Research Papers

Spectral Photon Monte Carlo With Energy Splitting Across Phases for Gas–Particle Mixtures

[+] Author and Article Information
Ricardo Marquez

School of Engineering,
University of California,
Merced, CA 95343

Michael F. Modest

ASME Life Fellow
School of Engineering,
University of California,
Merced, CA 95343
e-mail: MModest@ucmerced.edu

Jian Cai

Assistant Professor
University of Wyoming,
Laramie, WY 82071

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received May 30, 2014; final manuscript received April 17, 2015; published online August 11, 2015. Assoc. Editor: Sumanta Acharya.

J. Heat Transfer 137(12), 121012 (Aug 11, 2015) (10 pages) Paper No: HT-14-1368; doi: 10.1115/1.4030959 History: Received May 30, 2014

In multiphase modeling of fluidized beds, pulverized coal combustors, spray combustors, etc., where different temperatures for gas and solid phases are considered, the governing equations result in separate energy equations for each phase. For high-temperature applications, where radiation is a significant mode of heat transfer, accurately predicting the radiative source terms across each individual phase is an essential task. A spectral photon Monte Carlo (PMC) method is presented here with detailed description of the implementation features, including the spectral treatment of solid particles, random number correlations, and a scheme to split emission and absorption across phases. Numerical results from the PMC method are verified against direct numerical integration of the radiative transfer equation (RTE), for example, problems including a cylindrically enclosed homogeneous gas–particulate medium and a simple fluidized bed example. The PMC method is then demonstrated on a snapshot of a pulverized-coal combustion simulation.

Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.


