二维非均匀介质内辐射与瞬态导热耦合传热分析

Thermal Analysis of Coupled Radiation and Transient Conduction in Two-Dimensional Heterogeneous Media

充分利用间断谱元法对非规则区域良好适应性、数值稳定、局部高阶收敛性等优点,开展了二维非均匀介质内辐射与瞬态导热耦合传热分析。在求解过程中,将空间计算域离散为多个不重合的单元,并在单元内采用高阶谱节点进行离散。对于非均匀介质内离散坐标形式的辐射传递方程,根据离散角度上的辐射能传递方向,确定单元间的上下游关系,并采用迎风格式来实现单元间辐射信息的有效传递;对于瞬态能量守恒方程,采用全隐格式进行瞬态项离散。通过多组非均匀介质内辐射与瞬态导热耦合传热算例,发现了间断谱元法具有随单元数增加的线性收敛特性,以及随单元内节点数增加的指数收敛特性;通过与文献中结果对比,发现最大相对误差均小于1%,验证了间断谱元法的正确性和有效性;随着辐射与导热耦合参数的增加,导热在耦合传热所占比重会加大,非均匀介质带来的温度场非均匀性会减弱,达到稳态的时间变长。

Taking the advantages of the flexibility to deal with irregular geometry,numerical stability,and high-order local convergence,the discontinuous spectral element method(DSEM)was used for thermal analysis of coupled radiation and transient conduction in two-dimensional heterogeneous media.In the solving process,the spatial computational domain was discretized into several elements separated from each other,and high-order spectral nodes were used to discretize these elements.For the discrete coordinate form of the radiative transfer equation in a heterogeneous medium,the direction of radiant energy in a discrete angle was based to determine the upstream and downstream elements.Then,the upwind scheme was imposed to transmit radiation information in elements.For the transient energy conservation equation,the fully implicit difference scheme was adopted to discretize the transient term.Several examples of coupled radiation and transient conduction in the heterogeneous medium were chosen to test the linear convergence characteristic with increasing number of elements,and the exponential convergence characteristics with increasing nodes in the element.By comparing the results with those in the literature,it was found that the maximum relative error was less than 1%in all cases,which confirmed the accuracy and efficiency of the discontinuous spectral element method.With an increase in radiation and thermal coupling parameters,the proportion of heat conduction in coupled heat transfer increased while the non-uniformity of the temperature field caused by heterogeneous media decreased.Consequently,a longer time was required for it to reach steady-state.