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Title: On the late-time growth of the two-dimensional Richtmyer–Meshkov instability in shock tube experiments [On the late-time growth of the 2D Richtmyer–Meshkov instability in shock tube experiments]

Abstract

In the present study, shock tube experiments are used to study the very late-time development of the Richtmyer–Meshkov instability from a diffuse, nearly sinusoidal, initial perturbation into a fully turbulent flow. The interface is generated by two opposing gas flows and a perturbation is formed on the interface by transversely oscillating the shock tube to create a standing wave. The puncturing of a diaphragm generates a Mach$1. 2$shock wave that then impacts a density gradient composed of air and SF6, causing the Richtmyer–Meshkov instability to develop in the 2.0 m long test section. The instability is visualized with planar Mie scattering in which smoke particles in the air are illuminated by a Nd:YLF laser sheet, and images are recorded using four high-speed video cameras operating at 6 kHz that allow the recording of the time history of the instability. In addition, particle image velocimetry (PIV) is implemented using a double-pulsed Nd:YAG laser with images recorded using a single CCD camera. Initial modal content, amplitude, and growth rates are reported from the Mie scattering experiments while vorticity and circulation measurements are made using PIV. Amplitude measurements show good early-time agreement but relatively poor late-time agreement with existing nonlinear models. The model of Goncharovmore » agrees with growth rate measurements at intermediate times but fails at late experimental times. Measured background acceleration present in the experiment suggests that the late-time growth rate may be influenced by Rayleigh–Taylor instability induced by the interfacial acceleration. Numerical simulations conducted using the LLNL codes Ares and Miranda show that this acceleration may be caused by the growth of boundary layers, and must be accounted for to produce good agreement with models and simulations. Adding acceleration to the Richtmyer–Meshkov buoyancy–drag model produces improved agreement. It is found that the growth rate and amplitude trends are also modelled well by the Likhachev–Jacobs vortex model. Here, circulation measurements also show good agreement with the circulation value extracted by fitting the vortex model to the experimental data.« less

Authors:
 [1];  [1];  [1];  [2];  [2];  [1];  [1]
  1. The Univ. of Arizona, Tucson, AZ (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1559909
Report Number(s):
LLNL-JRNL-524231
Journal ID: ISSN 0022-1120; 553372
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Fluid Mechanics
Additional Journal Information:
Journal Volume: 712; Journal Issue: na; Journal ID: ISSN 0022-1120
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING

Citation Formats

Morgan, Robert V., Aure, R., Stockero, J. D., Greenough, J. A., Cabot, W., Likhachev, O. A., and Jacobs, J. W. On the late-time growth of the two-dimensional Richtmyer–Meshkov instability in shock tube experiments [On the late-time growth of the 2D Richtmyer–Meshkov instability in shock tube experiments]. United States: N. p., 2012. Web. doi:10.1017/jfm.2012.426.
Morgan, Robert V., Aure, R., Stockero, J. D., Greenough, J. A., Cabot, W., Likhachev, O. A., & Jacobs, J. W. On the late-time growth of the two-dimensional Richtmyer–Meshkov instability in shock tube experiments [On the late-time growth of the 2D Richtmyer–Meshkov instability in shock tube experiments]. United States. doi:10.1017/jfm.2012.426.
Morgan, Robert V., Aure, R., Stockero, J. D., Greenough, J. A., Cabot, W., Likhachev, O. A., and Jacobs, J. W. Mon . "On the late-time growth of the two-dimensional Richtmyer–Meshkov instability in shock tube experiments [On the late-time growth of the 2D Richtmyer–Meshkov instability in shock tube experiments]". United States. doi:10.1017/jfm.2012.426. https://www.osti.gov/servlets/purl/1559909.
@article{osti_1559909,
title = {On the late-time growth of the two-dimensional Richtmyer–Meshkov instability in shock tube experiments [On the late-time growth of the 2D Richtmyer–Meshkov instability in shock tube experiments]},
author = {Morgan, Robert V. and Aure, R. and Stockero, J. D. and Greenough, J. A. and Cabot, W. and Likhachev, O. A. and Jacobs, J. W.},
abstractNote = {In the present study, shock tube experiments are used to study the very late-time development of the Richtmyer–Meshkov instability from a diffuse, nearly sinusoidal, initial perturbation into a fully turbulent flow. The interface is generated by two opposing gas flows and a perturbation is formed on the interface by transversely oscillating the shock tube to create a standing wave. The puncturing of a diaphragm generates a Mach$1. 2$shock wave that then impacts a density gradient composed of air and SF6, causing the Richtmyer–Meshkov instability to develop in the 2.0 m long test section. The instability is visualized with planar Mie scattering in which smoke particles in the air are illuminated by a Nd:YLF laser sheet, and images are recorded using four high-speed video cameras operating at 6 kHz that allow the recording of the time history of the instability. In addition, particle image velocimetry (PIV) is implemented using a double-pulsed Nd:YAG laser with images recorded using a single CCD camera. Initial modal content, amplitude, and growth rates are reported from the Mie scattering experiments while vorticity and circulation measurements are made using PIV. Amplitude measurements show good early-time agreement but relatively poor late-time agreement with existing nonlinear models. The model of Goncharov agrees with growth rate measurements at intermediate times but fails at late experimental times. Measured background acceleration present in the experiment suggests that the late-time growth rate may be influenced by Rayleigh–Taylor instability induced by the interfacial acceleration. Numerical simulations conducted using the LLNL codes Ares and Miranda show that this acceleration may be caused by the growth of boundary layers, and must be accounted for to produce good agreement with models and simulations. Adding acceleration to the Richtmyer–Meshkov buoyancy–drag model produces improved agreement. It is found that the growth rate and amplitude trends are also modelled well by the Likhachev–Jacobs vortex model. Here, circulation measurements also show good agreement with the circulation value extracted by fitting the vortex model to the experimental data.},
doi = {10.1017/jfm.2012.426},
journal = {Journal of Fluid Mechanics},
number = na,
volume = 712,
place = {United States},
year = {2012},
month = {10}
}

