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

Title: Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime

Abstract

Experiments and large eddy simulation (LES) were performed to study the development of the Rayleigh–Taylor instability into the saturated, nonlinear regime, produced between two gases accelerated by a rarefaction wave. Single-mode two-dimensional, and single-mode three-dimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a non-constant acceleration, and a time decreasing Atwood number,$$A=(\unicode[STIX]{x1D70C}_{2}-\unicode[STIX]{x1D70C}_{1})/(\unicode[STIX]{x1D70C}_{2}+\unicode[STIX]{x1D70C}_{1})$$, where$$\unicode[STIX]{x1D70C}_{2}$$and$$\unicode[STIX]{x1D70C}_{1}$$are the densities of the heavy and light gas, respectively. Experiments and simulations are presented for initial Atwood numbers of$A=0.49$$,$$A=0.63$$,$$A=0.82$$and$$A=0.94$$. Nominally two-dimensional (2-D) experiments (initiated with nearly 2-D perturbations) and 2-D simulations are observed to approach an intermediate-time velocity plateau that is in disagreement with the late-time velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2-D bubbles in large wavenumber,$$k=2\unicode[STIX]{x03C0}/\unicode[STIX]{x1D706}=0.247~\text{mm}^{-1}$$, experiments and simulations, where$$\unicode[STIX]{x1D706}$is the wavelength of the initial perturbation. At moderate Atwood numbers, the bubble and spike velocities approach larger values than those predicted by Goncharov’s model. These late-time velocity trends are predicted well by numerical simulations using the LLNL Miranda code, and by the 2009 model of Mikaelian (Phys. Fluids., vol. 21, 2009, 024103) that extends Layzer type models to variable acceleration and density. Large Atwood number experiments show a delayed roll up, and exhibit a free-fall like behaviour. Finally, experiments initiated with three-dimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry.

Authors:
ORCiD logo [1];  [2];  [2];  [1]
  1. Univ. of Arizona, Tucson, AZ (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Univ. of Arizona, Tucson, AZ (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
Contributing Org.:
Lawrence Livermore National Laboratory
OSTI Identifier:
1419851
Alternate Identifier(s):
OSTI ID: 1568010
Report Number(s):
LLNL-JRNL-787438
Journal ID: ISSN 0022-1120; applab; PII: S002211201700893X; TRN: US1801403
Grant/Contract Number:  
NA0002929; AC52-07NA27344
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Fluid Mechanics
Additional Journal Information:
Journal Volume: 838; Journal ID: ISSN 0022-1120
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; gas dynamics; nonlinear instability; turbulent mixing; Engineering - Mechanical and civil engineering

