1,720,981 research outputs found
Phase-Function Normalization in the 3-D Discrete-Ordinates Solution of Radiative Transfer – PART II: Benchmark Comparisons
No full textRadiative transfer in a cubic enclosure, subject to varying conditions, is determined using the discrete-ordinates method (DOM) with the two normalization techniques introduced in Part I of this study. Their predictions are compared with Monte Carlo simulations. For all cases, false scattering due to directional discretization cannot be corrected when the old technique, which solely conserves scattered energy, is implemented; and thus, signifi- cant discrepancies exist when compared to Monte Carlo results. The new technique, which conserves both scattered energy and the asymmetry factor, is able to retain original scatter- ing properties after directional discretization, leading to improved accuracy when compared to Monte Carlo. In addition, a parametric study is presented to gauge the impact of asym- metry-factor conservation on media with various optical properties. Finally, the impact of normalization is investigated for both ultrafast radiative transfer and ballistic incidence with varying incident angle.Peer reviewed
A New and Simple Technique to Normalize the HG Phase Function for Conserving Scattered Energy and Asymmetry Factor
No full textA new, yet simple, technique is formulated for normalizing the Henyey-Greenstein (HG) phase function by ensuring conservation of both scattered energy and asymmetry factor simultaneously, and is analyzed for use in determining accurate radiative transfer predictions in strongly anisotropic scattering media using the discrete ordinates method (DOM). Two recently published simple normalization techniques are able to conserve either scattered energy or asymmetry factor after discretization solely by normalization of the forward- scattering HG phase-function value. However, normalization of only the forward-scattering term cannot conserve two quantities simultaneously. The present technique normalizes both the forward-scattering and backward-scattering terms in order to conserve both scattered energy and asymmetry factor simultaneously and maintain most of the phase-function shape while retaining simplicity and efficiency. Analysis of radiative transfer predictions shows that results generated using the present technique conform accurately to finite-volume method (FVM) and Monte Carlo (MC) predictions, as well as to those generated using the authors’ previously developed matrix normalization technique, validating its accuracy.Peer reviewed
Comparison of the Discrete-Ordinates Method and the Finite-Volume Method for Steady-State and Ultrafast Radiative Transfer Analysis in Cylindrical Coordinates
No full textThe time-dependent equation of radiative transfer is solved for an axisymmetric cylindrical medium using both the discrete-ordinates method and the finite-volume method. Steady and transient flux profiles are determined for absorbing and scattering media. Results for each solution method are compared and shown for various grid numbers, scattering albedos, and optical thicknesses. A comparison of computational time and memory usage between the methods is presented. It is found that the finite-volume method uses more memory and has a longer convergence time than the discrete-ordinates method for all cases, due to the difference in angular treatment.Peer reviewed
Improved treatment of anisotropic scattering for ultrafast radiative transfer analysis
No full textThe 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.Paper No: HT-14-1024, available in the ASME Digital Collection at http://heattransfer.asmedigitalcollection.asme.org/article.aspx?articleID=2213448.
Copyright 2015 by ASME.Peer reviewed
Conservation of Asymmetry Factor in Phase Function Discretization for Radiative Transfer Analysis in Anisotropic Scattering Media
No full textA new phase function normalization technique is developed for use with anisotropic scattering media and is applied to the conventional discrete-ordinates method. The new approach is shown to ensure conservation of both scattered energy and phase function asymmetry factor after directional discretization when considering the Henyey-Greenstein phase function approximation. Results show the necessity of conservation of the asymmetry factor as well as of the scattered energy. Lack of either conservation can lead to false results for radiation analysis in highly anisotropic media. Wall flux profiles predicted by the normalized DOM in a highly anisotropic scattering cylinder are compared with FVM and isotropic scaling profiles. The effect of scattering albedo and optical thickness is examined. For the tested benchmark problem, it is found that heat flux profiles generated with the present normalization approach conform more accurately to both FVM and isotropic scaling profiles than when the previous normalization techniques are implemented.Peer reviewed
Numerical smearing, ray effect, and angular false scattering in radiation transfer computation
No full textSolutions of the integro-differential equation of radiation transfer via numerical methods were well known to suffer from two ‘‘separate’’ shortcomings: (1) numerical smearing error due to spatial domain discretization, and (2) ray effect error due to angular discretization. In this study, proportionality expressions for various orders of numerical smearing errors are derived, and the inherent dependence of such errors on both spatial and angular discretization is found. Ray effect is categorized into two components: local and propagation errors; and they are not independent of spatial discretization. Using DOM solution, the individual and combined impacts of the above-mentioned numerical errors together with the recently discovered angular false scattering error are examined for various spatial and angular discretizations and medium optical properties. The dependence of numerical errors on scattering anisotropy is investigated. It is found that, for low scattering anisotropy, either numerical smearing or ray effect errors dominate, depending on optical thickness and scattering albedo. For high scattering anisotropy, however, the ray effect and angular false scattering dominate.Peer reviewed
