High-order Spherical Harmonic Methods for Solving Radiative Transfer Equations: Model Development and Implementation in ANSYS-Fluent Software

PANG Jiajie; WANG Liang; ZENG Qi; CAO Jun; REN Tao

doi:10.19805/j.cnki.jcspe.2025.230654

English Version Reader LoginJournal Login

您当前的位置：

首页 >

文章列表页 >

High-order Spherical Harmonic Methods for Solving Radiative Transfer Equations: Model Development and Implementation in ANSYS-Fluent Software

更新时间：2026-02-05

- High-order Spherical Harmonic Methods for Solving Radiative Transfer Equations: Model Development and Implementation in ANSYS-Fluent Software
- Chinese Journal of Power Engineering Vol. 45, Issue 1, Pages: 1-9(2025)
- 作者机构：
  
  1. 上海交通大学中英国际低碳学院,上海,201306
  2. 中国航发湖南动力机械研究所,湖南,株洲,412002
- 作者简介：
- 基金信息：
- DOI：10.19805/j.cnki.jcspe.2025.230654
  CLC： TK124;O241.82
- Online First：15 January 2025，
  
  Published：2025
- 稿件说明：
移动端阅览
庞佳婕,王良,曾琦,曹俊,任涛. 高阶球形谐波法求解辐射传输方程:模型开发与ANSYS-Fluent软件实现动力工程学报, 2025, 45(1): 1-9 https://doi.

org/10.19805/j.cnki.jcspe.2025.230654
庞佳婕,王良,曾琦,曹俊,任涛. 高阶球形谐波法求解辐射传输方程:模型开发与ANSYS-Fluent软件实现动力工程学报, 2025, 45(1): 1-9 https://doi. DOI： 10.19805/j.cnki.jcspe.2025.230654.

org/10.19805/j.cnki.jcspe.2025.230654 DOI：

摘要

为了改善ANSYS-Fluent软件中用于辐射传热计算的球形谐波法仅限于其最低阶(P1)形式的现状

基于高阶球形谐波法求解辐射传输方程的基本原理

利用ANSYS-Fluent软件提供的用户自定义函数(UDF)和用户自定义标量(UDS)接口

通过对控制方程和边界条件的耦合数值求解

开发了适用ANSYS-Fluent软件的高阶球形谐波法辐射传输方程求解模型。模型的精度通过对一维、二维平板及二维轴对称火焰的辐射传热进行计算

并且与相应的精确解或光子蒙特卡罗(PMC)解进行对比来实现。结果表明:开发的P3模型相比于ANSYS-Fluent软件中自带的P1模型无论是在计算辐射强度的角空间分布还是在辐射传热的总体热源方面都更加准确。

Abstract

In order to improve the status that the spherical harmonics method in the ANSYS-Fluent software is limited to its lowest order (P1) form for radiation heat transfer calculations

based on the basic principles of solving the radiative transfer equation using high-order spherical harmonics

by coupling the numerical solution of the governing equations and boundary conditions using the user-defined function (UDF) and user-defined scalar (UDS) interfaces provided in the ANSYS-Fluent software

a high-order spherical harmonics radiation transfer equation solution model suitable for the software was developed. The model accuracy was verified by calculating the radiative heat transfer in one-dimensional

two-dimensional flat plates

and two-dimensional axisymmetric flame

and comparing with the corresponding analytical or photon Monte Carlo (PMC) solutions. Results show that the P3 model developed in this paper is more accurate than the built-in P1 model of ANSYS-Fluent software in calculating both the angular distribution of radiation intensity and the overall radiative heat source.

关键词

Keywords

references

刘林华. 炉膛传热计算方法的发展状况[J]. 动力工程, 2000, 20(1): 523-527, 538. LIU Linhua. Development status of heat transfer calculation methods in boiler furnaces[J]. Journal of Power Engineering, 2000, 20(1): 523-527, 538.

王鹏, 陈寅彪, 廖海燕, 等. 200 MW富氧燃烧锅炉配风优化数值模拟研究[J]. 动力工程学报, 2019, 39(2): 98-103. WANG Peng, CHEN Yinbiao, LIAO Haiyan, et al. Numerical simulation on optimization of air distribution mode for a 200 MW oxy-fuel combustion boiler[J]. Journal of Chinese Society of Power Engineering, 2019, 39(2): 98-103.

LEE C E. The discrete Sn approximation to transport theory[R]. Los Alamos: Los Alamos National Laboratory, 1961.

CHAI J C, LEE H S, PATANKAR S V. Finite volume method for radiation heat transfer[J]. Journal of Thermophysics and Heat Transfer, 1994, 8(3): 419-425.

HOWELL J R. Application of monte carlo to heat transfer problems[J]. Advances in Heat Transfer, 1969: 5:1-54.

MODEST M F. Radiative heat transfer[M]. 3rd ed. San Diego: Elsevier, 2013.

李村生. 煤粉燃烧放热及介质辐射特性参数的数值分析[J]. 动力工程, 1982, 2(4): 31-37, 75. LI Cunsheng. A numerical analysis of the heat-release rate due to combustion of pulverized coal and radiative properties of the media[J]. Power Engineering, 1982, 2(4): 31-37, 75.

BAYAZITOGLU Y, HIGENYI J. Higher-order differential equations of radiative transfer: P3 approximation[J]. AIAA Journal, 1979, 17(4): 424-431.

CHENG Ping. Study of the flow of a radiating gas by a differential approximation[D]. Palo Alto: Stanford University, 1965.

CANOSA J, PENAFIEL H R. A direct solution of the radiative transfer equation: application to Rayleigh and Mie atmospheres[J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 1973, 13(1): 21-39.

DAVE J V, CANOSA J. A direct solution of the radiative transfer equation: application to atmospheric models with arbitrary vertical nonhomogeneities[J]. Journal of the Atmospheric Sciences, 1974, 31(4): 1089-1101.

ARPACI V S, GZM D. Thermal stability of radiating fluids: the Bnard problem[J]. The Physics of Fluids, 1973, 16(5): 581-588.

MODEST M F. Further development of the elliptic PDE formulation of the P N approximation and its Marshak boundary conditions[J ] . Numerical Heat Transfer, Part B: Fundamentals, 2012, 62(2/3): 181-202.

ARSCOTT F M. Spherical Harmonics: an elementary treatise on harmonic functions with applications[J]. The Mathematical Gazette, 1969, 53(386): 452-453.

YANG Jun, MODEST M F. Elliptic PDE formulation of general, three-dimensional high-order P N approximations for radiative transfer[J ] . Journal of Quantitative Spectroscopy and Radiative Transfer, 2007, 104(2): 217-227.

VARSHALOVICH D A, MOSKALEV A N, KHERSONSKII V K. Quantum theory of angular momentum[M]. Teaneck: World Scientific Publishing, 1987.

REN Tao, MODEST M F. A hybrid wavenumber selection scheme for line-by-line photon Monte Carlo simulations in high-temperature gases[J]. Journal of Heat Transfer, 2013, 135(8): 084501.

BARLOW R S. Proceedings of the international workshop on measurement and computation of turbulent nonpremixed flames[R]. Livermore: Sandia National Laboratories, 1996.

REN Tao, MODEST M F, HAWORTH D C. Simulating turbulence-radiation interactions using a presumed probability density function method[J]. International Journal of Heat and Mass Transfer, 2018, 121: 911-923.

Views

下载量

CSCD

Alert me when the article has been cited

提交

Tools

Publicity Resources

No data

Related Author

No data

Related Institution

No data

AI问答

⁰