Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session MP: Instability: Rayleigh-Taylor |
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Chair: Jeffrey Jacobs, University of Arizona Room: 200D |
Tuesday, November 24, 2009 8:00AM - 8:13AM |
MP.00001: Experimental Study of Rayleigh-Taylor Instability Using Paramagnetic Fluids Vladimer Tsiklashvili, Oleg Likhachev, Jeffry Jacobs Experiments that take advantage of the properties of paramagnetic liquids are used to study Rayleigh-Taylor instability. A gravitationally unstable combination of a paramagnetic salt solution and a nonmagnetic solution is initially stabilized by a magnetic field gradient that is produced by the contoured pole-caps of a large electromagnet. Rayleigh-Taylor instability originates with the rapid removal of current from the electromagnet, which results in the heavy liquid falling into the light liquid due to gravity and, thus, mixing with it. The mixing zone is visualized by back-lit photography and is recorded with a digital video camera. For visualization purposes, a blue-green dye is added to the magnetic fluid. The mixing rate of the two liquids is determined from an averaged dye concentration across the mixing layer by means of the Beer-Lambert law. After removal of the suspending magnetic field, the initially flat interface between the two liquids develops a random surface pattern with the dominant length scale well approximated by the fastest growing wavelength in accordance with the viscous linear stability theory. Several combinations of paramagnetic and nonmagnetic solutions have been considered during the course of the research. A functional dependence of the mixing layer growth constant, $\alpha $, on the properties of the liquids is a primary subject of the present study. [Preview Abstract] |
Tuesday, November 24, 2009 8:13AM - 8:26AM |
MP.00002: The Experimental Study of Rayleigh-Taylor Instability using a Linear Induction Motor Accelerator Nicholas Yamashita, Jeffrey Jacobs The experiments to be presented utilize an incompressible system of two stratified miscible liquids of different densities that are accelerated in order to produce the Rayleigh-Taylor instability. Three liquid combinations are used: isopropyl alcohol with water, a calcium nitrate solution or a lithium polytungstate solution, giving Atwood numbers of 0.11, 0.22 and 0.57, respectively. The acceleration required to drive the instability is produced by two high-speed linear induction motors mounted to an 8 m tall drop tower. The motors are mounted in parallel and have an effective acceleration length of 1.7 m and are each capable of producing 15 kN of thrust. The liquid system is contained within a square acrylic tank with inside dimensions 76 x76x184 mm. The tank is mounted to an aluminum plate, which is driven by the motors to create constant accelerations in the range of 1-20 g's, though the potential exists for higher accelerations. Also attached to the plate are a high-speed camera and an LED backlight to provide continuous video of the instability. In addition, an accelerometer is used to provide acceleration measurements during each experiment. Experimental image sequences will be presented which show the development of a random three-dimensional instability from an unforced initial perturbation. Measurements of the mixing zone width will be compared with traditional growth models. [Preview Abstract] |
Tuesday, November 24, 2009 8:26AM - 8:39AM |
MP.00003: Experimental study of the Rayleigh-Taylor instability at multimode interfaces Jeremy White, Jason Oakley, Mark Anderson, Riccardo Bonazza The gravitationally driven 2-D Rayleigh-Taylor (RT) instability is studied experimentally using simple, quantifiable multimode interfaces for two different Atwood numbers, $A$=0.46 and A$\sim ~$1. This study is performed using a magnetic fluid suspension technique that allows for precise interfacial shaping by exploiting the unique properties of magnetorheological (MR) fluids. The multimode shapes examined include a handful of modes which were chosen to minimize the effects of the physical test section size and surface tension on the development of the instability. A high speed X-ray radiography based diagnostic system is used to measure the evolution of the RT bubbles and spikes. The method for prescribing the initial condition allows for individual modes, which are chosen a priori, to be tracked for studying saturation, merger, and their collective influence on the overall mixing width. [Preview Abstract] |
Tuesday, November 24, 2009 8:39AM - 8:52AM |
MP.00004: Two-Wheel Experiment for detailed measurements of Rayleigh-Taylor Turbulence Aaron Haley, Raghu Mutnuri, Arindam Banerjee A novel two-wheel experiment to investigate incompressible turbulent Rayleigh-Taylor (RT) instability is described. The experiment consists of two counter rotating wheels, placed side by side, such that the axes of the wheels are normal to gravity. A test section, carrying a pair of immiscible fluids, is loaded on one wheel such that the heavier fluid is held radially outwards ensuring a stable stratification (no mixing). The test section is then oscillated to impose controlled multi-mode initial perturbations on the interface and finally transferred to the adjacent wheel using a solenoid actuated transfer mechanism. Upon transfer, the fluid stratification in the test section is reversed which leads to development of RT instability. Large centrifugal accelerations (10g) produced by the rotation of the wheels allow investigation of late time RT turbulence. Details of the mixing layer development and growth constants are captured using high speed backlit imaging. A variety of immiscible fluid combinations are utilized to investigate development of the RT mixing over a large range of Atwood numbers (0.1-0.99) and the results are compared with similar data available in the literature. [Preview Abstract] |
Tuesday, November 24, 2009 8:52AM - 9:05AM |
