A Discontinuous Finite-Element Formulation for Radiative Transfer in Axisymmetric Finite Cylindrical Enclosures and Coupling with Other Mode Heat Transfer

ABSTRACT

This article presents a discontinuous finite-element formulation for numerical solution of internal thermal radiative transfer problems in axisymmetric cylindrical enclosures. While the computation of axisymmetric radiative transfer is essentially three-dimensional, an appropriate mapping procedure entailing the use of the axisymmetric and periodic conditions associated with the enclosures may be used to make it possible to compute the problem over a 2-D mesh only. This will result in a significant reduction in both computing time and memory storage requirement. Mathematical formulation and numerical implementation using the discontinuous Galerkin method for axisymmetric internal radiation heat transfer calculations are given. The procedures for incorporating the mapping in the discontinuous formulation to convert an essentially 3-D calculation into a 2-D calculation are discussed in detail. The computed results are given and compare well with the solutions reported in the literature using other methods. Examples include both nonscattering and scattering cases. The effects of both solid-angular and spatial discretization are discussed, and both the theory and results show that an even discretization of solid angle is important to ensure adequate numerical accuracy. The coupling of the discontinuous and conventional finite-element methods for mixed-mode heat transfer calculations, including swirling flow, conduction, natural convection, and thermal radiation in participating media, is illustrated in the last example.

The authors gratefully acknowledge the support of this work by the U.S. Air Force Office of Research, subcontracted through VLOC, Inc. (Grant VAN00138704451) and by NASA (Grant NAG8-1693). The assistance of Dr. Xin Ai with the unstructured mesh generation is also acknowledged.