Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session Q28: Flow Instability: Rayleigh-Taylor/Richtmyer-Meshkov III |
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Chair: Jacob McFarland, University of Missouri Room: Georgia World Congress Center B316 |
Tuesday, November 20, 2018 12:50PM - 1:03PM |
Q28.00001: Analysis of Second-Moment Budgets and Closure Models for Richtmyer-Meshkov Instability Man Long Wong, Daniel Livescu, Sanjiva K Lele An analysis of second moment budgets for variable density mixing induced by the interaction between a Mach 1.45 shock and subsequent re-shock with the interface between two ideal gases at high Atwood number (sulphur hexafluoride and air) is performed using high-resolution compressible Navier-Stokes simulations. The analysis first addresses the importance of the additional transport equations of second moment quantities: turbulent mass flux and density-specific-volume covariance for the closure of Reynolds-averaged Navier–Stokes (RANS) equations in this type of flow compared to single-species flows that only require Reynolds stress equations. Then, a short survey of RANS closures for Richtmyer-Meshkov instability is presented, together with an analysis of the requirements for capturing this type of flow. The analysis is further applied to the BHR-3 RANS model by [Schwarzkopf et al., 2011] and its extension with two separate length scales (decay and transport length scales) by [Schwarzkopf et al., 2016]. |
Tuesday, November 20, 2018 1:03PM - 1:16PM |
Q28.00002: Comparison of inclined and aligned interface Richtmyer-Meshkov instabilities Akshay Subramaniam, Sanjiva K Lele The classical Richtmyer-Meshkov instability arises from the interaction of a shock wave with a material interface that is nominally aligned with the shock. The problem is homogeneous in the directions perpendicular to the shock propagation direction. Shock interaction with a material interface that is nominally inclined with respect to the shock brings out the effects of inhomogeneity in the transverse direction. This creates large scale shear and large correlated vortex structures. The inclined interface RM simulations with a 1:1 crossectional domain target the experiment of McFarland et. al. (2014) and the aligned interface RM data is from Tritschler et. al. (2014). Turbulence energy budgets are characterized for both cases and compared. The inclined interface problem is found to have large scale shear that acts as a prolonged energy injection mechanism for the late time turbulent region while the turbulent kinetic energy decays in the aligned interface problem. Compressibility effects are characterized and are found to arise from coupling of the mixing region with the end wall. A scale decomposition analysis is also performed to assess the energetics of the problem as a function of scale. |
Tuesday, November 20, 2018 1:16PM - 1:29PM |
Q28.00003: Mixing layer growth from localized perturbations Britton Olson, Robin Williams We study the growth of Richtmyer-Meshkov mixing layers from an initial surface with spatially localized perturbations. We use two symmetric forms of the initial patch, which allow simulation data to be averaged to generate a two-dimensional statistical representation of the three dimensional turbulent flow. We find that as the mixing layer grows, the turbulent structures tend to form into discrete packets separated from the surface, with material entrainment into them dominated by a laminar entrainment flow inward from the surrounding regions where the surface was originally smooth. The entrainment appears to be controlled by the propagation of vortex pairs which appear at the boundary of the region of initial perturbations. This suggests that the growth of RM mixing from isolated features, as may be found in manufactured Inertial Confinement Fusion capsules, has a rather different mechanism than the growth of an RM mixing layer when the perturbations are uniform. This may be a challenge for some existing engineering models to accurately capture. |
Tuesday, November 20, 2018 1:29PM - 1:42PM |
Q28.00004: Modeling the Effects of Combustion on Reshocked Richtmyer−Meshkov Instability-Induced Turbulent Mixing Bryan W Reuter, Oleg Schilling The effects of heat release and combustion processes on integral scale quantities (such as mixing layer width and molecular mixing) and turbulent quantities (such as turbulent kinetic energy and turbulent viscosity) are investigated using one-dimensional Reynolds-averaged Navier−Stokes simulations using a recently proposed four-equation mechanical/scalar turbulence model [Schilling and Mueschke, Physical Review E 96, 063111 (2017)] augmented by the b PDF model to close the mean reaction rates in the species mean mass fraction equations. Quantities are compared for a nonreacting and reacting reshocked Richtmyer−Meshkov instability with a single-step reaction to quantitatively evaluate the effects of combustion on the hydrodynamic evolution. Comparisons of quantities are presented for a hierarchy of increasingly more complete and accurate models for the mean reaction rates, which also include the effects of temperature fluctuations. In addition, the budgets of the mean and turbulent transport equations are compared between the nonreacting and reacting cases to elucidate the mechanisms affecting the hydrodynamic evolution. |
