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 M10: General Instability I |
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Chair: Brent Houchens, Rice University Room: 25C |
Tuesday, November 20, 2012 8:00AM - 8:13AM |
M10.00001: Stability of Miscible Displacements in Porous Media for Time-Dependent Injection Velocities Qingwang Yuan, Jalel Azaiez Flow instabilities are often observed when a high-viscosity fluid is displaced by a low-viscosity fluid in porous media. Even though most existing studies have analyzed such instabilities in the case of constant injection velocity, in many practical processes such as ground water flows and enhanced oil recovery, the velocity is actually time dependent. This work presents linear stability analysis of miscible displacement with time-dependent injection velocities in rectilinear Hele-Shaw cell. Both quasi-steady-state approximation (QSSA) and initial value calculation (IVC) methods are used to analyze the stability of constant, sinusoidal, and step injection velocity models. For QSSA, it is found that the growth rate follows the behavior of the injection velocity, while it also tends to flatten out whenever the contribution to the velocity is negative. For such negative velocities, the inverse displacement is unconditionally stable. For IVC, the variation of growth rate is influenced by velocity amplitude $\Gamma$ and time. The growth rates at maximum and minimum velocities are nearly the same as their constant velocity counterparts when $\Gamma$ is small. For large $\Gamma$, they are different, with some special characteristics. [Preview Abstract] |
Tuesday, November 20, 2012 8:13AM - 8:26AM |
M10.00002: Stability and sensitivity analyses of the engulfment regime in a three dimensional T-shaped micromixer Andrea Fani, Simone Camarri, Chiara Galletti, Maria Vittoria Salvetti The recent research in micro-fluidics has focused on the development of efficient passive micromixers, in which mixing is promoted without the help of any external power. One among the simplest designs of a passive micromixer is a T shape, in which the inlets join the main channel with T-shaped branches. The range of Reynolds numbers, $Re$, of interest for practical applications is such that the flow inside such a mixer is laminar but it is characterized by peculiar fluid-dynamics instabilities, which significantly enhance mixing but are poorly investigated in the literature. As $Re$ is increased, the flow goes through a bifurcation which drives the system from a perfectly symmetric flow to a steady but asymmetric state, so enhancing mixing (engulfment regime). The onset of the engulfment has been found to be influenced by geometrical parameters and by inflow conditions. In the present work we characterize the engulfment instability by a global stability analysis on the 3D base flow in a T-mixer. Sensitivity analyses with respect to a structural perturbation of the linearized flow equations and to a base flow modification were carried out. Finally, we characterize the sensitivity of the considered instability with respect to a perturbation of the inlet velocity profile. [Preview Abstract] |
Tuesday, November 20, 2012 8:26AM - 8:39AM |
M10.00003: Investigation of Linear Stability Theory for Wavy Interface in Magnetic Pulse Welding Ali Nassiri, Gregory Chini, Brad Kinsey Magnetic Pulse Welding (MPW) is a solid state, high strain-rate joining process in which a weld of dissimilar or similar materials can be created via high-speed oblique impact of two workpieces.~ MPW is a lap welding method:~ the two workpieces are placed in a roughly parallel configuration with a small gap between them to achieve high impact velocity and pressure.~ Intriguingly, experiments routinely show the emergence of a distinctive wavy pattern, with a well defined amplitude and wavelength of approximately 20 and 70 micrometers, respectively, at the interface between the two welded materials.~ The mechanism underlying this wavy pattern is still not well understand.~ Some researchers have proposed that the interfacial waves are formed in a process akin to Kelvin-Helmholtz instability, with relative shear movement of the flyer and base plates providing an energy source for the vortical pattern. Here, we employ a linear stability analysis to investigate whether the wavy pattern could be the signature of a shear-driven high strain-rate instability of a perfectly plastic solid material.~ Preliminary results confirm that an instability giving rise to a wavy interfacial pattern is possible. [Preview Abstract] |
Tuesday, November 20, 2012 8:39AM - 8:52AM |
M10.00004: Analysis of Float-Zone Crystal Growth Instabilities Through Linear Stability Analysis and 3D Spectral Element Simulations Brent Houchens, Kenneth Davis, Yue Huang In the optically-heated floating zone crystal growth process, a region of polycrystalline rod is melted and resolidified as a single crystal. Increased heat flux causes the axisymmetric base flow to transition to a fully three-dimensional flow, leading to various defects in the grown crystals. Here we use linear stability analysis to determine the point of initial instability and to compute the eigenfunctions corresponding to the unstable growth modes. In addition, three-dimensional, time-dependent spectral element simulations are computed and the results for the initial bifurcation point as well as the flow field are then compared to the results from linear stability theory. Simulations beyond the initial instability show competition between two stationary modes, which mimic a quasi-periodic mode. Additionally, the melt region is subjected to an axial magnetic field to resist velocities in the radial and azimuthal directions, stabilizing the base state. Simulations and linear stability analyses are compared for cases with the applied magnetic field and both confirm the desired stabilization. [Preview Abstract] |
Tuesday, November 20, 2012 8:52AM - 9:05AM |
M10.00005: Sheared Electroconvective Instability Rhokyun Kwak, Van Sang Pham, Kiang Meng Lim, Jongyoon Han Recently, ion concentration polarization (ICP) and related phenomena draw attention from physicists, due to its importance in understanding electrochemical systems. Researchers have been actively studying, but the complexity of this multiscale, multiphysics phenomenon has been limitation for gaining a detailed picture. Here, we consider electroconvective(EC) instability initiated by ICP under pressure-driven flow, a scenario often found in electrochemical desalinations. Combining scaling analysis, experiment, and numerical modeling, we reveal unique behaviors of sheared EC: unidirectional vortex structures, its size selection and vortex propagation. Selected by balancing the external pressure gradient and the electric body force, which generates Hagen--Poiseuille(HP) flow and vortical EC, the dimensionless EC thickness scales as $(\phi ^2/U_{\mbox{HP}})^{1/3}$. The pressure-driven flow(or shear) suppresses unfavorably-directed vortices, and simultaneously pushes favorably-directed vortices with constant speed, which is linearly proportional to the total shear of HP flow. This is the first systematic characterization of sheared EC, which has significant implications on the optimization of electrodialysis and other electrochemical systems. [Preview Abstract] |
