Bulletin of the American Physical Society
64th Annual Meeting of the APS Division of Fluid Dynamics
Volume 56, Number 18
Sunday–Tuesday, November 20–22, 2011; Baltimore, Maryland
Session E19: Richtmeyer-Meshkov Instability II |
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Chair: Sam Paolucci, University of Notre Dame Room: 322 |
Sunday, November 20, 2011 4:40PM - 4:53PM |
E19.00001: Simulation of Richtmyer-Meshkov Instability using the Wavelet Adaptive Multiscale Representation (WAMR) Samuel Paolucci, Zachary Zikoski The parallel WAMR method is used to simulate the Richtmyer-Meshkov instability of a shocked and re-shocked thin varicose heavy gas layer. The problem is based on the experiments of Balakumar \textit{et al.},\footnote{Balakumar \textit{et al.}~Phys.~Fluids \textbf{20}, 124103 (2008).} and modelled by the compressible Navier-Stokes equations for a multi-component gas mixture. The WAMR method provides dynamic, spatial grid adaptivity to efficiently capture features over a wide range of physical scales. Results of the simulation are compared with experimental measurements. Additionally, sensitivity of the long-time behavior of the gas layer to various secondary perturbations is investigated. [Preview Abstract] |
Sunday, November 20, 2011 4:53PM - 5:06PM |
E19.00002: The Bipolar Behavior of the Richtmyer--Meshkov Instability Fernando Grinstein, Akshay Gowardhan, Raymond Ristorcelli A numerical study of the evolution of the multimode planar Richtmyer-Meshkov instability (RMI) in a light-heavy (air-SF6, Atwood number A=0.67) configuration involving a Mach number Ma=1.5 shock is carried out. Our results demonstrate that the initial material interface morphology controls the evolution characteristics of RMI (for fixed A, Ma), and provide a significant basis to develop metrics for transition to turbulence. Depending on initial rms slope of the interface, RMI evolves into linear or nonlinear regimes, with distinctly different flow features and growth rates, turbulence statistics, and material mixing rates. We have called this the bipolar behavior of RMI. [Preview Abstract] |
Sunday, November 20, 2011 5:06PM - 5:19PM |
E19.00003: Theory and simulation of moderately and strongly nonlinear dynamics of the classical Richtmyer-Meshkov instability M. Herrmann, A.L. Velikovich, S.I. Abarzhi There are many features of early- and late-time nonlinear Richtmyer-Meshkov instability growth that are not captured by simplified or ad hoc phenomenological models, such as Layzer's or drag-buoyancy. These include but are not limited to: late-time evolution of the bubble curvature, early-time acceleration of the spike, and effect of finite values of ripple amplitude and Atwood number on early-time bubble and spike growth. We compare the results of numerical simulations with the predictions of nonlinear theory, demonstrating good agreement. The influences of viscosity, the initial spectra, and other effects on the nonlinear dynamics are discussed. [Preview Abstract] |
Sunday, November 20, 2011 5:19PM - 5:32PM |
E19.00004: Numerical Investigation of Turbulence in a Reshocked Richtmyer Meshkov Unstable Curtain of Dense Gas Santhosh Shankar, Sanjiva Lele Moderate resolution numerical simulation of the impulsive acceleration of a dense gas curtain in air by a Mach 1.21 planar shock (modeling the experiments by Balakumar et al. PoF 2008) is carried out by solving the 3-D compressible multi-species Navier-Stokes equation coupled with a localized artificial diffusivity method to capture discontinuities in the flow-field. The simulations account for the presence of three species in the flow-field: air, SF$_{6}$~and acetone (used as a tracer species in the experiments). Simulations at different concentration levels of the species are conducted and the temporal evolution of the numerically computed curtain width is compared with the experimental data. The reshock process is studied by re-impacting the evolving curtain with a reflected shock wave. Turbulence statistics computed in the flow-field following reshock are reported and compared with experiment where possible. The reshock time is varied in the simulations to study the turbulence development. Inertial range scaling, vorticity anisotropy and Reynolds stress development are studied in the reshocked flow. [Preview Abstract] |
