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

Abstract

The ninth-order weighted essentially nonoscillatory ͑WENO͒ 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 ͑acetone͒/SF 6 shock tube experiment of Collins and Jacobs ͓J. Fluid Mech. 464, 113 ͑2002͔͒: the growth of the bubble and spike amplitudes from fifth-and ninth-order WENO simulations of this experiment were compared to the predictions of linear and nonlinear amplitude growth models, and were shown to be in very good agreement with the experimental data prior to reshock by Latini, Schilling, and Don ͓Phys. Fluids 19, 024104 ͑2007͔͒. In the present investigation, the density, vorticity, baroclinic vorticity production, and simulated density Schlieren fields are first presented to qualitatively describe the reshock process. The baroclinic circulation deposition on the interface is shown to agree with the predictions of the Samtaney-Zabusky model and with 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 magnitudes of the circulations are equal before as well as after reshock, until the interaction of the reflected rarefaction with the layer induces flow symmetry breaking and different evolutions of the magnitude of the positive and negative circulation. The post-reshock mixing layer growth is shown to be in generally 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 mixing fractions. The modal distribution of energy in the mixing layer is quantified using the spectra of the fluctuating kinetic energy, fluctuating enstrophy, 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 nontrivial spectral content from its inception. The comparison of the spectra to the predictions of classical inertial subrange scalings in two-dimensional turbulence shows that the post-reshock spectra may be consistent with many of these scalings over wave number ranges less than a decade. At reshock, fluctuations in all fields ͑except for the density͒ 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 exhibits an approach toward unity across the layer at the latest time, signify...

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

“…This effect is particularly visible at high A > 0. This suggests that the expansion waves have a segregating role in the evolution of the mixing zone, where two mixing sub-regions would coexist, as Schilling et al (2007) observed in their two-dimensional light-heavy simulations.…”

“…These simulations reproduce some of the observations of Collins & Jacobs (2002) obtained from membrane-free shock tube experiments on the RMI at a light-heavy (air (acetone)-SF 6 , A ≈ 0.60) single-mode interface impacted by a Mach 1.21 shock. Schilling et al (2007) compare the simulated mixing-layer amplitude with existing reshock models evaluated at the same Atwood ratio (Mikaelian 1989;Brouillette & Sturtevant 1994;Charakhchyan 2001) during the post-reshock/preexpansion phase. Lacking complications present in experimental studies, both Schilling et al (2007) and Hill et al (2006) were able to examine the flow evolution over a wider time period following reshock than is customarily reported.…”

“…Schilling et al (2007) compare the simulated mixing-layer amplitude with existing reshock models evaluated at the same Atwood ratio (Mikaelian 1989;Brouillette & Sturtevant 1994;Charakhchyan 2001) during the post-reshock/preexpansion phase. Lacking complications present in experimental studies, both Schilling et al (2007) and Hill et al (2006) were able to examine the flow evolution over a wider time period following reshock than is customarily reported. In particular, we summarize here conclusions by Schilling et al (2007) on the effect of the expansion wave on the growth of the two-dimensional mixing layer: the expansion wave has a modest effect on the mixing kinetic energy, enstrophy and density fluctuations, leads to an increase of the spanwise velocity fluctuations compared with the streamwise counterpart, contributes to the late-time isotropization of the velocity field, and is responsible for the symmetry breaking and stretching of the mixing layer.…”

Richtmyer–Meshkov instability on a low Atwood number interface after reshock

“…Although this model describes three-dimensional multimode interfaces, it has been shown previously to provide a good estimate of amplitude growth of single mode interfaces after reshock [13].…”

On the Kolmogorov inertial subrange developing from Richtmyer-Meshkov instability

“…Accordingly, the effect of viscosity was considerably underestimated in many Richtmyer-Meshkov investigations that solved only the Euler equations 13,14,17,18 or solved the Euler equations and additionally neglected compressibility effects [30][31][32] assuming a constant ratio of specific heats for all fluids involved. Fig.…”