谱方法求解三维辐射与导热耦合换热问题

Spectral methods for three-dimensional coupled radiation-conduction heat transfer

采用基于Chebyshev配置点的谱方法求解吸收、发射和散射介质内的三维辐射与导热耦合换热问题。对所需求解的辐射传递方程(RTE)和能量方程,空间上均采用Chebyshev配置点谱方法离散。对于RTE,在角度方向上采用离散坐标法离散。谱配置法的应用和离散显示其高效性。将谱配置法计算结果与文献中采用有限容积法的结果相比较,结果显示:即使选用比温度变化更为敏感的辐射热流和总热流作为参考标准,两种不同方法的计算结果吻合得很好。此外,计算相同问题时,采用谱配置法用到的节点数比文献中有限容积法用的节点数少得多。这表明,即使采用很少的节点数,谱配置法也能精确地求解三维辐射与导热耦合换热问题。谱配置法可以高效、高精度地求解三维辐射与导热耦合换热问题。之后,考虑导热-辐射比、光学厚度、反照率、壁面发射率等参数对温度、辐射热流及总热流的影响。

A spectral collocation method based on Chebyshev polynomial expansions is presented to solve three-dimensional coupled radiation-conduction heat transfer problems in absorbing,emitting and scattering media.For both the radiative transfer equation（RTE）and energy equation,the spatial domain is discretized by the Chebyshev spectral collocation method.The angular domain is discretized by the discrete ordinates method for RTE.The formulations and implementation of the spectral collocation-discrete ordinates method（SP-DOM）reveal its high efficiency.The numerical results in three-dimensional cube geometries by the SP-DOM are compared with the results in literature obtained by the finite volume method.It is found that even by the standard of the radiative heat flux and the total heat flux,which are more sensitive than temperature,the calculated results are in good agreement with the results in literature.In addition,the number of nodes used in SP-DOM is much less for the same problem.These results show that,even with a small number of nodes,the present method can provide high accuracy to solve radiative-conductive heat transfer problems in three-dimensional enclosure.The SP-DOM for three-dimensional radiative-conductive heat transfer is accurate and efficient.The predicted temperature,radiative heat flux and total heat flux distributions are presented for different parameters,such as conduction/radiation ratio,optical thickness,scattering albedo and wall emissivity.