Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session M21: Richtmeyer-Meshkov: Theory and ExperimentsInstabilities Reacting
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Chair: Devesh Ranjan, Georgia Tech Room: 706 |
Tuesday, November 21, 2017 8:00AM - 8:13AM |
M21.00001: Maximum initial growth-rate of strong-shock-driven Richtmyer-Meshkov instability Snezhana I. Abarzhi, Aklant K. Bhowmich, Zachary R. Dell, Arun Pandian, Milos Stanic, Robert F. Stellingwerf, Nora C. Swisher We focus on classical problem of dependence on the initial conditions of the initial growth-rate of strong shocks driven Richtmyer-Meshkov instability (RMI) by developing a novel empirical model and by employing rigorous theories and Smoothed Particle Hydrodynamics (SPH) simulations to describe the simulations data with statistical confidence in a broad parameter regime. For given values of the shock strength, fluids’ density ratio, and wavelength of the initial perturbation of the fluid interface, we find the maximum value of RMI initial growth-rate, the corresponding amplitude scale of the initial perturbation, and the maximum fraction of interfacial energy. This amplitude scale is independent of the shock strength and density ratio, and is characteristic quantity of RMI dynamics. We discover the exponential decay of the ratio of the initial and linear growth-rates of RMI with the initial perturbation amplitude that excellently agrees with available data. [Preview Abstract] |
Tuesday, November 21, 2017 8:13AM - 8:26AM |
M21.00002: Analytical scalings of the linear Richtmyer-Meshkov instability. Francisco Cobos, Juan Gustavo Wouchuk In the linear Richtmyer-Meshkov instability (RMI), hydrodynamic perturbations are generated behind the transmitted and reflected rippled fronts. The contact surface reaches an asymptotic normal velocity and two different tangential velocities at each side, which are always different for moderate to strong levels of compression, depending on the amount of vorticity generated by the corrugated shocks. We show analytical scaling laws for the ripple velocity ($\delta $v$_{\mathrm{i}}^{\mathrm{\infty }})$ in different physical limits and approximate formulas are provided, valid for arbitrary initial pre-shock parameters. An asymptotic growth for the contact surface ripple of the form $\psi_{\mathrm{i}}$(t)$\approx \psi_{\mathrm{\infty }}+\delta $v$_{\mathrm{i}}^{\mathrm{\infty }}$ t is obtained. The quantity $\psi_{\mathrm{\infty \thinspace }}$is in general different from the initial post-shock ripple amplitude, in agreement with the early finding of [1]. Comparison to simulations and experimental work is shown [2,3]. [1] K. A. Meyer and P. J. Blewett, Phys. Fluids \textbf{15}, 753 (1972). [2] F. Cobos Campos, and J. G. Wouchuk, Phys. Rev. E \textbf{93}, 053111 (2016). [3] F. Cobos-Campos, and J. G. Wouchuk, Phys. Rev. E \textbf{96}, 013102 (2017). [Preview Abstract] |
Tuesday, November 21, 2017 8:26AM - 8:39AM |
M21.00003: Scalings and statistics in shock-driven mixing flow Peter Vorobieff, Patrick Wayne, Sumanth Reddy Lingampally, C. Randall Truman Recent studies of shock-driven mixing in Richtmyer-Meshkov instability reveal that, as the flow transitions to turbulence and a mixing transition occurs, some statistical measures of the flow manifest values different from those one could expect from theory. One such statistical measure is the scaling of the second-order structure function of a scalar advected by the flow, in experiment, fluorescence intensity of a tracer tagging one of the gases undergoing mixing. Accordingly, this fluorescence intensity can be interpreted as local concentration of one of the species in the flow. We discuss possible reasons for the differences between experiments and theoretical predictions and present results describing the simultaneous evolution of the structure functions, mixing interface length and fractal dimension, and a histogram-based mixedness criterion. We also consider to what extent expectations driven by theories of fully-developed turbulence are applicable to a transitional flow that does not meet many idealized theoretical assumptions. [Preview Abstract] |
Tuesday, November 21, 2017 8:39AM - 8:52AM |
M21.00004: Kinetic energy in Richtmyer-Meshkov like flows Juan Gustavo Wouchuk, Francisco Cobos-Campos Richtmyer-Meshkov (RM) flows are driven by corrugated shocks/rarefactions. Those flows are characterized by acoustic, entropic and vorticity perturbations. Hence, the velocity perturbations are essentially rotational for moderate levels of compression. The vorticity distributed inside the compressed fluids is important to quantify the asymptotic linear velocities at the contact/piston surfaces that drive the shocks as well as to calculate the asymptotic velocity profiles in the compressed fluids. Usually, the vortices nearest to the piston/contact surface are the strongest and contain a significant amount of rotational kinetic energy. The size of the strongest vortices is analyzed as a function of the compression level [1] and the kinetic energy stored inside the vorticity field is also calculated. The calculations are done at first for different boundary conditions downstream in a single fluid: isolated shock, rigid piston and free surface. Besides, the kinetic energy in the classical RM environments with two fluids is also analyzed. [1] J. G. Wouchuk and F. Cobos-Campos, Plasma Phys. Contr. Fusion \textbf{59}, 014033 (2017). [Preview Abstract] |
Tuesday, November 21, 2017 8:52AM - 9:05AM |
