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Title: Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability

Abstract

The ninth-order weighted essentially non-oscillatory (WENO) shock-capturing method is used to investigate the physics of reshock and mixing in two-dimensional single-mode Richtmyer-Meshkov instability to late times. The initial conditions and computational domain were adapted from the Mach 1.21 air(acetone)/SF{sub 6} shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]: the growth of the bubble and spike perturbation amplitudes from fifth- and ninth-order WENO simulations of this experiment were compared to the predictions of amplitude growth models, and were shown to be in very good agreement with the experimental data prior to reshock [Latini, Schilling and Don, Phys. Fluids (2007), in press]. In the present investigation, the density, vorticity, baroclinic vorticity production, and simulated density Schlieren fields are first presented to qualitatively describe reshock. The baroclinic circulation deposition on the interface is shown to agree with the predictions of the Samtaney and Zabusky [J. Fluid Mech. 269, 45 (1994)] model and linear instability theory. The time-evolution of the positive and negative circulation on the interface is considered before and after reshock: it is shown that the circulations are equal before, as well as after reshock, until the interaction of the reflected rarefaction with the layer leads tomore » flow symmetry breaking and different evolutions of the positive and negative circulation. The post-reshock mixing layer growth is shown to be in very good agreement with three models predicting linear growth for a short time following reshock. Next, a comprehensive investigation of local and global mixing properties as a function of time is performed. The distribution and amount of mixed fluid along the shock propagation direction is characterized using averaged mole fraction profiles, a fast kinetic reaction model, and molecular mixing fractions. The modal distribution of energy in the mixing layer is quantified using the spectra of the fluctuating kinetic energy, fluctuating entropy, pressure variance, density variance, and baroclinic vorticity production variance. It is shown that a broad range of scales already exists prior to reshock, indicating that the single-mode Richtmyer-Meshkov instability develops non-trivial spectral content from its inception. At reshock, fluctuations in all fields (except for the density) are amplified across all scales. Reshock strongly amplifies the circulation, profiles and mixing fractions, as well as the energy spectra and statistics, leading to enhanced mixing, followed by a decay. The mole and mixing fraction profiles become nearly self-similar at late times following reshock; the mixing fraction approaches unity across the layer at the latest time, signifying nearly complete mixing. The comparison of the spectra to the predictions of classical inertial subrange scalings in two-dimensional turbulence shows that the post-reshock spectra are consistent with most of these scalings over short wave number ranges. To directly quantify the amplification of fluctuations by reshock, the previously considered quantities are compared immediately after and before reshock. Finally, to investigate the decay of fluctuations in the absence of additional waves interacting with the mixing layer following reshock, the boundary condition at the end of the computational domain is changed from reflecting to outflow to allow the reflected rarefaction wave to exit the domain. It is shown that the reflected rarefaction has an important role in breaking symmetry and achieving late-time statistical isotropy of the velocity field.« less

Authors:
; ;
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
936958
Report Number(s):
UCRL-JRNL-226932
TRN: US0806146
DOE Contract Number:  
W-7405-ENG-48
Resource Type:
Journal Article
Journal Name:
Physical Review E, vol. 76, N/A, May 1, 2007, pp. 026319-1-026319-28
Additional Journal Information:
Journal Volume: 76
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; AMPLIFICATION; AMPLITUDES; BOUNDARY CONDITIONS; BUBBLES; DECAY; DEPOSITION; ENERGY SPECTRA; ENTROPY; FLUCTUATIONS; INSTABILITY; ISOTROPY; KINETIC ENERGY; KINETICS; PHYSICS; SHOCK TUBES; SPECTRA; SYMMETRY; SYMMETRY BREAKING; TURBULENCE

Citation Formats

Schilling, O, Latini, M, and Don, W. Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability. United States: N. p., 2006. Web.
Schilling, O, Latini, M, & Don, W. Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability. United States.
Schilling, O, Latini, M, and Don, W. Wed . "Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability". United States. https://www.osti.gov/servlets/purl/936958.
@article{osti_936958,
title = {Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability},
author = {Schilling, O and Latini, M and Don, W},
abstractNote = {The ninth-order weighted essentially non-oscillatory (WENO) shock-capturing method is used to investigate the physics of reshock and mixing in two-dimensional single-mode Richtmyer-Meshkov instability to late times. The initial conditions and computational domain were adapted from the Mach 1.21 air(acetone)/SF{sub 6} shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]: the growth of the bubble and spike perturbation amplitudes from fifth- and ninth-order WENO simulations of this experiment were compared to the predictions of amplitude growth models, and were shown to be in very good agreement with the experimental data prior to reshock [Latini, Schilling and Don, Phys. Fluids (2007), in press]. In the present investigation, the density, vorticity, baroclinic vorticity production, and simulated density Schlieren fields are first presented to qualitatively describe reshock. The baroclinic circulation deposition on the interface is shown to agree with the predictions of the Samtaney and Zabusky [J. Fluid Mech. 269, 45 (1994)] model and linear instability theory. The time-evolution of the positive and negative circulation on the interface is considered before and after reshock: it is shown that the circulations are equal before, as well as after reshock, until the interaction of the reflected rarefaction with the layer leads to flow symmetry breaking and different evolutions of the positive and negative circulation. The post-reshock mixing layer growth is shown to be in very good agreement with three models predicting linear growth for a short time following reshock. Next, a comprehensive investigation of local and global mixing properties as a function of time is performed. The distribution and amount of mixed fluid along the shock propagation direction is characterized using averaged mole fraction profiles, a fast kinetic reaction model, and molecular mixing fractions. The modal distribution of energy in the mixing layer is quantified using the spectra of the fluctuating kinetic energy, fluctuating entropy, pressure variance, density variance, and baroclinic vorticity production variance. It is shown that a broad range of scales already exists prior to reshock, indicating that the single-mode Richtmyer-Meshkov instability develops non-trivial spectral content from its inception. At reshock, fluctuations in all fields (except for the density) are amplified across all scales. Reshock strongly amplifies the circulation, profiles and mixing fractions, as well as the energy spectra and statistics, leading to enhanced mixing, followed by a decay. The mole and mixing fraction profiles become nearly self-similar at late times following reshock; the mixing fraction approaches unity across the layer at the latest time, signifying nearly complete mixing. The comparison of the spectra to the predictions of classical inertial subrange scalings in two-dimensional turbulence shows that the post-reshock spectra are consistent with most of these scalings over short wave number ranges. To directly quantify the amplification of fluctuations by reshock, the previously considered quantities are compared immediately after and before reshock. Finally, to investigate the decay of fluctuations in the absence of additional waves interacting with the mixing layer following reshock, the boundary condition at the end of the computational domain is changed from reflecting to outflow to allow the reflected rarefaction wave to exit the domain. It is shown that the reflected rarefaction has an important role in breaking symmetry and achieving late-time statistical isotropy of the velocity field.},
doi = {},
journal = {Physical Review E, vol. 76, N/A, May 1, 2007, pp. 026319-1-026319-28},
number = ,
volume = 76,
place = {United States},
year = {2006},
month = {12}
}