一维辐射传递方程的谱方法求解
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摘要
对于辐射传递方程的求解已经发展了很多方法,区域法、热通量法、蒙特卡洛法、离散坐标法等。综合看来,基于微分形式辐射传递方程离散的方法具有很好的适应性,上述传统方法在求解辐射传递方程时各有优点,但也有其本身不可克服的缺点。发展一种高精度、高效率、简便的数值求解辐射传递方程的方法仍然必要。
谱方法可以很好的克服低阶方法的不足,能高效地得到高精度的计算结果,而其所用的计算方法简便。本文利用谱方法解决半透明介质中的辐射换热问题,主要工作分两部分：
1.利用谱方法求解一维直角坐标系下的辐射传递方程,分别对不考虑介质散射和考虑介质散射两种情况进行计算,研究了该方法的数值稳定性,并与精确解或其他方法的数值解进行比较。结果表明,谱方法适用于一维直角坐标下辐射传递方程的求解,而且相对于其他方法具有较高的精度。
2.利用谱方法解决一维球面坐标系下的辐射换热问题以及一维球面坐标系下辐射与导热耦合问题。通过对谱方法求解结果与文献的结果进行比较和误差分析,验证了谱方法能简便、高效、高精度的解决一维球面坐标系下辐射问题以及辐射与导热相耦合的问题。
Many numerical methods have been developed for solving radiative heat transfer problems in semitransparent media, such as, zonal method, heat flux method, Monte-Carlo method, and discrete ordinates method, etc. By comprehensive comparison, the methods based on discretization of the differential form of radiative transfer equation possess very good flexibility. However, there are still some disadvantages existing in the former methods. It is necessary to develop a high accurate, efficient and simple numerical method to solve radiative transfer equations.
Spectral methods can somewhat overcome the drawbacks of low order methods, and can provide accurate results, while their solution procedures of spectral methods are something efficient and simple. The author develops and studies the characteristics of spectral methods to solve radiative transfer equation in semitransparent media. The present research contains two parts:
1. The spectral method is used to solve radiative transfer equation in one-dimensional Cartesian coordinate systems. The numerical stability of spectral methods is investigated for solving radiative heat transfer under the both cases of non-scattering media and scattering media. The present numerical solutions are compared with those of references by exact or other numerical methods. The results show that the spectral methods have good accuracy and efficiency for solving one-dimensional radiative heat transfer problems.
2. Spectral methods are presented to solve radiative heat transfer equations and coupled conduction-radiation problems in spherical media. An error comparison is made between present results and those from references. The final conclusions can be obtained that:the spectral methods can be used to solve radiative heat transfer alone, and can also to solve the coupled conduction-radiation problems in one-dimensional spherical media system efficiently.
谱方法可以很好的克服低阶方法的不足,能高效地得到高精度的计算结果,而其所用的计算方法简便。本文利用谱方法解决半透明介质中的辐射换热问题,主要工作分两部分：
1.利用谱方法求解一维直角坐标系下的辐射传递方程,分别对不考虑介质散射和考虑介质散射两种情况进行计算,研究了该方法的数值稳定性,并与精确解或其他方法的数值解进行比较。结果表明,谱方法适用于一维直角坐标下辐射传递方程的求解,而且相对于其他方法具有较高的精度。
2.利用谱方法解决一维球面坐标系下的辐射换热问题以及一维球面坐标系下辐射与导热耦合问题。通过对谱方法求解结果与文献的结果进行比较和误差分析,验证了谱方法能简便、高效、高精度的解决一维球面坐标系下辐射问题以及辐射与导热相耦合的问题。
Many numerical methods have been developed for solving radiative heat transfer problems in semitransparent media, such as, zonal method, heat flux method, Monte-Carlo method, and discrete ordinates method, etc. By comprehensive comparison, the methods based on discretization of the differential form of radiative transfer equation possess very good flexibility. However, there are still some disadvantages existing in the former methods. It is necessary to develop a high accurate, efficient and simple numerical method to solve radiative transfer equations.
Spectral methods can somewhat overcome the drawbacks of low order methods, and can provide accurate results, while their solution procedures of spectral methods are something efficient and simple. The author develops and studies the characteristics of spectral methods to solve radiative transfer equation in semitransparent media. The present research contains two parts:
1. The spectral method is used to solve radiative transfer equation in one-dimensional Cartesian coordinate systems. The numerical stability of spectral methods is investigated for solving radiative heat transfer under the both cases of non-scattering media and scattering media. The present numerical solutions are compared with those of references by exact or other numerical methods. The results show that the spectral methods have good accuracy and efficiency for solving one-dimensional radiative heat transfer problems.