Citation Formats

Morgan, R. V., Cabot, W. H., Greenough, J. A., and Jacobs, J. W. Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime. United States: N. p., 2018. Web. doi:10.1017/jfm.2017.893.
Morgan, R. V., Cabot, W. H., Greenough, J. A., & Jacobs, J. W. Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime. United States. doi:10.1017/jfm.2017.893.
Morgan, R. V., Cabot, W. H., Greenough, J. A., and Jacobs, J. W. Fri . "Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime". United States. doi:10.1017/jfm.2017.893. https://www.osti.gov/servlets/purl/1419851.
@article{osti_1419851,
title = {Rarefaction-driven Rayleigh–Taylor instability. Part 2. Experiments and simulations in the nonlinear regime},
author = {Morgan, R. V. and Cabot, W. H. and Greenough, J. A. and Jacobs, J. W.},
abstractNote = {Experiments and large eddy simulation (LES) were performed to study the development of the Rayleigh–Taylor instability into the saturated, nonlinear regime, produced between two gases accelerated by a rarefaction wave. Single-mode two-dimensional, and single-mode three-dimensional initial perturbations were introduced on the diffuse interface between the two gases prior to acceleration. The rarefaction wave imparts a non-constant acceleration, and a time decreasing Atwood number,$A=(\unicode[STIX]{x1D70C}_{2}-\unicode[STIX]{x1D70C}_{1})/(\unicode[STIX]{x1D70C}_{2}+\unicode[STIX]{x1D70C}_{1})$, where$\unicode[STIX]{x1D70C}_{2}$and$\unicode[STIX]{x1D70C}_{1}$are the densities of the heavy and light gas, respectively. Experiments and simulations are presented for initial Atwood numbers of$A=0.49$,$A=0.63$,$A=0.82$and$A=0.94$. Nominally two-dimensional (2-D) experiments (initiated with nearly 2-D perturbations) and 2-D simulations are observed to approach an intermediate-time velocity plateau that is in disagreement with the late-time velocity obtained from the incompressible model of Goncharov (Phys. Rev. Lett., vol. 88, 2002, 134502). Reacceleration from an intermediate velocity is observed for 2-D bubbles in large wavenumber,$k=2\unicode[STIX]{x03C0}/\unicode[STIX]{x1D706}=0.247~\text{mm}^{-1}$, experiments and simulations, where$\unicode[STIX]{x1D706}$is the wavelength of the initial perturbation. At moderate Atwood numbers, the bubble and spike velocities approach larger values than those predicted by Goncharov’s model. These late-time velocity trends are predicted well by numerical simulations using the LLNL Miranda code, and by the 2009 model of Mikaelian (Phys. Fluids., vol. 21, 2009, 024103) that extends Layzer type models to variable acceleration and density. Large Atwood number experiments show a delayed roll up, and exhibit a free-fall like behaviour. Finally, experiments initiated with three-dimensional perturbations tend to agree better with models and a simulation using the LLNL Ares code initiated with an axisymmetric rather than Cartesian symmetry.},
doi = {10.1017/jfm.2017.893},
journal = {Journal of Fluid Mechanics},
issn = {0022-1120},
number = ,
volume = 838,
place = {United States},
year = {2018},
month = {1}
}

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

Figures / Tables:

TABLE 1 TABLE 1: Forcing amplitudes af , and frequencies ω used to generate nominally 2D waves in the test section for each of the gas pairs and wavenumbers used.

Save / Share:

Works referenced in this record:

Evolution of the Rayleigh–Taylor instability in the mixing zone between gases of different densities in a field of variable acceleration
journal, July 2003


A tensor artificial viscosity using a finite element approach
journal, December 2009


The mixing transition in turbulent flows
journal, April 2000


Solution to Rayleigh-Taylor instabilities: Bubbles, spikes, and their scalings
journal, May 2014


Experiments on the late-time development of single-mode Richtmyer–Meshkov instability
journal, March 2005

  • Jacobs, J. W.; Krivets, V. V.
  • Physics of Fluids, Vol. 17, Issue 3
  • DOI: 10.1063/1.1852574

An overview of Rayleigh-Taylor instability
journal, July 1984


Hyperviscosity for shock-turbulence interactions
journal, March 2005


Adaptive wavelet collocation method simulations of Rayleigh–Taylor instability
journal, December 2010


A membraneless experiment for the study of Richtmyer–Meshkov instability of a shock-accelerated gas interface
journal, October 1997

  • Jones, M. A.; Jacobs, J. W.
  • Physics of Fluids, Vol. 9, Issue 10
  • DOI: 10.1063/1.869416

Statistically steady measurements of Rayleigh-Taylor mixing in a gas channel
journal, March 2006

  • Banerjee, Arindam; Andrews, Malcolm J.
  • Physics of Fluids, Vol. 18, Issue 3
  • DOI: 10.1063/1.2185687

Three-dimensional Rayleigh-Taylor instability Part 2. Experiment
journal, February 1988


Asymptotic spike evolution in Rayleigh–Taylor instability
journal, January 1999


PLIF flow visualization and measurements of the Richtmyer–Meshkov instability of an air/SF 6 interface
journal, August 2002


Comprehensive numerical methodology for direct numerical simulations of compressible Rayleigh–Taylor instability
journal, May 2016

  • Reckinger, Scott J.; Livescu, Daniel; Vasilyev, Oleg V.
  • Journal of Computational Physics, Vol. 313
  • DOI: 10.1016/j.jcp.2015.11.002