MP.00005: Effect of inital conditions in low-Atwood Rayleigh-Taylor Mixing Yuval Doron, Andrew Duggleby The effects of interface initial conditions in low-Atwood number Rayleigh-Taylor mixing are reported. The low-Atwood number water channel at Texas A\&M is modified with a servo motor controlled flapper device at the end of a splitter plate. The familiar bubble and spike phenomena for different wave numbers are observed. Average mixing rates are measured optically with the application of Beer-Lambert law and are used to measure the effect of initial conditions on the mixing height growth rates. Results show that single mode initial conditions all achieve the same growth rates within uncertainty. Details of the experimental set up are included as well as a discussion of future work. [Preview Abstract] |
Tuesday, November 24, 2009 9:05AM - 9:18AM |
MP.00006: Hybrid WENO/Central Difference Navier-Stokes Simulation of Rayleigh-Taylor Instability Wai-Sun Don, Oleg Schilling A new hybrid weighted essentially non-oscillatory (WENO)/central finite-difference method has been developed for the high-resolution, multi-dimensional, efficient simulation of turbulent mixing induced by interfacial hydrodynamic instabilities. Multi-resolution analysis is used to dynamically determine regions in which large gradients or discontinuities exist (where upwinding is applied) and regions in which the flow is relatively smooth (where central differencing is applied). This method is used to solve the fluid dynamics equations describing Rayleigh--Taylor unstable flow at intermediate and large Atwood number, and is shown to be robust for large initial density contrasts. Comparisons of the mixing layer widths, molecular mixing parameter, energy spectra, and other quantities are used to explore the effects of Atwood number on the evolution of turbulence statistics. [Preview Abstract] |
Tuesday, November 24, 2009 9:18AM - 9:31AM |
MP.00007: Wavelet-Based Simulations of Single-Mode Rayleigh-Taylor Instability Scott J. Reckinger, Daniel Livescu, Oleg V. Vasilyev The single-mode compressible Rayleigh-Taylor instability is investigated using numerical simulations on an adaptive mesh, performed with the Adaptive Wavelet Collocation Method (AWCM). Due to the physics-based adaptivity and direct error control of the method, AWCM is ideal for resolving the wide range of scales present in the development of the instability. The problem is initialized consistent to the solutions to the linear stability theory. Of interest are the departure time from the linear growth, the onset of strong non-linear interactions, and the late-time behavior of the fluid structures. The late time buble/spike velocities are computed and compared to those obtained in the incompressible case. [Preview Abstract] |
Tuesday, November 24, 2009 9:31AM - 9:44AM |
MP.00008: A Three- or Four-Equation Reynolds-Averaged Navier-Stokes Model of Large Reynolds Number Rayleigh-Taylor Turbulence and Mixing Oleg Schilling, Gregory Burton Using data from a $3072^3$ direct numerical simulation of Rayleigh--Taylor flow [\textit{Nature Physics} \textbf{2}, 562 (2006)], it is shown \textit{a priori} that gradient-diffusion and scale-similarity closures provide a closed three- or four- equation Reynolds-averaged Navier--Stokes model that correlates well with the data. In particular, using order of magnitude estimates of the exact transport equations and their closures, it is shown that the turbulent production and destruction terms in the turbulent kinetic energy dissipation rate and density variance dissipation rate equations scale as the square root of the turbulent Reynolds number, resulting in scale-similarity model coefficients that asymptote. A simplified algebraic Reynolds stress tensor model, similar to that used in turbulent convection and other buoyancy-driven turbulent flows, is shown to provide a good model for the anisotropic Reynolds stress tensor. Exploration of other algebraic Reynolds stress modeling approaches for incorporating the early-time nonequilibrium production-to-dissipation mechanisms is also discussed. [Preview Abstract] |
Tuesday, November 24, 2009 9:44AM - 9:57AM |
MP.00009: The ``second-wind'' phenomenon in single-wavelength Rayleigh-Taylor Praveen Ramaprabhu, Karthik Muthuraman, Guy Dimonte, Paul Woodward, Chris Fryer, Yuan-Nan Young, Sung-Ik Sohn The late-time, single-mode Rayleigh-Taylor (RT) flow asymptotes to a Froude number approaching 1, higher than predicted by potential flow models. The reacceleration to a higher terminal velocity [1] appears to be triggered by the appearance of Kelvin-Helmholtz (KH) vortices at small Atwood numbers. At large density differences, the KH instability is stabilized, with the result that the terminal velocity is in agreement with Layzer-type models. We compare results from simulations using multiple codes, with recently published experiments of [2], and with a simple model. The appearance of KH is also complicated by the presence of additional effects such as viscosity and surface tension. The results are of relevance to bubble- competition models of fully turbulent RT. [1] Ramaprabhu, P., et al. 2006, Physical Review E. 74, 066308. [2] Wilkinson, J.P. \& Jacobs, J.W. 2007, Phys. Fluids 19, 124102. [Preview Abstract] |
Tuesday, November 24, 2009 9:57AM - 10:10AM |
MP.00010: Rayleigh-Taylor Instability in Nonlinear Schr\"{o}dinger Flow Shu Jia, Jason W. Fleischer We consider the Rayleigh-Taylor instability in nonlinear Schr\"{o}dinger flow. In this superfluid-like case, wave diffraction, rather than viscosity or surface tension, sets the spatial scale for long-wave growth. Theoretically, we apply a polar (Madelung) transformation to the complex wavefunction and map intensity to density and velocity to the gradient of the phase. We show analytically that, unlike the instability dynamics in normal fluids, the superfluid behavior is strongly nonlinear and compressible from the start. Experimentally, we demonstrate the instability all-optically in a photorefractive crystal, using a self-defocusing nonlinearity as an effective pressure and a refractive index gradient as the driving acceleration. Observations of the characteristic spatial period show excellent agreement with scaling calculations from perturbation theory. We find that density fingering is always accompanied by vortex generation and that pressure effects strongly influence the finger period and mixing depth. The results hold for any Schr\"{o}dinger fluid, e.g. superfluids and quantum plasma, and lay the foundation for a variety of fluid-inspired instabilities in nonlinear optics. [Preview Abstract] |
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