基于气体动理学方法的多尺度稳态热辐射计算

张华波; 周瑞睿; 李思达; 孙亚松

doi:10.7527/S1000-6893.2021.26411

航空学报 >

2021 , Vol. 42 >Issue S1: 726411 - 726411

DOI: https://doi.org/10.7527/S1000-6893.2021.26411

基于气体动理学方法的多尺度稳态热辐射计算

张华波 ,
周瑞睿 ,
李思达 ,
孙亚松

展开

1. 西北工业大学动力与能源学院, 西安 710129;
2. 上海理工大学能源与动力工程学院, 上海 200093;
3. 西北工业大学太仓长三角研究院, 太仓 215400

收稿日期: 2021-09-01

修回日期: 2021-09-24

网络出版日期: 2021-10-18

基金资助

国家自然科学基金（51976173，51976014）；上海市青年科技英才扬帆计划（21YF1430400）；江苏省自然科学基金（BK20201204）；太仓市基础研究计划面上项目（TC2019JC01）

收起

Multiscale steady-state thermal radiation calculation based on gas kinetics method

ZHANG Huabo ,
ZHOU Ruirui ,
LI Sida ,
SUN Yasong

Expand

1. School of Power and Energy, Northwestern Polytechnical University, Xi'an 710129, China;
2. School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China;
3. Yangtze River Delta Research Institute, Northwestern Polytechnical University, Taicang 215400, China

Received date: 2021-09-01

Revised date: 2021-09-24

Online published: 2021-10-18

Supported by

National Natural Science Foundation of China(51976173, 51976014);Shanghai Youth Technological Talent Sailing Project(21YF1430400);Natural Science Foundation of Jiangsu Province(BK20201204);General Project of Taicang Basic Research Plan(TC2019JC01)

Fold

摘要

随着航空发动机燃烧室内燃气温度的提升，高温区域的热辐射问题将会变得更为重要，同时由于高温气体辐射导致辐射特性的剧烈变化，将会呈现出多尺度的现象，增加了辐射计算的难度。文章通过稳态离散统一气体动力学格式（SDUGKS，Steady Discrete Unified Gas Kinetics Scheme）的思路实现稳态辐射问题的求解，SDUGKS格式通过特征线差分离散的方法实现单元界面的重构，通过某种迭代格式来实现单元数据的更新，这一过程实现了对网格内部的辐射特性的有效模拟，该过程可适用于任何具体的辐射尺度。因此就可以在任意网格条件下实现多尺度问题的计算。文章引入了修正的延迟修正法（Deferred-correction，DC）实现单元数据更新，对单一尺度和多尺度问题进行了计算，在单一尺度问题中，验证了SDUGKS格式求解稳态辐射问题的正确性，进一步构造多尺度问题进行求解，论证了SDUGKS在多尺度问题计算中的渐近保持性质和准确性。

关键词： 热辐射; 稳态; 多尺度; 离散统一气体动力学格式; 延迟修正法; 渐近保持

本文引用格式

张华波 , 周瑞睿 , 李思达 , 孙亚松 . 基于气体动理学方法的多尺度稳态热辐射计算[J]. 航空学报, 2021 , 42(S1) : 726411 -726411 . DOI: 10.7527/S1000-6893.2021.26411

Abstract

With the increase of the gas temperature in the combustion chamber of the aero engine, the problem of radiation in the high temperature area will become more important. At the same time, the radiation characteristics will change drastically due to high temperature gas radiation, which will show a multi-scale phenomenon and thus increase the difficulty of radiation calculation. This paper uses the idea of steady discrete unified gas kinetics scheme (SDUGKS) to solve the steady-state radiation problem. SDUGKS schemes uses the method of differential discretization by characteristic line to achieve reconstruction of the unit interface, and realizes update of cell data through a certain iterative format. This process realizes effective simulation of the radiation characteristics inside the grid. The process can be applied to any specific radiation scale, so that the calculation of multi-scale problems can be realized under any grid condition. This paper introduces the deferred-correction (DC) method to update unit data, and calculates the single-scale and multi-scale problems. For the single-scale problem, the SDUGKS format is verified to be applicable for the steady-state radiation problem. The multi-scale problem is further constructed to be solved, which verifies the asymptotic preservation and accuracy of SDUGKS in calculation of multi-scale problems.

Key words： thermal radiation; steady state; multiscale; discrete unified gas kinetics scheme; deferred-correction (DC) method; asymptotic preservation

