Journal of Quantitative Spectroscopy and Radiative Transfer
The high-order spherical harmonics () method for 2-D Cartesian domains is extracted from the 3-D formulation. The number of equations and intensity coefficients reduces to (N+1)2/4 in the 2-D Cartesian formulation compared with N(N+1)/2 for the general 3-D formulation. The Marshak boundary conditions are extended to solve problems with nonblack and mixed diffuse-specular surfaces. Additional boundary conditions for specified radiative wall flux, for symmetry/specular reflection boundaries have also been developed. The mathematical details of the formulations and their implementation in the OpenFOAM finite volume based CFD software platform are presented. The accuracy and computational cost of the 2-D Cartesian are compared with that of the 3-D solver and a Photon Monte Carlo solver for a square enclosure, as well as a 45° wedge geometry with variable radiative properties. The new boundary conditions have been applied for both test cases, and the boundary condition for mixed diffuse-specular surfaces is further illustrated by numerical examples of a rectangular geometry enclosed by walls with different surface characteristics.
Ge, Wenjun; Modest, Michael F.; and Roy, Somesh, "Development of High-Order PN Models for Radiative Heat Transfer in Special Geometries and Boundary Conditions" (2016). Mechanical Engineering Faculty Research and Publications. 238.
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