Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session NQ: Richtmyer-Meshkov Instability |
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Chair: Christopher Tomkins, Los Alamos National Laboratory Room: Hilton Chicago Stevens 2 |
Tuesday, November 22, 2005 11:01AM - 11:14AM |
NQ.00001: Statistical characterization of mixing induced by Richtmyer-Meshkov instability Christopher Tomkins, Sanjay Kumar, Greg Orlicz, Kathy Prestridge We quantitatively investigate mixing in the case of a heavy-gas (SF6) cylinder that is accelerated by a planar, Mach 1.2 shock wave. Concentration measurements of the heavy gas are acquired using planar laser-induced fluorescence (PLIF). The quantitative nature of the data permits a host of analysis, including estimation of the local mixing rate. The effects of the primary and secondary instabilities are revealed; these include the expected increase in molecular mixing due to increased stirring associated with transition to turbulence, and elevated mixing rate in pre-turbulent regions due to intensification of concentration gradients along stretched interfaces. Wavelets are used to characterize the transfer of energy between scales as a function of time. [Preview Abstract] |
Tuesday, November 22, 2005 11:14AM - 11:27AM |
NQ.00002: Reduced Reshock Growth in a Convergent/Divergent System Steven Batha, J.R. Fincke, J.M. Taccetti, N.D. Delamater, R.M. Hueckstaedt, N.E. Lanier, R.R. Magelssen, K.W. Parker, S.D. Rothman, C.J. Horsfield The interaction of a second shock with an already shocked, Richtmyer-Meshkov unstable interface causes the growth of the instability to increase in a planar geometry. Experiments on the Omega laser, however, have measured reduced growth rates when the second shock is diverging in cylindrical geometry. Illuminating the outside of a 1-mm-diameter cylinder with 18 kJ of laser light creates a strong shock. The shock passes through an embedded Al marker band. The outside surface of the Al is either smooth or has longitudinal perturbations (azimuthally symmetric) of wavelengths 2.5, 6, or 9 $\mu $m. The shock reflects off a hard inner cylinder that controls the timing, planarity, and strength of the rebounding shock (the reshock). Measurement of the mixing zone width after reshock show regrowth independent of the initial surface, contrary to single-shock results. Two possible explanations are considered. Freeze-out of the growth can occur by careful tailoring of the reshock timing. The loss of turbulent energy to the background strain field is also examined. This work was performed under the auspices of the United States Department of Energy under contract No. W-7405-ENG-36. [Preview Abstract] |
Tuesday, November 22, 2005 11:27AM - 11:40AM |
NQ.00003: Measurements of a re-shocked heavy-gas curtain using PLIF Katherine Prestridge, Christopher Tomkins, Gregory Orlicz, Sanjay Kumar We investigate Richtmyer-Meshkov instability developing in a heavy-gas curtain. The SF6 curtain is accelerated by a planar, Mach 1.2 shock, and then re-shocked by the nominally planar reflection from the end of the tube. We obtain preliminary concentration measurements of the transitioning heavy gas using acetone-based planar laser-induced fluorescence (PLIF). High-resolution images are acquired before and after re-shock. [Preview Abstract] |
Tuesday, November 22, 2005 11:40AM - 11:53AM |
NQ.00004: Experimental study of the two-mode Richtmyer-Meshkov instability. Vitaliy Krivets, Jeffrey Jacobs Experiments have been performed to study the Richtmyer-Meshkov instability of an Air /SF$_{6}$ interface initiated with a simple multi-mode initial perturbation. The experiments are conducted in a vertical shock tube and planar laser induced fluorescence is used to visualize the flow. The two gases flow from opposite ends of the shock tube driven section to form the interface. An initial perturbation in the form of the superposition of two two-dimensional normal modes is given to the interface by oscillating the tube in the horizontal direction at the combination of frequencies required to obtain the individual modes. Experiments with different relationships between the amplitudes and wavelengths of the sinusoidal modes will be presented. It is found that the amplitude of the multimode perturbation grows faster after interaction with the shock wave than its single-mode components. [Preview Abstract] |
Tuesday, November 22, 2005 11:53AM - 12:06PM |
NQ.00005: Richtmyer-Meshkov Instability of a Membraneless, Sinusoidal Gas Interface Bradley Motl, John Niederhaus, Mark Anderson, Jason Oakley, Riccardo Bonazza Results are presented from a series of shock tube experiments studying the Richtmyer-Meshkov instability (RMI) for the case of a 2-D single mode gas interface. The membraneless interface is formed by the head-on flow of nitrogen, seeded with acetone, and sulfur-hexafluoride which creates a stagnation surface. A sinusoidal interface is created by oscillating two rectangular pistons that are initially flush with the shock tube walls. The RMI is studied for varying incident shock strengths (1.3 $\le M \le $ 4) by imaging the interface with planar laser-induced fluorescence, once immediately before shock arrival and at two different post-shock times. The experimental images and the growth rates of non-dimensionalized geometrical features are compared to numerical simulations using the \textit{Raptor} code (LLNL) which takes advantage of the Piecewise Linear Method (PLM) with Adaptive Mesh Refinement (AMR) to solve the Navier-Stokes equations. [Preview Abstract] |
