漫反射与非漫反射表面间的辐射传递系数快速计算

Fast calculation of radiative heat transfer coefficient between diffuse and non-diffuse surfaces

针对蒙特卡洛方法计算目标表面间辐射传递系数耗时过长的问题,提出了一种计算漫反射灰体与非漫反射灰体表面间辐射传递系数的快速方法。首先,利用蒙特卡洛方法在漫反射表面生成发射光束集并进行射线追踪,计算漫反射表面对目标表面的辐射传递系数;然后,在非漫反射表面生成发射光束并进行射线追踪,如果射线在多次反射过程中击中任意漫反射表面,则利用反射光束的漫反射特性,直接调用漫反射表面的辐射传递系数对反射能量进行分配,并停止射线追踪。对正六面体模型内表面(两个漫反射面元、四个镜反射面元)的辐射传递系数进行仿真,结果表明,当表面反射率ρ=0.4时,镜反射表面的辐射传递系数计算时间仅为蒙特卡洛方法的1/3;ρ=0.8时,相应的计算时间占比低于1/10,并且保持良好的计算精度。理论推导并分析了影响该方法计算速度的模型参数,结果表明:表面反射率越高,系统中漫反射表面占比越大,快速方法中单束光线的平均追踪次数较蒙特卡洛方法越少,非漫反射表面的辐射传递系数计算优势越明显。

Objective Radiative heat transfer is one of the three basic modes of heat transfer and has an important impact on the study of the temperature distribution and infrared radiation characteristics of the outer surface of a space target.For solving the radiation heat transfer between incomplete gray-diffuse surfaces system(both diffuse surfaces and non-diffuse surfaces in the model),there is usually a lack of corresponding analytical solutions.The Monte-Carlo method has the advantage of good calculation accuracy,but it has the disadvantage of long calculation time.In order to solve this problem,this paper proposes a representation of the ray reflection energy of the diffuse surface and a calculation method for the radiative transfer coefficient of the incomplete diffuse surfaces system based on the diffuse reflection characteristics of the diffuse surface.This reduces multiple ray tracing before the ray energy threshold is reached and improves the calculation speed.Methods A method for expressing the reflected energy of diffuse surfaces is proposed.When the Monte-Carlo method is used to conduct ray tracing,if a ray hits a diffuse surface,the reflection energy of the ray is defined as the diffuse emission beam set in the upper half space of the surface using the diffuse reflection characteristics of the diffuse surface(Fig.2(b)).In addition,modifications were made to the Monte-Carlo tracking process.First,the radiative transfer coefficient of the diffuse surface was calculated using the Monte-Carlo method.Then,when calculating the radiative transfer coefficient of diffuse surfaces,if the light emitted from the surface intersects with the diffuse surface,the radiative transfer coefficient of the other surfaces is multiplied by the reflected energy,and the reflected energy absorbed by the other surfaces is calculated to end the ray tracing process,avoiding subsequent multiple ray tracing and achieving fast calculation of diffuse surfaces to improve the computational efficiency of the entire system(Fig.5).Results and Discussions Using the cube model and assuming that the No.1 and No.2 surfaces are diffuse and the rest of the surfaces are specular(Fig.4(a)),the radiative transfer coefficient from each surfaces to the other surfaces(including itself)are calculated using the Monte-Carlo method and the fast algorithm proposed in this paper,and the results of the calculations are shown(Tab.1-2).It can be seen that both of them have the same accuracy,but as for the computation time,the new method is more efficient due to the significant reduction of the number of ray tracing times in Monte-Carlo(Fig.6).In addition,the 13-facet L-type unenclosed cavity model is used as proof to show that the method is also applicable in complex models.Finally,taking the cube model as an example,the advantages of the fast method compared with the Monte-Carlo method are analyzed from the theoretical point of view.For the emitted beam on a non-diffuse surface,the average tracing times of its rays are much smaller than that of the Monte-Carlo method,and the higher the reflectivity of the surface element,the more significant the computational advantages are.For example,if the energy threshold is 0.001,the number of diffuse reflective surfaces in the model is 2.When the surface reflectance is 0.4,the calculation time of the non-diffuse reflective surfaces in the fast calculation method is 0.307 times that of the Monte-Carlo method.When the reflectance of the surface is increased to 0.8,the calculation time of the non-diffuse reflective surface is only 0.081 of that of the Monte-Carlo method,which is more than ten times higher.Conclusions Aiming at the problem of the traditional Monte-Carlo method in calculating the radiative transfer coefficient between diffuse surfaces and diffuse surfaces for a long time,a fast calculation method is proposed.Firstly,the realization principle of the method and the difference with Monte-Carlo method are introduced,and then the cube model and L-shape unenclosed cavity model are used to compare the calculation results and calculation time of the fast method to Monte-Carlo method,which illustrates the advantages of fast method over Monte-Carlo method in terms of the calculation efficiency,and then the coefficient affecting the calculation advantages of the method are illustrated through the theoretical analysis,and finally the outlook on the next step of how to improve the calculation time of the diffuse surface elements is proposed.