间断谱元法分析圆柱坐标系内非均质辐射传热

Analysis of Radiative Heat Transfer Within Heterogeneous Media in Cylindrical Coordinate by Discontinuous Spectral Element Method

在非均匀高温介质中,辐射能束的传输路径会发生弯曲;并且,圆柱坐标系下辐射传递方程存在角向微分项。这都将导致辐射传递过程的分析和求解变得更加复杂。本文利用间断谱元法数值稳定、易于适应复杂区域、能够捕捉单元边界物理量的大变化、且在单元内实现高阶离散的特点,构建一种圆柱坐标系下非均匀介质内辐射传热模型。在求解过程中,将计算域离散成相互独立的单元,在单元内利用高阶谱配置点离散,并且在单元边界上通过施加迎风格式的数值通量来传递上下游信息。通过与多组文献结果对比分析,验证了间断谱元法求解圆柱坐标系下非均匀介质内辐射传热问题的正确性和有效性。并分析了间断谱元法的收敛速度,以及介质折射率分布、光学厚度和壁面发射率对辐射传热的影响。

In the heterogeneous high-temperature media, the ray of radiant energy is transmitted along a curved path. The radiative transfer equation in cylindrical coordinate exists the angular derivative term. Thus, the solution of the radiative transfer equation with heterogeneous media in cylindrical coordinate is complex. The discontinuous spectral element method(DSEM) exits lots of advantages, such as numerical stability, flexibility to deal with complex geometry, capturing the large variation of quantity at the element boundary. In this paper, the thermal radiation model with heterogeneous media in cylindrical coordinate is established by the DSEM. In the solving process,the computational domain is discretized as independent elements, and the high order spectral collocation points are adopted to discretize these elements. In the element boundary, the numerical flux with an upwind scheme is used to transmit information from upstream to downstream. Several cases are chosen to validate the DSEM model in solving radiative heat transfer problems with heterogeneous media in cylindrical coordinate. Then, the convergence rate of the DSEM, the effects of refractive index distribution, optical thickness and boundary emissivity on radiative heat transfer are comprehensively investigated.