Bulletin of the American Physical Society
68th Annual Meeting of the APS Division of Fluid Dynamics
Volume 60, Number 21
Sunday–Tuesday, November 22–24, 2015; Boston, Massachusetts
Session L17: Flow Instability: Richtmyer-Meshkov III |
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Chair: Juan Gustavo Wouchuk, Universidad de Castilla-La Mancha Room: 205 |
Monday, November 23, 2015 4:05PM - 4:18PM |
L17.00001: Analytical expressions for the asymptotic velocities in the linear Richtmyer-Meshkov instability when a shock is reflected. Francisco Cobos, Juan Gustavo Wouchuk When a planar shock hits a corrugated contact surface between two fluids, hydrodynamic perturbations are generated in both fluids that result in asymptotic normal and tangential velocity perturbations in the linear stage. In this work, explicit and exact analytical expansions of the asymptotic velocities are presented for the general case in which a shock is reflected back. The expansions are derived from the conservation equations and takes into account the whole perturbation history between the transmitted and reflected fronts. The important physical limits of weak and strong shocks, high density ratio at the contact surface and very compressible/incompressible are studied. The expansions are compared with the exact solution obtained by iteration from a coupled set of functional equations and the limits of validity of those expansions are discussed. An approximate expression for the normal velocity, valid even for strong shocks in some regimes, is given. This work is a continuation of the calculations shown in Phys. Rev. E \textbf{90}, 053007 (2014) for a single shock moving into one fluid. [Preview Abstract] |
Monday, November 23, 2015 4:18PM - 4:31PM |
L17.00002: Richtmyer--Meshkov mixing: Modeling and simulation of experiments Nicholas Denissen, Susan Kurien Hydrodynamic instabilities that result from the interaction of a shock-wave with a perturbed interface are known as Richtmyer--Meshkov instabilities (RMI). RMI is important in a wide variety of applications including Inertial Confinement Fusion. Recent experiments at Los Alamos National Laboratory (LANL) have focused on careful measurement of initial conditions and repeated statistical measurements of the instability growth and transition to turbulence. This talk will discuss ongoing efforts to model these experiments using weakly non-linear theoretical models, one dimensional Reynolds--Averaged Navier--Stokes models and three-dimensional Implicit Large Eddy Simulations (ILES). Analysis of the experimental data supplies the initial condition for the theoretical model and the ILES calculations. The effect of different initial conditions and mesh resolutions will be examined in light of interest in international collaboration on an RMI test problem. Comparison of the different models to experimental data will be presented. All calculations are performed in the arbitrary Lagrangian/Eulerian (ALE) code FLAG, developed at LANL. The ALE framework allows us to assess the effects of numerical diffusion on RMI computations by varying the remap strategy. [Preview Abstract] |
Monday, November 23, 2015 4:31PM - 4:44PM |
L17.00003: Interactions of Blast Waves with Perturbed Interfaces Marc Henry de Frahan, Eric Johnsen Richtmyer-Meshkov and Rayleigh-Taylor instabilities induce hydrodynamic mixing in many important physical systems such as inertial confinement fusion, supernova collapse, and scramjet combustion. Blast waves interacting with perturbed interfaces are prevelant in such applications and dictate the mixing dynamics. This study increases our understanding of blast-driven hydrodynamic instabilities by providing models for the time-dependent perturbation growth and vorticity production mechanisms. The strength and length of the blast wave determine the different growth regimes and the importance of the Richtmyer-Meshkov or Rayleigh-Taylor growth. Our analysis is based on simulations of a 2D planar blast wave, modeled by a shock (instantaneous acceleration) followed by a rarefaction (time-dependent deceleration), interacting with a sinusoidal perturbation at an interface between two fluids. A high-order accurate Discontinuous Galerkin method is used to solve the multifluid Euler equations. [Preview Abstract] |
Monday, November 23, 2015 4:44PM - 4:57PM |
L17.00004: Evolution of the air/SF6 turbulent mixing zone for different lengths of SF6: shock tube visualizations and 3D simulations. Jean-Francois Haas, Jerome Griffond, Denis Souffland, Ghazi Bouzgarrou, Yannick Bury, Stephane Jamme A turbulent mixing zone (TMZ) is created in a vertical shock tube (based in ISAE DAEP) when a Mach 1.2 shock wave in air accelerates impulsively to 70 m/s an air/SF6 interface. The gases are initially separated by a thin nitrocellulose membrane maintained flat and parallel to the shock by two wire grids. The upper grid (SF6 side) of square mesh spacing h$_{\mathrm{u}}$ 1.8 or 12.1 mm is expected to seed perturbation for the Richtmyer-Meshkov instability (RMI) while the lower grid with h$_{\mathrm{l}}$ 1 mm is needed to prevent the membrane from bulging prior to the shot. The experiments were carried out for different lengths L of SF6 between the initial interface and the shock tube's end plate : 10, 15, 20, 25 and 30 cm. The time resolved Schlieren image processing based on space and frequency filtering yields similar evolution for the TMZ thickness. Before reshock, the thickness grows initially fast then slows down and reaches different values (10 to 14 mm) according to L. Soon after reshock, the TMZ thickness growths rate is 21 mm/ms independently of L and h$_{\mathrm{u}}$. Numerical Schlieren images generated from 3D numerical simulations (performed at CEA DAM IDF) are analyzed as the experimental ones for L 15 and 25 cm and for h$_{\mathrm{u}}$ 1.8 and 12.1 mm. The very weak experimental dependence on h$_{\mathrm{u}}$ is not obtained by simulation as expected from dimensional reasoning. This discrepancy remains paradoxical. [Preview Abstract] |
