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 R13: Richtmyer-Meshkov Instability II |
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Chair: Oleg Schilling, Lawrence Livermore National Laboratory Room: 27A |
Tuesday, November 20, 2012 1:00PM - 1:13PM |
R13.00001: Mixing at shocked interfaces with known perturbations Andrew Cook, Chris Weber, Riccardo Bonazza, Bill Cabot We derive a growth-rate model for the Richtmyer-Meshkov mixing layer, given arbitrary but known initial conditions. The initial growth rate is determined by the net mass flux through the center plane of the perturbed interface immediately after shock passage. The net mass flux is determined by the correlation between the post-shock density and streamwise velocity. The post-shock density field is computed from the known initial perturbations and the shock jump conditions. The streamwise velocity is computed via Biot-Savart integration of the vorticity field. The vorticity deposited by the shock is obtained from the baroclinic torque with an impulsive acceleration. Using the initial growth rate and characteristic perturbation wavelength as scaling factors, the model collapses growth rates over a broad range of Mach numbers, Atwood numbers and perturbation types. The mixing layer at late times exhibits a power-law growth with an average exponent of theta=0.23. [Preview Abstract] |
Tuesday, November 20, 2012 1:13PM - 1:26PM |
R13.00002: Simultaneous Measurements of Density and Velocity Fields in Single-interface Richtmyer-Meshkov Instabilities Ricardo Mejia-Alvarez, Brandon Wilson, Kathy Prestridge The Extreme Fluids Team at Los Alamos National Laboratory (LANL) has developed a new Vertical Shock Tube (VST). This facility is equipped with high-resolution diagnostics for simultaneous measurements of density and velocity fields in single-interface Richtmyer-Meshkov instabilities (RMI). The VST was conceived to provide high resolution PIV and PLIF data for a better understanding of the underlying phenomena of single-interface RMI. Additionally, these results will serve as a benchmark for RANS models and ILES. To reduce downtime and improve repeatability, a membraneless driver operates this VST. However, the Mach number response to the driver pressure differs from the one in membrane-based shock-tubes. Such differences are addressed in this talk. Additionally, this VST has the capability of introducing multi-modal 3-D perturbations in the interface between the working gases. Some examples of a perturbed air/SF$_6$ interface are presented. Finally, an instance of a simultaneous PIV-PLIF measurement at the initial conditions is presented. [Preview Abstract] |
Tuesday, November 20, 2012 1:26PM - 1:39PM |
R13.00003: Investigating Mach number dependence on Richtmyer-Meshkov mixing with high resolution velocity and density measurements Greg Orlicz, Sridhar Balasubramanian, Kathy Prestridge Experiments are performed to study the effect of incident shock Mach number (M) on the development of the Richtmyer-Meshkov instability after a shock wave impulsively accelerates a varicose-perturbed, heavy-gas curtain (air-SF$_{6}$-air). Incident shock strength is varied within the weak shock regime (M $\le $ 1.5), and the resulting instability and subsequent fluid mixing is measured using simultaneous Planar Laser-Induced Fluorescence (PLIF) and Particle Image Velocimetry (PIV). While large scale features of the evolving layer (e.g. total width) tend to grow similarly in scaled time, differences are observed in how the mixing occurs at smaller length scales. Presented are measures of mixing that can quantify some of these differences, as well as provide calibration and validation data for numerical models of this transitional flow. Through measurements of density PDFs, the instantaneous mixing rate, the density self-correlation parameter, and the area of the mixing layer, it is concluded that for fixed initial conditions, as incident shock Mach number is increased, the uniformity of the mixing layer increases, but the total amount of mixing decreases. [Preview Abstract] |
Tuesday, November 20, 2012 1:39PM - 1:52PM |
R13.00004: Turbulent Mixing in Late-Time Richtmyer-Meshkov Instability Experiments Chris Weber, Nick Haehn, Jason Oakley, David Rothamer, Riccardo Bonazza The Richtmyer-Meshkov instability is experimentally investigated in a vertical shock tube using a broadband initial condition imposed on an interface between a helium-acetone mixture and argon ($A $= 0.7). The initial condition is created, first by setting up a gravitationally stable stagnation plane between the gases, and then injecting the same two gases horizontally at the interface to create a shear layer. The perturbations along the shear layer create a statistically-repeatable broadband initial condition. The interface is accelerated by a $M$ = 1.6 or $M$ = 2.2 planar shock wave and develops into a fully-developed turbulent state. Mixing measurements are made using planar laser-induced fluorescence (PLIF). The spectra, length scales, and isotropy after the turbulent mixing transition are presented. [Preview Abstract] |
Tuesday, November 20, 2012 1:52PM - 2:05PM |
R13.00005: Evolution of the density self-correlation in developing RM turbulence Christopher Tomkins, B.J. Balakumar, G. Orlicz, K. Prestridge, J.R. Ristorcelli Turbulent mixing in a Richtmyer-Meshkov unstable light-heavy-light (air-SF$_6$-air) fluid layer subjected to a shock (Mach 1.20) and a reshock (Mach 1.17) is investigated using true ensemble statistics obtained from simultaneous velocity-density measurements. The mixing is found to be driven by an unstable array of initially symmetric vortices that induce rapid material mixing and create smaller scale vortices. The density self-correlation ($b$) and terms in its evolution equation are directly measured experimentally for the first time after reshock. Amongst other things, it is found that production terms are balanced by the dissipation terms, suggesting a form of equilibrium in $b$. Simultaneous velocity measurements are used to probe the state of the incipient turbulence. Results suggest that an inertial range is just beginning to form, consistent with the onset of a mixing transition. Second-order structure functions of the density field do not exhibit the classical 2/3 power-law behavior, which is discussed. [Preview Abstract] |
