A Fokker–Planck approach to a moment closure for mixing in variabledensity turbulence
Abstract
We develop a theory for the cascade mixing terms in a moment closure approach to binary active scalar mixing in variabledensity turbulence. To address the variabledensity 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 singlepoint 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 smallscale mixing is replaced with the determination of the drift and diffusion terms of a Fokker–Planck equation in a betaPDFconvergent stochastic process. We find that realisability of a betaconvergent process requires the mixing timescale 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 densityvolume correlation and moments of the density field. We develop and compare the new model with direct numerical simulations data of nonstationary homogeneous variabledensity turbulence.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE Laboratory Directed Research and Development (LDRD) Program
 OSTI Identifier:
 1569613
 Report Number(s):
 LAUR1823839
Journal ID: ISSN 14685248
 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 14685248
 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 variabledensity 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 variabledensity turbulence. United States. https://doi.org/10.1080/14685248.2019.1662030
Ristorcelli, J. R., and Bakosi, J. Mon .
"A Fokker–Planck approach to a moment closure for mixing in variabledensity turbulence". United States. https://doi.org/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 variabledensity 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 variabledensity turbulence. To address the variabledensity 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 singlepoint 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 smallscale mixing is replaced with the determination of the drift and diffusion terms of a Fokker–Planck equation in a betaPDFconvergent stochastic process. We find that realisability of a betaconvergent process requires the mixing timescale 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 densityvolume correlation and moments of the density field. We develop and compare the new model with direct numerical simulations data of nonstationary homogeneous variabledensity turbulence.},
doi = {10.1080/14685248.2019.1662030},
journal = {Journal of Turbulence (Online)},
number = 7,
volume = 20,
place = {United States},
year = {2019},
month = {9}
}
Web of Science
Figures / Tables:
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Figures / Tables found in this record: