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Title: Oscillations of a standing shock wave generated by the Richtmyer-Meshkov instability

Abstract

In a typical Richtmyer-Meshkov experiment a fast moving flat shock strikes a stationary perturbed interface between fluids A and B creating a transmitted and a reflected shock, both of which are perturbed. We propose shock tube experiments in which the reflected shock is stationary in the laboratory. Such a standing perturbed shock undergoes well-known damped oscillations. We present the conditions required for producing such a standing shock wave, which greatly facilitates the measurement of the oscillations and their rate of damping. We define a critical density ratio Rcritical, in terms of the adiabatic indices of the two fluids, and a critical Mach number Mcriticals of the incident shock wave, which produces a standing reflected wave. If the initial density ratio R of the two fluids is less than Rcritical then a standing shock wave is possible at Ms=Mcriticals. Otherwise a standing shock is not possible and the reflected wave always moves in the direction opposite the incident shock. Examples are given for present-day operating shock tubes with sinusoidal or inclined interfaces. We consider the effect of viscosity, which affects the damping rate of the oscillations. Furthermore, we point out that nonlinear bubble and spike amplitudes depend relatively weakly on themore » viscosity of the fluids and that the interface area is a better diagnostic.« less

Authors:
 [1]
  1. 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
OSTI Identifier:
1297656
Alternate Identifier(s):
OSTI ID: 1262445
Report Number(s):
LLNL-JRNL-681121
Journal ID: ISSN 2469-990X
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Fluids
Additional Journal Information:
Journal Volume: 1; Journal Issue: 3; Journal ID: ISSN 2469-990X
Publisher:
APS
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Mikaelian, Karnig O. Oscillations of a standing shock wave generated by the Richtmyer-Meshkov instability. United States: N. p., 2016. Web. doi:10.1103/PhysRevFluids.1.033601.
Mikaelian, Karnig O. Oscillations of a standing shock wave generated by the Richtmyer-Meshkov instability. United States. doi:10.1103/PhysRevFluids.1.033601.
Mikaelian, Karnig O. Wed . "Oscillations of a standing shock wave generated by the Richtmyer-Meshkov instability". United States. doi:10.1103/PhysRevFluids.1.033601. https://www.osti.gov/servlets/purl/1297656.
@article{osti_1297656,
title = {Oscillations of a standing shock wave generated by the Richtmyer-Meshkov instability},
author = {Mikaelian, Karnig O.},
abstractNote = {In a typical Richtmyer-Meshkov experiment a fast moving flat shock strikes a stationary perturbed interface between fluids A and B creating a transmitted and a reflected shock, both of which are perturbed. We propose shock tube experiments in which the reflected shock is stationary in the laboratory. Such a standing perturbed shock undergoes well-known damped oscillations. We present the conditions required for producing such a standing shock wave, which greatly facilitates the measurement of the oscillations and their rate of damping. We define a critical density ratio Rcritical, in terms of the adiabatic indices of the two fluids, and a critical Mach number Mcriticals of the incident shock wave, which produces a standing reflected wave. If the initial density ratio R of the two fluids is less than Rcritical then a standing shock wave is possible at Ms=Mcriticals. Otherwise a standing shock is not possible and the reflected wave always moves in the direction opposite the incident shock. Examples are given for present-day operating shock tubes with sinusoidal or inclined interfaces. We consider the effect of viscosity, which affects the damping rate of the oscillations. Furthermore, we point out that nonlinear bubble and spike amplitudes depend relatively weakly on the viscosity of the fluids and that the interface area is a better diagnostic.},
doi = {10.1103/PhysRevFluids.1.033601},
journal = {Physical Review Fluids},
number = 3,
volume = 1,
place = {United States},
year = {2016},
month = {7}
}

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Works referenced in this record:

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