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Works referenced in this record:

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


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

Nonlinear evolution of an interface in the Richtmyer-Meshkov instability
journal, March 2003


Hyperviscosity for shock-turbulence interactions
journal, March 2005


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

Asymptotic growth in the linear Richtmyer–Meshkov instability
journal, April 1997

  • Wouchuk, Juan Gustavo; Nishihara, Katsunobu
  • Physics of Plasmas, Vol. 4, Issue 4
  • DOI: 10.1063/1.872191

The dynamics of shock accelerated light and heavy gas cylinders
journal, September 1993

  • Jacobs, J. W.
  • Physics of Fluids A: Fluid Dynamics, Vol. 5, Issue 9
  • DOI: 10.1063/1.858562

Nonlinear regime of a multimode Richtmyer–Meshkov instability: A simplified perturbation theory
journal, March 2002

  • Vandenboomgaerde, Marc; Gauthier, Serge; Mügler, Claude
  • Physics of Fluids, Vol. 14, Issue 3
  • DOI: 10.1063/1.1447914

Richtmyer–Meshkov turbulent mixing arising from an inclined material interface with realistic surface perturbations and reshocked flow
journal, April 2011

  • Hahn, M.; Drikakis, D.; Youngs, D. L.
  • Physics of Fluids, Vol. 23, Issue 4
  • DOI: 10.1063/1.3576187

A vortex model for Richtmyer–Meshkov instability accounting for finite Atwood number
journal, March 2005

  • Likhachev, Oleg A.; Jacobs, Jeffrey W.
  • Physics of Fluids, Vol. 17, Issue 3
  • DOI: 10.1063/1.1863276

Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability
journal, August 2007


Numerical Investigation of the Stability of a Shock-Accelerated Interface between Two Fluids
journal, January 1972


Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)
journal, March 1965

  • Abramowitz, Milton; Stegun, Irene A.; Miller, David
  • Journal of Applied Mechanics, Vol. 32, Issue 1
  • DOI: 10.1115/1.3625776

Richtmyer–Meshkov instability growth: experiment, simulation and theory
journal, June 1999


Optimization of particle image velocimeters: II. Multiple pulsed systems
journal, October 1991


Vortex-accelerated secondary baroclinic vorticity deposition and late-intermediate time dynamics of a two-dimensional Richtmyer–Meshkov interface
journal, December 2003

  • Peng, Gaozhu; Zabusky, Norman J.; Zhang, Shuang
  • Physics of Fluids, Vol. 15, Issue 12
  • DOI: 10.1063/1.1621628

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


An aerosol generator of high stability
journal, December 1975

  • Liu, Benjamin Y. H.; Lee, K. W.
  • American Industrial Hygiene Association Journal, Vol. 36, Issue 12
  • DOI: 10.1080/0002889758507357

Optimization of particle image velocimeters. I. Double pulsed systems
journal, November 1990


An experimental investigation of mixing mechanisms in shock-accelerated flow
journal, September 2008


Rayleigh–Taylor and Richtmyer–Meshkov instabilities of flat and curved interfaces
journal, April 2009


Analytical linear theory for the interaction of a planar shock wave with a two- or three-dimensional random isotropic density field
journal, May 2011


Inviscid and viscous vortex models for Richtmyer–Meshkov instability
journal, November 2011


On Flow Duration in Low-Pressure Shock Tubes
journal, January 1960


Hot Flow Length and Testing Time in Real Shock Tube Flow
journal, January 1964


Nonlinear theory of unstable fluid mixing driven by shock wave
journal, April 1997