参考文献

[1] 廉筱纯, 吴虎. 航空发动机原理[M].西安: 西北工业大学出版社, 2005: 147-182. LIAN X C, WU H. Principle of aeroengine[M].Xi'an: Northwest University of Technology Press, 2005: 147-182 (in Chinese).
[2] MODEST M F. Radiative heat transfer[M].3th ed. Salt Lake City:Academic Press, 2013: 279-302.
[3] 索建秦, 馮翔洲, 梁紅俠, 等. 航空发动机燃烧室研发中的数值仿真探讨[J]. 航空动力, 2021(2): 61-65. SUO J Q, FENG X Z, LIANG H X, et al. Numerical simulation for research and development of aero engine combustor[J]. Aerospace Power, 2021(2): 61-65 (in Chinese).
[4] HOWELL J R, MENGVÇ M P, DAUN K, et al. Thermal radiation heat transfer[M].6th ed. New York: CRC Press, 2015: 573-664.
[5] 余其铮. 辐射换热原理[M].哈尔滨: 哈尔滨工业大学出版社, 2000: 144-160. YU Q Z. Principle of radiant heat transfer[M].Harbin: Harbin Institute of Technology Press, 2000: 144-160 (in Chinese).
[6] SUN W J, JIANG S, XU K. An asymptotic preserving implicit unified gas kinetic scheme for frequency-dependent radiative transfer equations[J]. International Journal of Numerical Analysis and Modeling, 2018, 15(1-2): 134-153.
[7] CERCIGNANI C. The boltzmann equation[M]//The Boltzmann equation and its applications. New York: Springer New York, 1988: 40-103.
[8] 刘沙, 王勇, 袁瑞峰, 等. 统一气体动理学方法研究进展[J]. 气体物理, 2019, 4(4): 1-13. LIU S, WANG Y, YUAN R F, et al. Advance in unified methods based on gas-kinetic theory[J]. Physics of Gases, 2019, 4(4): 1-13 (in Chinese).
[9] 刘畅, 徐昆. 离散时空直接建模思想及其在模拟多尺度输运中的应用[J]. 空气动力学学报, 2020, 38(2): 197-216. LIU C, XU K. Direct modeling methodology and its applications in multiscale transport process[J]. Acta Aerodynamica Sinica, 2020, 38(2): 197-216 (in Chinese).
[10] LI Z H, ZHANG H X. Study on gas kinetic unified algorithm for flows from rarefied transition to continuum[J]. Journal of Computational Physics, 2004, 193(2): 708-738.
[11] WU J L, LI Z H, ZHANG Z B, et al. On derivation and verification of a kinetic model for quantum vibrational energy of polyatomic gases in the gas-kinetic unified algorithm[J]. Journal of Computational Physics, 2021, 435: 109938.
[12] XU K, HUANG J C. A unified gas-kinetic scheme for continuum and rarefied flows[J]. Journal of Computational Physics, 2010, 229(20): 7747-7764.
[13] XU K, HUANG J C. An improved unified gas-kinetic scheme and the study of shock structures[J]. IMA Journal of Applied Mathematics, 2011, 76(5): 698-711.
[14] GUO Z L, XU K, WANG R J. Discrete unified gas kinetic scheme for all Knudsen number flows: Low-speed isothermal case[J]. Physical Review E, 2013, 88(3): 033305.
[15] ZHU L H, GUO Z L, XU K. Discrete unified gas kinetic scheme on unstructured meshes[J]. Computers & Fluids, 2016, 127: 211-225.
[16] 姚博, 张创, 郭照立. 考虑分子转动自由度的离散统一气体动理学格式[J]. 航空学报, 2019, 40(7): 122914. YAO B, ZHANG C, GUO Z L. Discrete unified gas kinetic scheme for diatomic gas with rotational degrees of freedom[J]. Acta Aeronautica et Astronautica Sinica, 2019, 40(7): 122914 (in Chinese).
[17] CHEN Y P, ZHU Y J, XU K. A three-dimensional unified gas-kinetic wave-particle solver for flow computation in all regimes[J]. Physics of Fluids, 2020, 32(9): 096108.
[18] SUN W J, JIANG S, XU K, et al. An asymptotic preserving unified gas kinetic scheme for frequency-dependent radiative transfer equations[J]. Journal of Computational Physics, 2015, 302: 222-238.
[19] SUN W J, JIANG S, XU K, et al. Multiscale simulation for the system of radiation hydrodynamics[J]. Journal of Scientific Computing, 2020, 85(2): 1-24.
[20] LUO X P, WANG C H, ZHANG Y, et al. Multiscale solutions of radiative heat transfer by the discrete unified gas kinetic scheme[J]. Physical Review E, 2018, 97(6-1): 063302.
[21] SONG X L, ZHANG C, ZHOU X F, et al. Discrete unified gas kinetic scheme for multiscale anisotropic radiative heat transfer[J]. Advances in Aerodynamics, 2020, 1: 50-64.
[22] 谈和平, 夏新林, 刘林华,等. 红外辐射特性与传输的数值计算: 计算热辐射学[M].哈尔滨: 哈尔滨工业大学出版社, 2006: 18-41. TAN H P,XIA X L, LIU L H,et al. Numerical calculation of infrared radiation characteristics and transmission: Computational thermal radiation[M].Harbin: Harbin Institute of Technology Press, 2006: 18-41 (in Chinese).
[23] ZHOU X F, GUO Z L. Discrete unified gas kinetic scheme for steady multiscale neutron transport[J]. Journal of Computational Physics, 2020, 423: 109767.
[24] ZHANG C, GUO Z L, CHEN S Z. Unified implicit kinetic scheme for steady multiscale heat transfer based on the phonon Boltzmann transport equation[J]. Physical Review E, 2017, 96(6-1): 063311.
[25] DEMBO R S, EISENSTAT S C, STEIHAUG T. Inexact Newton methods[J]. SIAM Journal on Numerical Analysis, 1982, 19(2): 400-408.
[26] CROCKATT M M, CHRISTLIEB A J, GARRETT C K, et al. An arbitrary-order, fully implicit, hybrid kinetic solver for linear radiative transport using integral deferred correction[J]. Journal of Computational Physics, 2017, 346: 212-241.
[27] DARWISH M S, MOUKALLED F. The normalized weighting factor method: A novel technique for accelerating the convergence of high-resolution convective schemes[J]. Numerical Heat Transfer, Part B: Fundamentals, 1996, 30(2): 217-237.
[28] XAMÁN J, ZAVALA-GUILLÉN I, HERNÁNDEZ-LÓPEZ I, et al. Evaluation of the CPU time for solving the radiative transfer equation with high-order resolution schemes applying the normalized weighting-factor method[J]. Journal of Quantitative Spectroscopy and Radiative Transfer, 2018, 208: 45-63.
[29] TRUELOVE J S. Discrete-ordinate solutions of the radiation transport equation[J]. Journal of Heat Transfer, 1987, 109(4): 1048-1051.

Options

文章导航

模态框（Modal）标题

摘要

本文引用格式

Abstract

参考文献