Improved Treatment of Anisotropic Scattering in Radiation Transfer Analysis Using the Finite Volume Method

Discretization 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.

[1]  J. Cuevas,et al.  Radiative Heat Transfer , 2018, ACS Photonics.

[2]  D. Kukulka,et al.  Development of Vipertex EHT Solar Surfaces for Enhanced Energy Transfer Applications , 2014 .

[3]  B. Hunter,et al.  Normalization of Various Phase Functions for Radiative Heat Transfer Analysis in a Solar Absorber Tube , 2014 .

[4]  B. Hunter,et al.  Phase-Function Normalization in the 3-D Discrete-Ordinates Solution of Radiative Transfer—PART I: Conservation of Scattered Energy and Asymmetry Factor , 2012 .

[5]  B. Hunter,et al.  Phase-Function Normalization in the 3-D Discrete-Ordinates Solution of Radiative Transfer—PART II: Benchmark Comparisons , 2012 .

[6]  B. Hunter,et al.  Phase-function normalization for accurate analysis of ultrafast collimated radiative transfer. , 2012, Applied optics.

[7]  B. Hunter,et al.  Reduction of angle splitting and computational time for the finite volume method in radiative transfer analysis via phase function normalization , 2012 .

[8]  Zhixiong Guo,et al.  Conservation of asymmetry factor in phase function discretization for radiative transfer analysis in anisotropic scattering media , 2012 .

[9]  G. Krishnamoorthy.  A Comparison of Angular Discretization Strategies for Modeling Radiative Transfer in Pool Fire Simulations , 2012 .

[10]  B. Hunter,et al.  Comparison of the Discrete-Ordinates Method and the Finite-Volume Method for Steady-State and Ultrafast Radiative Transfer Analysis in Cylindrical Coordinates , 2011 .

[11]  Subhash C. Mishra,et al.  Analysis of the Transport of a Train of Short-Pulse Radiation of Gaussian Temporal Profile Through a 2-D Participating Medium , 2009 .

[12]  Kyunghan Kim,et al.  Bio-heat transfer analysis during short pulse laser irradiation of tissues , 2008 .

[13]  B. Yilbas,et al.  Laser Evaporative Heating: Influence of Laser Pulse Intensity on the Cavity Formation , 2008 .

[14]  M. Borjini,et al.  Modeling of radiative heat transfer in 3D complex boiler with non-gray sooting media , 2007 .

[15]  Kyunghan Kim,et al.  Multi-time-scale heat transfer modeling of turbid tissues exposed to short-pulsed irradiations , 2007, Comput. Methods Programs Biomed..

[16]  Pascal Boulet,et al.  On the finite volume method and the discrete ordinates method regarding radiative heat transfer in acute forward anisotropic scattering media , 2007 .

[17]  G. Kamel,et al.  Formulation and testing of the FTn finite volume method for radiation in 3-D complex inhomogeneous participating media , 2006 .

[18]  Zhixiong Guo,et al.  ULTRAFAST RADIATION HEAT TRANSFER IN LASER TISSUE WELDING AND SOLDERING , 2004 .

[19]  Y. Lam,et al.  Three-dimensional transient radiative transfer modeling using the finite-volume method , 2004 .

[20]  S. Kumar,et al.  Discrete-ordinates solution of short-pulsed laser transport in two-dimensional turbid media. , 2001, Applied optics.

[21]  Vladimir P. Solovjov,et al.  An Efficient Method for Modeling Radiative Transfer in Multicomponent Gas Mixtures With Soot , 2001 .

[22]  J. H. Park,et al.  UNSTRUCTURED FINITE-VOLUME METHOD FOR RADIATIVE HEAT TRANSFER IN A COMPLEX TWO-DIMENSIONAL GEOMETRY WITH OBSTACLES , 2001 .

[23]  Man Young Kim, Seung Wook Baek, Jae Hyun Park.  UNSTRUCTURED FINITE-VOLUME METHOD FOR RADIATIVE HEAT TRANSFER IN A COMPLEX TWO-DIMENSIONAL GEOMETRY WITH OBSTACLES , 2001 .

[24]  S. Kumar,et al.  Equivalent isotropic scattering formulation for transient short-pulse radiative transfer in anisotropic scattering planar media. , 2000, Applied optics.

[25]  Shigenao Maruyama,et al.  Radiative heat transfer in inhomogeneous, nongray, and anisotropically scattering media , 2000 .

[26]  Kang Y. Huh,et al.  A new angular discretization scheme of the finite volume method for 3-D radiative heat transfer in absorbing, emitting and anisotropically scattering media , 2000 .

[27]  S. Maruyama,et al.  Scaling anisotropic scattering in radiative transfer in three-dimensional nonhomogeneous media , 1999 .

[28]  G. Raithby.  Discussion of the finite-volume method for radiation, and its application using 3D unstructured meshes , 1999 .

[29]  Shigenao Maruyama,et al.  Combined heat transfer in floating zone growth of large silicon crystals with radiation on diffuse and specular surfaces , 1998 .

[30]  Seung Wook Baek,et al.  Nonorthogonal finite-volume solutions of radiative heat transfer in a three-dimensional enclosure , 1998 .

[31]  S. Patankar,et al.  Finite volume method for radiation heat transfer , 1994 .

[32]  Suhas V. Patankar,et al.  RAY EFFECT AND FALSE SCATTERING IN THE DISCRETE ORDINATES METHOD , 1993 .

[33]  G. D. Raithby,et al.  Implementation of the Finite Volume Method for Calculating Radiative Transfer in a Pulverized Fuel Flame , 1993 .

[34]  G. Raithby,et al.  COMPUTATION OF RADIANT HEAT TRANSFER ON A NONORTHOGONAL MESH USING THE FINITE-VOLUME METHOD , 1993 .

[35]  G. Raithby,et al.  Prediction of radiative transfer in cylindrical enclosures with the finite volume method , 1992 .

[36]  G. D. Raithby,et al.  A Finite-Volume Method for Predicting a Radiant Heat Transfer in Enclosures With Participating Media , 1990 .

[37]  Tae-Kuk Kim,et al.  Effect of anisotropic scattering on radiative heat transfer in two-dimensional rectangular enclosures , 1988 .

[38]  Amir Y. Sajjadi,et al.  THERMAL ANALYSIS AND EXPERIMENTS OF LASER−TISSUE INTERACTIONS: A REVIEW , 2013 .

[39]  S. Acharya,et al.  Dynamics, NOx and flashback characteristics of confined premixed hydrogen-enriched methane flames , 2009 .

[40]  Michael F. Modest,et al.  CHAPTER 9 – THE EQUATION OF RADIATIVE TRANSFER IN PARTICIPATING MEDIA , 2003 .

[41]  Zhixiong Guo,et al.  Three-Dimensional Discrete Ordinates Method in Transient Radiative Transfer , 2002 .

[42]  Kang Y. Huh,et al.  ASSESSMENT OF THE FINITE-VOLUME METHOD AND THE DISCRETE ORDINATE METHOD FOR RADIATIVE HEAT TRANSFER IN A THREE-DIMENSIONAL RECTANGULAR ENCLOSURE , 1999 .

[43]  S. R. Mathur,et al.  Finite Volume Method for Radiative Heat Transfer Using Unstructured Meshes , 1998 .