Angular False Scattering in Radiative Heat Transfer Analysis Using the Discrete-Ordinates Method With Higher-Order Quadrature Sets

2013 ◽  
Author(s):  
Brian Hunter ◽  
Zhixiong Guo
Keyword(s):  
Monte Carlo ◽  
Radiative Transfer ◽  
Phase Function ◽  
Radiative Heat ◽  
Higher Order ◽  
Heat Transfer Analysis ◽  
Discrete Ordinates ◽  
Equal Weight ◽  
Participating Media ◽  
Discrete Ordinates Method

The SN quadrature set for the discrete-ordinates method is limited in overall discrete direction number in order to avoid physically unrealistic negative directional weight factors. Such a limitation can adversely impact radiative transfer predictions. Directional discretization results in errors due to ray effect, as well as angular false scattering error due to distortion of the scattering phase function. The use higher-order quadrature schemes in the discrete-ordinates method allows for improvement in discretization errors without an overall directional limitation. In this analysis, four higher-order quadrature sets (Legendre-Equal Weight, Legendre-Chebyshev, Triangle Tessellation, and Spherical Ring Approximation) are implemented for determination of radiative transfer in a 3-D cubic enclosure containing participating media. Radiative heat fluxes, calculated at low direction number, are compared to the SN quadrature and Monte Carlo predictions to gauge quadrature accuracy. Additionally, investigation into the reduction of angular false scattering with sufficient increase in direction number using higher-order quadrature, including heat flux accuracy with respect to Monte Carlo and computational efficiency, is presented. While higher-order quadrature sets are found to effectively minimize angular false scattering error, it is found to be much more computationally efficient to implement proper phase function normalization for accurate radiative transfer predictions.

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.

scholarly journals Ray Effects and False Scattering in Improved Discrete Ordinates Method

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6839
Author(s):  
Yong Cheng ◽  
Shuihua Yang ◽  
Zhifeng Huang
Keyword(s):  
Heat Flux ◽  
Radiative Transfer ◽  
Radiative Heat ◽  
Anisotropic Scattering ◽  
Radiative Heat Flux ◽  
Discrete Ordinates ◽  
Discrete Ordinates Method ◽  
Computation Efficiency ◽  
Scattering Phase ◽  
Ray Effects

The improved discrete ordinates method (IDOM) developed in our previous paper is extended to solve radiative transfer in three-dimensional radiative systems with anisotropic scattering medium. In IDOM, radiative intensities in a large number of new discrete directions are calculated by direct integration of the conventional discrete ordinates method (DOM) results, and radiative heat flux is obtained by integrating radiative intensities in these new discrete directions. Ray effects and false scattering, which tend to compensate each other, are investigated together in IDOM. Results show that IDOM can mitigate both of them effectively with high computation efficiency. Finally, the effect of scattering phase function on radiative transfer is studied. Results of radiative heat flux at boundaries containing media with different scattering phase functions are compared and analyzed. This paper indicates that the IDOM can overcome the shortages of the conventional DOM well while inheriting its advantages such as high computation efficiency and easy implementation.

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.

Analytical Delta-Four-Stream Doubling–Adding Method for Radiative Transfer Parameterizations

2013 ◽  
Vol 70 (3) ◽  
pp. 794-808 ◽  
Author(s):  
Feng Zhang ◽  
Zhongping Shen ◽  
Jiangnan Li ◽  
Xiuji Zhou ◽  
Leiming Ma
Keyword(s):  
Optical Properties ◽  
Radiative Transfer ◽  
Transfer Process ◽  
Solar Spectrum ◽  
Single Layer ◽  
Discrete Ordinates ◽  
Discrete Ordinates Method ◽  
Atmospheric Profile ◽  
Relative Errors ◽  
Transmission And Absorption

Abstract Although single-layer solutions have been obtained for the δ-four-stream discrete ordinates method (DOM) in radiative transfer, a four-stream doubling–adding method (4DA) is lacking, which enables us to calculate the radiative transfer through a vertically inhomogeneous atmosphere with multiple layers. In this work, based on the Chandrasekhar invariance principle, an analytical method of δ-4DA is proposed. When applying δ-4DA to an idealized medium with specified optical properties, the reflection, transmission, and absorption are the same if the medium is treated as either a single layer or dividing it into multiple layers. This indicates that δ-4DA is able to solve the multilayer connection properly in a radiative transfer process. In addition, the δ-4DA method has been systematically compared with the δ-two-stream doubling–adding method (δ-2DA) in the solar spectrum. For a realistic atmospheric profile with gaseous transmission considered, it is found that the accuracy of δ-4DA is superior to that of δ-2DA in most of cases, especially for the cloudy sky. The relative errors of δ-4DA are generally less than 1% in both the heating rate and flux, while the relative errors of δ-2DA can be as high as 6%.

Experimental and Numerical Studies of Short Pulse Propagation in Model Systems

2002 ◽  
Author(s):  
Sunil Kumar ◽  
Zhixiong Guo ◽  
Janice Aber ◽  
Bruce Garetz
Keyword(s):  
Monte Carlo ◽  
Pulse Propagation ◽  
Short Pulse ◽  
Model Systems ◽  
Discrete Ordinates ◽  
Pulsed Lasers ◽  
Discrete Ordinates Method ◽  
Numerical Studies ◽  
Tissue Phantoms ◽  
Good Agreement

In this paper experimental and numerical studies of the propagation of short-pulsed lasers through scattering and absorbing media are presented. Experimental results of a 60 ps pulse laser transmission in tissue phantoms are obtained and compared with Monte Carlo simulations. Good agreement between the Monte Carlo simulation and experimental measurement is found. Three models are developed for the simulation of short pulse transport. Benchmark comparisons among the Monte Carlo (MC), transient discrete ordinates method (TDOM) and transient radiation element method (TREM) are conducted.

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