The ray effect is a serious problem in radiative heat transfer computations. Continuously varying radiation fields are approximated numerically by sampling a limited number of angular directions. The discrete transfer method (DTM) is a conceptually simple technique suitable for general-purpose calculations of thermal radiation in complex geometries. Over the years a large variety of quadratures based on fixed ray firing patterns has been suggested for use in conjunction with the DTM. Arguably, in absence of a comprehensive error analysis, the efficacy of all these quadratures has only been proved for limited collections of radiation problems. Recently, sharp error bounds for the heat flux integral in the DTM have been established for irradiation distributions of three different continuity classes: smooth fields, fields with discontinuous angular derivatives and piecewise constant fields. The resulting error formulas have paved the way for a new adaptive quadrature strategy. Results are presented of its application to an idealized jet flame and to radiative exchanges inside a cube-shaped enclosure, along with brief comments on the viability of this approach in general-purpose CFD/radiation computations. In this paper, the following capabilities of the new adaptive angular quadrature are demonstrated: Evaluation of DTM heat flux integrals to a pre-specified tolerance for any intensity distribution; Excellent accuracy with very low ray numbers for irradiation due to small view factor sources; and Good heat flux estimates for piecewise constant sources, provided that the starting mesh is selected carefully.

Modified formulations of the discrete transfer and Monte Carlo methods are presented for the prediction of radiative heat transfer in three-dimensional, nonhomogeneous, participating media.Numerical solutions found with both algorithms are in good agreement with published benchmark results which used contemporary methods to determine the radiative transport in a unit cube. New solutions in an arbitrary L-shaped geometry using a nonorthogonal, body-fitted mesh are also presented. The average deviation between the two methods is less than 1.2% for both the boundary surface flux and the divergence of radiative flux or gas emissive power within the enclosed, isotropically scattering media. Henson,

Most practical combustion systems involve complex geometry configurations and CFD techniques used for the calculation of flow and combustion in such geometries use body-fitted non-orthogonal mesh systems. This paper reviews some of the currently available radiative heat transfer calculation techniques suitable for such CFD applications. The Monte Carlo method, the discrete transfer method, the YIX method, the discrete ordinates method and the finite volume method are discussed and some notable applications related to combustion problems are reviewed. Comparative results using all the methods outlined are presented for bench mark problems and their applicability to complex geometry situations are discussed. Radiative heat flux predictions for an S.I. engine simulation are presented to demonstrate the capability of the discrete transfer method in a pent-roof complex geometry combustion chamber. The paper also describes a ray based technique for the handling of turbulence-radiation interactions in combustion and its application is demonstrated in the prediction of a methane diffusion flame.

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