基于改进蒙特卡洛法求解辐射传热问题的计算精度评价  

Evaluation on Computational Accuracy for Improved Monte Carlo Method of Radiative Heat Transfer Problem

作　　者：李国军 钟佳琪 李定勇 王晓东 LI Guojun;ZHONG Jiaqi;LI Dingyong;WANG Xiaodong(College of Metallurgy,Northeastern University,Shenyang 110000,China;Research Institute of Automobile,Geely Auto,Ningbo 315000,China)

机构地区：[1]东北大学冶金学院,辽宁沈阳110000 [2]吉利汽车自动化研究所,浙江宁波315000

出　　处：《湖南大学学报（自然科学版）》2022年第2期55-62,共8页Journal of Hunan University:Natural Sciences

基　　金：国家重点研发计划资助项目(2017YFA0700300);国家自然科学基金资助项目(52106079)。

摘　　要：针对传统蒙特卡洛法计算辐射传输耗时问题,提出了一种改进蒙特卡洛方法,通过比例迭代累加法来求解反射及散射能量,从而大幅减少了计算时间.引入直接评价方法,以包含参与性介质的密闭系统(方形和圆形为例)为例,分析了网格密度、发射能束数及物性参数对改进蒙特卡洛法计算精度的影响.当光学厚度为0.005时,采用改进蒙特卡洛方法求得方腔及圆形腔的表面微元辐射通量的相对均方根误差值分别为0.002 5及0.002 3,而采用传统蒙特卡洛方法时对应误差分别为0.008 0及0.003 7.可见,相同计算条件下,改进蒙特卡洛方法对辐射换热问题具有更高的精度.进一步研究了追踪能束数对计算误差的影响规律,给出了计算误差与追踪能束数拟合关系式,为计算该类问题的能束数选取提供了支撑.Aiming at the time-consuming problem of traditional Monte Carlo calculation for radiation transmission,this paper develops an improved Monte Carlo method,which solves the reflection and scattering energy through proportional iterative accumulation method,thereby greatly reducing the calculation time.The direct evaluation method is introduced,and the closed system containing participating media(square and circular as examples)is used as an example to analyze the influence of the grid density,the number of emitted energy beams and the physical parameters on the calculation accuracy of the improved Monte Carlo method.When the optical thickness is0.005,the relative root mean square error of radiation flux for the square cavity and the circular cavity is 0.002 5 and0.002 3 respectively by using the improved Monte Carlo method,while the corresponding errors are 0.008 0 and0.003 7 respectively when the traditional Monte Carlo method is used.It can be seen that under the same calculation conditions,the improved Monte Carlo method has higher accuracy for the radiation heat transfer problem.The influence of the tracking energy beam number on the calculation error is further studied,and the fitting relationship between the calculation error and the tracking energy beam number is given,which provides support for the selection of the energy beam number.

关 键 词：蒙特卡洛法 评价 计算精度 计算效率 

分 类 号：TK124[动力工程及工程热物理—工程热物理]