Abstract
Abstract A novel, computationally inexpensive method is proposed to study the combined effects of turbulent mixing, molecular diffusion, and chemical reaction, of a scalar in a homogeneous, isotropic, turbulent flow. Single-scalar, two-point probability density functions (pdf's) are used in the analysis. The reaction terms of the pdf equations are closed; the diffusion terms are artificially closed by using Linear Mean Square Estimation (LMSE) theory. The convection terms are modelled by generalizing equations developed for the scalar correlation function from Eddy Damped Quasi-Normal Markovian (EDQNM) theory. Time-splitting techniques are used for the numerical calculations. The evolution of scalar two-point pdfs and related statistical quantities are obtained for a numerical example. Qualitatively satisfactory behavior is obtained in all cases. The present methods seem to be quite easy to extend to multiple-scalar two-point pdf's.
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