Modified δ-M Scaling Results for Mie-Anisotropic Scattering Media

1990 ◽  
Vol 112 (4) ◽  
pp. 988-994 ◽  
Author(s):  
T.-K. Kim ◽  
H. S. Lee
Keyword(s):  
Phase Function ◽  
Anisotropic Scattering ◽  
Asymmetry Factor ◽  
Discrete Ordinates ◽  
Scattering Media ◽  
Scattering Problems ◽  
Anisotropic Scaling ◽  
M Phase ◽  
Phase Functions ◽  
Transfer Problems

A modified δ-M scaling method, which adjusts the δ-M scaled phase functions to be always positive, is applied to radiative transfer problems in two-dimensional square enclosures. The scaled anisotropic results are compared with the results obtained from an accurate model of the full anisotropic scattering problems using the S-N discrete ordinates method. The modified δ-M anisotropic scaling is shown to improve the isotropic scaled results of a collimated incidence problem, but the required number of terms increases as the phase function complexity and the asymmetry factor increase. For the diffuse incidence problems, even a low-order modified δ-M phase function significantly improves the accuracy of scaled solutions over the isotropic scaling. Significant savings in the computer times are observed when the modified δ-M method is applied.

A New Phase Function Normalization Approach for Radiative Transfer Analysis in Highly Anisotropic Scattering Media

2011 ◽  
Author(s):  
Brian Hunter ◽  
Zhixiong Guo
Keyword(s):  
Phase Function ◽  
Solid Angle ◽  
Scaling Law ◽  
Anisotropic Scattering ◽  
Convergence Time ◽  
Extreme Condition ◽  
Asymmetry Factor ◽  
Scattering Media ◽  
Scattered Energy ◽  
New Phase

A new phase function normalization approach is applied to both the DOM and FVM for predicting radiative heat transfer in an extreme condition — highly anisotropic scattering media. Previous attempts to normalize the DOM result in a distortion of the overall phase function asymmetry factor. The splitting of each solid angle into numerous sub-angles in the FVM is shown to also produce a lack of conservation of asymmetry factor, even though scattered energy is conserved. The current normalization technique is crafted such that scattered energy and asymmetry factor are accurately conserved after both DOM and FVM discretization. The change in scattering effect when asymmetry factor is not conserved is examined for both methods. Wall flux profiles generated by DOM with old and new normalization techniques as well as FVM with and without phase function normalization are compared to isotropic scaling law profiles to gauge the accuracy of the techniques. The effects of changes in both optical thickness and scattering albedo are investigated. It is found that the current normalization approach vastly improves accuracy of flux profiles. The current procedure also greatly decreases FVM convergence time by eliminating the need for large amounts of solid angle splitting.

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.

Transient Radiative Transfer in Anisotropically Scattering Media Using Monotonicity-Preserving Schemes

2000 ◽  
Author(s):  
M. Sakami ◽  
K. Mitra ◽  
P.-F. Hsu
Keyword(s):  
Radiative Transfer ◽  
Research Work ◽  
Discrete Ordinates ◽  
Scattering Media ◽  
Discrete Ordinates Method ◽  
Piecewise Parabolic ◽  
Phase Functions ◽  
Monotonicity Preserving ◽  
Made In ◽  
Thick Medium

Abstract This research work deals with the analysis of transient radiative transfer in one-dimensional scattering medium. The time-dependant discrete ordinates method was used with an upwind monotonic scheme: the piecewise parabolic scheme. This scheme was chosen over a total variation diminishing version of the Lax-Wendroff scheme. These schemes were originally developed to solve Eulerian advection problem in hydrodynamics. The capability of these schemes to handle sharp discontinuity in a propagating electromagnetic wave front was compared. The accuracy and the efficiency of the discrete ordinates method associated with the piecewise parabolic advection scheme were studied. Comparisons with Monte Carlo and integral formulation methods show the accuracy and the efficiency of this proposed method. Parametric study for optically thin and thick medium, different albedos and phase functions is then made in the unsteady state zone.

