Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session JM: Instability: Richtmyer-Meshkov I |
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Chair: B.J. Balakumar, Los Alamos National Laboratory Room: Salt Palace Convention Center 251 A |
Monday, November 19, 2007 3:35PM - 3:48PM |
JM.00001: Startup process in Richtmyer-Meshkov instability Manuel Lombardini, D.I. Pullin A simple analytical model is presented for the initial growth of the planar Richtmyer-Meshkov instability in the case of a reflected shock. The model captures the main features of the interfacial perturbation growth before the asymptotic linear regime is attained, over a wide range of incident shock Mach number and Atwood ratio. The problem is formulated in the general framework of the compressible Euler equations for ideal gases, and consists of solving the initial-value problem describing a shock impacting a slightly sinusoidally perturbed density interface. The equations are linearized about a base flow corresponding to the 1D Riemann problem of the shock interaction with an unperturbed interface. An appropriate scaling, similar to the Rayleigh-Jansen method, is then used to construct a perturbation expansion about the basic state. Linearized boundary conditions are applied at both reflected and transmitted perturbed shocks and at the contact interface. The zeroth order of the expansion is retained and leads to an explicit expression for the growth of the interface perturbation. Results are compared with computations obtained from two-dimensional, highly-resolved numerical simulations of the Richtmyer-Meshkov instability. [Preview Abstract] |
Monday, November 19, 2007 3:48PM - 4:01PM |
JM.00002: Experimental Study of the Richtmyer-Meshkov Instability for a He -- SF$_{6}$ Interface Bradley Motl, Devesh Ranjan, Jason Oakley, Mark Anderson, Riccardo Bonazza Results are presented from a series of experiments studying the Richtmyer-Meshkov (RM) instability for the case of a perturbed gas interface at the Wisconsin Shock Tube Laboratory. A membraneless interface is formed by the head-on flow of helium and sulfur-hexafluoride (seeded with smoke) which creates a stagnation surface. A sinusoidal interface is created at the gas stagnation plane in the test section by oscillating pistons that are initially flush with the shock tube walls. Flow visualization for the initial condition and post-shock images is carried out using Mie scattering from a planar laser sheet. The RM instability is studied for varying incident shock wave strengths (1.1 $\le M \le $ 2), and results are reported in the form of experimental images and perturbation growth rates which are compared to several analytic models. [Preview Abstract] |
Monday, November 19, 2007 4:01PM - 4:14PM |
JM.00003: Computational Study of the Richtmyer-Meshkov Instability for a He-SF6 Interface Christopher Weber, Nicholas Haehn, Bradley Motl, Jason Oakley, Mark Anderson, Riccardo Bonazza, Jeffrey Greenough Computational simulations of the Richtmyer-Meshkov (RM) instability are performed using the 2D Eulerian AMR code \textit{Raptor} (LLNL) for a perturbed gas interface of helium over sulfur-hexafluoride. The interfacial modal content of the initial conditions for these simulations are directly obtained from the recent experiments carried out at the University of Wisconsin Shock Tube Laboratory. In the simulation, performed at a resolution of 128 grid points per wavelength, the interface is accelerated by a planar shock wave of varying strength (1.1 $<$ M $<$ 2). These very high Atwood number (A=0.95) interfaces result in asymmetrical bubble/sphere growth in the early stages of the RM instability development and a near pinch-off of the heavy fluid located at the spike tip in the very late stages. The computed solutions are compared to experimental results and several analytic models. [Preview Abstract] |
Monday, November 19, 2007 4:14PM - 4:27PM |
JM.00004: Experimental and numerical study of the single-mode three-dimensional Richtmyer-Meshkov instability. Vitaliy Krivets, Christopher Long, Jeffrey Jacobs, Jeffrey Greenough A vertical shock tube is used to perform experiments on the single-mode three-dimensional Richtmyer-Meshkov instability. The interface is formed using apposed flows of air and SF$_{6}$ (with an Atwood number of 0.66) and the three-dimensional single-mode perturbation is created by the periodic vertical motion of the gases within the shock tube. Planar laser induced fluorescence still images in addition to planar Mie scattering movies are acquired. Richtmyer-Meshkov instability is produced by impulsive acceleration by a weak shock wave ($M_{s} = 1.2$). A three-dimensional numerical simulation of this experiment utilizing the Eulerian adaptive mesh refinement code Raptor was also conducted. The results of this simulation are compared with the experimental images and measurements. [Preview Abstract] |
