Analyzing thermal radiation in cylindrical anisotropic scattering medium with element differential method

微分单元法分析圆柱内各向异性散射介质热辐射

¹ School of Power and Energy, Northwestern Polytechnical University, Xi'an 710072, China
² Yangtze River Delta Research Institute, Northwestern Polytechnical University, Taicang 215400, China
³ School of Automobile, Chang'an University, Xi'an 710064, China

Received: 18 April 2022

Abstract

The spontaneous radiation combustion diagnosis technology has high requirements for obtaining the radiation intensity of highly directional resolution in a combustion system. Taking advantage of the numerical stability and easy implementation of the element differential method, this paper constructs a radiation model that can achieve the radiation intensity of spatial and angular high-resolution in cylindrical anisotropic scattering medium. In analyzing the radiation model, the radiation intensity is discretized in three dimensions. An upwind scheme is proposed to suppress the numerical oscillation of the strong convection characteristics of the radiation transfer equation. The double-layer node algorithm is used to capture the strong discontinuous singularities at the radiation boundary. The comparison with the analytical solution shows that the radiation model based on the element differential method can achieve the high-resolution description of radiation intensity with high-order accuracy. The accuracy and validity of the radiation model are verified through comparing with the results on the Monte Carlo method. The further description of the three-dimensional distribution of radiation intensity in angle and space proves that the up-wind scheme can effectively suppress numerical oscillation and realize stable calculation.

摘要

自发辐射燃烧诊断技术对获取燃烧系统内高方向分辨率辐射强度有强烈需求。利用微分单元法数值稳定、易于实施的特点, 构建一种能在圆柱坐标系各向异性散射介质中, 获取角度和空间上高分辨率辐射强度的辐射模型。在模型分析中, 将辐射强度进行三维高阶离散; 针对辐射传递方程的强对流特性, 提出一种迎风方案抑制数值振荡; 对于辐射边界存在的强间断奇异点, 采用双层节点方案进行捕捉。与解析解对比发现, 基于微分单元法的辐射模型能够实现辐射强度的高分辨率刻画, 且具有高阶精度; 与蒙特卡罗法结果对比, 验证了此模型的准确性和有效性。进一步刻画辐射强度在角度和空间上的三维分布, 证明迎风方案可以有效抑制数值振荡、实现稳定计算。