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

Journal Article · · Journal of Turbulence (Online)
 [1]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
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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.

Research Organization:
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Sponsoring Organization:
USDOE Laboratory Directed Research and Development (LDRD) Program
Grant/Contract Number:
89233218CNA000001
OSTI ID:
1569613
Report Number(s):
LA-UR-18-23839
Journal Information:
Journal of Turbulence (Online), Vol. 20, Issue 7; ISSN 1468-5248
Publisher:
Taylor & FrancisCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 1 work
Citation information provided by
Web of Science

References (15)

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

Figures / Tables (12)

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Figure 11(p. 25)figure Figure 11
Figure 12(p. 26)figure Figure 12

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Favre averages
mean turbulent reaction rates
variable density turbulence