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

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 SF 6, 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 ofmore » 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.« 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:
Journal Article: 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. https://doi.org/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. https://doi.org/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},
url = {https://www.osti.gov/biblio/1559909}, journal = {Journal of Fluid Mechanics},
issn = {0022-1120},
number = na,
volume = 712,
place = {United States},
year = {2012},
month = {10}
}

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

Citation Metrics:
Cited by: 19 works
Citation information provided by
Web of Science

Save / Share:

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


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


Hyperviscosity for shock-turbulence interactions
journal, March 2005


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


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


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


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


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


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


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


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


An aerosol generator of high stability
journal, December 1975


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


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


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


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


Über laminare und turbulente Reibung
journal, January 1921


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


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
  • https://doi.org/10.1098/rsta.2009.0252

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


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


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


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


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


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


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


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


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


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


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


    Works referencing / citing this record:

    The Richtmyer–Meshkov instability of a ‘V’ shaped air/ interface
    journal, August 2016


    Evaluation of turbulent mixing transition in a shock-driven variable-density flow
    journal, October 2017


    The transition to turbulence in shock-driven mixing: effects of Mach number and initial conditions
    journal, May 2019


    Richtmyer–Meshkov instability on a quasi-single-mode interface
    journal, June 2019


    Direct simulation Monte Carlo investigation of the Richtmyer-Meshkov instability
    journal, August 2015