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.

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.

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.

Comparison of Phase Function Normalization Techniques for Radiative Transfer Analysis Using DOM

2014 ◽  
Author(s):  
Brian Hunter ◽  
Zhixiong Guo ◽  
Matthew Frenkel
Keyword(s):  
Phase Function ◽  
Radiation Heat Transfer ◽  
Mathematical Formulation ◽  
Diffuse Radiation ◽  
Asymmetry Factor ◽  
Participating Media ◽  
Scattered Energy ◽  
Volume Method ◽  
The Impact ◽  
Angular Discretization

Five phase-function (PF) normalization techniques are compared using the discrete-ordinate method (DOM) for modeling diffuse radiation heat transfer in participating media. Both the mathematical formulation and the impact on the conservation of both scattered energy and PF asymmetry factor for both Henyey-Greenstein (HG) and Legendre PF distributions are presented for each technique. DOM radiation transfer predictions generated using the five normalization techniques are compared to high-order finite-volume method, to gauge their accuracy. The commonly implemented scattered energy averaging technique cannot correct asymmetry factor distortion after angular discretization, and thus large errors due to angular false scattering are prevalent. Another three simple techniques via correction of one or two terms in the PF are shown to reduce normalization complexity whilst retaining diffuse radiation computation accuracy for HG PFs. However, for Legendre PFs, such simple normalization is found to result in unphysical negative PF values at one or few correction directions. The relatively complex Hunter and Guo 2012 technique, in which normalization is realized through a correction matrix covering all discrete directions, is shown to be highly applicable for both PF types.

Application of the Discrete Ordinates Method to a Continuous Glass Furnace Model

1999 ◽  
Author(s):  
Sandra Coutín Rodicio ◽  
Kirby S. Chapman
Keyword(s):  
Glass Furnace ◽  
Radiant Heat ◽  
Heat Fluxes ◽  
Discrete Ordinates ◽  
Surface Emissivity ◽  
Continuous Glass ◽  
Discrete Ordinates Method ◽  
Radiant Intensity ◽  
Control Volumes ◽  
The Impact

Abstract The radiative behavior of the glass as it flows through a continuous glass furnace is studied by applying the Discrete Ordinates Method (DOM). Through the application of the DOM the radiant intensity is calculated at each of the control volumes inside the glass tank domain. Consequently, the heat fluxes of the emitted and irradiated energy in the glass are obtained. The results are presented in terms of the radiant heat fluxes distribution and temperature profile of the glass. In addition, the variation of the glass surface emissivity is studied in order to provide further understanding of the impact of this property in the glass overall thermal behavior.

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%.

Discrete ordinates method in the analysis of the radiative transfer in high intensity discharge lamps

2005 ◽  
Vol 38 (22) ◽  
pp. 4053-4065 ◽  
Author(s):  
Mohamed Bouaoun ◽  
Hatem Elloumi ◽  
Kamel Charrada ◽  
Mounir Ben El Hadj Rhouma ◽  
Mongi Stambouli
Keyword(s):  
Radiative Transfer ◽  
High Intensity ◽  
Discrete Ordinates ◽  
Discrete Ordinates Method
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