Solution Methods for Radiative Transfer in Participating Media

2015 ◽  
pp. 607-698
Keyword(s):  
Radiative Transfer ◽  
Participating Media ◽  
Solution Methods

The Weighted-Sum-of-Gray-Gases Model for Arbitrary Solution Methods in Radiative Transfer

1991 ◽  
Vol 113 (3) ◽  
pp. 650-656 ◽  
Author(s):  
M. F. Modest
Keyword(s):  
Radiative Transfer ◽  
Integral Equations ◽  
Solution Method ◽  
Weighted Sum ◽  
Arbitrary Solution ◽  
Absorption Coefficients ◽  
Zonal Method ◽  
Radiation Problem ◽  
Participating Media ◽  
Solution Methods

The weighted-sum-of-gray-gases approach for radiative transfer in nongray participating media, first developed by Hottel in the context of the zonal method, has been shown to be applicable to the general radiative equation of transfer. Within the limits of the weighted-sum-of-gray-gases model (nonscattering media within a black-walled enclosure), any nongray radiation problem can be solved by any desired solution method after replacing the medium by an equivalent small number of gray media with constant absorption coefficients. Some examples are presented for isothermal media and media at radiative equilibrium, using the exact integral equations as well as the popular P-I approximation for the equivalent gray media solutions. The results demonstrate the equivalency of the method with the quadrature of spectral results, as well as the tremendous computer times savings (by a minimum of 95 percent) that are achieved.

Accelerate Iteration of Least-Squares Finite Element Method for Radiative Heat Transfer in Participating Media With Diffusely Reflecting Walls

2012 ◽  
Vol 134 (4) ◽  
Author(s):  
Wei An ◽  
Tong Zhu ◽  
NaiPing Gao
Keyword(s):  
Heat Transfer ◽  
Finite Element Method ◽  
Boundary Condition ◽  
Finite Element ◽  
Radiative Transfer ◽  
Radiative Heat Transfer ◽  
Radiative Heat ◽  
Present Model ◽  
Participating Media ◽  
Element Method

A high reflectivity of walls often leads to prohibitive computation time in the numerical simulation of radiative heat transfer. Such problem becomes very serious in many practical applications, for example, metal processing in high-temperature environment. The present work proposes a modified diffusion synthetic acceleration model to improve the convergence of radiative transfer calculation in participating media with diffusely reflecting boundary. This model adopts the P1 diffusion approximation to rectify the scattering source term of radiative transfer equation and the reflection term of the boundary condition. The corrected formulation for boundary condition is deduced and the algorithm is realized by finite element method. The accuracy of present model is verified by comparing the results with those of Monte Carlo method and finite element method without any accelerative technique. The effects of emissivity of walls and optical thickness on the convergence are investigated. The results indicate that the accuracy of present model is reliable and its accelerative effect is more obvious for the optically thick and scattering dominated media with intensive diffusely reflecting walls.

Finite-Volume Solution of the P3 Equations of Radiative Transfer and Coupling to Reacting Flow Calculations

2009 ◽  
Author(s):  
Mahesh Ravishankar ◽  
Sandip Mazumder ◽  
Ankan Kumar
Keyword(s):  
Radiative Transfer ◽  
Finite Volume ◽  
Unstructured Mesh ◽  
Laminar Flame ◽  
Cell Group ◽  
Reacting Flow ◽  
Computational Domain ◽  
Algebraic Equations ◽  
Participating Media ◽  
Cpu Time

The method of spherical harmonics (or PN) is a popular method for approximate solution of the radiative transfer equation (RTE) in participating media. A rigorous conservative finite-volume (FV) procedure is presented for discretization of the P3 equations of radiative transfer in two-dimensional geometry—a set of four coupled second-order partial differential equations. The FV procedure, presented here, is applicable to any arbitrary unstructured mesh topology. The resulting coupled set of discrete algebraic equations are solved implicitly using a coupled solver that involves decomposition of the computational domain into groups of geometrically contiguous cells using the Binary Spatial Partitioning algorithm, followed by fully implicit coupled solution within each cell group using a pre-conditioned Generalized Minimum Residual (GMRES) solver. The RTE solver is first verified by comparing predicted results with published Monte Carlo (MC) results for a benchmark problem. For completeness, results using the P1 approximation are also presented. As expected, results agree well with MC results for large/intermediate optical thicknesses, and the discrepancy between MC and P3 results increase as the optical thickness is decreased. The P3 approximation is found to be more accurate than the P1 approximation for optically thick cases. Finally, the new RTE solver is coupled to a reacting flow code and demonstrated for a laminar flame calculation using an unstructured mesh. It is found that the solution of the 4 P3 equations requires 14.5% additional CPU time, while the solution of the single P1 equation requires 9.3% additional CPU time over the 10 equations that are solved for the reacting flow calculations.

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