von Zedtwitz, P. , and Steinfeld, A. , 2005, “Steam-Gasification of Coal in a Fluidized-Bed/Packed-Bed Reactor Exposed to Concentrated Thermal Radiation—Modeling and Experimental Validation,” Ind. Eng. Chem. Res, 44(11), pp. 3852–3861. [CrossRef]
Consalvi, J. , Porterie, B. , and Loraud, J. , 2002, “A Formal Averaging Procedure for Radiation Heat Transfer in Particulate Media,” Int. J. Heat Mass Transfer, 45(13), pp. 2755–2768. [CrossRef]
Lipiński, W. , Petrasch, J. , and Haussener, S. , 2010, “Application of the Spatial Averaging Theorem to Radiative Heat Transfer in Two-Phase Media,” J. Quant. Spectrosc. Radiat. Transfer, 111(1), pp. 253–258. [CrossRef]
Lipiński, W. , Keene, D. , Haussener, S. , and Petrasch, J. , 2010, “Continuum Radiative Heat Transfer Modeling in Media Consisting of Optically Distinct Components in the Limit of Geometrical Optics,” J. Quant. Spectrosc. Radiat. Transfer, 111(16), pp. 2474–2480. [CrossRef]
Petrasch, J. , Haussener, S. , and Lipiński, W. , 2011, “Discrete vs. Continuum-Scale Simulation of Radiative Transfer in Semitransparent Two-Phase Media,” J. Quant. Spectrosc. Radiat. Transfer, 112(9), pp. 1450–1459. [CrossRef]
Hodkinson, J. R. , 1963, “Light Scattering and Extinction by Irregular Particles Larger Than the Wavelength,” Electromagnetic Scattering, M. Kerker , ed., Macmillan, New York, pp. 87–100.
Lee, S. C. , 1986, “Radiative Transfer Through a Fibrous Medium: Allowance for Fiber Orientation,” J. Quant. Spectrosc. Radiat. Transfer, 36(3), pp. 253–263. [CrossRef]
Singh, B. P. , and Kaviany, M. , 1991, “Independent Theory Versus Direct Simulation of Radiation Heat Transfer in Packed Beds,” Int. J. Heat Mass Transfer, 34(11), pp. 2869–2882. [CrossRef]
Singh, R. I. , Brink, A. , and Hupa, M. , 2013, “CFD Modeling to Study Fluidized Bed Combustion and Gasification,” Appl. Therm. Eng., 52(2), pp. 585–614. [CrossRef]
Modest, M. F. , 2013, Radiative Heat Transfer, 3rd ed., Academic, New York.
Cai, J. , and Modest, M. F. , 2012, “Absorption Coefficient Regression Scheme for Splitting Radiative Heat Sources Across Phases in Gas–Particulate Mixtures,” Powder Tech., 265, pp. 76–82. [CrossRef]
von Zedtwitz, P. , Lipinski, W. , and Steinfeld, A. , 2007, “Numerical and Experimental Study of Gas–Particle Radiative Heat Exchange in a Fluidized-Bed Reactor for Steam-Gasification of Coal,” Chem. Eng. Sci., 62(1–2), pp. 599–607. [CrossRef]
Adzeriho, K. , Nogotov, E. F. , and Trofimov, V. P. , 1993, Radiative Heat Transfer in Two-Phase Media, CRC Press, Boca Raton, FL.
Siegel, R. , and Howell, J. R. , 2002, Thermal Radiation Heat Transfer, 4th ed., Taylor & Francis, New York.
Snegirev, A. Y. , 2004, “Statistical Modeling of Thermal Radiation Transfer in Buoyant Turbulent Diffusion Flames,” Combust. Flame, 136(1–2), pp. 51–71. [CrossRef]
Tessé, L. , Duporieux, F. , Zamuner, B. , and Taine, J. , 2002, “Radiative Transfer in Real Gases Using Reciprocal and Forward Monte Carlo Methods and a Correlated-k Approach,” Int. J. Heat Mass Transfer, 45(13), pp. 2797–2814. [CrossRef]
Tessé, L. , Duporieux, F. , Zamuner, B. , and Taine, J. , 2004, “Monte Carlo Modeling of Radiative Transfer in a Turbulent Sooty Flame,” Int. J. Heat Mass Transfer, 47(3), pp. 555–572. [CrossRef]
Wang, A. , and Modest, M. F. , 2006, “Photon Monte Carlo Simulation for Radiative Transfer in Gaseous Media Represented by Discrete Particle Fields,” ASME J. Heat Transfer, 128(10), pp. 1041–1049. [CrossRef]
Wang, A. , and Modest, M. F. , 2007, “An Adaptive Emission Model for Monte Carlo Ray-Tracing in Participating Media Represented by Statistical Particle Fields,” J. Quant. Spectrosc. Radiat. Transfer, 104(2), pp. 288–296. [CrossRef]
Xia, X. L. , Ren, D. P. , and Tan, H. P. , 2006, “A Curve Monte Carlo Method for Radiative Heat Transfer in Absorbing and Scattering Gradient-Index Medium,” Numer. Heat Transfer, Part B, 50(2), pp. 181–192. [CrossRef]
Ruan, L. M. , Tan, H. P. , and Yan, Y. Y. , 2002, “A Monte Carlo (MC) Method Applied to the Medium With Nongray Absorbing–Emitting-Anisotropic Scattering Particles and Gray Approximation,” Numer. Heat Transfer, Part A, 42(2), pp. 253–268. [CrossRef]
Mazumdar, S. , and Kersch, A. , 2000, “A Fast Monte Carlo Scheme for Thermal Radiation in Semiconductor Processing Applications,” Numer. Heat Transfer, Part B, 37(2), pp. 185–199. [CrossRef]
Wang, A. , and Modest, M. F. , 2007, “Spectral Monte Carlo Models for Nongray Radiation Analyses in Inhomogeneous Participating Media,” Int. J. Heat Mass Transfer, 50(19–20), pp. 3877–3889. [CrossRef]
Ren, T. , and Modest, M. F. , 2013, “Hybrid Wavenumber Selection Scheme for Line-by-Line Photon Monte Carlo Simulations in High-Temperature Gases,” ASME J. Heat Transfer, 135(8), p. 084501. [CrossRef]
Mehta, R. S. , Haworth, D. C. , and Modest, M. F. , 2010, “Composition PDF/Photon Monte Carlo Modeling of Moderately Sooting Turbulent Jet Flames,” Combust. Flame, 157(5), pp. 982–994. [CrossRef]
Feldick, A. M. , and Modest, M. F. , 2012, “A Spectrally Accurate Tightly-Coupled 2-D Axisymmetric Photon Monte Carlo RTE Solver for Hypersonic Entry Flows,” ASME J. Heat Transfer, 134(12), p. 122701. [CrossRef]
Modest, M. F. , 2013, Radiative Heat Transfer, 3rd ed., Academic Press, New York.
Rothman, L. S. , Gordon, I. E. , Barber, R. J. , Doth, H. , Gamache, R. R. , Goldman, A. , Prevalov, V. I. , Tashkun, S. A. , and Tennyson, J. , 2010, “HITEMP, the High Temperature Molecular Spectroscopic Database,” J. Quant. Spectrosc. Radiat. Transfer, 111(15), pp. 2139–2150. [CrossRef]
Buckius, R. O. , and Hwang, D. C. , 1980, “Radiation Properties for Polydispersions: Application to Coal,” ASME J. Heat Transfer, 102(1), pp. 99–103. [CrossRef]
Feldick, A. M. , and Modest, M. F. , 2011, “An Improved Wavelength Selection Scheme for Monte Carlo Solvers Applied to Hypersonic Plasmas,” J. Quant. Spectrosc. Radiat. Transfer, 112(8), pp. 1394–1401. [CrossRef]
Cai, J. , Masato, H. , and Modest, M. F. , 2014, “Eulerian–Eulerian Multi-Fluid Methods for Pulverized Coal Flames With Nongray Radiation,” Combust. Flame, 162(4), pp. 1550–1565. [CrossRef]
Hwang, S. M. , Kurose, R. , Akamatsu, F. , Tsuji, H. , Makino, H. , and Katsuki, M. , 2005, “Application of Optical Diagnostics Techniques to a Laboratory-Scale Turbulent Pulverized Coal Flame,” Energy Fuels, 19(2), pp. 382–392. [CrossRef]
Magnussen, B. F. , 2005, “The Eddy Dissipation Concept: A Bridge Between Science and Technology,” ECCOMAS Thematic Conference on Computational Combustion, Lisbon, Portugal, June 21–24.
Ubhayakar, S. K. , Stickler, D. B. , von Rosenberg, C. W., Jr. , and Gannon, R. E. , 1977, “Rapid Devolatilization of Pulverized Coal in Hot Combustion Gases,” Symp. (Int.) Combust., 16(1), pp. 427–436. [CrossRef]
Hamor, R. J. , Smith, I. W. , and Tyler, R. J. , 1973, “Kinetics of Combustion of a Pulverized Brown Coal Char Between 630 and 2200 K,” Combust. Flame, 21(2), pp. 153–162. [CrossRef]
Syamlal, M. , Rodgers, W. , and O'Brien, T. , 1993, “MFIX Documentation: Theory Guide,” U.S. Department of Energy, Office of Fossil Energy, Morgantown, WV, Technical Note No. DOE/METC-94/1004.
Cai, J. , and Modest, M. F. , 2013, “Improved Full-Spectrum k-Distribution Implementation for Inhomogeneous Media Using a Narrow-Band Database,” J. Quant. Spectrosc. Radiat. Transfer, 141, pp. 65–72. [CrossRef]
Wang, A. , Modest, M. F. , Haworth, D. C. , and Wang, L. , 2008, “Monte Carlo Simulation of Radiative Heat Transfer and Turbulence Interactions in Methane/Air Jet Flames,” J. Quant. Spectrosc. Radiat. Transfer, 109(2), pp. 269–279. [CrossRef]
Cai, J. , Marquez, R. , Masato, H. , and Modest, M. F. , 2013, “Comparisons of Radiative Heat Transfer Calculations in a Jet Diffusion Flame Using Spherical Harmonics and k-Distributions,” ASME J. Heat Transfer, 136(11), p. 112702. [CrossRef]
Ge, W. , Marquez, R. , Modest, M. F. , and Roy, S. P. , 2015, “Implementation of High Order Spherical Harmonics Methods for Radiative Heat Transfer on OpenFOAM,” ASME J. Heat Transfer, 137(5), p. 052701. [CrossRef]