M21.00005: Investigation of Atwood ratio influence on turbulent mixing transition of a shock-driven variable density flow after reshock Mohammad Mohaghar, John Carter, Gokul Pathikonda, Devesh Ranjan The current study experimentally investigates the influence of the initial Atwood ratio (At) on the evolution of Richtmyer-Meshkov instability at the Georgia Tech Shock Tube and Advanced Mixing Laboratory. Two Atwood numbers (At$=$0.22 and 0.67) are studied, which correspond to the gas combinations of nitrogen seeded with acetone vapor (light) over carbon dioxide (heavy) and same light gas over sulfur hexafluoride (heavy) respectively. A perturbed, multi-mode, inclined interface (with an amplitude to wavelength ratio of 0.088) is impulsively accelerated by the incident shock traveling vertically from light to heavy gas with a Mach number $\approx $1.55. The effect of Atwood ratio on turbulent mixing transition after reshock at the same non-dimensional times between the two cases is examined through ensemble-averaged turbulence statistics from simultaneous planar laser induced ?uorescence (PLIF) and particle image velocimetry (PIV) measurements. Preliminary studies over the smaller Atwood number indicates that turbulent mixing transition criteria can be satisfied after reshock. [Preview Abstract] |
Tuesday, November 21, 2017 9:05AM - 9:18AM |
M21.00006: Richtmyer-Meshkov instability experiments of miscible and immiscible incompressible fluids. Vitaliy Krivets, Brason Holt, Matthew Mokler, Jeffrey Jacobs Experiments were conducted in a 3 m tall vertical drop tower setup. A flat interface separating two liquids of differing density is formed in the Plexiglas tank with the heavier fluid in the bottom and the lighter one on top. Two liquids pairs were utilized, one - miscible (isopropyl alcohol and a calcium nitrate water mixture) and the other immiscible (silicone oil with the same heavy liquid), both with Atwood near 0.2. The tank is mounted on a rail mounted sled at 2 m initial height where an initial perturbation is generated using vertical periodic motion with 10 Hz frequency and 1 mm displacement, thus producing 3D interfacial waves. An impulsive acceleration, with approximately 100g magnitude, is imparted to the sled by a rail mounted weight released and allowed to fall, impacting the sled from above. Both weight and sled then travel freely down the rails where they are smoothly decelerated at the bottom of drop tower by magnetic brakes. PLIF is used to visualize mixing process by seeding fluorescein in the bottom fluid and illuminating using laser diode from above forming thin vertical sheet. The resulting fluorescent image sequences are captured using a digital camera mounted to the sled operating at a 100 Hz framing rate. Comparisons of the measured growth of the mixing zone for both immiscible and miscible liquid combinations with theoretical models are presented. [Preview Abstract] |
Tuesday, November 21, 2017 9:18AM - 9:31AM |
M21.00007: Studies of Shock Wave Interaction with a Curtain of Massive Particles Sumanth Reddy Lingampally, Patrick Wayne, Sean Cooper, Ricardo Gonzalez Izard, Gustaaf Jacobs, Peter Vorobieff Interaction of a shock wave with planar and perturbed curtain of massive particles is studied experimentally. To form the curtain, solid soda lime particles (30-50 micron diameter) are dropped from a hopper fitted with mesh sieves and vibrated with a motor. The curtain forms when the particles move through a rectangular slot in the top of the test section of the shock tube used in experiment. The curtain can be either planar or perturbed in the horizontal plane (parallel to the shock direction) based on the shape of the slot. This setup generates a particle curtain with a volume fraction varying between 2 and 8 percent along its vertical height. A laser illuminates the curtain in vertical and horizontal planes. When the diaphragm separating the driver and the driven section is ruptured, shock waves with Mach numbers ranging from 1 to 2, depending on the pressure, propagate down the driven section and into test section. The phenomena following the shock wave impingement on the particle curtain are captured using an Apogee Alta U42 camera. [Preview Abstract] |
Tuesday, November 21, 2017 9:31AM - 9:44AM |
M21.00008: Simultaneous measurements of concentration and velocity in the Richtmyer-Meshkov instability Dan Reese, Alex Ames, Chris Noble, Jason Oakley, David Rothamer, Riccardo Bonazza The Richtmyer-Meshkov instability (RMI) is studied experimentally in the Wisconsin Shock Tube Laboratory (WiSTL) using a broadband, shear layer initial condition at the interface between a helium-acetone mixture and argon. This interface (Atwood number $A$=0.7) is accelerated by either a $M$=1.6 or $M$=2.2 planar shock wave, and the development of the RMI is investigated through simultaneous planar laser-induced fluorescence (PLIF) and particle image velocimetry (PIV) measurements at the initial condition and four post-shock times. Three Reynolds stresses, the planar turbulent kinetic energy, the Taylor microscale are calculated from the concentration and velocity fields. The external Reynolds number is estimated from the Taylor scale and the velocity statistics. The results suggest that the flow transitions to fully developed turbulence by the third post-shock time for the high Mach number case, while it may not at the lower Mach number. [Preview Abstract] |
Tuesday, November 21, 2017 9:44AM - 9:57AM |
M21.00009: Time-resolved Particle Image Velocimetry measurements of the 3D random Richtmyer-Meshkov Instability. Everest Sewell, Vitaliy Krivets, Jeffrey Jacobs The vertical shock tube at the University of Arizona is used to perform experiments on the multi-mode three-dimensional Richtmyer-Meshkov Instability (RMI). An interface of air and sulfur hexafluoride is formed in a counter flow configuration, and is excited using voice coils to produce faraday-like multi-modal perturbations.This interface is shock accelerated by an approximately Mach 1.2 shockwave to form the RMI. Time resolved Particle Image Velocimetry (PIV) is used to perform analysis of the evolving instability. [Preview Abstract] |
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