Monday, November 19, 2007 4:27PM - 4:40PM |
JM.00005: Investigation of Late-Time Nonlinear Effects in Richtmyer-Meshkov Instability Using Compressible and Incompressible Simulations Marco Latini, Oleg Schilling The WENO method is used to investigate the late-time dynamics of the single-mode Richtmyer-Meshkov instability using a model of the Mach 1.3 air(acetone)/SF$_6$ Jacobs-Krivets shock tube experiment. The effects of compressibility are explored by varying the Mach number in the WENO simulations and comparing the results to an incompressible vorticity-streamfunction (VS) simulation. The WENO density fields capture the small-scale disordered structure resembling that in the experimental PLIF images, while the VS densities do not. The amplitudes agree with the experimental data points up to reshock. The bubble and spike amplitudes from the two methods agree at early times. At later times, the WENO bubble amplitude is smaller than the VS amplitude and vice versa for the spike: this difference is attributed to pressure perturbations that are absent in the incompressible simulations. The amplitudes from the WENO and VS simulations are also compared with the predictions of nonlinear instability growth models. [Preview Abstract] |
Monday, November 19, 2007 4:40PM - 4:53PM |
JM.00006: Investigation of the Richtmyer-Meshkov Instability Using a New Higher Resolution, Lower Dissipation Hybrid Central-Difference WENO-Z Method Wai Sun Don, Oleg Schilling A recently developed high-order hybrid central-difference WENO-Z method for the Euler equations is extended to the two- fluid compressible fluid equations. This new method is applied to simulate the two- and three-dimensional Richtmyer-Meshkov instability using a model of the Mach $1.3$ air(acetone)/SF$_6$ Jacobs-Krivets shock tube experiment. Fields, as well as quantities representative of the large- and small-scales of the flow, are compared to the corresponding fields and quantities obtained using the pure WENO method and the same grid resolution. The comparisons show that the new method provides better resolution properties and lower implicit numerical dissipation compared to the original WENO method. In particular, it is shown that the multi-resolution strategy used to select either the WENO or central differencing scheme yields better quality numerical solutions in the relatively smooth post-shock flow region than the pure WENO method. [Preview Abstract] |
Monday, November 19, 2007 4:53PM - 5:06PM |
JM.00007: Preliminary considerations of shock driven interfacial instability as a delta function impulse source in the transition to turbulence Erik Vold Previous work (Vold and Tomkins) compared computations to experiments for a shock driven interfacial instability (Richtmyer-Meshkov, R-M, instability) in a shocked gas cylinder. Mixing proceeds from an initially diffuse interface to a complex dipole vortex flow, then to a secondary instability with a characteristic unstable mode scale of about one tenth the initial gas cylinder diameter, and finally to a `fully' mixed state. We consider the impulsive source driving that fluid mixing source in the shocked system as a delta function for application to the continuous energy source driving the transition to turbulence in more general shear flow cases. The baroclinic vorticity source and resultant pressure field in the shocked case is contrasted to the vorticity source arising from the velocity profile near a wall or in free shear layer turbulent flow and to the pressure profiles seen along the surface of a cylinder in a high speed flow. Transition to turbulence in shear flows is hypothesized to follow through multiple and successive instabilities, each similar to the secondary instability transition observed in the R-M experiments, and with each instability cascading to a successfully smaller scale until molecular dissipation can accommodate the flow energy. [Preview Abstract] |
Monday, November 19, 2007 5:06PM - 5:19PM |