Grahic Jump Location
Fig. 1

Random-number relations and regression coefficients for particles as functions of grouped variables γ and ξ. The regression coefficients a1 and a2 were computed directly using least squares regression from the random-number relations, then approximated through a second regression function. (a) Random-number relations for solids and (b) regression coefficients.

Grahic Jump Location
Fig. 2

Directly calculated and approximated Planck-mean absorption coefficients for particles as functions of γ. The linear function b32 lg γ + b33 represents the right asymptote of lgκ¯/(fAγ) versus lg γ. (a) Normalized Planck-mean absorption coefficient and (b) ratio of normalized Planck-mean absorption coefficient and solids property variable γ.

Grahic Jump Location
Fig. 3

Illustration of a single ray emitted from cell i and traversing cell j. The absorbed energy depends on the absorptivity of cell j, the distance traversed Sijk, and the energy of the photon bundle as it enters the absorbing cell Qi,jk.

Grahic Jump Location
Fig. 4

Comparison of PMC/LBL, PMC/gray, PMC/LBL applied separately to the gas and solid phases, and an exact solution for Qabs''' for first example problem. Profiles taken at z = 0.5 m.

Grahic Jump Location
Fig. 6

∇⋅ q for gas and solid phases computed on a snapshot at steady state conditions for pulverized coal flame case. Included in the profiles are the full spectral PMC method (PMC/LBL), OT approximation, and full-spectrum k-distributions spectral model with P1 RTE solver (P1/FSK). (a) Computed ∇⋅ q using PMC/LBL and (b) profiles at z = 1.2 m.

Grahic Jump Location
Fig. 5

PMC/LBL solutions of Qabs''' gas and particle phases for fluidized bed example problem. Profiles are taken along the centerline axis (r = 0).




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In