Kinetic Mechanism, Structure and Properties of Premixed Flames in Hydrogen-Oxygen-Nitrogen Mixtures”, Phil. Trans. R. Soc., London, 292, 45–99 (1979).

    Article  Google Scholar 

  13. G. Tsatsaronis, “Prediction of Propagating Laminar Flames in Methane, Oxygen, Nitrogen Mixtures”, Combust. and Flame 33, 217–239 (1978).

    Article  Google Scholar 

  14. D.B. Spalding and P.L. Stephenson, “Laminar Flame Propagation in Hydrogen and Bromine Mixtures”, Proc. R. Soc., London A 324, 315–337 (1971).

    Google Scholar 

  15. P.L. Stephenson and R.G. Taylor, “Laminar Flame Propaga-tion in Hydrogen, Oxygen, Nitrogen Mixtures”, Combust. and Flame 20, 231–244 (1973).

    Article  Google Scholar 

  16. L.D. Smoot, W.C. Hecker and G.A. Williams, “Prediction of Propagating Methane-Air Flames”, Combust. and Flame 26, 323–342 (1976). — •

    Google Scholar 

  17. J. Warnatz, “Calculation of the Structure of Laminar Flat Flames II; Flame Velocity and Structure of Freely Propa-gating hydrogen-Oxygen and Hydrogen-Air Flames”, Ber. Bunsenges. Phys. Chem. 82, 643–649 (1978).

    Article  Google Scholar 

  18. D.B. Spalding, P.L. Stephenson and R.G. Taylor, “A Calculation Procedure for the Prediction of Laminar Flame Speeds”, Combust. and Flame 17, 55–64 (1971).

    Article  Google Scholar 

  19. L. Bledjian, “Computation of Time-Dependent Laminar Flame Structure”, Combust. and Flame 20, 5–17 (1973).

    Google Scholar 

  20. E. Cramarossa and G. Dixon-Lewis, “Ozone Decomposition in Relation to the Problem of the Existance of Steady-State Flames”, Combust. and Flame 16, 243–251 (1971).

    Article  Google Scholar 

  21. T.P. Coffee and J.M. Heimerl, “Transport Algorithms for Premixed, Laminar Steady-State Flames”, Combustion and Flame 43, 273–289 (1981).

    Google Scholar 

  22. T.P. Coffee and J.M. Heimerl, “A Method for Computing the Flame Speed for a Laminar, Premixed, One-Dimensional Flame’; BRL Technical Report, ARBRL-TR-02212, Jan. 1980.

    Google Scholar 

  23. T.P. Coffee, “A Computer Code for the Solution of the Equations Governing a Laminar, Premixed. One-Dimensional Flame’; BRL Memorandum Report, in press.

    Google Scholar 

  24. T.P. Coffee and J.M. Heimerl, “Transport Algorithms for Premixed Laminar Steady-State Flames”, BRL Technical Report, ARBRL-TR-02302, March 1981. Also see Ref. 21.

    Google Scholar 

  25. G. Dixon-Lewis, “Flame Structure and Flame Reaction Kinetics II. Transport Phenomena in Multicomponent Systems”, Proc. R. Soc., London A 307, 111–135 (1968).

    Article  Google Scholar 

  26. J.0. Hirshfelder, “Heat Conductivity in Polyatomic, Electronically Excited, or Chemical Reacting Mixtures III”, Sixth International Combustion Symposium, Reinhold Publishing Corporation, NY, 351–366 (1957).

    Google Scholar 

  27. J.0. Hirshfelder and C.F. Curtiss, “Theory of Propagation of Flames Part I: General Equations”, Third International Combustion Symposium Williams and Wilkins Co., Baltimore, 121–127 (1949).

    Google Scholar 

  28. E.S. Oran and J.P. Boris, “Detailed Modeling of Combustion Systems”, Proj. Energy Combust. Sci. 7, 1–71 (1981).

    Google Scholar 

  29. E.A. Mason and S.C. Saxena, “Approximate Formula for the Thermal Conductivity of Gas Mixtures”, Phys. Fluids 1, 361–369 (1958).

    Article  MathSciNet  Google Scholar 

  30. J.H. Burgoyne and F. Weinberg, “A Method of Analysis of a Plane Combustion Wave”, Fourth Symposium on Combustion Williams and Wilkins Co., Baltimore, 294–302 (1953).

    Google Scholar 

  31. R.B. Bird, W.S. Stewart and E.N. Lightfoot, “Transport Phenomena”, John Wiley and Sons, NY, 1960.

    Google Scholar 

  32. S. Chapman and T.G. Cowling, The Mathematical Theory of Non-Uniform Gases third edition, Cambridge University Press (1970).

    Google Scholar 

  33. Suggestion of R.D. Reitz, Princeton University, 1981.

    Google Scholar 

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© 1982 Springer Fachmedien Wiesbaden

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Heimerl, J.M., Coffee, T.P. (1982). Results of a Study of Several Transport Algorithms for Premixed, Laminar Steady-State Flames. In: Peters, N., Warnatz, J. (eds) Numerical Methods in Laminar Flame Propagation. Notes on Numerical Fluid Mechanics, vol 6. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14006-1_7

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  • DOI: https://doi.org/10.1007/978-3-663-14006-1_7

  • Publisher Name: Vieweg+Teubner Verlag, Wiesbaden

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