Experimental investigation of Rayleigh-Taylor instability
journal, January 1973


Limitations and failures of the Layzer model for hydrodynamic instabilities
journal, July 2008


Reshocks, rarefactions, and the generalized Layzer model for hydrodynamic instabilities
journal, February 2009


Validation of the Sharp–Wheeler bubble merger model from experimental and computational data
journal, January 1988

  • Glimm, J.; Li, X. L.
  • Physics of Fluids, Vol. 31, Issue 8
  • DOI: 10.1063/1.866660

Dimensionality dependence of the Rayleigh–Taylor and Richtmyer–Meshkov instability late-time scaling laws
journal, June 2001

  • Oron, D.; Arazi, L.; Kartoon, D.
  • Physics of Plasmas, Vol. 8, Issue 6
  • DOI: 10.1063/1.1362529

The late-time dynamics of the single-mode Rayleigh-Taylor instability
journal, July 2012

  • Ramaprabhu, P.; Dimonte, Guy; Woodward, P.
  • Physics of Fluids, Vol. 24, Issue 7
  • DOI: 10.1063/1.4733396

Experiments on the Richtmyer–Meshkov instability with an imposed, random initial perturbation
journal, March 2013


Vortex simulations of the Rayleigh–Taylor instability
journal, January 1980

  • Baker, Gregory R.; Meiron, Daniel I.; Orszag, Steven A.
  • Physics of Fluids, Vol. 23, Issue 8
  • DOI: 10.1063/1.863173

Limits of the potential flow approach to the single-mode Rayleigh-Taylor problem
journal, December 2006


A high-wavenumber viscosity for high-resolution numerical methods
journal, April 2004


Enthalpy diffusion in multicomponent flows
journal, May 2009


Time dependent boundary conditions for hyperbolic systems
journal, January 1987


Bubble Acceleration in the Ablative Rayleigh-Taylor Instability
journal, November 2006


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


Single-mode dynamics of the Rayleigh-Taylor instability at any density ratio
journal, March 2005


Nonlinear evolution of the Rayleigh–Taylor and Richtmyer–Meshkov instabilities
journal, May 1999


Rayleigh-Taylor instability and the use of conformal maps for ideal fluid flow
journal, July 1983


Analytical Solutions of Layzer-Type Approach to Unstable Interfacial Fluid Mixing
journal, October 1998


Rayleigh-Taylor Instability in Elastic-Plastic Materials
journal, February 1998


Production of reproducible Rayleigh–Taylor instabilities
journal, October 1979

  • Popil, R.; Curzon, F. L.
  • Review of Scientific Instruments, Vol. 50, Issue 10
  • DOI: 10.1063/1.1135698

Rarefaction-driven Rayleigh–Taylor instability. Part 1. Diffuse-interface linear stability measurements and theory
journal, February 2016

  • Morgan, R. V.; Likhachev, O. A.; Jacobs, J. W.
  • Journal of Fluid Mechanics, Vol. 791
  • DOI: 10.1017/jfm.2016.46

Shock tube experiments and numerical simulation of the single-mode, three-dimensional Richtmyer–Meshkov instability
journal, November 2009

  • Long, C. C.; Krivets, V. V.; Greenough, J. A.
  • Physics of Fluids, Vol. 21, Issue 11
  • DOI: 10.1063/1.3263705

Small Atwood number Rayleigh–Taylor experiments
journal, April 2010

  • Andrews, Malcolm J.; Dalziel, Stuart B.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 368, Issue 1916
  • DOI: 10.1098/rsta.2010.0007

Boundary conditions for direct simulations of compressible viscous flows
journal, July 1992


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


Comparison of two- and three-dimensional simulations of miscible Rayleigh-Taylor instability
journal, April 2006


On the Instability of Superposed Fluids in a Gravitational Field.
journal, July 1955

  • Layzer, David
  • The Astrophysical Journal, Vol. 122
  • DOI: 10.1086/146048