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 MQ: Instability: General |
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Chair: Patrick Huerre, Ecole Polytechnique Room: 200E |
Tuesday, November 24, 2009 8:00AM - 8:13AM |
MQ.00001: Nonlinear transient growth and detecting the laminar-turbulent boundary Rich Kerswell, Chris Pringle The area of transition to turbulence has experienced a spurt of activity recently in wall-bounded shear flows where transition is triggered by finite amplitude disturbances. This has been stimulated by the discovery of new solutions to the governing equations which are disconnected from the steady unidirectional ``base'' flow in, for example, pipe flow and plane Couette flow. Understanding how all this new (nonlinear) work fits together with transient growth ideas which focus on linear mechanisms based around the base state presents an interesting challenge. In this talk, we attempt to bridge the gap from linear optimals to the (very nonlinear) laminar-turbulent boundary in phase space which determines whether a given disturbance will trigger turbulence or not. [Preview Abstract] |
Tuesday, November 24, 2009 8:13AM - 8:26AM |
MQ.00002: Transient growth in Rayleigh-Benard-Poiseuille and Rayleigh-Benard-Couette flows John Soundar Jerome Joseph, Jean-Marc Chomaz, Patrick Huerre A study on the effect of buoyancy in plane Poiseuille flow and Couette flow has been carried out through linear temporal stability analysis, in the normal and non-normal framework. Here, the buoyancy is solely induced by a constant thermal stratification in the wall-normal direction. In the context of linear temporal stability analysis, a parametric study of the marginally stable modes with respect to Reynolds and Rayleigh numbers has been presented. It is found that the wall-normal temperature gradient has a negligible effect on the Tollmien-Schlichting instability. Nevertheless, the nonmodal analysis shows that the coupling between the body force and shear has a favorable effect on the transient growth of longitudinal disturbances in both plane Poiseuille flow and Couette flow. The transient growth characteristics have been illustrated by making use of different energy norms. [Preview Abstract] |
Tuesday, November 24, 2009 8:26AM - 8:39AM |
MQ.00003: Flow induced oscillation of a cylinder in a Hele-Shaw cell B. Semin, H. Auradou, J.-P. Hulin, A. Decoene, V. Scelles, A. Lefebvre Spontaneous regular oscillations of a confined cylinder in a steady Poiseuille flow are observed down to small Reynolds numbers ($Re=15$). In this study, the cylinder is perpendicular to the mean flow, parallel to the walls of a Hele-Shaw cell and free to move only in the direction perpendicular to them; the ratio of the diameter of the cylinder by the cell aperture is $0.7$. Experimentally, the cylinder is held by long thin threads. This flow-structure coupling, resulting from the confinement, has also been modelled successfully using $2D$ finite elements simulations. The oscillations are quasi-sinusoidal in a wide range of $Re$ value ($Re$ is defined using the mean velocity and the diameter of the cylinder). The threshold value ($Re=15$) is much smaller than for classical vortex shedding past a nonconfined cylinder ($Re=45$). The amplitude increases with the Reynolds number until saturation. The frequency increases almost linearly with $Re$ (Strouhal number close to $1$) even when contact with the walls occurs; it increases with the diameter of the cylinder and decreases with its density. [Preview Abstract] |
Tuesday, November 24, 2009 8:39AM - 8:52AM |
MQ.00004: Transient growth in Core-Annular Flow Gennaro Coppola, Annagrazia Orazzo, Luigi De Luca The classical problem of the stability of Core-Annular Flow (CAF) in pipes is here reconsidered from the point of view of linear non modal analysis. An accurate Chebyshev pseudospectral code in polar coordinates has been developed in order to separately discretize the two phases of the flow. The classical tools of non modal analysis have been employed in order to assess the effects of non normality on transient evolution of small perturbations to core-annular base flow. Linear transient growths of three dimensional perturbations are computed for typical potentially stable configurations, by taking into account the effects of viscosity and volume ratios between the two liquids, as well as of Reynolds number and surface tension. A detailed numerical investigation has been conducted on wide regions of the parameters space and the occurrence of substantial transient growth has been found for asymptotical stable configurations. Optimal perturbations for the most critical parameters have been determined and their structure during the unsteady evolution has been considered. It is found that in situations in which axisymmetric modes of disturbance are expected to constitute the most dangerous ones, in subcritical conditions spiral disturbances can provide higher levels of energy amplification. [Preview Abstract] |
Tuesday, November 24, 2009 8:52AM - 9:05AM |
MQ.00005: The Effect of Brownian Motion of Nano-Catalysts on the Stability of Reactive Fronts in Porous Media Karim Ghesmat, Hassan Hassanzadeh, Jalal Abedi, John Chen The reactive flows in porous media that involve the displacement of fluids by different physical properties may lead to a hydrodynamic instability. The use of nano-particles as catalysts in porous media has recently been increased and is generally relevant to applications that include \textit{in-situ} heavy oil upgrading and removal of reactive and non-reactive pollutants in groundwater. The objective is to investigate the effects of \textit{nano-catalysts} and \textit{chemical} \textit{reactions} on this instability. In order to understand the physics of this flow displacement, the basic equations of conservation of mass and momentum are linearized and solved numerically for a homogenous porous medium. The analysis reveals that increasing the reaction rate enhances the instability around an interface including nano-catalysts while increasing the nano-catalysts deposition rate in porous media usually stabilizes the front. The effects of the interface sharpness, nano-particle diffusion coefficient, permeability of porous media, and viscosity ratios of different phases will also be discussed. [Preview Abstract] |