  • Zhang, Qiang; Sohn, Sung-Ik
  • Physics of Fluids, Vol. 9, Issue 4
  • DOI: 10.1063/1.869202

Experimental study of incompressible Richtmyer–Meshkov instability
journal, February 1996

  • Jacobs, J. W.; Sheeley, J. M.
  • Physics of Fluids, Vol. 8, Issue 2
  • DOI: 10.1063/1.868794

Nonlinear growth of the shock-accelerated instability of a thin fluid layer
journal, July 1995


Coherent density gradients in water compressed by a modulated shock wave
journal, January 1984

  • Benjamin, Robert F.; Trease, Harold E.; Shaner, John W.
  • Physics of Fluids, Vol. 27, Issue 10
  • DOI: 10.1063/1.864541

Über laminare und turbulente Reibung
journal, January 1921

  • Kármán, Th. V.
  • ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 1, Issue 4
  • DOI: 10.1002/zamm.19210010401

Growth of a Richtmyer-Meshkov turbulent layer after reshock
journal, September 2011

  • Thornber, B.; Drikakis, D.; Youngs, D. L.
  • Physics of Fluids, Vol. 23, Issue 9
  • DOI: 10.1063/1.3638616

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution
journal, April 2010

  • Nishihara, K.; Wouchuk, J. G.; Matsuoka, C.
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 368, Issue 1916
  • DOI: 10.1098/rsta.2009.0252

A numerical simulation of boundary layer effects in a shock tube
journal, May 1992

  • Badcock, K. J.
  • International Journal for Numerical Methods in Fluids, Vol. 14, Issue 10
  • DOI: 10.1002/fld.1650141003

The experimental plan for cryogenic layered target implosions on the National Ignition Facility—The inertial confinement approach to fusion
journal, May 2011

  • Edwards, M. J.; Lindl, J. D.; Spears, B. K.
  • Physics of Plasmas, Vol. 18, Issue 5
  • DOI: 10.1063/1.3592173

Particle image velocimetry study of the shock-induced single mode Richtmyer–Meshkov instability
journal, July 2008


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


Dependence of growth patterns and mixing width on initial conditions in Richtmyer–Meshkov unstable fluid layers
journal, October 2008


Simulations and model of the nonlinear Richtmyer–Meshkov instability
journal, January 2010

  • Dimonte, Guy; Ramaprabhu, P.
  • Physics of Fluids, Vol. 22, Issue 1
  • DOI: 10.1063/1.3276269

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

X‐ray measurements of growth rates at a gas interface accelerated by shock waves
journal, September 1996

  • Bonazza, R.; Sturtevant, B.
  • Physics of Fluids, Vol. 8, Issue 9
  • DOI: 10.1063/1.869033

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


Padé approximation to an interfacial fluid mixing problem
journal, September 1997


Instability growth patterns of a shock-accelerated thin fluid layer
journal, February 1993


A Theoretical and Experimental Study of Shock-Tube Flows
journal, February 1955

  • Glass, I. I.; Patterson, G. N.
  • Journal of the Aeronautical Sciences, Vol. 22, Issue 2
  • DOI: 10.2514/8.3282

Nonlinear evolution of the Richtmyer–Meshkov instability
journal, October 2008


The late-time development of the Richtmyer–Meshkov instability
journal, August 2000

  • Prasad, J. K.; Rasheed, A.; Kumar, S.
  • Physics of Fluids, Vol. 12, Issue 8
  • DOI: 10.1063/1.870456

Atwood ratio dependence of Richtmyer–Meshkov flows under reshock conditions using large-eddy simulations
journal, February 2011


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

Study of Nonlinear Evolution of Single-Mode and Two-Bubble Interaction under Richtmyer-Meshkov Instability
journal, February 1998


Computational parametric study of a Richtmyer-Meshkov instability for an inclined interface
journal, August 2011


Experiments on the Richtmyer-Meshkov instability of an air/SF6 interface
journal, March 1995


Taylor instability in shock acceleration of compressible fluids
journal, May 1960

  • Richtmyer, Robert D.
  • Communications on Pure and Applied Mathematics, Vol. 13, Issue 2
  • DOI: 10.1002/cpa.3160130207

Simulations of Richtmyer–Meshkov instabilities in planar shock-tube experiments
journal, March 2011

  • Grinstein, F. F.; Gowardhan, A. A.; Wachtor, A. J.
  • Physics of Fluids, Vol. 23, Issue 3
  • DOI: 10.1063/1.3555635

Experimental Study for ICF-Related Richtmyer-Meshkov Instabilities
journal, November 2007

  • Motl, B. J.; Niederhaus, J. H. J.; Ranjan, D.
  • Fusion Science and Technology, Vol. 52, Issue 4
  • DOI: 10.13182/FST07-A1640

Investigation of the Richtmyer-Meshkov Instability with Stereolithographed Interfaces
journal, June 2008


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

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