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

Ristorcelli, J. R.; Bakosi, J.

doi:10.1080/14685248.2019.1662030

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:

Ristorcelli, J. R. ^[1];

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: Mon Sep 09 00:00:00 EDT 2019

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):: 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.

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                    Ristorcelli, J. R., & Bakosi, J. A Fokker–Planck approach to a moment closure for mixing in variable-density turbulence.  United States.  https://doi.org/10.1080/14685248.2019.1662030

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                    Ristorcelli, J. R., and Bakosi, J. Mon .  
"A Fokker–Planck approach to a moment closure for mixing in variable-density turbulence".  United States.  https://doi.org/10.1080/14685248.2019.1662030.  https://www.osti.gov/servlets/purl/1569613.

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@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         = {Mon Sep 09 00:00:00 EDT 2019},

  month        = {Mon Sep 09 00:00:00 EDT 2019}

}

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Journal Article:

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https://doi.org/10.1080/14685248.2019.1662030

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Cited by: 1 work

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Figures / Tables:

Figure 1: Time evolution of the density PDF extracted from DNS [2,4] for various Atwood numbers and initial conditions.

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Works referenced in this record:

Implicit large-eddy simulation of passive scalar mixing in statistically stationary isotropic turbulence
journal, February 2013

Wachtor, A. J.; Grinstein, F. F.; DeVore, C. R.
Physics of Fluids, Vol. 25, Issue 2
DOI: 10.1063/1.4783924

Exact statistical results for binary mixing and reaction in variable density turbulence
journal, February 2017

Ristorcelli, J. R.
Physics of Fluids, Vol. 29, Issue 2
DOI: 10.1063/1.4974517

Application of the Fokker-Planck molecular mixing model to turbulent scalar mixing using moment methods
journal, June 2017

Madadi-Kandjani, E.; Fox, R. O.; Passalacqua, A.
Physics of Fluids, Vol. 29, Issue 6
DOI: 10.1063/1.4989421

The Fokker–Planck closure for turbulent molecular mixing: Passive scalars
journal, June 1992

Fox, R. O.
Physics of Fluids A: Fluid Dynamics, Vol. 4, Issue 6
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PDF methods for turbulent reactive flows
journal, January 1985

Pope, S. B.
Progress in Energy and Combustion Science, Vol. 11, Issue 2
DOI: 10.1016/0360-1285(85)90002-4

Turbulent Flows
book, July 2012

Pope, Stephen B.
DOI: 10.1017/CBO9780511840531

A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing
journal, September 2015

Schwarzkopf, J. D.; Livescu, D.; Baltzer, J. R.
Flow, Turbulence and Combustion, Vol. 96, Issue 1
DOI: 10.1007/s10494-015-9643-z

Variable-density mixing in buoyancy-driven turbulence
journal, May 2008

Livescu, D.; Ristorcelli, J. R.
Journal of Fluid Mechanics, Vol. 605
DOI: 10.1017/S0022112008001481

Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids
journal, January 2011

Schwarzkopf, John D.; Livescu, Daniel; Gore, Robert A.
Journal of Turbulence, Vol. 12
DOI: 10.1080/14685248.2011.633084

Assumed β-pdf Model for Turbulent Mixing: Validation and Extension to Multiple Scalar Mixing
journal, August 1991

Girimaji, S. S.
Combustion Science and Technology, Vol. 78, Issue 4-6
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A vortex-based model for the subgrid flux of a passive scalar
journal, September 2000

Pullin, D. I.
Physics of Fluids, Vol. 12, Issue 9
DOI: 10.1063/1.1287512

Buoyancy-driven variable-density turbulence
journal, October 2007

Livescu, D.; Ristorcelli, J. R.
Journal of Fluid Mechanics, Vol. 591
DOI: 10.1017/S0022112007008270

High-Reynolds number Rayleigh–Taylor turbulence
journal, January 2009

Livescu, D.; Ristorcelli, J. R.; Gore, R. A.
Journal of Turbulence, Vol. 10
DOI: 10.1080/14685240902870448

Passive scalar mixing: Analytic study of time scale ratio, variance, and mix rate
journal, July 2006

Ristorcelli, J. R.
Physics of Fluids, Vol. 18, Issue 7
DOI: 10.1063/1.2214704

Turbulent Flows
journal, October 2001

Pope, Stephen B.
Measurement Science and Technology, Vol. 12, Issue 11
DOI: 10.1088/0957-0233/12/11/705

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Similar Records

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

Abstract

Citation Formats

Figures / Tables:

Implicit large-eddy simulation of passive scalar mixing in statistically stationary isotropic turbulence journal, February 2013

Exact statistical results for binary mixing and reaction in variable density turbulence journal, February 2017

Application of the Fokker-Planck molecular mixing model to turbulent scalar mixing using moment methods journal, June 2017

The Fokker–Planck closure for turbulent molecular mixing: Passive scalars journal, June 1992

PDF methods for turbulent reactive flows journal, January 1985

Turbulent Flows book, July 2012

A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing journal, September 2015

Variable-density mixing in buoyancy-driven turbulence journal, May 2008

Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids journal, January 2011

Assumed β-pdf Model for Turbulent Mixing: Validation and Extension to Multiple Scalar Mixing journal, August 1991

A vortex-based model for the subgrid flux of a passive scalar journal, September 2000

Buoyancy-driven variable-density turbulence journal, October 2007

High-Reynolds number Rayleigh–Taylor turbulence journal, January 2009

Passive scalar mixing: Analytic study of time scale ratio, variance, and mix rate journal, July 2006

Turbulent Flows journal, October 2001

Implicit large-eddy simulation of passive scalar mixing in statistically stationary isotropic turbulence
journal, February 2013

Exact statistical results for binary mixing and reaction in variable density turbulence
journal, February 2017

Application of the Fokker-Planck molecular mixing model to turbulent scalar mixing using moment methods
journal, June 2017

The Fokker–Planck closure for turbulent molecular mixing: Passive scalars
journal, June 1992

PDF methods for turbulent reactive flows
journal, January 1985

Turbulent Flows
book, July 2012

A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing
journal, September 2015

Variable-density mixing in buoyancy-driven turbulence
journal, May 2008

Application of a second-moment closure model to mixing processes involving multicomponent miscible fluids
journal, January 2011

Assumed β-pdf Model for Turbulent Mixing: Validation and Extension to Multiple Scalar Mixing
journal, August 1991

A vortex-based model for the subgrid flux of a passive scalar
journal, September 2000

Buoyancy-driven variable-density turbulence
journal, October 2007

High-Reynolds number Rayleigh–Taylor turbulence
journal, January 2009

Passive scalar mixing: Analytic study of time scale ratio, variance, and mix rate
journal, July 2006

Turbulent Flows
journal, October 2001