skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation

Abstract

High-fidelity large eddy simulation (LES) of a low-Atwood number (A = 0.05) Rayleigh-Taylor mixing layer is performed using the tenth-order compact difference code Miranda. An initial multimode perturbation spectrum is specified in Fourier space as a function of mesh resolution such that a database of results is obtained in which each successive level of increased grid resolution corresponds approximately to one additional doubling of the mixing layer width, or generation. The database is then analyzed to determine approximate requirements for self-similarity, and a new metric is proposed to quantify how far a given simulation is from the limit of self-similarity. It is determined that mixing layer growth reaches a high degree of self-similarity after approximately 4.5 generations. Statistical convergence errors and boundary effects at late time, however, make it impossible to draw similar conclusions regarding the self-similar growth of more sensitive turbulence parameters. Finally, self-similar turbulence profiles from the LES database are compared with one-dimensional simulations using the k-L-a and BHR-2 Reynolds-averaged Navier-Stokes (RANS) models. The k-L-a model, which is calibrated to reproduce a quadratic turbulence kinetic energy profile for a self-similar mixing layer, is found to be in better agreement with the LES than BHR-2 results.

Authors:
ORCiD logo [1];  [1];  [2];  [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
  2. Univ. of Missouri, Columbia, MO (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1430929
Report Number(s):
LLNL-JRNL-681041
Journal ID: ISSN 1468-5248
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Turbulence (Online)
Additional Journal Information:
Journal Name: Journal of Turbulence (Online); Journal Volume: 18; Journal Issue: 10; Journal ID: ISSN 1468-5248
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; 70 PLASMA PHYSICS AND FUSION

Citation Formats

Morgan, B. E., Olson, B. J., White, J. E., and McFarland, J. A. Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation. United States: N. p., 2017. Web. doi:10.1080/14685248.2017.1343477.
Morgan, B. E., Olson, B. J., White, J. E., & McFarland, J. A. Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation. United States. doi:10.1080/14685248.2017.1343477.
Morgan, B. E., Olson, B. J., White, J. E., and McFarland, J. A. Thu . "Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation". United States. doi:10.1080/14685248.2017.1343477. https://www.osti.gov/servlets/purl/1430929.
@article{osti_1430929,
title = {Self-similarity of a Rayleigh–Taylor mixing layer at low Atwood number with a multimode initial perturbation},
author = {Morgan, B. E. and Olson, B. J. and White, J. E. and McFarland, J. A.},
abstractNote = {High-fidelity large eddy simulation (LES) of a low-Atwood number (A = 0.05) Rayleigh-Taylor mixing layer is performed using the tenth-order compact difference code Miranda. An initial multimode perturbation spectrum is specified in Fourier space as a function of mesh resolution such that a database of results is obtained in which each successive level of increased grid resolution corresponds approximately to one additional doubling of the mixing layer width, or generation. The database is then analyzed to determine approximate requirements for self-similarity, and a new metric is proposed to quantify how far a given simulation is from the limit of self-similarity. It is determined that mixing layer growth reaches a high degree of self-similarity after approximately 4.5 generations. Statistical convergence errors and boundary effects at late time, however, make it impossible to draw similar conclusions regarding the self-similar growth of more sensitive turbulence parameters. Finally, self-similar turbulence profiles from the LES database are compared with one-dimensional simulations using the k-L-a and BHR-2 Reynolds-averaged Navier-Stokes (RANS) models. The k-L-a model, which is calibrated to reproduce a quadratic turbulence kinetic energy profile for a self-similar mixing layer, is found to be in better agreement with the LES than BHR-2 results.},
doi = {10.1080/14685248.2017.1343477},
journal = {Journal of Turbulence (Online)},
number = 10,
volume = 18,
place = {United States},
year = {2017},
month = {6}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 6 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

The mixing transition in turbulent flows
journal, April 2000


Large and Small Scale Structure in Rayleigh-Taylor Mixing
journal, April 1998


Development and validation of a turbulent-mix model for variable-density and compressible flows
journal, October 2010


