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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

Professor
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.

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Figures

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).

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