Reduction of Angle Splitting and Computational Time for the Finite Volume Method in Radiative Transfer Analysis via Phase Function Normalization
No full textThe commonly implemented splitting of solid angles to ensure scattered energy conservation in the finite volume method does not exactly conserve phase function asymmetry factor after directional discretiza- tion, leading to significant changes in scattering effect for radiative transfer analysis in highly anisotropic scattering media. In addition, use of a large number of split sub-angles results in drastic increases in com- putational CPU time and computer memory. The phase function normalization approach considered in this study is found to guarantee accurate conservation of both scattered energy and asymmetry factor simultaneously after directional discretization as well as depress solid angle splitting, vastly reducing the computational convergence time with improved accuracy. As a test, radial and axial radiative heat flux profiles in a scattering cylinder generated both with and without the phase function normalization are compared among different levels of angle discretization and splitting as well as with the discrete- ordinates method. The effects of changes in optical thickness, angular resolution, scattering albedo, and phase function approximation are examined.Peer reviewed
Normalization of Various Phase Functions for Radiative Heat Transfer Analysis in a Solar Absorber Tube
No full textNormalization of various phase functions is considered for accurately predicting radiative heat transfer. A solar absorber tube filled with anisotropic scattering working medium is used as an example. Analysis of previous normalization techniques show that while they do conserve scattered energy exactly after DOM discretization, the overall asymmetry factor of the phase function is distorted, leading to substantial changes in overall scattering effect. An innovative normalization technique which conserves asymmetry factor and scattered energy simultaneously is investigated. The impact of lack of asymmetry factor conservation is analyzed for both the Legendre polynomial and HG phase function approximations. Heat flux at the surface and energy absorbing rate inside the solar absorber tube are predicted using the new normalization technique. Variations of medium optical thickness, scattering albedo, asymmetry factor, and side wall emissivity are scrutinized to determine the effect of said parameters on wall heat flux and energy absorbing rate inside the absorber tube. Side wall heat flux is found to increase with increases in asymmetry factor, optical thickness, and wall emissivity, and with decreases in scattering albedo. Energy absorbing rate profiles are found to depend greatly on optical thickness and scattering albedo.Peer reviewed.Paper presented at the First International Workshop on Heat Transfer Advances for Energy Conservation and Pollution Control (IWHT2011), October 17-20, 2011, Xi'an, China
Phase Function Normalization for Accurate Analysis of Ultrafast Collimated Radiative Transfer
No full textThe scattering of radiation from collimated irradiation is accurately treated via normalization of phase function. This approach is applicable to any numerical method with directional discretization. In this study it is applied to the transient discrete-ordinates method for ultrafast collimated radiative transfer analysis in turbid media. A technique recently developed by the authors, which conserves a phase-function asymmetry factor as well as scattered energy for the Henyey–Greenstein phase function in steady-state diffuse radiative transfer analysis, is applied to the general Legendre scattering phase function in ultrafast collimated radiative transfer. Heat flux profiles in a model tissue cylinder are generated for various phase functions and compared to those generated when normalization of the collimated phase function is neglected. Energy deposition in the medium is also investigated. Lack of conservation of scattered energy and the asymmetry factor for the collimated scattering phase function causes overpredictions in both heat flux and energy deposition for highly anisotropic scattering media. In addition, a discussion is presented to clarify the time-dependent formulation of divergence of radiative heat flux.Peer reviewed
Improved treatment of anisotropic scattering in radiation transfer analysis using the finite volume method
No full textDiscretization of the integral anisotropic-scattering term in the equation of radiative transfer will result in two kinds of numerical errors: alterations in scattered energy and asymmetry factor. Though quadrature flexibility with large angular directions and further solid-angle splitting in the finite volume method (FVM) allow for reduction/minimization of these errors, computational efficiency is adversely impacted. A phase-function normalization technique to get rid of these errors is simpler and is applied to the three-dimensional (3-D) FVM for the first time to improve anisotropic radiation transfer computation accuracy and efficiency. FVM results are compared to Monte Carlo and discrete-ordinates method predictions of radiative heat transfer in a cubic enclosure housing a highly anisotropic participating medium. It is found that the FVM results generated using the normalization technique conform accurately to the results of the other two methods with little impact on computational efficiency.Peer reviewed
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