Improved Treatment of Anisotropic Scattering for Ultrafast Radiative Transfer Analysis

2013 ◽  
Author(s):  
Brian Hunter ◽  
Zhixiong Guo
Keyword(s):  
Radiative Transfer ◽  
Phase Function ◽  
Energy Deposition ◽  
Radiant Energy ◽  
Diffuse Radiation ◽  
Anisotropic Scattering ◽  
Heat Fluxes ◽  
Asymmetry Factor ◽  
Conservation Of Energy ◽  
Numerical Predictions

The necessity of conserving both scattered energy and asymmetry factor for ballistic incidence after either FVM or DOM discretization is convincingly shown by analyzing ultrafast laser radiative transfer in a cubic enclosure housing a participating medium. A phase-function normalization technique introduced previously by the present authors to correct for non-conservation of energy and asymmetry factor in diffuse radiant energy scattering is applied to scattering of ballistic incidence for the first time in 3-D FVM/DOM in order to improve treatment of anisotropic scattering through reduction of angular false scattering errors. Treatment of only the diffuse radiation will not conserve ballistic properties if the direction of ballistic incidence differs from a predetermined discrete direction. Our ultrafast radiative transfer predictions generated using the FVM and DOM are compared to benchmark Monte Carlo predictions in the literature to gauge accuracy and to illustrate the necessity of ballistic phase-function normalization. Additionally, numerical predictions of energy deposition in a tissue-phantom medium are analyzed to further clarify the importance of accurate numerical predictions. It is shown that the addition of 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.

Implementation of SLW model in the radiative heat transfer problems with particles and high temperature gradients

2017 ◽  
Vol 27 (5) ◽  
pp. 1128-1141 ◽  
Author(s):  
Rahul Yadav ◽  
C. Balaji ◽  
S.P. Venkateshan
Keyword(s):  
High Temperature ◽  
Radiative Heat ◽  
Anisotropic Scattering ◽  
Heat Fluxes ◽  
Temperature Gradients ◽  
Discrete Ordinates ◽  
Content Type ◽  
Practical Applications ◽  
Transfer Problems ◽  
Rocket Exhaust

Purpose The paper aims to test the spectral line-based weighted sum of gray gases (SLW) method in axisymmetric geometries with particles and high temperature gradients. Design/methodology/approach An SLW model is coupled with Trivic’s mean wavelength approach to estimate the radiative heat fluxes at the wall of an enclosure and to the base wall of the rocket exhaust, thereby subsequently studying the effect of concentration variation of the gases and particles in these cases. Radiative transfer equation is solved using modified discrete ordinates method. Anisotropic scattering is modeled using transport approximation. Findings Two cases considered show the importance of particle emission and scattering in the rocket plume base heating problems. In cases involving only gases, the concentration of H2O tends to have more impact on the flux values than any other gas. Originality/value A full model of gases with particles in an axially varying temperature field is reported. Such cases are very common in practical applications. The present methodology gives more insight and a firm handle on the problem vis-a-vis other traditional techniques.

Least-Squares Finite Element Analysis for Transient Radiative Transfer in Absorbing and Scattering Media

2005 ◽  
Vol 128 (5) ◽  
pp. 499-503 ◽  
Author(s):  
W. An ◽  
L. M. Ruan ◽  
H. P. Tan ◽  
H. Qi
Keyword(s):  
Finite Element ◽  
Radiative Transfer ◽  
Least Squares ◽  
Present Model ◽  
Element Model ◽  
Discrete Ordinates ◽  
Scattering Media ◽  
Element Analysis ◽  
Volume Method ◽  
Transfer Problems

In some radiative transfer processes, the time scales are usually on the order of 10−9-10−15s, so the transient effect of radiation should be considered. In present research, a finite element model, which is based on the discrete ordinates method and least-squares variational principle, is developed to simulate the transient radiative transfer in absorbing and scattering media. The numerical formulations and detailed steps are given. Moreover, two transient radiative transfer problems are investigated and the results are compared with those by integral method and finite volume method. It indicates that the present model can simulate the transient radiative transfer effectively and accurately.

scholarly journals ON INCREASING THE EFFICIENCY OF A DISCRETE ORDINATES RADIATIVE TRANSFER METHOD WITH PERIODIC RELATIONS

2005 ◽  
Vol 4 (2) ◽  
pp. 181
Author(s):  
M. P. De Abreu
Keyword(s):  
Radiative Transfer ◽  
Computer Time ◽  
Anisotropic Scattering ◽  
Discrete Ordinates ◽  
Coupling Coefficients ◽  
Radiation Beam ◽  
Component Method ◽  
Two Component ◽  
Transfer Method ◽  
Transfer Problems

In this article, improvements in a recently developed discrete ordinates method – the two-component method - are reported. The method solves conservative and non-conservative radiative heat transfer problems with anisotropic scattering on a multislab domain irradiated from one side with a radiation beam. The beam here consists of a monodirectional (singular) stream and of a continuous (regular) distribution in angle. Specifically, the computational efficiency of this two-component method has been increased with the help of new periodic relations for the coupling coefficients that appear in the numerical component of the method. With these periodic relations, memory usage requirement for storing the (usually large number of) coupling coefficients has been halved, while saving computer time from unnecessary computation of redundant coefficients. The increased efficiency of the two-component method has been illustrated with numerical results and discussion of a model problem in shortwave radiative transfer.

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