Tuesday, November 22, 2005 12:06PM - 12:19PM |
NQ.00006: Numerical Investigation of Incompressible Richtmyer-Meshkov Instability Wayne Kraft, Nicholas Mueschke, Malcolm Andrews, Jeffrey Jacobs The Richtmyer-Meshkov (RM) instability occurs when a shock passes through a perturbed interface separating fluids of different densities. Similarly, RM instabilities may also occur when a perturbed interface between two incompressible fluids of different density is impulsively accelerated. We report work that investigates RM instabilities between incompressible media through numerical simulations that are matched to experiments reported by Niederhaus {\&} Jacobs (2003). In this work, we present a simplified set of initial conditions that may be used as an alternative to more complicated initial conditions, which require simulating impulse dynamics prior to instability growth. As an alternative an initial velocity impulse has been used to model the impulsive acceleration history found in the experiments of Niederhaus \textit{et. al}. We report accurate simulation of the experimentally measured early-, intermediate-, and late-time penetrations of one fluid into another. In addition we find good agreement in structure morphology between the experiments of Niederhaus \textit{et. al.} and our simulation. As a result, the initial conditions and results of this work can be used as a physical validation for a range of variable density, incompressible algorithms. We present such a validation for numerical code which solves the variable density Navier-Stokes equation. [Preview Abstract] |
Tuesday, November 22, 2005 12:19PM - 12:32PM |
NQ.00007: A shocked gas cylinder as an example of Richtmyer-Meshkov transitional mixing Erik Vold, Chris Tomkins Previously, simulations of Richtmyer-Meshkov (R-M) instability-driven mixing in a gas cylinder after passage of a shock (Ma = 1.2) were shown to agree with experimental data, and indicated there is an order of magnitude increase in post-shock mixing rates attributed to the increased gas interface area and slope steepening in the post-shock roll-up and formation of secondary instabilities (Vold and Tomkins, Bull. Am. Phys. Soc., DFD04, GP.007). We re-examine the results as an example of a general transition from instability to a fully mixed state, with large scales evolving to smaller scales via stretching and secondary instabilities, and subsequently to a fully (molecularly) mixed state. Three phases in the transition to mixing (similar to those identified in Zhang, et.al., Phys. Fluids 16(5) p.1203, 2004) are examined and relations between vorticity, shock deposited circulation, an evolving `baroclinic circulation', and late time mixing are described. The stretching due to the circulation and secondary instabilities during late time mixing contributes to the increased interfacial area resulting in the enhanced molecular mixing observed in the simulations. The evolution to the final mixed state appears to be consistent with the assumption that small scales are resolved in the experiment, and thus, the experiment and simulations exemplify a resolved scale transition to a fully mixed state. [Preview Abstract] |
Tuesday, November 22, 2005 12:32PM - 12:45PM |
NQ.00008: Evolution and diagnositcs of the nonlinear Richtmyer-Meshkov instability Snezhana I. Abarzhi, Marcus Herrmann, Parviz Moin We report analytical and numerical solutions describing the dynamics of the two-dimensional coherent structure of bubbles and spikes in the Richtmyer-Meshkov instability for fluids with a finite density ratio. The theory accounts for the non-local properties of the interface evolution and the simulations treat the interface as a discontinuity. Good agreement between the analytical and numerical solutions is achieved. To quantify accurately the interface evolution in the observations, new diagnostics and scalings are suggested. The velocity, at which the interface would move if it would be ideally planar, is used to set the flow time-scale as well as the reference point for the bubble (spike) position. The data sampling has high temporal resolution and captures the velocity oscillations caused by sound waves. The bubble velocity and curvature are both monitored, and the bubble curvature is shown to be the relevant diagnostic parameter. In the nonlinear regime of the Richtmyer-Meshkov instability, the bubbles flatten and decelerate. The flattening of the bubble front indicates a multi-scale character of the coherent dynamics. [Preview Abstract] |
