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# Analysis of Radiation Modeling for Turbulent Combustion: Development of a Methodology to Couple Turbulent Combustion and Radiative Heat Transfer in LES

[+] Author and Article Information
Damien Poitou

CERFACS, 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, Francepoitou@cerfacs.fr

Mouna El Hafi

Centre RAPSODEE, École des Mines d’Albi, Campus Jarlard, 81013 Albi, France

Bénédicte Cuenot

CERFACS, 42 Avenue Gaspard Coriolis, 31057 Toulouse Cedex 01, France

PRISSMA: parallel radiation solver with spectral integration on multicomponent media, http://www.cerfacs.fr/prissma.

J. Heat Transfer 133(6), 062701 (Mar 10, 2011) (10 pages) doi:10.1115/1.4003552 History: Received July 19, 2010; Revised January 17, 2011; Published March 10, 2011; Online March 10, 2011

## Abstract

Radiation exchanges must be taken into account to improve large eddy simulation (LES) prediction of turbulent combustion, in particular, for wall heat fluxes. Because of its interaction with turbulence and its impact on the formation of polluting species, unsteady coupled calculations are required. This work constitutes a first step toward coupled LES-radiation simulations, selecting the optimal methodology based on systematic comparisons of accuracy and CPU cost. Radiation is solved with the discrete ordinate method (DOM) and different spectral models. To reach the best compromise between accuracy and CPU time, the performance of various spectral models and discretizations (angular, temporal, and spatial) is studied. It is shown that the use of a global spectral model combined with a mesh coarsening (compared with the LES mesh) and a minimal coupling frequency $Nit$ allows to compute one radiative solution faster than $Nit$ LES iterations while keeping a good accuracy. It also appears that the impact on accuracy of the angular discretization in the DOM is very small compared with the impact of the spectral model. The determined optimal methodology may be used to perform unsteady coupled calculations of turbulent combustion with radiation.

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## Figures

Figure 1

Test configuration (15)

Figure 2

Instantaneous field of temperature, heat release, and magnitude velocity in the plane y=0

Figure 3

(a) SCS) and (b) PCS

Figure 4

Radiative source term along the central axis for the LC11 (96 directions) and the S4 (24 directions) angular discretization

Figure 5

Radiative source term for different spectral models along the central axis SNBcK (Nq=5), FS-SNBcK for Nq=7,10,15 and WSGG; influence of the tabulation for the FS-SNBcK model with Nq=15

Figure 6

(a) Grid 1 where the cell size cell in the fluctuating zone of temperature is kept constant in the original mesh (1 mm). In grid 2, the cell size in the fluctuating zone of temperature is twice the original mesh (2 mm). (b) Mean and rms temperature fields in the y=0 plane. (c) Mean Planck absorption coefficient (m−1) from the temporally averaged solution ⟨T⟩, ⟨Xi⟩ in the plane z=0.

Figure 7

Radiative source term along the central axis calculated with FS-SNBcK model, Nq=15, S4 with black walls (no reflection) for the three grids

Figure 8

Radiative source term along the central axis for the SNBcK model on grid 2 with an S4 quadrature; line: without reflection and dashed: with reflection

Figure 9

Wall radiative flux along the x axis at y=2.5 cm and z=0 (quartz wall) for the SNBcK model on grid 2 with an S4 quadrature; line: without reflection and dashed: with reflection

Figure 10

Ratio of calculation times PRISSMA/AVBP for the different models and discretizations of the radiative solver

## Errata

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