Grid-free simulation of radiative transport in a participating medium

Department of Mechanical Engineering, Rm 3-339 Massachusetts Institute of Technology Cambridge, MA 02139, U.S.A

Abstract

Radiative transport in a participating medium transfroms the energy equation into an integro-differential equation which must be solved if radiation is considered as an important mechanism of heat transfer in a convective-diffusive-reactive environment. In most cases, especially in combustion problems, the temperature gradients are so steep that the region where the radiative flux, which is proportional to the fourth power of temperature, is significant in a small subset of the entire flow domain. Especially when utilizing a grid-free Lagrangian scheme to perform the convective-diffusive-reactive simulations, it is desirable to develop a compatible scheme which does not require a grid to perform the computations of the radiative flux and its gradient (needed in the energy equation.) We have developed the discrete source method in which the radiative flux and irradiance are computed by summing over a collection of radiating elements distributed over the region of high temperature. In an axisymmetric domain, the irradiance and radiative flux, both are triple integrals of the radiation kernel over the elemental volume, are reduced to double integrals which are then approximated by single integrals that are evaluated semi-analytically. We demonstrate the accuracy of the scheme by comparing the results with direct numerical evaluation of the original integrals for cases relevant to combustion problems.