作者：
Zhou, Rui-RuiSun, Ya-SongLi, Ben-WenMa, JingUniv Shanghai Sci & Technol
Sch Energy & Power Engn Shanghai Key Lab Multiphase Flow & Heat Transfer Shanghai 200093 Peoples R China Northwestern Polytech Univ
Sch Power & Energy Shaanxi Key Lab Thermal Sci Aeroengine Syst Xian 710072 Peoples R China NPU
Ctr Computat Phys & Energy Sci Yangtze River Delta Res Inst Taicang 215400 Peoples R China Dalian Univ Technol
Sch Energy & Power Engn Key Lab Ocean Energy Utilizat & Energy Conservat Minist Educ Dalian 116024 Peoples R China Changan Univ
Sch Automobile Key Lab Shaanxi Prov Dev & Applicat New Transport Xian 710064 Peoples R China
Recently, the Chebyshev integration method was developed to solve the radiative integral transfer equations (RITEs) after singularity removing (IJTS, 149 (2020) 106,158), and shown fourth order convergence accuracy. T...
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Recently, the Chebyshev integration method was developed to solve the radiative integral transfer equations (RITEs) after singularity removing (IJTS, 149 (2020) 106,158), and shown fourth order convergence accuracy. This superior property makes the Chebyshev integration method attractive to produce results with quite high accuracy to be benchmark solutions. However, the Chebyshev integration method, which is a global method, is only suitable for problems with smooth parameters and temperature distribution. To overcome this drawback, in this paper, the composite Chebyshev integration method is proposed. The computational domain is divided into several subdomains, and then the Chebyshev quadrature is applied in each subdomain. Several benchmark problems in the rectangular medium with continuous/stepwise-change scattering albedo and emissions are solved. Increasing the grid number with fixed subdomains, one can observe that the composite Chebyshev integration method still has the high order convergence accuracy. Besides, the solutions rounded to seven significant digits are given in tabular form for convenience. They are also used as benchmark solutions to assess the collocation spectral method (CSM) and its modified version for radiative transfer equation (RTE). The results indicate that the CSM suffers from severe ray effect when the discontinuities appear in the scattering albedo and temperature distribution. Though the modified CSM can avoid the ray effect due to stepwise-change emissions, it requires heavier computational load but produces less accurate results than the composite Chebyshev integration method for RITEs under the same spatial grid system. Compared with the CSM or modified CSM to solve the RTE, the composite Chebyshev integration method for RITEs can achieve much higher accuracy with acceptable computational time, thus could also be a good alternative for thermal radiation calculations in simple geometry.
In this paper, an investigation of radiative transfer in a rectangular medium with one-dimensional or two-dimensional graded index is presented. The integral equations of intensity moments are derived and then the cas...
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In this paper, an investigation of radiative transfer in a rectangular medium with one-dimensional or two-dimensional graded index is presented. The integral equations of intensity moments are derived and then the cases of a cold medium exposed to diffuse irradiation at the left boundary are solved by the Nystrom method. The results obtained by solving integral equations are in excellent agreement with those obtained by the Monte Carlo method and the discrete ordinates method. For the case with an increasing refractive index in the direction to the right boundary, the distribution of refractive index enhances the radiation in the direction to the right, and so the half-range flux toward the right boundary increases with the increase of the gradient of refractive index. Besides, the half-range flux toward the right boundary decreases as the position considered approaches the top or bottom boundary. (C) 2013 Elsevier Ltd. All rights reserved.
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