PDF methods for turbulent reactive flows

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Abstract

The aim of the methods described is to calculate the properties of turbulent reactive flow fields. At each point in the flow field, a complete statistical description of the state of the fluid is provided by the velocity-composition joint pdf. This is the joint probability density function (pdf) of the three components of velocity and of the composition variables (species mass fractions and enthalpy). The principal method described is to solve a modelled transport equation for the velocity-composition joint pdf. For a variable-density flow with arbitrarily complex and nonlinear reactions, it is remarkable that in this equation the effects of convection, reaction, body forces and the mean pressure gradient appear exactly and so do not have to be modelled. Even though the joint pdf is a function of many independent variables, its transport equation can be solved by a Monte Carlo method for the inhomogeneous flows of practical interest. A second method that is described briefly is to solve a modelled transport equation for the composition joint pdf.

The objective of the paper is to provide a comprehensive and understandable of the theoretical foundations of the pdf approach.

References (131)

  • W.P. Jones et al.

    Combust. Flame

    (1982)
  • F.C. Lockwood et al.

    Combust. Flame

    (1975)
  • C. Dopazo et al.

    Acta astronaut.,

    (1974)
  • S.B. Pope

    Combust. Flame

    (1976)
  • S.B. Pope
  • L.A. Spielman et al.

    Chem. Engng Sci.,

    (1965)
  • R.C. Flagan et al.

    Combust. Flame

    (1974)
  • M.C. Drake et al.
  • D.B. Spalding

    Chem. Engng Sci.

    (1971)
  • S.B. Pope

    Combust. Flame

    (1979)
  • P.A. Libby et al.

    A. Rev. Fluid Mech.,

    (1976)
  • H.W. Liepmann

    Am. Sci.,

    (1979)
  • B.E. Launder et al.

    Mathematical Models of Turbulence

    (1972)
  • J.L. Lumley

    Adv. appl. Mech.,

    (1978)
  • W.R. Hawthorne et al.
  • K.N.C. Bray et al.

    University of Southampton Report AASU335

    (1974)
  • R.P. Rhodes

    Turbulent Mixing in Nonreactive and Reactive Flows

  • S.B. Pope

    J. Non-Equilib. Thermodyn.,

    (1979)
  • S.B. Pope

    Phil. Trans. R. Soc. Lond.,

    (1979)
  • S.B. Pope
  • T.S. Lundgren

    Phys. Fluids

    (1969)
  • B.E. Launder et al.

    J. Fluid Mech.,

    (1975)
  • C. Dopazo et al.

    Phys. Fluids

    (1975)
  • C. Dopazo et al.

    Combust. Sci. Technol.,

    (1976)
  • J. Janicka et al.
  • J. Janicka et al.

    J. Non-equilib. Thermodyn.,

    (1978)
  • T.V. Nguyen et al.

    Combust. Sci. Technol.,

    (1984)
  • D.G. McNutt
  • S.V. Sherikar et al.
  • P. Givi et al.

    Combust. Sci. Technol.,

    (1984)
  • S.B. Pope

    Combust. Sci. Technol.,

    (1981)
  • C. Dopazo

    Phys. Fluids

    (1987)
  • W. Kollmann et al.

    Phys. Fluids

    (1982)
  • W. Kollmann et al.
  • M.-Z. Wu et al.

    Combust. Sci. Technol.,

    (1982)
  • D.C. Handscomb et al.

    Monte Carlo Methods

    (1965)
  • G. Dahlquist et al.

    Numerical Methods

    (1974)
  • S.B. Pope

    MIT Report EL-80-012

    (1980)
  • S.B. Pope
  • S.B. Pope

    AIAA J.

    (1984)
  • M.S. Anand et al.
  • S.B. Pope et al.
  • Pope, S. B. (in preparation)...
  • V.A. Frost
  • Cited by (0)

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