Scaled Isotropic Results for Two-Dimensional Anisotropic Scattering Media

1990 ◽  
Vol 112 (3) ◽  
pp. 721-727 ◽  
Author(s):  
T.-K. Kim ◽  
H. S. Lee
Keyword(s):  
Boundary Conditions ◽  
Phase Function ◽  
Side Wall ◽  
Incident Radiation ◽  
Anisotropic Scattering ◽  
Isotropic Scattering ◽  
Isotropic Phase ◽  
Two Dimensional ◽  
Scattering Media ◽  
Net Flux

The full anisotropic scattering solutions of the radiative equation of transfer are compared with the scaled isotropic scattering solutions. Square enclosures with a collimated incidence, a diffuse incidence, or an isothermal emission are considered for comparison. The isotropic scaling approximation is found to predict accurately the radiative flux and the average incident radiation for the isothermal emission problem and for most diffuse incidence problems. For the collimated incidence problem, the isotropic scaling solutions are acceptable only for weakly scattering media. For large scattering albedo the error in the isotropic scaling is appreciable for the diffuse incidence problem and unacceptably large for the collimated incidence problem. The largest error in the y-direction net flux is found at the side wall regions when the medium is purely scattering. The isothermal emission problem or problems with symmetric boundary conditions can be accurately modeled by a scaled isotropic phase function, since the effect of the phase function anisotropy is negligible in such problems.

Anisotropic Two-Dimensional Scattering: Comparison of Experiment with Theory

1981 ◽  
Vol 103 (1) ◽  
pp. 127-134 ◽  
Author(s):  
D. C. Look ◽  
H. F. Nelson ◽  
A. L. Crosbie
Keyword(s):  
Laser Beam ◽  
Water Solution ◽  
Anisotropic Scattering ◽  
Infinite Medium ◽  
Isotropic Scattering ◽  
Asymmetry Factor ◽  
Two Dimensional ◽  
Scattering Media ◽  
Uniform Size ◽  
Scattering Centers

Anisotropic scattering from a semi-infinite medium exposed to a laser beam is studied. The situation is two-dimensional and cylindrical because the laser beam is incident normal to the purely scattering media. The back scattered radiation in the normal direction is predicted and measured as a function of the distance from the beam. The latex particles of uniform size with diameters ranging from 0.03 up to 1.011 μ are used as scattering centers in a water solution. The influence of anisotropic scattering shifts the maximum of the radial distribution of the scattered intensity to larger optical radii as the particle size increases. For large optical thicknesses, the asymmetry factor is used as a correlation coefficient to reduce the anisotropic results to those of isotropic scattering.

Diffuse Reflectance of Highly Anisotropic Nonconservative Media

1976 ◽  
Vol 30 (6) ◽  
pp. 610-614 ◽  
Author(s):  
Harry G. Hecht
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
Excellent Agreement ◽  
Phase Function ◽  
Entire Range ◽  
Approximate Formula ◽  
Diffuse Reflectance ◽  
Incident Radiation ◽  
Scattering Media ◽  
Reflectance Data

With the use of methods described by Chandrasekhar, integrals have been tabulated which allow the diffuse reflectance of highly anisotropic nonconservative scattering media to be calculated. Solutions obtained in this way are compared for normally incident radiation with those given by an approximate formula due to Pitts. It is found that the Pitts formula is in excellent agreement with the exact solution and can be used to interpret reflectance data throughout the entire range of positive x values for which exact solutions exist for the phase function ω0 (1 + x cos θ).

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.

An Approximate Solution to Radiative Transfer in Two-Dimensional Rectangular Enclosures

1997 ◽  
Vol 119 (4) ◽  
pp. 738-745 ◽  
Author(s):  
J. B. Pessoa-Filho ◽  
S. T. Thynell
Keyword(s):  
Radiative Transfer ◽  
Iterative Solution ◽  
Anisotropic Scattering ◽  
Solution Procedure ◽  
Two Dimensional ◽  
Scattering Media ◽  
Discontinuous Nature ◽  
Selection Of ◽  
Iterative Solution Procedure ◽  
Numerical Approaches

The application of a new approximate technique for treating radiative transfer in absorbing, emitting, anisotropically scattering media in two-dimensional rectangular enclosures is presented. In its development the discontinuous nature of the radiation intensity, stability of the iterative solution procedure, and selection of quadrature points have been addressed. As a result, false scattering is eliminated. The spatial discretization can be formed without considering the chosen discrete directions, permitting a complete compatibility with the discretization of the conservation equations of mass, momentum, and energy. The effects of anisotropic scattering, wall emission, and gray-diffuse surfaces are considered for comparison with results available in the literature. The computed numerical results are in excellent agreement with those obtained by other numerical approaches.

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