Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session M13: Richtmyer-Meshkov Instability I |
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Chair: Snezha Abarzhi, University of Chicago Room: 27A |
Tuesday, November 20, 2012 8:00AM - 8:13AM |
M13.00001: Richtmyer-Meshkov growth of a granular layer Stuart Dalziel This paper explores the mechanism responsible for the growth of Richtmyer-Meshkov instability in the novel context of the impulsive acceleration of a granular layer. With the classical instability, when a density interface is impulsively accelerating towards the medium with a lower density, the phase of interfacial perturbations is reversed and the deposited kinetic energy leads to growth of the perturbations. The higher density medium forms ``spikes'' as it penetrates into the lower density medium, while the lower density medium forms ``bubbles'' as it penetrates into the denser medium. Simple laboratory experiments are used to demonstrate that this Richtmyer-Meshkov growth mechanism can act on the surface of a granular layer, forming structures reminiscent of the classical case. This happens despite the fundamental differences in the way stresses are communicated. [Preview Abstract] |
Tuesday, November 20, 2012 8:13AM - 8:26AM |
M13.00002: Richtmyer-Meshkov instability induced by strong shocks Milos Stanic, Robert Stellingverf, Jason Cassibry, Snezhana Abarzhi We systematically study the Richtmyer-Meshkov instability (RMI) induced by strong shocks for fluids with contrasting densities and with small and large amplitude initial perturbations imposed at the fluid interface. The Smoothed particle hydrodynamics code (SPHC) is employed to ensure accurate shock capturing, interface tracking, and accounting for the dissipation processes. Simulations results achieve good agreement with existing experiments and with the theoretical analyses including zero-order theory describing the post-shock background motion of the fluids, linear theory providing RMI growth-rate in a broad range of the Mach and Atwood numbers, weakly nonlinear theory accounting for the effect of the initial perturbation amplitude on RMI growth-rate, and highly nonlinear theory describing evolution of RM bubble front. We find that for strong-shock-driven RMI the background motion is supersonic, and the interfacial mixing can be sub-sonic or supersonic. Significant part of the shock energy goes into compression and background motion of the fluids, and only a small portion remains for interfacial mixing. The initial perturbation amplitude appears a key factor of RMI evolution. It strongly influences the dynamics of the interface, in the fluid bulk, and the transmitted shock. [Preview Abstract] |
Tuesday, November 20, 2012 8:26AM - 8:39AM |
M13.00003: Scale coupling in Richtmyer-Meshkov flows induced by strong shocks R.F. Stellingverf, M. Stanic, J.T. Cassibry, S.I. Abarzhi We report an integrated study of the Richtmyer-Meshkov (RM) flows under high energy density relevant conditions by means of smoothed particle hydrodynamics simulations and theoretical analysis. We show that significant amount of the shock energy goes into the compression and background of the fluids (that is supersonic), and only a small portion remains for interfacial mixing (that can be sub-sonic or supersonic). At late times, the RM bubbles flatten and decelerate, specific drag force decays quickly, the interfacial motion tends to be inertial, and the flow remains laminar rather than turbulent. At early times, shear-driven Kelvin-Helmholtz structures appear at the interface. At late times the velocity field is non-uniform and is characterized by intense dynamics in a vicinity of the front, effectively no motion in the bulk (rather than the background motion), and the checkerboard velocity patterns, which are induced by reverse cumulative jets. These jets appear in the fluid bulk and are accompanied by hot spots - local heterogeneous microstructures with temperature substantially higher than that in the ambient. Our results show that RMI dynamics is a multi-scale and heterogeneous process with a complicated character of scale coupling at the interface and in the bulk. [Preview Abstract] |
Tuesday, November 20, 2012 8:39AM - 8:52AM |
M13.00004: Three-dimensional modeling of Richtmyer-Meshkov instability Michael Anderson, Peter Vorobieff, C. Randall Truman, Sanjay Kumar We explore the use of CFD to accurately model the three-dimensional structure of Richtmyer-Meshkov instability (RMI), matching numerical data with new experimental results. Earlier experimental work focused on visualizing planar slices of the initial conditions to observe the formation and growth of the RMI. It was often assumed in the past that the initial conditions are relatively constant in the third dimension and any variation that existed had little effect on the resulting instabilities. Recent experiments have provided quantitative data revealing the three-dimensional structure of the flow. Two computational tools were used in this work, the commerical CFD code FLUENT and the Second-order Hydrodynamic Automatic Mesh Refinement Code (SHAMRC). To reproduce the experimental results, it was necessary to faithfully reproduce the initial conditions on a gaseous density interface prior to shock arrival. This was achieved with FLUENT. Then SHAMRC was used to model the shock interaction and subsequent formation of the RMI. Results are presented for 2D and 3D planar shock/heavy gas column interaction and explore the formation of structures observed experimentally. [Preview Abstract] |
Tuesday, November 20, 2012 8:52AM - 9:05AM |
M13.00005: Integrated study of non-uniform structures in Richtmyer-Meshkov unstable flows by means of theoretical analysis, Lagrangian and Eulerian numerical simulations, and experiments J.T. Cassibry, M. Stanic, R.F. Stellingverf, J. McFarland, D. Ranjan, R. Bonazza, S.I. Abarzhi We conducted the integrated study of the Richtmyer-Meshkov flow by means of theoretical analysis, Lagrangian and Eulerian numerical simulations, and experiments achieving good qualitative and quantitative agreement. In our study, Mach numbers are moderate, Atwood numbers are high, initial perturbation amplitudes are finite, and the initial perturbation is coherent. We showed that in this regime, the velocity at which the interface would move if it would be ideally planar is a relevant parameter, as it tracks the amount of momentum and energy deposited by shock at the interface. The amplitude of the initial perturbation is one of key factors of RMI evolution. In case of large amplitudes, the vector and scalar fields in the fluid bulk are non-uniform. The flow non-uniformities include cumulative reverse jets, checkerboards velocity pattern, shock-focusing effects, and local hot spots with temperature substantially higher than that in the ambient. The dynamics of the nonlinear flow is shown to have an essentially multi-scale character. [Preview Abstract] |
