Parallelization of the P-1 Radiation Model

In this work, the behavior of a 200-μm spherical carbon particle moving in a hot environment mainly consisting of O2 and CO2 was investigated numerically. The main goal of this work was to study the influence of the particle velocity, temperature, and composition of the surrounding gas on the carbon consumption rates. The particle investigated was placed in a uniform oxygen/carbon dioxide mixture at different Reynolds numbers corresponding to different laminar flow regimes. The ambient temperature was systematically varied in the range of 1000–3000 K, and the mass fraction of O2 was varied between 0.12 and 0.36. To solve the Navier–Stokes equations for the flow field coupled with the energy and species conservation equations, a finite volume solver was applied. In addition to the solid carbon, the model incorporates six gaseous chemical species (O2, CO, CO2, H2, H2O, and N2). The semiglobal reaction mechanism includes the forward and backward water–gas-shift reaction, one reaction for CO combustion, and four heterogeneous reactions. The ambient medium was assumed to be nearly dry (Y H2O = 0.001). The numerical results were carefully validated against experimental data published in the literature ( Bejarano Levendis Bejarano Levendis Combust. Flame2008153270287). In particular, it was shown that taking into account losses from radiation (gas–gas, gas–solid) brings the results closer to the experimental data. Additionally, the influence of the gas–gas radiation effect on the integral characteristics of the oxidizing particle was studied. In particular, the results are discussed with a focus on the systematic variation of the ambient-gas temperature and Reynolds number. We found out that increasing the Reynolds number enhances species transport to the particle surface and shifts particle oxidation from a diffusion-controlled to a kinetically controlled regime.

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“…Here, the P-1 radiation model is applied. 25 The incident radiation G is estimated by solving the transport equation…”

Section: Equationsmentioning

confidence: 99%

Numerical Investigation of a Chemically Reacting Carbon Particle Moving in a Hot O₂/CO₂ Atmosphere

Richter

Nikrityuk

Kestel

2013

Ind. Eng. Chem. Res.

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“…However, commercial unstructured CFD codes employ robust multigrid solution strategies to solve the discretized transport equations. For instance, Krishnamoorthy et al [24] demonstrated that through an appropriate choice of multigrid solver and preconditioner for solving the discretized P1 transport equation, accurate numerical solutions can be obtained efficiently that are also scalable when employed in parallel simulations across a wide range of medium opacities. Consequently, the computational cost of employing a model is more or less proportional to the number of transport equations being solved.…”

Section: Comparisons Of Do and P1 Modelsmentioning

confidence: 99%

“…Consequently, the computational cost of employing a model is more or less proportional to the number of transport equations being solved. As a result, the computational cost of the DO model that solves the transport equation along 128 directions (as in the T 4 model) would roughly be two orders of magnitude more than that of the P1 model . Therefore, the accuracies of the P1 model were examined for use in large‐scale parallel simulations of oxy‐combustion.…”

Section: Comparisons Of Do and P1 Modelsmentioning

confidence: 99%

A new weighted-sum-of-gray-gases model for oxy-combustion scenarios

Krishnamoorthy

2012

Int. J. Energy Res.

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SUMMARY A new weighted‐sum‐of‐gray gases (WSGG) model that is based on the statistical narrow band model (SNB) RADCAL is proposed for use in computational fluid dynamic (CFD) simulations of air and oxy‐combustion. When employed in conjunction with the discrete ordinates (DO) method, the model predictions compare well against line‐by‐line benchmark data that have been made available recently that are based on the latest spectroscopic databases. Furthermore, the model compares well against the EM2C SNB model calculations that have served as benchmark data in three‐dimensional geometries. Radiative transfer calculations in these prototypical problems therefore confirm recent experimental observations that SNB RADCAL and EM2C SNB serve as good model databases to develop approximate radiative property models. To achieve an optimum balance of speed and accuracy in computationally intensive CFD simulations, non‐gray formulations of the WSGG model are also employed with the P1 model and solutions are compared against those generated by the DO model. While the P1 model gave favorable comparisons when cold, black walls were present, the errors in the surface incident radiative flux predictions increased in the presence of hot, reflecting walls. Finally, in fully coupled simulations of natural gas combustion under air‐firing and oxy‐firing modes, the predicted incident radiative flux profiles were distinctly different between the gray and non‐gray calculations at regions of high temperature gradients, while the centerline temperature predictions were comparatively unaffected. The effects of turbulence radiation interactions were also accounted for through the temperature self‐correlation term. However, the magnitudes of the temperature fluctuations were small and localized within this furnace and did not significantly alter our predictions. Copyright © 2012 John Wiley & Sons, Ltd.

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“…This method also appears to be popular in some commercial software. Krishnamoorthy et al, discuss the process of a parallel implementation of the P1 method using a matrix formulation and various solution techniques [11]. Recently, Carrington and Mousseau demonstrated parallel solution methods developed for the P 1 (and diffusion) models for both 2-D and 3-D geometries [12].…”

Section: Introductionmentioning

confidence: 98%

A Parallel First-Order Spherical Harmonics (P₁) Matrix-Free Method for Radiative Transport

Carrington

2007

Numerical Heat Transfer, Part B: Fundamentals

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Radiative transfer in participating media is modeled using a first-order spherical harmonics (P 1 ), or its degenerate form, diffusion. The equations are discretized on an unstructured grid. The method uses a matrix-free algorithm employing an iterative solver from the Preconditioned Conjugate Gradient (PCG) solver package developed by Joubert and Carey [1]. The algorithm couples radiation transport and conduction, by casting them into a Picard iteration. Compared are solutions for two participating media problems indicating the method to be first-order accurate in time. Parallel scaling of the matrix-free method with use of in-situ preconditioners, symmetric successive overrelaxation (SSOR) and block Jacobi, are reported.

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Parallelization of the P-1 Radiation Model

Cited by 37 publications

References 21 publications

Numerical Investigation of a Chemically Reacting Carbon Particle Moving in a Hot O₂/CO₂ Atmosphere

Numerical Investigation of a Chemically Reacting Carbon Particle Moving in a Hot O₂/CO₂ Atmosphere

A new weighted-sum-of-gray-gases model for oxy-combustion scenarios

A Parallel First-Order Spherical Harmonics (P₁) Matrix-Free Method for Radiative Transport

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Parallelization of the P-1 Radiation Model

Cited by 37 publications

References 21 publications

Numerical Investigation of a Chemically Reacting Carbon Particle Moving in a Hot O2/CO2 Atmosphere

Numerical Investigation of a Chemically Reacting Carbon Particle Moving in a Hot O2/CO2 Atmosphere

A new weighted-sum-of-gray-gases model for oxy-combustion scenarios

A Parallel First-Order Spherical Harmonics (P1) Matrix-Free Method for Radiative Transport

Contact Info

Product

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Numerical Investigation of a Chemically Reacting Carbon Particle Moving in a Hot O₂/CO₂ Atmosphere

Numerical Investigation of a Chemically Reacting Carbon Particle Moving in a Hot O₂/CO₂ Atmosphere

A Parallel First-Order Spherical Harmonics (P₁) Matrix-Free Method for Radiative Transport