Development of high-order PN models for radiative heat transfer in special geometries and boundary conditions. (March 2016) - Ge, Wenjun; Modest, Michael F.; Roy, Somesh P.
Abstract: The high-order spherical harmonics ( P N ) 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 P N 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 P N are compared with that of the 3-D P N 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. Abstract : Highlights: Derivation of the 2-D Cartesian formulation for the high order spherical harmonics (PN) methods. Derivation of the boundary condition of PN for the mixed diffuse-specular surfaces. Derivation of the boundary condition of PN for specified radiative heat flux at the wall. Derivation of the boundary condition of PN for symmetry/specular boundaries.