Tuesday, November 20, 2018 1:42PM - 1:55PM |
Q28.00005: Vorticity Dynamics of the Richtmyer-Meshkov Instability Samuel Pellone, Eric Johnsen The interaction between a shock wave and a material interface separating two fluids of different densities gives rise to the Richtmyer-Meshkov instability, ubiquitous in both nature and engineering applications, such as high energy density physics and scramjet combustion. The initial baroclinic vorticity deposited along the interface by the incoming shock is the dominant and driving mechanism of the evolution of the interface in time. This study explores the evolution of an initially perturbed interface dominated by the vorticity dynamics of the interface. The use of a vortex-sheet approach allows us to identify the mechanisms responsible for the dynamics of the interfacial vorticity, and enhances our understanding of the vortex cores behavior. We identify three consecutive phases for the temporal evolution of the circulation, and quantify secondary vorticity appearing in the non-linear regime. A scaling analysis of the secondary vorticity is performed based on the parameters of the problem. |
Tuesday, November 20, 2018 1:55PM - 2:08PM |
Q28.00006: Evolution of vortex surfaces in the Richtmyer-Meshkov instability Naifu Peng, Yue Yang We study the vortex dynamics in the Richtmyer-Meshkov instability (RMI) using the vortex-surface field (VSF). The VSF is a Lagrangian-based structure-identification method, whose isosurface is a vortex surface consisting of vortex lines. For the RMI with a single-mode interface separating two different fluids, we derive the initial VSF from the vorticity generated by the baroclinic effect after the normal shock wave interacting with the perturbed interface. Then the evolving VSF is calculated using the two-time method from a series of velocity fields obtained from direct numerical simulation. The typical vortex surfaces in the evolution display signature spike and bubble structures, and are slightly different from the isosurfaces of the density and vorticity magnitude before significant vortex reconnection. Based on the evolving vortex surfaces, we elucidate the development of asymmetric spike and bubble and estimate the growth rate of the mixing zone. |
Tuesday, November 20, 2018 2:08PM - 2:21PM |
Q28.00007: An Improved Ejecta Production Model Based on Richtmyer-Meshkov Instability Spike Dynamics Alan K. Harrison The FLAG Lagrange/ALE hydrocode employs a subgrid model of mass ejection as a Richtmyer-Meshkov instability (RMI), including (1) a description of RMI spike and bubble growth rates to due to Buttler et al. [W. T. Buttler et al., J. Fluid Mech, 703, 2012, pp. 60-84], (2) the Self-Similar Velocity Distribution (SSVD) model of the velocity field within a spike (in the fluid frame) as varying linearly from zero at the base to a maximum value at the tip [J. E. Hammerberg et al., AIP Conference Proceedings 1979, 080006 (2018)], and (3) a model of spike breakup. In this work, we improve on model (2) by accounting for inflow of matter at the base of the spike. This allows us to self-consistently reconcile the evolving shape of the spikes (elongation and thinning) with the inflow, and with the corresponding properties of the bubbles, under the assumption of incompressibility. Since the model enables the description of the motion of a fluid element into and along the spike, a more realistic prediction of the velocities and sizes of the resulting ejecta can result. We describe the new self-consistent model and its implementation in FLAG, and indicate how it will be coupled to the breakup model to predict sizes and speeds of the resulting particles. |
Tuesday, November 20, 2018 2:21PM - 2:34PM |
