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Maxime Roger – One of the best experts on this subject based on the ideXlab platform.

  • Radiative heat transfer in strongly forward scattering media using the discrete ordinates method
    Journal of Quantitative Spectroscopy and Radiative Transfer, 2016
    Co-Authors: Pedro Granate, Pedro J Coelho, Maxime Roger

    Abstract:

    The discrete ordinates method (DOM) is widely used to solve the radiative transfer equation, often yielding satisFactory results. However, in the presence of strongly forward scattering media, this method does not generally conserve the scattering energy and the phase function Asymmetry Factor. Because of this, the normalization of the phase function has been proposed to guarantee that the scattering energy and the Asymmetry Factor are conserved. Various authors have used different normalization techniques. Three of these are compared in the present work, along with two other methods, one based on the finite volume method (FVM) and another one based on the spherical harmonics discrete ordinates method (SHDOM). In addition, the approximation of the Henyey–Greenstein phase function by a different one is investigated as an alternative to the phase function normalization. The approximate phase function is given by the sum of a Dirac delta function, which accounts for the forward scattering peak, and a smoother scaled phase function. In this study, these techniques are applied to three scalar radiative transfer test cases, namely a three-dimensional cubic domain with a purely scattering medium, an axisymmetric cylindrical enclosure containing an emitting–absorbing–scattering medium, and a three-dimensional transient problem with collimated irradiation. The present results show that accurate predictions are achieved for strongly forward scattering media when the phase function is normalized in such a way that both the scattered energy and the phase function Asymmetry Factor are conserved. The normalization of the phase function may be avoided using the FVM or the SHDOM to evaluate the in-scattering term of the radiative transfer equation. Both methods yield results whose accuracy is similar to that obtained using the DOM along with normalization of the phase function. Very satisFactory predictions were also achieved using the delta-M phase function, while the delta-Eddington phase function and the transport approximation may perform poorly.

  • Radiative heat transfer in strongly forward scattering media using the discrete ordinates method
    , 2015
    Co-Authors: Pedro Granate, Pedro J Coelho, Maxime Roger

    Abstract:

    The discrete ordinates method is widely used to solve the radiative transfer equation, often yielding satisFactory results. However, in the presence of strongly forward scattering media, this method does not generally conserve the scattering energy and the phase function Asymmetry Factor. Because of this, the phase function should be normalized so that the scattering energy and the Asymmetry Factor are conserved. Various authors have proposed different normalization techniques. Three of these are compared in the present work, along with two other methods, one based on the finite volume method (FVM) and another one based on the spherical harmonics discrete ordinates method (SHDOM). In this study, these techniques are applied to three benchmark test cases, namely a three-dimensional cubic domain with a purely scattering medium, an axisymmetric cylindrical enclosure containing an emitting-absorbing-scattering medium, and a three-dimensional transient problem with collimated radiation. The present results confirm previous findings concerning the need to normalize the phase function in such a way that both the scattered energy and the phase function Asymmetry Factor are conserved. Whenever the normalization guarantees that, the predictions are satisFactory. This may be difficult to achieve when the FVM is used and the Asymmetry Factor is close to unity. The accuracy of the SHDOM seems also to decrease when that Factor is close to one, even though the influence of the various optical parameters on the results needs to be further investigated.

Zhixiong Guo – One of the best experts on this subject based on the ideXlab platform.

  • A New and Simple Technique to Normalize the HG Phase Function for Conserving Scattered Energy and Asymmetry Factor
    Numerical Heat Transfer Part B: Fundamentals, 2014
    Co-Authors: Brian Hunter, Zhixiong Guo

    Abstract:

    A 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 presen…

  • Normalization of Various Phase Functions for Radiative Heat Transfer Analysis in a Solar Absorber Tube
    Heat Transfer Engineering, 2013
    Co-Authors: Brian Hunter, Zhixiong Guo

    Abstract:

    Normalization 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 a previous normalization technique shows that while it does conserve scattered energy exactly after discrete-ordinates method (DOM) discretization, the overall Asymmetry Factor of the phase function is distorted, leading to substantial changes in overall scattering effect. A new normalization technique that 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 the Henyey–Greenstein phase function approximations. Variations of medium optical thickness, scattering albedo, Asymmetry Factor, and side-wall emissivity are scrutinized to determine the effects of said parameters on wall heat flux and energy absorbing rate inside the absorber tube. Side-wall heat flux is found to …

