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EXTENDED LMSE AND LANGEVIN MODELS OF THE SCALAR MIXING IN THE TURBULENT FLOW

Vladimir Sabel'nikov
ONERA, Fundamental and Applied Energetics Department, Fort de Palaiseau, Chemin de la Hunière 91761 Palaiseau Cedex, France

Mikhael Gorokhovski
CORIA UMR 6614 CNRS University of Rouen, Site Universitaire du Madrillet BP12, 76801 Saint Etienne du Rouvray; and LMFA UMR 5509 CNRS Ecole Centrale de Lyon, 36 avenue Guy de Collongue, 69131 Ecully Cedex, France

Abstract

A further developments of the LMSE and Langevin micro-mixing models are proposed in order to account for the entire spectrum of time scales in the turbulent flow. The evolution of these scales are described in the framework of the log-normal stochastic process. The equation for the scalar pdf conditional on the given mixing frequency is derived and numerically solved for each of considered models in the simple case of the statistically homogeneous flow. Then, by integration over all range of the mixing frequency, the unconditional pdf s are obtained and compared against DNS data. It is shown that at late times, the modeled pdf has exponential tails. The model of the forcing mixing with injection of unmixed concentrations is proposed in the last part of the paper.