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A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state

Ward, G. M. and Pullin, D. I. (2011) A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state. Physics of Fluids, 23 (7). Art. No. 076101. ISSN 1070-6631. https://resolver.caltech.edu/CaltechAUTHORS:20110906-081413985

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Abstract

We present a numerical comparison study of planar Richtmyer-Meshkov instability with the intention of exposing the role of the equation of state. Results for Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state derived from a linear shock-particle speed Hugoniot relationship (Jeanloz, J. Geophys. Res. 94, 5873, 1989; McQueen et al., High Velocity Impact Phenomena (1970), pp. 294–417; Menikoff and Plohr, Rev. Mod. Phys. 61(1), 75 1989) are compared to those from perfect gases under nondimensionally matched initial conditions at room temperature and pressure. The study was performed using Caltech’s Adaptive Mesh Refinement, Object-oriented C++ (AMROC) (Deiterding, Adaptive Mesh Refinement: Theory and Applications (2005), Vol. 41, pp. 361–372; Deiterding, “Parallel adaptive simulation of multi-dimensional detonation structures,” Ph.D. thesis (Brandenburgische Technische Universität Cottbus, September 2003)) framework with a low-dissipation, hybrid, center-difference, limiter patch solver (Ward and Pullin, J. Comput. Phys. 229, 2999 (2010)). Results for single and triple mode planar Richtmyer-Meshkov instability when a reflected shock wave occurs are first examined for mid-ocean ridge basalt (MORB) and molybdenum modeled by Mie-Grüneisen equations of state. The single mode case is examined for incident shock Mach numbers of 1.5 and 2.5. The planar triple mode case is studied using a single incident Mach number of 2.5 with initial corrugation wavenumbers related by k_1 = k_2+k_3. Comparison is then drawn to Richtmyer-Meshkov instability in perfect gases with matched nondimensional pressure jump across the incident shock, post-shock Atwood ratio, post-shock amplitude-to-wavelength ratio, and time nondimensionalized by Richtmyer’s linear growth time constant prediction. Differences in start-up time and growth rate oscillations are observed across equations of state. Growth rate oscillation frequency is seen to correlate directly to the oscillation frequency for the transmitted and reflected shocks. For the single mode cases, further comparison is given for vorticity distribution and corrugation centerline shortly after shock interaction. Additionally, we examine single mode Richtmyer-Meshkov instability when a reflected expansion wave is present for incident Mach numbers of 1.5 and 2.5. Comparison to perfect gas solutions in such cases yields a higher degree of similarity in start-up time and growth rate oscillations. The formation of incipient weak waves in the heavy fluid driven by waves emanating from the perturbed transmitted shock is observed when an expansion wave is reflected.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1063/1.3607444DOIUNSPECIFIED
http://pof.aip.org/resource/1/phfle6/v23/i7/p076101_s1PublisherUNSPECIFIED
http://link.aip.org/link/doi/10.1063/1.3607444PublisherUNSPECIFIED
Additional Information:© 2011 American Institute of Physics. Received 28 June 2010; accepted 23 May 2011; published online 15 July 2011.
Group:GALCIT
Subject Keywords:equations of state, flow instability, fluid oscillations, Mach number, mesh generation, shock wave effects, supersonic flow, vortices
Issue or Number:7
Classification Code:PACS: 47.20.-k; 47.32.C-; 47.40.Ki; 47.40.Nm; 02.70.Dh; 47.11.Fg
Record Number:CaltechAUTHORS:20110906-081413985
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110906-081413985
Official Citation:A study of planar Richtmyer-Meshkov instability in fluids with Mie-Grüneisen equations of state G. M. Ward and D. I. Pullin Phys. Fluids 23, 076101 (2011); doi:10.1063/1.3607444 (17 pages)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:25223
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:06 Sep 2011 15:43
Last Modified:03 Oct 2019 03:04

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