Tuesday, November 22, 2005 12:45PM - 12:58PM |
NQ.00009: Scaling behavior for vorticity ``drift'' from high-gradient interfaces in Richtmyer-Meshkov flows Norman Zabusky, Gaozhu Peng It is well known that vorticity is generated on high-gradient interfaces by \textit{vortex --acceleration }baroclinic processes during early-to-intermediate times of Richtmyer-Meshkov (RM) evolutions. The accumulated circulation after six multivalue times can be much larger than that deposited by the initial shock passage. These vorticity layers are observed to \textit{drift }away from the interface into the lower density domain. We quantify and scale the circulation\textit{ drift rate }as well as cascade to small scales for the two and three dimensional inviscid and viscous RM evolutions at various Atwood and Mach numbers. If time permits we will discuss these behaviors for Rayleigh-Taylor flows. [Preview Abstract] |
Tuesday, November 22, 2005 12:58PM - 1:11PM |
NQ.00010: Quantitative analysis of three-dimensional reshocked Richtmyer-Meshkov instability-induced mixing using different orders of WENO flux reconstruction Marco Latini, Oleg Schilling, Wai-Sun Don The formally high-order, Eulerian, shock-capturing weighted essentially non-oscillatory (WENO) method is applied to a three- dimensional model of the Mach 1.5 air/SF$_6$ Vetter-Sturtevant shock tube experiment with reshock. Results from fifth-, ninth- , and eleventh-order simulations are compared to quantitatively investigate the dependence of the dynamics and flow structure (including time-evolution of the mixing layer width, global and local mixing statistics, and spectra) on the order of flux reconstruction. Some of the benefits of high-order methods are discussed, including implications for assessing turbulent transport and mixing models for complex hydrodynamic flows. This work was performed under the auspices of the U.S. Department of Energy by the University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. This work was also supported by the Caltech ASC-Alliance Program. UCRL-ABS-214353. [Preview Abstract] |
Tuesday, November 22, 2005 1:11PM - 1:24PM |
NQ.00011: Assessment of gradient-diffusion closures for modeling turbulent transport in three-dimensional Richtmyer-Meshkov instability-induced mixing with reshock Oleg Schilling, Marco Latini, Wai-Sun Don The turbulent transport properties of multi-mode Richtmyer- Meshkov instability with reshock are investigated using data from a three-dimensional, ninth-order weighted essentially non- oscillatory (WENO) simulation of the Mach 1.5 air/SF$_6$ Vetter- Sturtevant shock tube experiment. A spatial average over the periodic directions is used to define averaged and fluctuating quantities. Quantities needed in gradient-diffusion closure models, such as the turbulent viscosity, turbulent kinetic energy, and turbulent kinetic energy dissipation rate, are computed and used to model the unclosed terms in the turbulent kinetic energy and dissipation rate equations. These terms are then compared a priori to the analogous quantities obtained by directly averaging the data to assess the validity of the gradient-diffusion approximation. Implications for two-equation turbulence modeling of Richtmyer-Meshkov instability induced mixing with reshock are discussed. This work was performed under the auspices of the U.S. Department of Energy by the University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. This work was also supported by the Caltech ASC-Alliance Program. UCRL-ABS-214351. [Preview Abstract] |
Tuesday, November 22, 2005 1:24PM - 1:37PM |
NQ.00012: Atomistic dynamics and the evolution of the Richtmyer-Meshkov instability Vasilii Zhakhovskii, Sergey Zybin, Snezhana I. Abarzhi, Katsunobu Nishihara For the first time the molecular dynamics (MD) approach is applied to study the evolution of the shock-driven Richtmyer- Meshkov instability(RMI), which develops at the corrugated interface separating two Lennard-Jones (LJ) liquids or two solids with different densities. Compared to traditional hydrodynamic simulations, MD has a number of fundamental advantages. It accounts for strong gradients of the pressure and temperature, and captures accurately the heat transfer and the viscous or plastic flow at early (shock passage) as well as late (turbulent mixing) stages of the instability evolution. MD has no limitations for the spatial resolution and does not require the assumption of thermodynamic equilibrium. We analyze the influence of the critical parameters, energy and mass transfer, and the governing stresses on the growth of the interface perturbations, and compare the cases of LJ liquids and solids. In liquids, RMI is driven by the non-uniform velocity shear and vorticity production. In solids, the development of visco-plastic flow, shear stresses, and elastic anisotropy influences significantly the evolution of initial perturbations. [Preview Abstract] |
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