圆柱坐标系下辐射换热离散坐标法的影响因素分析

Discrete ordinates method for radiative transfer equation in cylindrical coordinate

以辐射平衡条件下的一维无限长同心圆环之间的发射、吸收、非散射介质的辐射换热问题为例,探讨了辐射传递方程的离散坐标求解方法,并分析了角积分方案、空间差分格式及角度差分格式对圆柱坐标系下离散坐标法的影响。研究结果表明:角积分方案近似阶数越高,计算结果的精度越高,但随着积分方案阶数的增加,所需计算时间也相应增大;对于同一近似阶数的角积分方案,FN角积分方案的计算精度高于SN角积分方案;空间差分格式对计算精度的影响较小,其中阶梯格式精度最高,正格式所需计算时间最长,菱形格式所需时间最短;角度差分格式对计算精度的影响较大,其中菱形格式计算精度最高,阶梯格式和正格式的计算精度相当,同时三种角度差分格式所需计算时间相当。因此,角积分方案一定的情况下,建议空间与角度差分格式分别选用阶梯格式和菱形格式。

Based on the radiative heat transfer of infinite concentric cylinders containing an absorbing,emitting,and non-scattering gray medium under radiative equilibrium,discrete ordinates method（DOM） in cylindrical coordinate system was studied.The effects of angular quadrature schemes,spatial differencing schemes and angular differencing schemes on DOM were analyzed.It shows that the accuracy of DOM increases with the increasing of the orders of quadrature schemes,but the computational time for higher order quadrature schemes increase dramatically at the same time.For the same approximation order of angular quadrature scheme,the accuracy of FN is higher than that of SN.The effect of spatial differencing schemes on the accuracy of DOM is negligible,and step scheme is a little bit better.It takes the longest computation time for positive scheme and the shortest computation time for diamond scheme.The effect of angular differencing scheme on the accuracy of DOM is more remarkable than that of spatial differencing scheme.Among the three angular differencing schemes,diamond scheme is the best,and step scheme and positive scheme are equally well in terms of accuracy.Furthermore,the three angular differencing schemes require almost same computational time.Therefore,step and diamond scheme for spatial and angular differencing schemes is recommended respectively with certain angular quadrature scheme.