Collocation Spectral Method to Solve Radiative Heat Transfer in Inhomogeneous Medium

With changing of composition and concentration of high-temperature gas in an aero-engine, the refractive index is inhomogeneous. The heat ray goes along a curved path. As a result, the corresponding radiative heat transfer process in the inhomogeneous medium is more difficult than that in the uniform medium. To avoid the complicated computation of the curved ray tracing method and improve the calculation efficiency, a collocation spectral method (CSM) was proposed to solve the radiative heat transfer problem in two-dimensional inhomogeneous medium. In the process of solving, the discrete ordinates method is adopted to discretize the angular term, and the spatial domain is discretized by the CSM. Three different cases of radiative heat transfer in an inhomogeneous medium are chosen. The CSM results are compared with available results in references. The comparisons indicate that the CSM has good accuracy and efficiency even using very litter nodes. Furthermore, the calculational times of these three cases by using CSM are less than 20 minutes. The CSM will provide a basis for rapid simulation of high-temperature gas radiation in the complex structure of the aero-engine. © 2021, Editorial Department of Journal of Propulsion Technology. All right reserved.