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EFFECTS OF TEMPERATURE AND CONCENTRATION FLUCTUATIONS IN TURBULENT GAS FLOWS ON COMBINED RADIATIVE AND CONDUCTIVE WALL FLUXES

F. El Ammouri
Laboratoire EM2C, UPR288 du CNRS et de L'ECP, Ecole Centrale Paris, 92295 Chatenay-Malabry Cedex, FRANCE

Anouar Soufiani
Laboratoire EM2C, CNRS, CentraleSupélec, Université Paris-Saclay, Châtenay-Malabry, France

Jean Taine
Laboratoire d'Energetique Moleculaire et Macroscopique, Combustion, UPR 288 du CNRS et de l'ECP. Ecole Centrale Paris, 92295 Chatenay-Malabry Cedex, France

Abstract

The effects of temperature and concentration turbulent fluctuations on combined heat transfer by conduction, convection and radiation are studied in the case of a 2D flow of a binary gas mixture. A random statistical narrow-band (RSNB) model associated with the Curtis-Godson approximation is used for gas radiative properties. Second order Taylor expansions of the local instantaneous equilibrium intensities and column element transmissivities versus temperature and molar fraction fluctuations T '(s) and Xα'(s') are carried out in order to obtain the expressions of the local time averaged intensities as functions of two-point turbulence moments xα'(s) Xα(s'), T'(s)T'(s') and Xα'(s)T '(s'). These fields are computed from a turbulence model with six supplementary equations, related to turbulent kinetic energy k, temperature variance θ, mass fraction variance χ and their respective dissipation rates ε, εθ and εχ. Global results, such as wall fluxes, are very sensitive to the degree of accuracy and completeness of the modelling of both temperature and concentration fluctuating terms in the balance equations of energy, θ and εθ. The effects of temperature fluctuations on equilibrium radiative intensities increase the wall fluxes but the same effects on gas transmissivities decrease these fluxes. The part of the wall flux due to temperature and molar fraction fluctuations can be as high as that due to the contributions of the mean fields T and xα, especially around 1000 K and when positive cross correlations xα'T' are considered.

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