  • phase function normalization in the 3 d discrete ordinates solution of radiative transfer part i conservation of scattered energy and Asymmetry Factor
    Numerical Heat Transfer Part B-fundamentals, 2012
    Co-Authors: Brian Hunter, Zhixiong Guo

    Abstract:

    The conditions for which conversation of scattered energy and phase-function Asymmetry Factor after discrete-ordinates methods (DOM) directional discretization for 3-D radiative transfer in anisotropic scattering media breaks down are examined. Directional discretization in anisotropic scattering media is found to alter the scattering Asymmetry Factor—a second-type of “false scattering.” Phase-function normalization which conserves scattered energy alone cannot correct this problem, and conservation of the Asymmetry Factor is simultaneously required. A normalization technique developed by the authors, which was successfully tested in 2-D asymmetric cylindrical-coordinate radiative transfer analysis, is intensively examined and validated with benchmark problems in 3-D Cartesian coordinates. In Part I of this study, the degree of anisotropy for which normalization is necessary to conserve these inherent quantities is presented for various phase-function approximations and discrete quadrature sets.

F. Monteleone – One of the best experts on this subject based on the ideXlab platform.

  • Aerosol optical properties at Lampedusa (Central Mediterranean). 2. Determination of single scattering albedo at two wavelengths for different aerosol types
    Atmospheric Chemistry and Physics, 2006
    Co-Authors: D. Meloni, A. Di Sarra, G. Pace, F. Monteleone

    Abstract:

    Aerosol optical properties were retrieved from direct and diffuse spectral irradiance measurements made by a multi-filter rotating shadowband radiometer (MFRSR) at the island of Lampedusa (35.5° N, 12.6° E), in the Central Mediterranean, in the period July 2001?September 2003. In a companion paper (Pace et al., 2006) the aerosol optical depth (AOD) and Ångström exponent were used together with airmass backward trajectories to identify and classify different aerosol types. The MFRSR diffuse-to-direct ratio (DDR) at 415.6 nm and 868.7 nm for aerosol classified as “biomass burning-urban/industrial”, originating primarily from the European continent, and desert dust, originating from the Sahara, is used in this study to estimate the aerosol single scattering albedo (SSA). A detailed radiative transfer model is initialised with the measured aerosol optical depth; calculations are performed at the two wavelengths varying the SSA values until the modelled DDR matches the MFRSR observations. Sensitivity studies are performed to estimate how uncertainties on AOD, DDR, Asymmetry Factor (g), and surface albedo influence the retrieved SSA values. The results show that a 3% variation of AOD or DDR produce a change of about 0.02 in the retrieved SSA value at 415.6 and 868.7 nm; a ±0.06 variation of the Asymmetry Factor g produces a change of the estimated SSA of

  • Aerosol optical properties at Lampedusa (Central Mediterranean) ? 2. Determination of single scattering albedo at two wavelengths for different aerosol types
    Atmospheric Chemistry and Physics Discussions, 2005
    Co-Authors: D. Meloni, A. Di Sarra, G. Pace, F. Monteleone

    Abstract:

    Aerosol optical properties were retrieved from direct and diffuse spectral irradiance measurements made by a multi-filter rotating shadowband radiometer (MFRSR) at the island of Lampedusa (35.5° N, 12.6° E), in the Central Mediterranean, in the period July 2001?September 2003. In a companion paper (Pace et al., 2005) the aerosol optical depth (AOD) and Ångström exponent were used together with airmass backward trajectories to identify and classify different aerosol types. The MFRSR diffuse-to-direct ratio (DDR) at 415.6 nm and 868.7 nm for aerosol classified as biomass burning-urban/industrial, originating primarily from the European continent, and desert dust, originating from the Sahara, is used in this study to estimate the aerosol single scattering albedo (SSA). A detailed radiative transfer model is initialized with the measured aerosol optical depth; calculations are performed at the two wavelengths varying the SSA values until the modelled DDR matches the MFRSR observations. Sensitivity studies are performed to estimate how uncertainties on AOD, DDR, Asymmetry Factor (g), and surface albedo influence the retrieved SSA values. The results show that a 3% variation of AOD or DDR produce a change of about 0.02 in the retrieved SSA value at 415.6 and 868.7 nm; a ±0.06 variation of the Asymmetry Factor g produces a change of the estimated SSA of