Date of download: 12/26/2017 Copyright © ASME. All rights reserved. From: Spectral Photon Monte Carlo With Energy Splitting Across Phases for Gas–Particle Mixtures J. Heat Transfer. 2015;137(12):121012-121012-10. doi:10.1115/1.4030959 Figure Legend: 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.

Date of download: 12/26/2017 Copyright © ASME. All rights reserved. From: Spectral Photon Monte Carlo With Energy Splitting Across Phases for Gas–Particle Mixtures J. Heat Transfer. 2015;137(12):121012-121012-10. doi:10.1115/1.4030959 Figure Legend: 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.

Date of download: 12/26/2017 Copyright © ASME. All rights reserved. From: Spectral Photon Monte Carlo With Energy Splitting Across Phases for Gas–Particle Mixtures J. Heat Transfer. 2015;137(12):121012-121012-10. doi:10.1115/1.4030959 Figure Legend: 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.

Date of download: 12/26/2017 Copyright © ASME. All rights reserved. From: Spectral Photon Monte Carlo With Energy Splitting Across Phases for Gas–Particle Mixtures J. Heat Transfer. 2015;137(12):121012-121012-10. doi:10.1115/1.4030959 Figure Legend: 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.

Date of download: 12/26/2017 Copyright © ASME. All rights reserved. From: Spectral Photon Monte Carlo With Energy Splitting Across Phases for Gas–Particle Mixtures J. Heat Transfer. 2015;137(12):121012-121012-10. doi:10.1115/1.4030959 Figure Legend: PMC/LBL solutions of Qabs''' gas and particle phases for fluidized bed example problem. Profiles are taken along the centerline axis (r = 0).

Date of download: 12/26/2017 Copyright © ASME. All rights reserved. From: Spectral Photon Monte Carlo With Energy Splitting Across Phases for Gas–Particle Mixtures J. Heat Transfer. 2015;137(12):121012-121012-10. doi:10.1115/1.4030959 Figure Legend: ∇⋅ 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.