Tuesday, November 20, 2012 9:05AM - 9:18AM |
M10.00006: A localized relaxation scheme for the computation of steady flows Jean-Marc Chomaz, Xavier Garnaud The computation of steady flow solutions in unstable settings is often the first step in studying the instability features. For this purpose, we present a method inspired by the Selective Frequency Damping of Akervik \emph{et al.} (2006). A low-pass temporal filter is applied at a small number of locations in the flow, and these values are used to relax the nonlinear system. If the relaxation points are properly selected, such a scheme may stabilize the dynamics. In this case, the steady flow can be computed using a regular time marching procedure with almost the same computational cost and memory requirements as a regular simulation. The relation between the optimal location of the relaxation points and the wavemaker region will be discussed. [Preview Abstract] |
Tuesday, November 20, 2012 9:18AM - 9:31AM |
M10.00007: A spectral representation of oscillators Shervin Bagheri We investigate Koopman modes as an expansion basis for describing the nonlinear dynamics of self-sustained oscillating flows. The method decomposes the flow evolving on a limit cycle and on its stable manifold into asymptotic/transient and steady/oscillatory components, providing an accurate prediction of both frequencies and relaxation rates. We find that the leading Koopman modes of an oscillator correspond to the mean flow, shift modes and nonlinear global modes. Close to the critical bifurcation threshold the modes are explicitly formed using multiple scale expansion of the flow field and a spectral expansion of the corresponding amplitudes. The analytic modes are in good agreement with Ritz vectors obtained computationally using the dynamic mode decomposition algorithm. We further discuss the ability of the Koopman modes and Ritz vectors of a nonlinear system to approximate the dynamics of unstable equilibria and the transient dynamics characterized by non-exponential behavior. [Preview Abstract] |
Tuesday, November 20, 2012 9:31AM - 9:44AM |
M10.00008: Criterion of Turbulent Transition in Pressure Driven Flows Hua-Shu Dou, Boo Cheong Khoo It has been found from numerical simulations and experiments that velocity inflection could result in turbulent transition in viscous parallel flows. However, there are exceptions, for example, in the plane Poiseuille-Couette flow. Thus, whether velocity inflection necessarily leads to turbulent transition is still not clear. To-date, there is still no consensus on the physics of turbulence transition in the scientific community. In this study, the mechanism of turbulent transition is investigated using the energy gradient method. It is found that the transition to turbulence from a laminar flow depends on the magnitudes of the energy gradient function and the energy of the disturbance imposed (including both the amplitude and the frequency). Our study further reveals that the criterion of turbulent transition is different in pressure and shear driven flows. In pressure driven parallel flows, it is found that the necessary and sufficient condition of turbulent transition is the existence of an inflection point on the velocity profile. This criterion is found to be consistent with the available experimental data and numerical simulation results. On contrast, velocity inflection in shear driven flows does not necessarily lead to turbulent transition. [Preview Abstract] |
Tuesday, November 20, 2012 9:44AM - 9:57AM |
M10.00009: Experimental Study of Transition to Turbulence in a Kolmogorov-Like Flow Balachandra Suri, Jeffrey Tithof, Radford Mitchell, Roman Grigoriev, Michael Schatz Recent theoretical advances suggest that turbulence can be characterized using exact unstable solutions of the Navier Stokes equations, called Exact Coherent Structures (ECS). Due to their experimental accessibility and theoretical tractability, two-dimensional flows provide an ideal setting for the exploration of turbulence from a dynamical systems perspective. Here, we present results from an experimental implementation of a Kolmogorov-like flow where a thin layer of electrolyte is driven electromagnetically. Using PIV to extract the velocity fields, we quantitatively study the bifurcations that the system undergoes as it transitions to turbulence. These results are in good quantitative agreement with those from a direct numerical simulation of a two-dimensional flow model. We also discuss our on-going work on identifying ECS in these flows and studying their role in the weakly turbulent regime. [Preview Abstract] |
Tuesday, November 20, 2012 9:57AM - 10:10AM |
M10.00010: On the added-mass effects of mean compressible and incompressible flows in fluid-solid interaction R. Jaiman, M. Parmar, Pardha Saradhi The unsteady fluid-structure interaction (FSI) is of fundamental interest in its own right. It is also of practical interest in a wide range of natural phenomena and industrial applications. Understanding the effects of flexible wall and estimates of added-mass forces can provide insights to coupled fluid-structure dynamics as well the improvements of numerical algorithms and closed-form empirical relations. Starting from the seminal work of Kramer (M.O. Kramer. Readers Forum, J. Aerospace Sci., 27(68), 1960.) numerous work have been published describing experiments, theoretical analysis and computations to understand how flexible elastic walls affect hydrodynamic stability. Most of the prior analysis focused on inviscid incompressible flow interacting with an elastic flat plate. In this work we present further theoretical investigation of the added-mass effect and the instability of an elastic plate as well as a string under a variety of uniform mean flows consisting of incompressible and compressible, inviscid and viscous conditions. We discuss the influence of viscosity and compressibility on the instability modes of fluid-solid interaction. We note that the added-mass effect for incompressible flow has a global character and for compressible flow it is time dependent. [Preview Abstract] |
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