Mean Coefficients of Radiation in Sooty Media in Light of the Lorenz-Mie and Lorentz-Drude Theories 920112

The Planck and Rosseland mean absorption coefficients for particle laden media such as diesel combustion-generated soot are developed in terms of the complete Lorenz-Mie theory. They are found to depend on the complex refractive index m=n-ik of particles, n and k being refractive and absorptive indices, respectively, and the dimensionless number πDT/C₂; D being the particle diameter, T the absolute temperature, and C₂ the second radiation constant. Being applicable for an arbitrary πDT/C₂, the development also provides a criterion for the upper bound of the Penndorf-based mean coefficients. In view of the fact that the radiative heat flux represents a significant fraction of the total heat transport in the luminous, compression-ignition engine combustion, these mean properties coupled with the spectrally integrated radiative-transport equation are expected to be useful for the in-cylinder modeling of these engines.

The effect of wavelength on the optical properties of soot used in the Planck and Rosseland mean coefficients are also investigated in terms of the Lorentz-Drude dispersion theory and comparisons are made for three sets of model parameters currently available. Results exhibit a marked sensitivity to n and k, which indicates a need for better estimation of optical properties of particles for accurate interpretation of optical diagnostics, as well as for improved predictive capability of radiative heat transfer models. The use of the complete Lorenz-Mie theory becomes more important in the infrared with larger values of n and k, leading to marked deviations from Rayleigh-based expressions.