配置点谱方法求解非均匀介质内辐射传热问题

发动机内的燃气等高温介质随着组分和浓度的变化，会引起折射率在空间上的非均匀分布，从而导致辐射能束沿着曲线传播，其相应的辐射传热过程也更为复杂。为了避免射线追踪方法的复杂计算、提高计算效率，本文提出了配置点谱方法求解二维非均匀介质内辐射传热问题。在求解过程中，角向采用离散坐标法处理，空间采用配置点谱方法处理。通过将三种非均匀介质内辐射传热问题的配置点谱方法结果与文献结果进行对比分析，发现配置点谱方法可以在较少的节点数下，获得准确、有效地计算结果。并且，采用配置点谱方法求解三种算例的计算时间均消耗较少，均在20分钟以内。这将为进一步开展发动机复杂结构内高温燃气辐射快速仿真提供基础。

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, this paper proposes a collocation spectral method (CSM) to solve the radiative heat transfer problem in two-dimensional inhomogeneous medium. In the process of solving, the discrete ordinates method is adopted to discrete 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.