Q28.00008: An ejecta model created from combining nonlinear growth and empirical asymptotic spike velocity models Jonathan D. Regele, Alan K Harrison, Marianne M Francois Ejecta models can be formulated from Richtmyer-Meshkov instability behavior where initial ejecta properties are based on wave amplitude, wave number, and spike velocity. While many models employ nonlinear factors, most models are based on incompressible theory and do not account for compressible effects when the incident shock Mach number becomes large. Karkhanis et al. [V. Karkhanis et al., J. Appl. Phys., 2018] developed an empirical model for the asymptotic spike velocity that includes compressibility. The distance particles travel can be overestimated by using the asymptotic speed for initial ejecta formation. For a more accurate trajectory, the ejecta particles can be initialized with an initial spike velocity and then integrated with a nonlinear growth model until the particles reach the asymptotic spike velocity. In this work, the Karkhanis model is combined with the nonlinear growth model in Buttler et al. [W. T. Buttler et al., J. Fluid Mech, 703, 2012, pp. 60-84] to obtain a time varying solution where the asymptotic velocity is recovered in the late time limit. |
Tuesday, November 20, 2018 2:34PM - 2:47PM |
Q28.00009: Ejecta velocities from twice-shocked metals Praveen K Ramaprabhu, Varad A Karkhanis, William T Buttler, Frank J Cherne, James E Hammerberg |
Tuesday, November 20, 2018 2:47PM - 3:00PM |
Q28.00010: Abstract Withdrawn Hydrodynamic Instabilities (HI) are of critical concern in many fields of science and engineering such as aerospace engineering, chemical engineering or astrophysics. Those of interest in this work, the Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities, emerge at the perturbed interface between fluids of different densities. Under the excitation of a continuous (RT) or impulsive acceleration (RM), the initial perturbations at an unstable density interface grow via baroclinic torque and eventually turbulent mixing is induced. Recently, much attention has turned to RT and RM instabilities in converging geometries driven by progress made and new knowledge gained in Inertial Confinement Fusion experiments. In the present work, we report an analysis of the mixing ensuing a shock wave converging in radially-stratified fluids using Proper Orthogonal Decomposition (POD) as a tool for order reduction. A transfer function (or state space model) is extracted by the POD and a Galerkin projection of the governing equations. Then, a model of the mixing state is constructed using the most dominant modes and validated with simulation data. |
Tuesday, November 20, 2018 3:00PM - 3:13PM |
Q28.00011: Simulations of a Shock-Driven Instability Developing from a Curtain of Particles Bertrand Rollin, Rahul Babu Koneru, Frederick Ouellet, Joshua R Garno The problem of a shock wave interacting with a corrugated curtain of solid particles is investigated using point-particle simulations. This gas-solid analog to the classic Richtmyer-Meshkov instability in which two fluids of different densities are at play may be relevant to phenomena such as the late time formation of aerodynamically stable particle jets in the context of explosive dispersal of particles or supernovae dust processing. Tracking trajectories of computational particles in the Eulerian-Lagrangian framework, the study aims to characterize the particle curtain development following the passing of a strong pressure discontinuity as a function of the initial conditions. Using a numerical shock tube containing a two-millimeter-thick particle curtain composed of heavy solid particles, we explore the effects of initial shape, particle volume fraction and shock strength on the curtain evolution in two- and three-dimensional planar geometries. Throughout the investigation, compaction phenomena are avoided by constraining simulations to initial particle volume fractions of less than 25%. |
Tuesday, November 20, 2018 3:13PM - 3:26PM |
Q28.00012: Effect of plasma parameters on magnetic suppression of the Richtmyer-Meshkov instability in two-fluid plasmas Vincent Wheatley, Daryl M Bond, Yuan Li, Ravi Samtaney, Dale I. Pullin The Richtmyer-Meshkov instability (RMI) of a shock accelerated perturbed density interface is important in both inertial confinement fusion and astrophysics, where the materials involved are typically in the plasma state. In the single-fluid magnetohydrodynamic model, it has been demonstrated that the plasma RMI can be mitigated by magnetizing the plasma with a sufficiently strong field. We will show that this is also the case in the two-fluid plasma model, which couples a separate set of conservation laws for each species to Maxwell’s equations. We will explore how the suppression mechanism varies with plasma parameters. For low density plasmas with larger plasma length-scales, the mechanism is a Lorentz force driven inversion of the sign of vorticity on the interface. As plasma density increases and plasma length-scales decrease, the vorticity generated by the shock interaction is increasingly transported from the interface by plasma waves. |
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