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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 20:01:45 +0000High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability: Comparison to experimental data and to amplitude growth model predictions
https://resolver.caltech.edu/CaltechAUTHORS:LATpof07
Authors: Latini, Marco; Schilling, Oleg; Don, Wai Sun
Year: 2007
DOI: 10.1063/1.2472508
The reshocked single-mode Richtmyer-Meshkov instability is simulated in two spatial dimensions using the fifth- and ninth-order weighted essentially nonoscillatory shock-capturing method with uniform spatial resolution of 256 points per initial perturbation wavelength. The initial conditions and computational domain are modeled after the single-mode, Mach 1.21 air(acetone)/SF6 shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]. The simulation densities are shown to be in very good agreement with the corrected experimental planar laser-induced fluorescence images at selected times before reshock of the evolving interface. Analytical, semianalytical, and phenomenological linear and nonlinear, impulsive, perturbation, and potential flow models for single-mode Richtmyer-Meshkov unstable perturbation growth are summarized. The simulation amplitudes are shown to be in very good agreement with the experimental data and with the predictions of linear amplitude growth models for small times, and with those of nonlinear amplitude growth models at later times up to the time at which the driver-based expansion in the experiment (but not present in the simulations or models) expands the layer before reshock. The qualitative and quantitative differences between the fifth- and ninth-order simulation results are discussed. Using a local and global quantitative metric, the prediction of the Zhang and Sohn [Phys. Fluids 9, 1106 (1997)] nonlinear Padé model is shown to be in best overall agreement with the simulation amplitudes before reshock. The sensitivity of the amplitude growth model predictions to the initial growth rate from linear instability theory, the post-shock Atwood number and amplitude, and the velocity jump due to the passage of the shock through the interface is also investigated numerically.https://authors.library.caltech.edu/records/7jzm2-7re45Physics of reshock and mixing in single-mode Richtmyer-Meshkov instability
https://resolver.caltech.edu/CaltechAUTHORS:SCHIpre07
Authors: Schilling, Oleg; Latini, Marco; Don, Wai Sun
Year: 2007
DOI: 10.1103/PhysRevE.76.026319
The ninth-order weighted essentially nonoscillatory (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)/SF6 shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]: 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 (2007)]. 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 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 exhibits an approach toward unity across the layer at the latest time, signifying nearly complete mixing of the gases. 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 demonstrated that the reflected rarefaction has an important role in breaking symmetry and achieving late-time statistical isotropy of the velocity field.https://authors.library.caltech.edu/records/46mpa-gf718High-order WENO simulations of three-dimensional reshocked Richtmyer-Meshkov instability to late times: Dynamics, dependence on initial conditions, and comparisons to experimental data
https://resolver.caltech.edu/CaltechAUTHORS:20100527-141603536
Authors: Schilling, Oleg; Latini, Marco
Year: 2010
DOI: 10.1016/S0252-9602(10)60064-1
The dynamics of the reshocked multi-mode Richtmyer–Meshkov instability is
investigated using 513 × 257^2 three-dimensional ninth-order weighted essentially nonoscillatory
shock-capturing simulations. A two-mode initial perturbation with superposed random
noise is used to model the Mach 1.5 air/SF_6 Vetter–Sturtevant shock tube experiment.
The mass fraction and enstrophy isosurfaces, and density cross-sections are utilized to show
the detailed flow structure before, during, and after reshock. It is shown that the mixing
layer growth agrees well with the experimentally measured growth rate before and after
reshock. The post-reshock growth rate is also in good agreement with the prediction of the
Mikaelian model. A parametric study of the sensitivity of the layer growth to the choice
of amplitudes of the short and long wavelength initial interfacial perturbation is also presented.
Finally, the amplification effects of reshock are quantified using the evolution of
the turbulent kinetic energy and turbulent enstrophy spectra, as well as the evolution of
the baroclinic enstrophy production, buoyancy production, and shear production terms in
the enstrophy and turbulent kinetic transport equations.https://authors.library.caltech.edu/records/k23md-rpd86A comparison of two- and three-dimensional single-mode reshocked Richtmyer–Meshkov instability growth
https://resolver.caltech.edu/CaltechAUTHORS:20190919-113941696
Authors: Latini, Marco; Schilling, Oleg
Year: 2020
DOI: 10.1016/j.physd.2019.132201
The growth dynamics of two- and three-dimensional single-mode reshocked Richtmyer–Meshkov instability are compared systematically using data from high-resolution implicit large-eddy simulations of a model of the Mach 1.3 air(acetone) and sulfur hexafluoride (Jacobs and Krivets, 2005) shock tube experiment. The vorticity deposition by the incident shock and the dynamics of interface evolution are examined quantitatively and qualitatively. The perturbation amplitudes from the two- and three-dimensional simulations are compared to the experimental data and to the predictions of several nonlinear instability growth models. It is shown that the perturbation amplitudes from the two- and three-dimensional simulations with matching initial Richtmyer velocity are in excellent agreement with the experimental data. In addition, the dynamics of reshock (not considered in the experiment) are described in detail, and the post-reshock mixing layer amplitude growth rate is compared to the predictions of several reshock models. It is shown that using two-dimensional simulations to understand three-dimensional dynamics is valid only at early-to-intermediate times before reshock; at intermediate-to-late times after reshock the three-dimensional growth is generally larger than the corresponding two-dimensional growth. The reshock dynamics are also different between two and three dimensions. The quantitative results, together with visualizations of the flow field, were also used to contrast the difference between two- and three-dimensional vorticity and enstrophy dynamics.https://authors.library.caltech.edu/records/0p4mt-zgr21