Analysis of turbulent transport and mixing in transitional Rayleigh–Taylor unstable flow using direct numerical simulation data
journal, October 2010

  • Schilling, Oleg; Mueschke, Nicholas J.
  • Physics of Fluids, Vol. 22, Issue 10
  • DOI: 10.1063/1.3484247

Measurements of molecular mixing in a high-Schmidt-number Rayleigh–Taylor mixing layer
journal, July 2009

  • Mueschke, Nicholas J.; Schilling, Oleg; Youngs, David L.
  • Journal of Fluid Mechanics, Vol. 632
  • DOI: 10.1017/S0022112009006132

A numerical study of bubble interactions in Rayleigh–Taylor instability for compressible fluids
journal, November 1990

  • Glimm, J.; Li, X. L.; Menikoff, R.
  • Physics of Fluids A: Fluid Dynamics, Vol. 2, Issue 11
  • DOI: 10.1063/1.857679

The Role of Mixing in Astrophysics
journal, April 2000

  • Arnett, D.
  • The Astrophysical Journal Supplement Series, Vol. 127, Issue 2
  • DOI: 10.1086/313364

The dynamics of the k –ϵ mix model toward its self-similar Rayleigh–Taylor solution
journal, November 2014


Two-equation and multi-fluid turbulence models for Rayleigh–Taylor mixing
journal, December 2015


Nonlinear effects in the combined Rayleigh-Taylor/Kelvin-Helmholtz instability
journal, November 2011

  • Olson, Britton J.; Larsson, Johan; Lele, Sanjiva K.
  • Physics of Fluids, Vol. 23, Issue 11
  • DOI: 10.1063/1.3660723

Experimental study of Rayleigh–Taylor instability with a complex initial perturbation
journal, March 2009

  • Olson, D. H.; Jacobs, J. W.
  • Physics of Fluids, Vol. 21, Issue 3
  • DOI: 10.1063/1.3085811

Artificial fluid properties for large-eddy simulation of compressible turbulent mixing
journal, May 2007


Large-eddy and unsteady RANS simulations of a shock-accelerated heavy gas cylinder
journal, April 2015


Detailed measurements of a statistically steady Rayleigh–Taylor mixing layer from small to high Atwood numbers
journal, August 2010

  • Banerjee, Arindam; Kraft, Wayne N.; Andrews, Malcolm J.
  • Journal of Fluid Mechanics, Vol. 659
  • DOI: 10.1017/S0022112010002351

Progress toward Ignition and Burn Propagation in Inertial Confinement Fusion
journal, September 1992

  • Lindl, John D.; McCrory, Robert L.; Campbell, E. Michael
  • Physics Today, Vol. 45, Issue 9
  • DOI: 10.1063/1.881318

K-L turbulence model for the self-similar growth of the Rayleigh-Taylor and Richtmyer-Meshkov instabilities
journal, August 2006

  • Dimonte, Guy; Tipton, Robert
  • Physics of Fluids, Vol. 18, Issue 8
  • DOI: 10.1063/1.2219768

The Tilted Rocket Rig: A Rayleigh–Taylor Test Case for RANS Models1
journal, July 2014

  • Denissen, Nicholas A.; Rollin, Bertrand; Reisner, Jon M.
  • Journal of Fluids Engineering, Vol. 136, Issue 9
  • DOI: 10.1115/1.4027776

Three-equation model for the self-similar growth of Rayleigh-Taylor and Richtmyer-Meskov instabilities
journal, April 2015


Large eddy simulation requirements for the Richtmyer-Meshkov instability
journal, April 2014

  • Olson, Britton J.; Greenough, Jeff
  • Physics of Fluids, Vol. 26, Issue 4
  • DOI: 10.1063/1.4871396

On generating initial conditions for turbulence models: the case of Rayleigh–Taylor instability turbulent mixing
journal, March 2013


Numerical simulation of turbulent mixing by Rayleigh-Taylor instability
journal, July 1984


