Radiative energy flux of diffusive supersonic wave in a cylinder

Abstract

The calculation of radiative energy flux is very important in the study of diffusive supersonic wave transfer when the radiative thermal conduction approximation is used. In this paper, a formula of radial position-dependent spectral energy flux is given for the diffusive supersonic wave in a low density filled cylinder with a high density wall. A geometrical factor is defined to describe the influence of the radial size of the cylinder on the radiative energy flux. From the formula, the geometrical factor decreases with the radial position from center to edge, due to the much shorter mean free path in the wall than in the fill. This is another important reason in causing a significant curvature in the radiation front, which was observed in recent diffusive supersonic wave experiments. In addition, expressions for calculating the averaged spectral energy flux over the cylinder cross-section and the energy flux in local thermal equalibrium are given. The geometrical factor in the expression of the averaged spectral energy flux is compared with the conventional geometrical factor obtained via geometrical free path which people usually used in their simulation. Finally, to make the simulation easy, approximate expressions are given for the geometrical factors.