Tuesday, November 24, 2009 9:05AM - 9:18AM |
MQ.00006: Experiments on two- and three-dimensional vortex flows in lid-driven cavities Tanja Siegmann-Hegerfeld, Stefan Albensoeder, Hendrik C. Kuhlmann Vortex flows in one-sided lid-driven cavities with different cross-sectional aspect ratios ($\Gamma $ = 0.26 up to $\Gamma $ = 6.3) are investigated experimentally. In all cases the spanwise aspect ratio $\Lambda >>\Gamma $ is very large and much larger than most previous experiments. Flow-structure visualizations will be presented together with quantitative LDA and PIV measurements. The experimental results are in good agreement with the critical data from numerical stability analyses and with nonlinear simulations. Experimentally, we find four different three-dimensional instabilities. Particular attention is paid to the so-called C$_{4}$ mode which arises at large cross-sectional aspect ratios. When the spanwise aspect ratio is small the first bifurcation of the C$_{4}$ mode is strongly imperfect. [Preview Abstract] |
Tuesday, November 24, 2009 9:18AM - 9:31AM |
MQ.00007: Thickness dependence of drag and kinematic viscosity in quasi-two-dimensional flows Paul W. Fontana, Edward Titmus, Adrian Kirn In many experimental and natural quasi-two-dimensional (Q-2D) flows the effects of internal viscosity and surface friction are significant but difficult to distinguish. We have made precise, independent measurements of both kinematic viscosity and coefficient of external drag as functions of film thickness in a Q-2D experiment using soap films in a circular Couette cell configuration, using a combination of vortex decay rates and steady-state shear lengths. Both the kinematic viscosity and the drag coefficient are found to depend inversely on film thickness, as expected theoretically. This result is enabling quantitative experimental study of stability thresholds in Q-2D basic flows. [Preview Abstract] |
Tuesday, November 24, 2009 9:31AM - 9:44AM |
MQ.00008: The structure of the transition boundary for shear flows Norman Lebovitz The shape and properties of the basin of attraction of the stable laminar point is investigated for finite-dimensional models of shear flows. In some of these models, the basin boundary is the stable manifold of an equilibrium point Xlb, the lower-branch point. As parameters change, the boundary undergoes a topological change at which a periodic orbit P emerges via a homoclinic bifurcation, and thereafter the major part of the basin boundary coincides with the stable manifold of P. The stable manifold of Xlb is then detectable only as an ``edge,'' i.e., the boundary between sets having different relaminarization properties. Implications for the nature of the edge are discussed. [Preview Abstract] |
Tuesday, November 24, 2009 9:44AM - 9:57AM |
MQ.00009: The Formation of Packets of Hairpins in Shear Flows Jacob Cohen, Michael Karp, Ilia Shukhman In the present work we utilize a recently developed new method in an attempt to understand the generation of packets of hairpin vortices from a pair of counter rotating streamwise vortices embedded in uniform shear flow. This analytical-based solution method is capable of following (numerically) the evolution of finite-amplitude localized vortical disturbances embedded in shear flows. Due to their localization in space, the surrounding base flow is assumed to have homogeneous shear to leading order. The method can solve in a novel way the interaction between a general family of unbounded planar homogeneous shear flows and any localized disturbance. The solution is carried out using Lagrangian variables in Fourier space which is convenient and enables fast computations. The revealed mechanism for generation of packets of hairpins seems to be universal and has been observed in the past both in fully developed wall-bounded shear flows as well as in wall-bounded transitional shear flows. [Preview Abstract] |
Tuesday, November 24, 2009 9:57AM - 10:10AM |
MQ.00010: Lock exchange and autocatalytic reaction front Ibrahim Bou Malham, Nolwenn Jarrige, Jerome Martin, Nicole Rakotomalala, Laurent Talon, Dominique Salin Lab FAST, UPMC Paris6 UPS Paris11 and CNRS, Bat. 502, Orsay, F-91405, France. Viscous lock-exchange is the reciprocal exchange of two fluids of different density in a horizontal channel: the front between the two fluids spreads as the square root of time with a diffusion coefficient reflecting the buoyancy, viscosity and geometry of the current. Iodate Arsenous Acid (IAA) autocatalytic reaction front between reactant and product propagates as solitary waves (constant velocity and stationary concentration profile) resulting from a balance between molecular diffusion and chemical reaction. The fluid left behind the front has a different density leading to a lock-exchange configuration. We revisit, with chemical reaction, the lock exchange situation. We present an experimental analysis of buoyancy effects on IAA reaction fronts, propagating in horizontal rectangular channels of different aspect ratio. We observe stationary-shaped fronts, spanning the height of the cell and propagating along the cell axis. As the result of the data analysis, we find out that the product of the front velocity times its extension is nothing but the diffusion coefficient of the lock-exchange in the absence of chemical reaction. The analysis accounts for results in other geometries and for other chemical reactions. [Preview Abstract] |
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