New phenomena in variable-density Rayleigh–Taylor turbulence
journal, December 2010


Density ratio dependence of Rayleigh–Taylor mixing for sustained and impulsive acceleration histories
journal, February 2000

  • Dimonte, Guy; Schneider, Marilyn
  • Physics of Fluids, Vol. 12, Issue 2
  • DOI: 10.1063/1.870309

Rayleigh-Taylor and Richtmyer-Meshkov instabilities and mixing in stratified spherical shells
journal, September 1990


An overview of Rayleigh-Taylor instability
journal, July 1984


The mixing transition in RayleighTaylor instability
journal, January 1999


Self-similarity and internal structure of turbulence induced by Rayleigh–Taylor instability
journal, November 1999


Inertial-range anisotropy in Rayleigh-Taylor turbulence
journal, February 2012

  • Soulard, Olivier; Griffond, Jérôme
  • Physics of Fluids, Vol. 24, Issue 2
  • DOI: 10.1063/1.3680871

Effect of shear on Rayleigh-Taylor mixing at small Atwood number
journal, March 2013


Modelling turbulent mixing by Rayleigh-Taylor instability
journal, July 1989


Dynamics and structure of unstably stratified homogeneous turbulence
journal, June 2016


Modal interactions between a large-wavelength inclined interface and small-wavelength multimode perturbations in a Richtmyer-Meshkov instability
journal, July 2015


Rayleigh–Taylor turbulence: self-similar analysis and direct numerical simulations
journal, May 2004


Enthalpy diffusion in multicomponent flows
journal, May 2009


Rayleigh–Taylor instability in complex stratifications
journal, October 2005


The role of directionality on the structure and dynamics of strongly anisotropic turbulent flows
journal, January 2013


Applications of shock-induced mixing to supersonic combustion
journal, May 1993

  • Yang, Joseph; Kubota, Toshi; Zukoski, Edward E.
  • AIAA Journal, Vol. 31, Issue 5
  • DOI: 10.2514/3.11696

Self-similarity and universality in Rayleigh–Taylor, Boussinesq turbulence
journal, January 2009

  • Vladimirova, Natalia; Chertkov, Michael
  • Physics of Fluids, Vol. 21, Issue 1
  • DOI: 10.1063/1.3054152

Bubble merger model for the nonlinear Rayleigh–Taylor instability driven by a strong blast wave
journal, November 2004


Experimental investigation of RayleighTaylor mixing at small Atwood numbers
journal, January 1999


Reynolds number effects on Rayleigh–Taylor instability with possible implications for type Ia supernovae
journal, July 2006

  • Cabot, William H.; Cook, Andrew W.
  • Nature Physics, Vol. 2, Issue 8
  • DOI: 10.1038/nphys361

Statistics of mixing in three-dimensional Rayleigh–Taylor turbulence at low Atwood number and Prandtl number one
journal, March 2010

  • Boffetta, G.; Mazzino, A.; Musacchio, S.
  • Physics of Fluids, Vol. 22, Issue 3
  • DOI: 10.1063/1.3371712

Rayleigh–Taylor shock waves
journal, December 2007

  • Olson, Britton J.; Cook, Andrew W.
  • Physics of Fluids, Vol. 19, Issue 12
  • DOI: 10.1063/1.2821907

Comparison of two- and three-dimensional simulations of miscible Richtmyer-Meshkov instability with multimode initial conditions
journal, October 2014

  • Olson, Britton J.; Greenough, Jeffrey A.
  • Physics of Fluids, Vol. 26, Issue 10
  • DOI: 10.1063/1.4898157

Experimental characterization of initial conditions and spatio-temporal evolution of a small-Atwood-number Rayleigh–Taylor mixing layer
journal, October 2006

  • Mueschke, Nicholas J.; Andrews, Malcolm J.; Schilling, Oleg
  • Journal of Fluid Mechanics, Vol. 567
  • DOI: 10.1017/S0022112006001959

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

Transition stages of Rayleigh–Taylor instability between miscible fluids
journal, September 2001