Discrete Ordinates Solutions of Nongray Radiative Transfer With Diffusely Reflecting Walls

1993 ◽  
Vol 115 (1) ◽  
pp. 184-193 ◽  
Author(s):  
J. A. Menart ◽  
HaeOk Skarda Lee ◽  
Tae-Kuk Kim
Keyword(s):  
Radiative Transfer ◽  
Numerical Solutions ◽  
Correlation Effect ◽  
Heat Fluxes ◽  
Discrete Ordinates ◽  
Band Model ◽  
Multiple Reflections ◽  
Spectral Correlation ◽  
Closure Approximation ◽  
Spectral Equation

Nongray gas radiation in a plane parallel slab bounded by gray, diffusely reflecting walls is studied using the discrete ordinates method. The spectral equation of transfer is averaged over a narrow wavenumber interval preserving the spectral correlation effect. The governing equations are derived by considering the history of multiple reflections between two reflecting walls. A closure approximation is applied so that only a finite number of reflections have to be explicitly included. The closure solutions express the physics of the problem to a very high degree and show relatively little error. Numerical solutions are obtained by applying a statistical narrow-band model for gas properties and a discrete ordinates code. The net radiative wall heat fluxes and the radiative source distributions are obtained for different temperature profiles. A zeroth-degree formulation, where no wall reflection is handled explicitly, is sufficient to predict the radiative transfer accurately for most cases considered, when compared with increasingly accurate solutions based on explicitly tracing a larger number of wall reflections without any closure approximation applied.

Nongray Radiative Gas Analyses Using the S-N Discrete Ordinates Method

1991 ◽  
Vol 113 (4) ◽  
pp. 946-952 ◽  
Author(s):  
T. K. Kim ◽  
J. A. Menart ◽  
H. S. Lee
Keyword(s):  
Radiative Heat ◽  
Narrow Band ◽  
Wide Band ◽  
Heat Fluxes ◽  
Discrete Ordinates ◽  
Band Model ◽  
Spectral Correlation ◽  
Discrete Ordinates Method ◽  
Computational Speed ◽  
Wide Band Model

The S-N discrete ordinates method is applied to analyze radiative heat transfer in nongray gases. Spectral correlation between the terms in the equation of transfer is considered for black or nearly nonreflecting walls. Formulations to apply the S-N method using a narrow-band or the exponential wide-band model are presented. The net radiative wall heat fluxes and the radiative source distributions are obtained for uniform, parabolic, and boundary layer type temperature profiles, as well as for a parabolic concentration profile. The narrow- and wide-band nongray solutions are compared with gray-band approximations using the same band models. The computational speed of the gray-band approximation is obtained at the expense of accuracy in the internal fluxes and radiative source distributions. The wall radiative flux predictions by the gray-band approximation are satisfactory.

Investigation of Radiative Transfer in Nongray Gases Using a Narrow Band Model and Monte Carlo Simulation

1994 ◽  
Vol 116 (1) ◽  
pp. 160-166 ◽  
Author(s):  
J. Liu ◽  
S. N. Tiwari
Keyword(s):  
Monte Carlo ◽  
Radiative Transfer ◽  
Narrow Band ◽  
Heat Fluxes ◽  
Radiative Energy ◽  
Band Model ◽  
Spectral Correlation ◽  
The Monte Carlo Method ◽  
Finite Volume Element ◽  
Narrow Band Model

The Monte Carlo method (MCM) is applied to analyze radiative heat transfer in nongray gases. The nongray model employed is based on the statistical narrow band model with an exponential-tailed inverse intensity distribution. The amount and transfer of the emitted radiative energy in a finite volume element within a medium are considered in an exact manner. The spectral correlation between transmittances of two different segments of the same path in a medium makes the statistical relationship different from the conventional relationship that only provides the noncorrelated results for nongray analysis. Two features of the MCM that are different from other nongray numerical methods are discussed. The simplicity of the MCM is demonstrated by considering the case of radiative transfer between two reflecting walls. The results for the radiative dissipation distributions and the net radiative wall heat fluxes are obtained for uniform, parabolic, and boundary layer type temperature profiles, as well as for a parabolic concentration profile. They are compared with available results of other methods. Good agreements are found for all the cases considered.

scholarly journals Numerical Solutions of Three-Dimensional Non-Grey Gas Radiative Transfer Using the Statistical Narrow-Band Model

1999 ◽  
Vol 121 (1) ◽  
pp. 200-203 ◽  
Author(s):  
F. Liu
Keyword(s):  
Radiative Transfer ◽  
Numerical Solutions ◽  
Radiative Transfer Equation ◽  
Narrow Band ◽  
Pure Water ◽  
Three Dimensional ◽  
Band Model ◽  
Real Gas ◽  
Gas Radiation ◽  
Narrow Band Model

Three-dimensional non-grey gas radiation analyses were conducted using the statistical narrow-band model along with up-dated band parameters. The exact narrow-band averaged radiative transfer equation was solved using a ray-tracing method. Accurate numerical results were presented for non-grey real gas radiative transfer in a three-dimensional rectangular enclosure containing (i) an isothermal pure water vapor at 1000 K and 1 atm, (ii) an isothermal and inhomogeneous H2O/N2 mixture at 1000 K and 1 atm, and (iii) a nonisothermal and homogeneous mixture of CO2/H2O/N2 at 1 atm.