Sunday, November 20, 2011 5:32PM - 5:45PM |
E19.00005: A Computation Study of the RIchtmyer-Meshkov Instability for an Inclined Interface Jacob McFarland, Jeffery Greenough, Devesh Ranjan A computational study of the Richtmyer-Meshkov instability is presented for an inclined interface perturbation in support of experiments to be performed in the Texas A{\&}M shock tube facility. Simulations were performed using the ARES code developed at Lawrence Livermore National Laboratory. A parametric study was performed for two high Atwood number gas pairs, air-SF6 and helium-SF6, where interface inclination angle and incident shock wave Mach number were varied. From this parametric study selected cases were run to late times where reshock occurs. The total circulation for these cases and the circulation production over time is presented. Mix mass and mixing width growth rate are found for before and after reshock. [Preview Abstract] |
Sunday, November 20, 2011 5:45PM - 5:58PM |
E19.00006: Simulations of Single-mode Richtmyer-Meshkov and Rayleigh-Taylor Instabilities in Spherical Geometries Anthony Nelson, Praveen Ramaprabhu We describe recent numerical simulations of the single-mode Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities in a spherical geometry. The simulations were performed using the astrophysical FLASH code in two- and three-dimensions. Our results are compared to previously published simulation results\footnote{Sakagami, H. and Nishihara, K., Phys. Rev. Lett. 65, 432, 1990a.} and linear\footnote{K.O. Mikaelian, Phys. Rev. A., 42 (6), 3400, 1990.} and nonlinear\footnote{D. S. Clark, M. Tabak, Phys. Fluids 18, 064106, 2006.} theories. The RM problem was setup with an air-SF6 interface, subject to a Mach 1.2 shock, and a convergence ratio of 10. We studied the variation of initial amplitude, shock strength, and convergence ratio. We expect the single-mode results to inform multimode growth in applications through bubble merger and competition mechanisms. [Preview Abstract] |
Sunday, November 20, 2011 5:58PM - 6:11PM |
E19.00007: Turbulent mixing in spherically converging Richtmyer--Meshkov flows Manuel Lombardini, D.I. Pullin, D.I. Meiron, R.A. Gore We discuss large-eddy simulations of the mixing induced at a perturbed, spherical density interface initially impacted by a spherically converging shock wave of Mach number $\simeq1.2$. Two configurations are investigated: i) air inside and SF$_6$ (five times denser than air) outside, i.e. heavy--light configuration; ii) SF$_6$ inside and air outside, or light--heavy configuration. A superposition of spherical harmonics with given power spectrum is used to prescribe an initially small perturbation at the interface while avoiding the pole singularity. Adaptive mesh refinement is employed in the regions of interest around the density interface and shock waves. Interest is focused on the strong turbulent mixing generated by the re-shock. In particular, from data interpolated over spherical surfaces, the power spectra of velocity and density are computed as well as extensive surface-averaged statistics involved in the budget of turbulent kinetic energy and enstrophy density. [Preview Abstract] |
Sunday, November 20, 2011 6:11PM - 6:24PM |
E19.00008: Reynolds-Averaged Navier--Stokes Model Predictions of Self-Similar Richtmyer--Meshkov Instability-Induced Mixing Oleg Schilling A high-order, multicomponent, weighted essentially nonoscillatory implementation of a two-equation $K$-$\epsilon$ Reynolds-averaged Navier--Stokes model is used to simulate reshocked Richtmyer--Meshkov turbulent mixing at various Atwood numbers. The predicted mixing layer evolution is compared with analytical, late-time self-similar solutions of the transport equations. The terms in the transport equation budgets are compared in detail to self-similar profiles across the mixing layer. Additionally, the sensitivity of the turbulence model solutions to variations in the initial conditions and in the model coefficients is explored. [Preview Abstract] |
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