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Title: A Fokker–Planck approach to a moment closure for mixing in variable-density turbulence

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.

Authors:
 [1]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1569613
Report Number(s):
LA-UR-18-23839
Journal ID: ISSN 1468-5248
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Turbulence (Online)
Additional Journal Information:
Journal Name: Journal of Turbulence (Online); Journal Volume: 20; Journal Issue: 7; Journal ID: ISSN 1468-5248
Publisher:
Taylor & Francis
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Favre averages; mean turbulent reaction rates; variable density turbulence

Citation Formats

Ristorcelli, J. R., and Bakosi, J. A Fokker–Planck approach to a moment closure for mixing in variable-density turbulence. United States: N. p., 2019. Web. doi:10.1080/14685248.2019.1662030.
Ristorcelli, J. R., & Bakosi, J. A Fokker–Planck approach to a moment closure for mixing in variable-density turbulence. United States. doi:10.1080/14685248.2019.1662030.
Ristorcelli, J. R., and Bakosi, J. Mon . "A Fokker–Planck approach to a moment closure for mixing in variable-density turbulence". United States. doi:10.1080/14685248.2019.1662030. https://www.osti.gov/servlets/purl/1569613.
@article{osti_1569613,
title = {A Fokker–Planck approach to a moment closure for mixing in variable-density turbulence},
author = {Ristorcelli, J. R. and Bakosi, J.},
abstractNote = {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.},
doi = {10.1080/14685248.2019.1662030},
journal = {Journal of Turbulence (Online)},
number = 7,
volume = 20,
place = {United States},
year = {2019},
month = {9}
}

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