Normalization for Ultrafast Radiative Transfer Analysis With Collimated Irradiation

2012 ◽  
Author(s):  
Brian Hunter ◽  
Zhixiong Guo
Keyword(s):  
Radiative Transfer ◽  
Phase Function ◽  
Function Approximation ◽  
Energy Deposition ◽  
Heat Fluxes ◽  
Asymmetry Factor ◽  
Discrete Ordinates ◽  
Discrete Ordinates Method ◽  
Scattered Energy ◽  
The Impact

Normalization of the scattering phase function is applied to the transient discrete ordinates method for ultrafast radiative transfer analysis in a turbid medium subject to a normal collimated incidence. Previously, the authors have developed a normalization technique which accurately conserves both scattered energy and phase function asymmetry factor after directional discretization for the Henyey-Greenstein phase function approximation in steady-state diffuse radiative transfer analysis. When collimated irradiation is considered, additional normalization must be applied to ensure that the collimated phase function also satisfies both scattered energy and asymmetry factor conservation. The authors’ technique is applied to both the diffuse and collimated components of scattering using the general Legendre polynomial phase function approximation for accurate and efficient ultrafast radiative transfer analysis. The impact of phase function normalization on both predicted heat fluxes and overall energy deposition in a model tissue cylinder is investigated for various phase functions and optical properties. A comparison is shown between the discrete ordinates method and the finite volume method. It is discovered that a lack of conservation of asymmetry factor for the collimated component of scattering causes over-predictions in both energy deposition and heat flux for highly anisotropic media.

Improved Treatment of Anisotropic Scattering for Ultrafast Radiative Transfer Analysis

2015 ◽  
Vol 137 (9) ◽  
Author(s):  
Brian Hunter ◽  
Zhixiong Guo
Keyword(s):  
Radiative Transfer ◽  
Phase Function ◽  
Energy Deposition ◽  
Anisotropic Scattering ◽  
Heat Fluxes ◽  
Asymmetry Factor ◽  
Discrete Ordinates ◽  
Improve Treatment ◽  
Scattered Energy ◽  
Volume Method

The necessity of conserving both scattered energy and asymmetry factor for ballistic incidence after finite volume method (FVM) or discrete-ordinates method (DOM) discretization is shown. A phase-function normalization technique introduced previously by the present authors is applied to scattering of ballistic incidence in 3D FVM/DOM to improve treatment of anisotropic scattering through reduction of angular false scattering errors. Ultrafast radiative transfer predictions generated using FVM and DOM are compared to benchmark Monte Carlo to illustrate the necessity of ballistic phase-function normalization. Proper ballistic phase-function treatment greatly improves predicted heat fluxes and energy deposition for anisotropic scattering and for situations where accurate numerical modeling is crucial.

Numerical Modeling of Radiative and Reactive Flow Field Around a Blunt Body at Hypersonic Regimes

2010 ◽  
Author(s):  
Morteza Rahmanpour ◽  
Reza Ebrahimi ◽  
Mehrzad Shams
Keyword(s):  
Flow Field ◽  
Differential Equations ◽  
Heat Fluxes ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Discrete Ordinates ◽  
Two Dimensional ◽  
Fully Implicit ◽  
Time Marching

A numerical method for calculation of strong radiation for two-dimensional reactive air flow field is developed. The governing equations are taken to be two dimensional, compressible Reynolds-average Navier-Stokes and species transport equations. Also, radiation heat flux in energy equation is evaluated using a model of discrete ordinate method. The model used S4 approximation to reduce the governing system of integro-differential equations to coupled set of partial differential equations. A multiband model is used to construct absorption coefficients. Tangent slab approximation is assumed to determine the characteristic parameters needed in the Discrete Ordinates Method. The turbulent diffusion and heat fluxes are modeled by Baldwin and Lomax method. The flow solution is obtained with a fully implicit time marching method. A thermochemical nonequilibrium formulation appropriate to hypersonic transitional flow of air is presented. The method is compared with existing experimental results and good agreement is observed.

An Efficient Sparse Finite Element Solver for the Radiative Transfer Equation

2009 ◽  
Author(s):  
Gisela Widmer
Keyword(s):  
Linear System ◽  
Radiative Transfer ◽  
Transfer Equation ◽  
Degrees Of Freedom ◽  
Radiative Transfer Equation ◽  
Three Dimensional ◽  
Discrete Ordinates ◽  
Five Dimensions ◽  
Computational Costs ◽  
Dimensional Domain

The stationary monochromatic radiative transfer equation (RTE) is posed in five dimensions, with the intensity depending on both a position in a three-dimensional domain as well as a direction. For non-scattering radiative transfer, sparse finite elements [1, 2] have been shown to be an efficient discretization strategy if the intensity function is sufficiently smooth. Compared to the discrete ordinates method, they make it possible to significantly reduce the number of degrees of freedom N in the discretization with almost no loss of accuracy. However, using a direct solver to solve the resulting linear system requires O(N3) operations. In this paper, an efficient solver based on the conjugate gradient method (CG) with a subspace correction preconditioner is presented. Numerical experiments show that the linear system can be solved at computational costs that are nearly proportional to the number of degrees of freedom N in the discretization.

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