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Title: Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing

Abstract

The three-equation k-L-a turbulence model [B. Morgan and M. Wickett, Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meshkov instabilities," Phys. Rev. E 91 (2015)] is extended by the addition of a second length scale equation. It is shown that the separation of turbulence transport and turbulence destruction length scales is necessary for simultaneous prediction of the growth parameter and turbulence intensity of a Kelvin-Helmholtz shear layer when model coeficients are constrained by similarity analysis. Constraints on model coeficients are derived that satisfy an ansatz of self-similarity in the low-Atwood-number limit and allow the determination of model coeficients necessary to recover expected experimental behavior. The model is then applied in one-dimensional simulations of Rayleigh-Taylor, reshocked Richtmyer-Meshkov, Kelvin{Helmholtz, and combined Rayleigh-Taylor/Kelvin-Helmholtz instability mixing layers to demonstrate that the expected growth rates are recovered numerically. Finally, it is shown that model behavior in the case of combined instability is to predict a mixing width that is a linear combination of Rayleigh-Taylor and Kelvin-Helmholtz mixing processes.

Authors:
 [1];  [1];  [1]
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  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1430927
Alternate Identifier(s):
OSTI ID: 1416418
Report Number(s):
LLNL-JRNL-740721
Journal ID: ISSN 2470-0045; PLEEE8; TRN: US1802766
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 97; Journal Issue: 1; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 70 PLASMA PHYSICS AND FUSION

Citation Formats

Morgan, Brandon E., Schilling, Oleg, and Hartland, Tucker A. Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing. United States: N. p., 2018. Web. doi:10.1103/PhysRevE.97.013104.
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Morgan, Brandon E., Schilling, Oleg, & Hartland, Tucker A. Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing. United States. https://doi.org/10.1103/PhysRevE.97.013104
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Morgan, Brandon E., Schilling, Oleg, and Hartland, Tucker A. Wed . "Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing". United States. https://doi.org/10.1103/PhysRevE.97.013104. https://www.osti.gov/servlets/purl/1430927.
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@article{osti_1430927,
title = {Two-length-scale turbulence model for self-similar buoyancy-, shock-, and shear-driven mixing},
author = {Morgan, Brandon E. and Schilling, Oleg and Hartland, Tucker A.},
abstractNote = {The three-equation k-L-a turbulence model [B. Morgan and M. Wickett, Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meshkov instabilities," Phys. Rev. E 91 (2015)] is extended by the addition of a second length scale equation. It is shown that the separation of turbulence transport and turbulence destruction length scales is necessary for simultaneous prediction of the growth parameter and turbulence intensity of a Kelvin-Helmholtz shear layer when model coeficients are constrained by similarity analysis. Constraints on model coeficients are derived that satisfy an ansatz of self-similarity in the low-Atwood-number limit and allow the determination of model coeficients necessary to recover expected experimental behavior. The model is then applied in one-dimensional simulations of Rayleigh-Taylor, reshocked Richtmyer-Meshkov, Kelvin{Helmholtz, and combined Rayleigh-Taylor/Kelvin-Helmholtz instability mixing layers to demonstrate that the expected growth rates are recovered numerically. Finally, it is shown that model behavior in the case of combined instability is to predict a mixing width that is a linear combination of Rayleigh-Taylor and Kelvin-Helmholtz mixing processes.},
doi = {10.1103/PhysRevE.97.013104},
journal = {Physical Review E},
number = 1,
volume = 97,
place = {United States},
year = {Wed Jan 10 00:00:00 EST 2018},
month = {Wed Jan 10 00:00:00 EST 2018}
}
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https://doi.org/10.1103/PhysRevE.97.013104
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Cited by: 28 works
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Figures / Tables:

TABLE I TABLE I: Summary of model coefficients and the experimental values that constrain them.
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      Figures / Tables found in this record:

      TABLE I (p. 8)table
      FIG. 1 (p. 9)figure
      FIG. 2 (p. 9)figure
      FIG. 3 (p. 10)figure
      FIG. 4 (p. 10)figure
      FIG. 5 (p. 11)figure
      FIG. 6 (p. 12)figure
      FIG. 7 (p. 12)figure
      FIG. 8 (p. 13)figure
      FIG. 10 (p. 14)figure
      FIG. 9 (p. 14)figure
      FIG. 11 (p. 15)figure
      FIG. 12 (p. 16)figure
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