Tuesday, November 20, 2012 9:05AM - 9:18AM |
M13.00006: Numerical simulations of cylindrical Richtmyer-Meshkov instability at a solid-gas interface A. L\'{o}pez Ortega, M. Lombardini, P.T. Barton, D.I. Pullin, D.I. Meiron Richtmyer--Meshkov flows occur in a wide range of physical phenomena and are of particular interest in shock compression of condensed matter. In this presentation, we discuss numerical simulations of a perturbed, solid--gas interface following the passage of a shock wave in cylindrical geometries. Results are obtained using a shock-capturing scheme applied to the equations of motion for contiguous gaseous and elastic--plastic solid media in a level set-based, multi--material and fully compressible Eulerian framework. Multiple Atwood ratios, initial amplitudes and shock strengths are investigated. Results show that fluid--solid interfaces become unstable when a plasticity model is added to the description of the solid. Under certain initial conditions, ejecta can be formed. This contrasts to previous results (L\'{o}pez Ortega et. al, {\it PRE}, 2010) for purely elastic solids, in which the interface exhibited stable behavior. [Preview Abstract] |
Tuesday, November 20, 2012 9:18AM - 9:31AM |
M13.00007: Shock-accelerated gas cylinder: a Mach number study Tennille Bernard, Patrick Wayne, Clint Corbin, C. Randall Truman, Peter Vorobieff, Sanjay Kumar, Michael Anderson We present an experimental study of the evolution of Richtmyer-Meshkov instability and secondary instabilities at a nominally cylindrical density interface under the influence of a planar shock wave traveling at Mach numbers from 1.2 to 2.4. Shock acceleration of the heavy gas (SF$_6$) cylinder creates not only the expected primary instability resulting in the formation of a pair of counter-rotating vortex columns, but also produces a prominent spike-like feature. Secondary instabilities (\emph{e.g.,} shear-driven) then develop in the spike. The spike formation most likely occurs due to shock focusing as the shock passes through the initial conditions. It is noteworthy that secondary instabilities in the spike were first observed numerically, and then their existence was confirmed experimentally using laser-induced fluorescence. [Preview Abstract] |
Tuesday, November 20, 2012 9:31AM - 9:44AM |
M13.00008: Characteristics of Richtmyer Meshkov Instability in a Spherical Geometry Anthony Nelson, Praveen Ramaprabhu We describe recent numerical simulations of the single-mode Richtmyer-Meshkov (RM) instability in a spherical geometry. The simulations were performed using the astrophysical FLASH code in two-dimensions in spherical coordinates. Two kinds of RM problems were setup to exploit the effect of shock convergence on perturbation growth. The first set of simulations had low Atwood number interfaces with large perturbations, subject to a Mach 1.2 shock. This set was established to investigate the result of direct contact between the interface and the converging/strengthening shock wave. Secondly, we investigated high Atwood number interfaces with high wavenumber perturbations, subject to a Mach 6 shock. For these simulations, we studied the interaction between the contact discontinuity and a strong converging shock when in close proximity. We expect the single-mode results to inform multimode growth relevant to applications. [Preview Abstract] |
Tuesday, November 20, 2012 9:44AM - 9:57AM |
M13.00009: RANS Initialization and Validation in Shock-Driven Turbulent Mixing Fernando Grinstein, Brian Haines, John Schwarzkopf We investigate a working framework for testing unsteady engineering model initialization and closures based on comparing moments extracted from ensemble-averaged 3D LES data and those predicted directly by a 2D, variable-density, compressible, RANS model. The particular focus is shock-driven turbulent material mixing, and the prototypical case considered is the inverse chevron shock-tube configuration for which laboratory and LES studies have been previously reported. LES results are validated through comparison with previous LES and available experimental data; sensitivity to initial material interface conditions, grid resolution, model, and closure specifics are examined. [Preview Abstract] |
Tuesday, November 20, 2012 9:57AM - 10:10AM |
M13.00010: Reacting H2-O2 Richtmyer-Meshkov Instability Simulations Using Detailed Chemistry Praveen Ramaprabhu, Nitesh Attal, Sukesh Roy, James Gord Interaction of a shockwave with a flame enhances supersonic mixing and detonation, and is of importance to the design of supersonic combustors, internal combustion engines and fire safety. The Richtmyer-Meshkov instability plays a significant role in these phenomena. We present numerical results of a reacting Richtmyer-Meshkov instability (RMI) triggered by the interaction of a shock with a sinusoidally perturbed H2-O2 diffusion flame. The simulations were performed using a modified version of the astrophysical FLASH code [1]. A detailed H2-O2 reaction mechanism [2] coupled with an operator-split, 2nd order PPM method in FLASH was used to investigate the effect of RMI induced mixing on the flame. A parametric study for shock Mach numbers ranging from 1.2-3 over Atwood numbers of 0.4-0.65 was carried out, and the results will be presented. The detailed flame dynamics upon reshock will also be discussed.\\[4pt] [1] B. Fryxell, K. Olson, P. Ricker, F. Timmes, M. Zingale, D. Lamb, P. MacNeice, R. Rosner, J. Truran and H. Tufo, Astrophys. J., Suppl. Ser. 131, 273 (2000).\\[0pt] [2] G. Billet, J. Comput. Phys. 204, 319 (2005). [Preview Abstract] |
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