An improved Monte Carlo method for radiative heat transfer in participating media. (August 2020) - Li, Guo-Jun; Zhong, Jia-Qi; Wang, Xiao-Dong
Highlights: Energy beams emitted from a surface micro-element are divided into M ( M ≥ 1) point. The sampling of surface reflection is eliminated. The sampling of surface emission and gas scattering are only arranged one time. More efficient and time-saving. Abstract: An improved Monte Carlo method (IMCM) is developed in this paper to solve the total radiant exchange areas (TEAs), which can greatly improve calculation accuracy and save CPU time. This approach, features two main improvements on the basis of the Monte Carlo method (MCM). First, the location of the surface emission points and the number of emission energy beams are subdivided, thereby improving the calculation accuracy. Specifically, it is assumed that the energy beams emitted by one micro-element are emitted from M points on average. Second, the energy beams emitted by the surface and gas micro-elements are only arranged once, and the sampling of surface reflection is eliminated, thereby improving the calculation efficiency. Specifically, the ratio of the energy beams emitted by one micro-element directly to other micro-elements can be calculated. The reflection and scattering energy of one micro-element to other micro-elements are obtained by iterative accumulation. This approach can greatly save CPU time compared with sampling the reflected and scattered energy beams. The application of IMCM to a two-dimensional (2D) square cavity is considered in this study. The effects of surface emissivity and boundary temperature on radiative heat transfer are analyzed. IMCM was used to solve the TEAs, and the calculated results of IMCM, MCM and the pathlength method (PLMCM) were compared based on the results of the reduced integration scheme (RIS). The all results show that the IMCM is more accurate than the MCM and PLMCM and is more efficient than the MCM and PLMCM for calculating the TEAs. Graphical abstract: As shown in the figure, the flow chart for solving the TEAs, the left side is the basic steps of IMCM, and the right side is the basic step of MCM. The basic steps of IMCM mainly include: calculating the share and proportion of the emitted energy beams of each micro-element to other micro-elements, calculating the energy of each micro-element reflected and scattered to the specified micro-element and store it, determining whether the accuracy is met. The basic steps of MCM mainly include: determining whether the energy beam is in the enclosure, if yes, reaching to gas micro-elements, determining whether the energy beam is scatter, if yes, resampling determine the scattering direction and distance; if the energy beams reaching to surface micro-elements, determining whether the energy beam is reflect, if yes, resampling determine the reflecting direction and distance. By comparing MCM with IMCM to solve the TEAs, it can be found that IMCM reduces the number of steps for needed to resample the distance and angle of the reflected and scattered energy beams, thereby reducing the CPU time. Image, graphical abstract