A discrete probability function method for the equation of radiative transfer

https://doi.org/10.1016/0022-4073(93)90089-ZGet rights and content

Abstract

A discrete probability function (DPF) method for the equation of radiative transfer is derived. The DPF is defined as the integral of the probability density function (PDF) over a discrete interval. The derivation allows the evaluation of the DPF of intensities leaving desired radiation paths including turbulence-radiation interactions without the use of computer intensive stochastic methods. The DPF method has a distinct advantage over conventional PDF methods since the creation of a partial differential equation from the equation of transfer is avoided. Further, convergence of all moments of intensity is guaranteed at the basic level of simulation unlike the stochastic method where the number of realizations for convergence of higher order moments increases rapidly. The DPF method is described for a representative path with approximately integral-length scale-sized spatial discretization. The results show good agreement with measurements in a propylene/air flame except for the effects of intermittency resulting from highly correlated realizations. The method can be extended to the treatment of spatial correlations as described in the Appendix. However, information regarding spatial correlations in turbulent flames is needed prior to the execution of this extension.

References (19)

  • R. Viskanta et al.

    Prog. Energy Combust. Sci.

    (1987)
  • S.B. Pope

    Combust. Flame

    (1976)
  • J.Y. Chen

    Combust. Flame

    (1987)
  • A.F. Sarofim

    Twenty-First Symposium (International) on Combustion

  • G.M. Faeth et al.
  • G. Cox

    Combust. Sci. Technol.

    (1977)
  • V.P. Kabashnikov et al.

    Appl. Spectrosc.

    (1979)
  • W.L. Grosshandler et al.
  • J.P. Gore et al.

    Twenty-First Symposium (International) on Combustion

There are more references available in the full text version of this article.

Cited by (0)

View full text