2. Spectral methods are presented to solve radiative heat transfer equations and coupled conduction-radiation problems in spherical media. An error comparison is made between present results and those from references. The final conclusions can be obtained that:the spectral methods can be used to solve radiative heat transfer alone, and can also to solve the coupled conduction-radiation problems in one-dimensional spherical media system efficiently.
引文
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5. W.H. Sutton and X.L. Chen. A General Intergration Method for Radiative Transfer in 3-D Non-Homogeneous Cylindrical Media with Anisotropic Scattering [J]. Journal of Quantitative Spectroscopy and Radiative Transfer.2004,84:65-103
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9.郭印诚,林文漪.马蹄形火焰玻璃熔窑燃烧空间流动与传热的数值模拟[J].燃烧科学与技术.2000,6(3)：244-248.
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38. S. A. Orszag and L. C. Kells. Transition to turbulence in plane Poiseuille and plane Couette flow [J]. J. Fluid Mech.1980,96:159-205.
39. A.T. Partera. A spectral element method for fluid dynamics:laminar flow in a channel expansion [J]. J. Comput. Phys.1984,54:468-488
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41. K. Abeand O. Inoue. Fourier expansion solution of the KDV equation [J]. J. Comp. Phys. 34:202-210,1980.
42. D. Kosloff and R. Kosloff. A Fourier method solution for the time dependent Schrodinger equation as a tool in molecular dynamics [J]. J. Comp. Phys.52:35-53,1983.
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2.范维澄等.计算燃烧学[M].安徽科学技术出版社,1988.
3. E.P. Keramidaa, H.H. Liakosa, M.A. Fountib. A.G. Boudouvisa and N.C. Markatos. Radiative Heat Transfer in Natural Gas-Fired Furances [J]. International Journal of Heat and Mass Transfer.2000,43:1801-1809.
4. B.Zheng, C.X.Lin and M.A. Ebadian. Combined Turbulent Forced Convection and Thermal Radiation in a Curved Pipe with Uniform Wall Temperature [J]. Numerical Heat Transfer Part A.2003,44 (2)149-167.
5. W.H. Sutton and X.L. Chen. A General Intergration Method for Radiative Transfer in 3-D Non-Homogeneous Cylindrical Media with Anisotropic Scattering [J]. Journal of Quantitative Spectroscopy and Radiative Transfer.2004,84:65-103
6.侯晓春,季鹤鸣,刘庆国,严传俊,赵坚行.高性能航空燃气轮机燃烧技术[M].北京：国防工业出版社,2002.
7. H. Miyama, H. Kaiji, Y. Hirose and N. Arai. Heat Transfer Characteristics of a Rotary Regenerative Combustion System (RRX) [J]. Heat Transfer-Japanese Research.1998,27 (8):585-596.
8. J. Abraham and V. Magi. Application of Discrete Ordinates Method to Compute Radiant Heat Loss in a Diesel Engine [J]. Numerical Heat Transfer Part A.1997,31 (6):597-610.
9.郭印诚,林文漪.马蹄形火焰玻璃熔窑燃烧空间流动与传热的数值模拟[J].燃烧科学与技术.2000,6(3)：244-248.
10.闵桂荣,郭舜.航天器热控制[M].第二版.北京：科学出版社,1998.
11. S.S. Penner and D.B. Olfe. Radiation and Reentry [M]. New York:Academic Press,1968.
12 T. Nakamura and T.Kai. Combined Radiation-Conduction Analysis and Experiment of Ceramic Insulation for Reentry Vehicles [J]. Journal of Thermophysics and Heat Transfer. 2004,18 (1):24-29
13.P.J. Coelho. Detailed Numerical Simulation of Radiative Transfer in a Nonluminous Turbulent Jet Diffusion Flame [J]. Combustion and Flame.2004,136:481-492
14.张文普,丰镇平.级间分离的流畅及热流分析研究[J].推进技术.2003,24(3)：240-243.
15.谈和平,夏新林,刘林华,阮立明.红外辐射特性与传输数值计算[M].哈尔滨：哈 尔滨工业大学出版社,2006,
16.强希文,王铁良,吴乃清.多光束激光大气传输[J].光子技术.1999.19(3)：167-172.
17.李现勤,程兆谷,蒋金波.激光束在大气中长距离传输聚焦特性的研究[J].光学学报.2001,21(3)：324-329
18.曹百灵,邬乘就,饶瑞中,魏合理,袁译谦HF/DF激光传输的大气衰减特性[J].强激光与粒子束.2003,15(1)：17-20
19. S. Lahsasni, M. Kouhila, M. Mahrouz, A. Idlimam and A. Jamali. Thin Layer Convective Solar Drying and Mathematical Modeling of Prickly Pear Peel [J]. Energy.2004,29:211-224.