Tuesday, November 20, 2012 2:05PM - 2:18PM |
R13.00006: Evaluation of the Predictive Capability of a Reynolds-Averaged Navier-Stokes Model Applied to Reshocked Richtmyer-Meshkov Instability Tiberius Moran-Lopez, James P. Holloway, Oleg Schilling Reshocked Richtmyer--Meshkov turbulent mixing of sulfur hexafluoride and air for various Atwood numbers and shock Mach numbers is simulated using a third-order weighted essentially nonoscillatory implementation of a $K$-$\epsilon$ multicomponent Reynolds-averaged Navier--Stokes model. Mixing layer widths from simulations with Mach number $Ma = 1.45$ and Atwood number $At = -0.67$ are compared to the experimental data of Poggi, Thorembey and Rodriguez, and widths from simulations with $Ma = 1.24$, $1.50$, and $1.98$ with $At = 0.67$ are compared to the experimental data of Vetter and Sturtevant. The sensitivity of the mixing layer widths to variations in the initial conditions and key model coefficients is considered. Budgets of the turbulent transport equations are also considered to further elucidate the mechanisms contributing to turbulent mixing in reshocked Richtmyer--Meshkov instability experiments. [Preview Abstract] |
Tuesday, November 20, 2012 2:18PM - 2:31PM |
R13.00007: Simulations of Material Mixing in a Laser-Driven Reshock Experiment Brian Haines, Fernando Grinstein, Leslie Welser-Sherrill, James Fincke We perform simulations of a laser-driven reshock experiment in order to better understand material mixing driven by the Richtmeyer-Meshkov instability. Due to high sensitivities to target imperfections in the experimental data, direct comparisons of simulation and x-ray data are insufficient for validation. Therefore, we supplement these comparisons by performing spectral analysis. We also compare statistics of the data to results from DNS and theory of homogeneous isotropic turbulence. Our results show that in shock-driven transitional flows, some turbulent features, such as self-similarity and isotropy, only fully develop once others have decayed significantly. Finally. we evaluate a presumed PDF model for mixing at subgrid scales. [Preview Abstract] |
Tuesday, November 20, 2012 2:31PM - 2:44PM |
R13.00008: Comparative Study of the Predictions of Four-Equation Reynolds-Averaged Navier-Stokes Models Applied to Richtmyer-Meshkov Instability-Induced Mixing Oleg Schilling A multicomponent, weighted essentially nonoscillatory implementation of several four-equation $K$-$\epsilon$ and $K$-$L$ based Reynolds-averaged Navier--Stokes models is used to simulate reshocked Richtmyer--Meshkov turbulent mixing at various Mach and Atwood numbers. One class of models is based on mechanical turbulence coupled to scalar variance and its dissipation rate, and the other is based on mechanical turbulence coupled to mass flux and the density--specific volume correlation. The predicted evolution of the mixing layer, molecular mixing and other quantities obtained from these models are systematically intercompared, as well as compared to experimental shock tube data. The relative advantages and disadvantages of the various models are discussed. [Preview Abstract] |
Tuesday, November 20, 2012 2:44PM - 2:57PM |
R13.00009: Numerical investigation of three-dimensional effects in Richtmyer-Meshkov induced mixing processes Nikolaus Adams, Volker Tritschler The Richtmyer-Meshkov instability (RMI) occurs when a perturbed interface between two fluids with different densities is impulsively accelerated by a passing shock wave. The misalignment of pressure gradient and density gradient between the fluids upon shock passing causes baroclinic vorticity production. The deposited vorticity drives the primary instability that causes the small initial perturbations at the interface to grow. In two-dimensional simulations of RMI the vortex stretching and tilting term vanishes and vorticity is confined to be perpendicular to the flow. However, for realistic Richtmyer-Meshkov induced mixing processes the vortex stretching term can be essential. The assessment of three-dimensional effects on RMI is the objective of our numerical investigation. We report on simulations of three-dimensional Navier-Stokes simulations of shock-cylinder interaction with re-shock. A SF6-gas cylinder is impacted by a Mach 1.2 shock wave propagating in air. The cylinder surface has an initial sinusoidal single-mode perturbation in the axial direction. The initial surface perturbation triggers an instability and vorticity evolution in all three space dimensions. Three-dimensional effects are further reinforced by the re-shock. [Preview Abstract] |
Tuesday, November 20, 2012 2:57PM - 3:10PM |
R13.00010: High Resolution Numerical Investigation of Turbulence in a Reshocked Richtmyer Meshkov Unstable Curtain of Dense Gas Santhosh Shankar, Sanjiva Lele High 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). 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. Inertial range scaling, vorticity anisotropy and Reynolds stress development are studied in the reshocked flow. The high resolution data set is used to test certain modeling assumptions appearing in mixing models (BHR model) that have been traditionally used to study variable density flows. [Preview Abstract] |
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