A Fokker–Planck approach to a moment closure for mixing in variable-density turbulence. Issue 7 (3rd July 2019)

• Record Type: Journal Article
• Authors: Ristorcelli, J. R.; Bakosi, J.
• Is Part Of: Journal of turbulence. Volume 20:Issue 7(2019)
• Page Start: 393
• Page End: 423
• Publication Date: 2019-07-03
• Subjects: Favre averages -- mean turbulent reaction rates -- variable-density turbulence; Turbulence -- Periodicals; Turbulence -- Périodiques; 532.0527
• DOI: 10.1080/14685248.2019.1662030
• Languages: English
• ISSNs: 1468-5248

Abstract

ABSTRACT: We develop a theory for the cascade mixing terms in a moment closure approach to binary active scalar mixing in variable-density turbulence. To address the variable-density complications we apply, as a principle and constraint, the conservation of the probability density function (PDF) through a Fokker–Planck equation with bounded sample space whose attractor is the beta PDF with skewness. Mixing is related to a single-point PDF as a realisability principle to provide mathematically rigorous expressions for the small scale statistics in terms of largescale moments. The problem of the unknown small-scale mixing is replaced with the determination of the drift and diffusion terms of a Fokker–Planck equation in a beta-PDF-convergent stochastic process. We find that realisability of a beta-convergent process requires the mixing time-scale ratio, taken as a constant in passive scalar mixing, to be a function of the mean mass fraction, mean fluid density, the Atwood number, the density-volume correlation and moments of the density field. We develop and compare the new model with direct numerical simulations data of non-stationary homogeneous variable-density turbulence.