JM.00008: Features of vorticity evolution in two- and three-dimensional simulations for shock-bubble interactions John Niederhaus, Jeffrey Greenough, Jason Oakley, Riccardo Bonazza Results are presented from a series of high-resolution Eulerian AMR simulations for planar shock wave interaction with a spherical gas bubble, which contrast the flowfield evolution under axisymmetry to the evolution when symmetry is relaxed and a small-amplitude, short-wavelength non-axisymmetric perturbation is imposed on the interface. For incident-shock Mach numbers 1.1$<$M$<$5, the solution in two-dimensional axisymmetric (r-z) simulations differs significantly from that in three-dimensional non-axisymmetric simulations when the bubble gas density is greater than the ambient density such that the Atwood number is greater than 0.2. In that case, a vorticity field characterized by disordered motion arises in the mixing region in three-dimensional simulations, while vortex projectiles and interface shearing dominate in the two-dimensional simulations. In cases with Atwood number A$<$0.2, and in cases with bubble gas lighter than the ambient gas, stable vortices persist without significant development of disordered motion in both two-dimensional and three-dimensional simulations for 1.2$<$M$<$3.5. This behavior is characterized here using integral diagnostics on the datasets, and physical mechanisms are proposed. [Preview Abstract] |
Monday, November 19, 2007 5:19PM - 5:32PM |
JM.00009: Planar concentration and velocity measurements of a shock-accelerated gas curtain at multiple Mach numbers Greg Orlicz, B.J. Balakumar, Kathy Prestridge, Chris Tomkins Concentration and velocity measurements are obtained in a shock-accelerated gas curtain for three values of the incident shock strength: Ma = 1.2, 1.5, and 2.0. Qualitative PLIF images yield planar concentration maps at approximately 12 times to capture the evolution of the transitioning curtain, from which mixing widths are estimated as a function of time. The concentration results are complemented by planar velocity measurements (using combined PIV/PLIF) at one or two times for each Mach number. Vorticity and circulation estimates are computed from the PIV data and used in determining appropriate scaling of the flow. [Preview Abstract] |
Monday, November 19, 2007 5:32PM - 5:45PM |
JM.00010: Simultaneous PIV-PLIF measurements in a Richtmyer-Meshkov-unstable gas curtain at Mach 1.2 B.J. Balakumar, G.C. Orlicz, K.P. Prestridge, C.D. Tomkins The effects of re-shocking an already Richtmyer-Meshkov-unstable gas curtain at Mach 1.2 will be presented. Concentration measurements reveal growth rate amplification associated with the reshock and vorticity measurements before and after reshock quantify circulation changes. Turbulence statistics obtained using simultaneous PIV-PLIF techniques, from tightly controlled and well quantified initial conditions, will also be presented. Methods to select a subset of initial conditions (from many shots) that correlate well with each other are shown. Further, the compression of the initial conditions due to the shock wave are quantitatively measured. Finally, we show some results that point towards the tendency of such flows to approach homogeneity upon reshock. [Preview Abstract] |
Monday, November 19, 2007 5:45PM - 5:58PM |
JM.00011: Point measurements of density and velocity in RMI induced turbulent mixing zones. Jean-Francois Haas, Denis Counilh, Christian Mariani, Lazhar Houas, Georges Jourdan, Laurent Schwaederle We measure a RMI air/SF6 mix induced by a Mach 1.2 shock wave using Schlieren, a constant temperature hot wire anemometer (CTHWA) in IUSTI and a 2 components laser Doppler velocimeter (LDV) at CEA/DIF. The discontinuous interface is materialized by a nitrocellulose microfilm set against a square wire mesh with a wire spacing of 1.8 mm. The CTHWA output voltage is a function of several local gas characteristics. Using some simplifying assumptions and an inverse method we obtain velocity and concentration evolutions before the reshock. The LDV provides a velocity data point whenever a seeding particle crosses the measuring volume and the diffused light reaches the receiving optics. The membrane fragments reduce the data rate in the mixing zone. Many identical runs are needed to measure the velocity mean and variance in the mix. Before reshock, the variance is just above the one measured in SF6. After reshock, the much larger variance indicates anisotropic amplification. The post reshock variance is higher for 25 cm SF6 length than for 20 cm at abscissa 13.5 and 10.5 cm respectively, as confirmed by the thicker mix from the Schlieren images. We compare the data to the results from 3D Euler simulation and Reynolds stress tensor modelling at CEA/DIF. [Preview Abstract] |
Monday, November 19, 2007 5:58PM - 6:11PM |
JM.00012: Stochastic model of Rayliegh-Taylor turbulent mixing S.I. Abarzhi, M. Cadjan, S. Fedotov We propose a stochastic model to describe the random character of the dissipation process in the Rayleigh-Taylor turbulent mixing. The parameter alpha, used conventionally to characterize the mixing growth-rate, is not a universal constant and is very sensitive to the statistical properties of the dissipation. The ratio between the rates of momentum loss and momentum gain is the statistic invariant and a robust parameter to diagnose with or without turbulent diffusion accounted for. [Preview Abstract] |
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