Monday, November 23, 2015 4:57PM - 5:10PM |
L17.00005: Initial condition spectral content effects on shock-driven turbulent mixing. Fernando Grinstein, Nicholas Nelson We report simulations of a shocked heavy band using the RAGE code in the implicit LES context [1]. We consider a shock-tube conÞguration with a band of high density SF6 gas embedded in low density air. A shock with Mach number 1.26 is transported through the band, resulting in transition to turbulence driven by the Richtmyer-Meshkov instability. The evolution of the system is followed as the primary shock traverses the SF6 band, reflects off the end-wall, propagates back and reshocks the mixing layers. We apply a variety of initial perturbations to the interfaces between the two ßuids in which the physical standard deviation, wave number range, and the spectral slope of the perturbations are held constant, but the number of modes initially present is varied. By decreasing the density of initial spectral modes of the interface, we Þnd that we can achieve as much as 25{\%} less total mixing at late times. Analysis is based on the evolution of mixing widths, mixedness, turbulent kinetic energy, and effective Reynolds number estimates. [1] Phys. Rev. E92, 013014, 2015. [Preview Abstract] |
Monday, November 23, 2015 5:10PM - 5:23PM |
L17.00006: shock driven instability of a multi-phase particle-gas system Jacob McFarland, Wolfgang Black, Jeevan Dahal, Brandon Morgan A computational study of a shock driven instability of a multiphse particle-gas system is presented. This instability can evolve in a similar fashion to the Richtmyer-Meshkov (RM) instability, but has addition parameters to be considered. Particle relaxation times, and density differences of the gas and particle-gas system can be adjusted to produce results which are different from the classical RM instability. We will show simulation results from the Ares code, developed at Lawrence Livermore National Laboratory, which uses a particle-in-cell approach to study the effects of the particle-gas system parameters. Mixing parameters will be presented to highlight the suppression of circulation and gas mixing by the particle phase. [Preview Abstract] |
Monday, November 23, 2015 5:23PM - 5:36PM |
L17.00007: Freeze-out of the linear Richtmyer-Meshkov instability Juan Gustavo Wouchuk, Francisco Cobos Campos, Takayoshi Sano When a planar shock refracts a corrugated contact surface separating two fluids with different thermodynamic properties, a transmitted and reflected wavefronts run inside each fluid. Due to the surface ripple, pressure, density and velocity perturbations are generated in both materials. When the fronts separate away, a steady normal velocity develops at the contact surface. For specific choices of the pre-shock parameters, the final value of the normal velocity at the surface ripple may become zero. This effect, known as ``freeze-out'' has been proposed by G.Fraley [Phys. Fluids \textbf{29}, 376 (1986)] and has been later on studied by K. Mikaelian [Phys. Fluids \textbf{6}, 356 (1994)]. We present here an analytical to study freeze-out in both situations of shock and rarefaction reflected at the contact surface. Freeze-out contours are derived as well as the detailed temporal evolution of the pressure and velocity perturbations in linear theory. Weak/strong incident shock limits are discussed. \\[4pt] [1] J. G. Wouchuk and K. Nishihara, Phys. Rev. E \textbf{70}, 026305 (2004).\\[0pt] [2] J. G. Wouchuk and T. Sano, Phys. Rev. E \textbf{91}, 023005 (2015). [Preview Abstract] |
Monday, November 23, 2015 5:36PM - 5:49PM |
L17.00008: Effect of pressure field fluctuations on the nonlinear evolution of Richtmyer-Meshkov coherent structure Aklant Bhowmick, Snezhana Abarzhi We consider the effect of pressure fluctuations on the evolution of Richtmyer-Meshkov (RM) flows. The pressure fluctuations are induced by non-uniformity in the fluid bulk and are modeled as a time dependent acceleration with the power-law exponent (-2). We consider a large scale periodic coherent structure of bubbles and spikes in a two-dimensional RM flow, and obtain asymptotic solutions describing nonlinear dynamics of the structure using group theory analysis. We show that regular asymptotic solutions describing the bubble dynamics form a one-dimensional family. The family can be parametrized by the curvature of the bubble front. The stability of the family solutions is analyzed. The physically significant solution in the family is interpreted as the stable solution with the maximum velocity. The associated flow fields in the vicinity of the bubble tip indicate the formation of vortices and the presence of shear at the interface, which may lead to cascading of energy of smaller scales. The fluids move intensively near the interface, and there is effectively no motion away from the interface. Dependence of the asymptotic dynamics to pressure fluctuations is studied both qualitatively and quantitatively, including the limiting cases of strong and weak fluctuations. [Preview Abstract] |