20. D.A. Lashof and D.R. Ahuja. Relative Contributions of Greenhouse Gas Emissions to Global Warming [J]. Nature.1990,344:529-531.
21. R.S. Linden. Some Coolness Concerning Global Warming [J]. Bulletin of the American Meteorological Society.1990,71 (3):288-199
22.史光梅,刘朝.工业炉内辐射换热模型研究进展[J].工业加热,2004,33(5),9-12.
23.刘林华.炉膛传热计算方法的发展状况[J].动力工程,2000,20(1),523-538.
24. H.C. Hottel and E.S. Cohen. Radiant Heat Exchange in a Gas-Filled Enclosure Allowance for Nonuniformity of Gas Temperature [J].AICE Joural.1958,4:3-14.
25. M.S. Patterson, B.C. Wilson and D.R. Wyman. The Propagation of Optical Radiation in Tissue I [J]. Models of Radiation Transport and Their Application Lasers in Medical Science. 1991,6(2):155-168.
26. J.T. Farmer and J.R. Howell. Monte Carlo Prediction of Radiative Heat Transfer in Inhomogeneous, Anisotropic, Nongray Media [J]. Journal of Thermophysics and Heat Transfer. 1994,8(1):133-139.
27. J.R. Howell. Application of Monte Carlo to Heat Transfer Problems [J].Advances in Heat Transfer.1968,5:1-54.
28. J.R. Howell and M. Perlmutter. Monte Carlo Solution of Thermal Transfer through Radiat Media between Gray Walls [J]. ASME Journal of Heat Transfer.1964,86 (1):116-122
29. TJ. Love, R.J. Grosh. Radiative heat transfer in absorbing, emitting and scattering media [J]. ASME Heat Transfer,1965,87:161-166.
30. J.S. Troulove. Discrete-Oridinates Solutions of the Radiative Transport Equation for Rectangular Enclosures [J]. ASME.J.Heat Transfer,1987,109:1048-1051.
31.刘林华,余其铮,阮立明,谈和平.求解辐射传递方程的离散坐标方法[J].中国工程热物理学会传热传值学学术会议论文集(下册).中国工程热物理学会编.北京：1996：47-54.
32.李本文.辐射换热新的离散坐标方法(第一部分)[D].浙江大学博士后(第二站)研究工作报告.浙江大学,1998：3-12
33.李本文,陈海耿,宁宝林,陶文铨,复杂炉型内有非均匀介质参与的热过程数学模型[J].化工学报.1996,47(3)：273-278.
34.杨占春,武文斐,李义科.模拟辐射传热的离散坐标法的改进[J].计算物理,2005,22(3).
35. S.A. Orszag. Numerical simulation of incompressible flows within simple boundaries Garlerkin (spectral) representation [J]. Studie in Appl. Math,1971,50:395-401
36. S.A. Orszag. Turbulence and transition:A progress report, Proc. Fifth International Conference on Numerical Methods in Fluid Dynamics, A.I. Van de Vooren and P.J. Zandbergen eds [J]. Springer-Verlag, Berlin,1976.
37. H. Wengle and J. H. Seifeld. Pseudospectral solution of atmospheric diffusion problems [J]. J. Comp. phys.1978,26:87-106.
38. S. A. Orszag and L. C. Kells. Transition to turbulence in plane Poiseuille and plane Couette flow [J]. J. Fluid Mech.1980,96:159-205.
39. A.T. Partera. A spectral element method for fluid dynamics:laminar flow in a channel expansion [J]. J. Comput. Phys.1984,54:468-488
40. D. B. Haidvogel. A.R. Robinson and E.E. Schulman. The accuracy efficiency and stability of three numerical models with application to open ocean problems [J]. J. Comp. phy.34:1-53, 1980.
41. K. Abeand O. Inoue. Fourier expansion solution of the KDV equation [J]. J. Comp. Phys. 34:202-210,1980.
42. D. Kosloff and R. Kosloff. A Fourier method solution for the time dependent Schrodinger equation as a tool in molecular dynamics [J]. J. Comp. Phys.52:35-53,1983.
43.张公礼,潘爱玲.数字谱方法的理论与应用.国防工业出版社,1992.
44. D. Gottlieb and S. Orszag. Numerical Analysis of Spectral Methods:Theroy and Applications [J]. SCAM-CBMS, Phiadelphia,1977.
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