Monday, November 23, 2015 5:49PM - 6:02PM |
L17.00009: Influence of interference of perturbation waves on the dynamics of Richtmyer-Meshkov flows Arun Pandian, Snezhana Abarzhi We study the dynamics of structures that are formed due to Richtmyer-Meshkov instability (RMI) at the interface between two fluids with different densities when a strong shock wave refracts it [1]. While previous research in this area was focused on the effects of the wavelength and amplitude of the interface perturbation, the information was largely ignored on the influences of the relative phase of a multi-wave perturbation and the interference of the perturbation waves on RMI evolution. Applying group theory analysis and Smooth Particle Hydrodynamics simulations, we study the effects of the relative phase of the interfacial sinusoidal waves on the structure of bubbles and spikes that is formed at the interface after the shock passage. A number of new qualitative and quantitative effects are found, and the effect of the wave interference on RMI evolution is observed. In particular, evidences so far indicate that the symmetry of the interface strongly influences the spike morphology as compared to asymmetric cases. We discuss how one may control the growth of RMI by controlling the phases of waves of the initial perturbation [Preview Abstract] |
Monday, November 23, 2015 6:02PM - 6:15PM |
L17.00010: Direct Numerical Simulation of Richtmeyer-Meshkov Instability Using pWAMR Temistocle Grenga, Samuel Paolucci The parallel Wavelet Adaptive Multiresolution Representation (pWAMR) method is used to simulate the Richtmyer-Meshkov instability caused by a shock interacting with a density-stratified interface. The physical problem is studied in several configurations. We present results of numerical studies that investigate the influence of initial condition parameters (amplitude and wavelength of perturbations) on mixing and transition. In addition, the evaluation of turbulence statistics provides a measure of the mixing across the scales and the correlation with the initial condition parameters. The problem is modeled using the compressible reactive Navier-Stokes equations for a gas mixture, including multi-component diffusion, Soret and Dufour effects, and state dependent thermodynamic and transport properties. Since the amplitudes of wavelets provide a direct measure of the local error, the method is able to efficiently capture to any desired accuracy a wide range of spatial scales using a relatively small number of degrees of freedom by evolving the dynamically adaptive grid. In an effective fashion, the multilevel structure of the algorithm provides a simple way to adapt computational refinements to local demands of the solution, thus automatically producing verified solutions. [Preview Abstract] |
Monday, November 23, 2015 6:15PM - 6:28PM |
L17.00011: Measurements of the turbulent development of Richtmyer-Meshkov instability Vitaliy Krivets, Everest Sewell, Qian Xu, Jeffrey Jacobs A vertical shock tube is used for experiments on the Richtmyer-Meshkov instability in which a membrane-less interface is formed by opposed gas flows where the light and heavy gases enter the shock tube from the top and from the bottom of the driven section. An air/SF$_{\mathrm{6}}$ gas combination is used and an $M =$\textit{ 1.2} incident shock wave impulsively accelerates the interface. Initial perturbations are generated by harmonically oscillating the gases vertically, using two loudspeakers mounted in the shock tube walls, to produce Faraday resonance resulting in a random short wavelength perturbation. Planar Mie scattering is used to visualize the flow using a laser sheet to illuminate smoke particles seeded in one of the two gases. In addition, particle image velocimetry is used to obtain velocity measurements in which both gases are seeded. Image sequences are captured using high-speed video cameras. New experiments are presented quantifying the growth of the integral mixing layer width in addition to the molecular mixing evolution produced by the instability. [Preview Abstract] |
Monday, November 23, 2015 6:28PM - 6:41PM |
L17.00012: Experimental Investigation of Velocity Evolution in the Richtmyer-Meshkov Instability Daniel Reese, Jason Oakley, Dave Rothamer, Riccardo Bonazza The present work describes the evolution of the Richtmyer-Meshkov instability through a focus on the development of velocity fluctuations. In the Wisconsin Shock Tube Laboratory at the University of Wisconsin, a broadband, shear-layer initial condition is created at the interface between helium and argon. This shear layer is seeded with particulate TiO$_{\mathrm{2}}$, which is used to track the flow and allow for the Mie scattering of light. Once impulsively accelerated by a M$=$1.4 shock wave, the interface is imaged twice in close succession using planar laser imaging to create particle image pairs. Velocity fields are obtained from these particle images using the Insight 4G software package from TSI. This process is repeated, capturing a total of four different times in the development of the instability, allowing for the study of velocity development in the RMI. For each post-shock time, velocity field structure is investigated, and probability density functions of velocity fluctuations are compared. Using known length scales from previous studies, these newfound RMS velocity values are also used to give an estimate of the Reynolds number. [Preview Abstract] |
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