Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session M30: Instability: General V - Elastic and Pulsating Flows |
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Chair: Tareneh Sayadi, Ecole Polytechnique Room: 408 |
Tuesday, November 26, 2013 8:00AM - 8:13AM |
M30.00001: Saffman-Taylor Instability for a non-Newtonian fluid Prabir Daripa Motivated by applications, we study classical Saffman-Taylor instability involving displacement of an Oldroyd-B fluid displaced by air in a Hele-Shaw cell. The lubrication approximation is used by neglecting the vertical component of the velocity. We obtain an explicit expression of one of the components of the extra-stress perturbations tensor in terms of the horizontal velocity perturbations. The main result is an explicit formula for the growth constant (in time) of perturbations, given by a ratio in which a term depending on the relaxation and retardation (time) constants appears in the denominator of the ratio. This exact result compares extremely well with known numerical results. It is found that flow is more unstable than the corresponding Newtonian case. This is a joint work with Gelu Pasa. [Preview Abstract] |
Tuesday, November 26, 2013 8:13AM - 8:26AM |
M30.00002: Influence of Fluid, Solid, and Geometric Parameters on the Fluid-Structure Interaction Response and Stability of Flexible Lifting Surfaces Eun Jung Chae, Deniz Tolga Akcabay, Yin Lu Young There is an increasing interest to use innovative passive/active flexible lifting surfaces to take advantage of the fluid-structure interaction (FSI) response to improve performance or harvest energy. However, design and testing of flexible lifting surfaces are quite complicated, particularly for lightweight structures in a dense, viscous fluid. The objectives of this work are to (1) investigate the influence of varying fluid, material, and geometric parameters on the FSI response and stability boundaries, and (2) to develop generic parametric maps to facilitate the design of flexible lifting surfaces In particular, the focus is on the influence of solid-to-fluid density ratio, Reynolds number, relative stiffness ratio, and relative excitation frequency ratio on the FSI response and static/dynamic divergence and flutter stability boundaries. The results show that the governing failure mode transitions from flutter to dynamic divergence to static divergence when the solid-to-fluid added mass ratio decreases. In addition, classic linear potential theory is severely under-conservative in predicting the flutter boundary, and cannot predict the transition to dynamic divergence for cases in the low mass ratio regimes due to the strong nonlinear, viscous FSI response that develops when the fluid forces are comparable or greater than the solid forces. [Preview Abstract] |
Tuesday, November 26, 2013 8:26AM - 8:39AM |
M30.00003: Stability theory for the synchronized waving of marine grass Ravi Singh, Shreyas Mandre, Amala Mahadevan, L. Mahadevan, Mahesh Bandi Synchronized waving of grass blades in the presence of fluid flow has been observed in cases such as wheat field in wind, marine grass in tidal currents. The synchronous motion can have important environmental and ecological impact via mixing of fluid due to waving. When the hydrodynamic and elastic time scales are well separated, this waving is the manifestation of a shear instability. We extend the Orr-Sommerfeld equation for the stability of a shear flow to include a continuum mean-field approximation for the vegetation, thus capturing the essential ingredients for waving. Our model exhibits an hydrodynamic instability due to different amounts of drag experienced by fluid with in and above the grass. We will also present some numerical results exhibiting existence of a threshold flow speed for waving, which have been observed in case of submerged marine vegetation [Preview Abstract] |
Tuesday, November 26, 2013 8:39AM - 8:52AM |
M30.00004: Travelling waves and fold localization in hovercraft seals Andrew Wiggins, Steve Zalek, Marc Perlin, Steve Ceccio The seal system on hovercraft consists of a series of open-ended fabric cylinders that contact the free surface and, when inflated, form a compliant pressure barrier. Due to a shortening constraint imposed by neighboring seals, bow seals operate in a post-buckled state. We present results from large-scale experiments on these structures. These experiment show the hydroelastic response of seals to be characterized by striking stable and unstable post-buckling behavior. Using detailed 3-d measurements of the deformed seal shape, dominant response regimes are identified. These indicate that mode number decreases with wetted length, and that the form of the buckling packet becomes localized with increased velocity and decreased bending stiffness. Eventually, at a critical pressure, travelling waves emerge. To interpret the wide range of observed behavior, a 2-d nonlinear post-buckling model is developed and compared with the experimental studies. The model shows the importance of seal shortening and the buckling length, which is driven by the balance of hydrodynamic and bending energies. Preliminary scaling laws for the fold amplitude and mode number are presented. The experiments may ultimately provide insight into the bedeviling problem of seal wear. [Preview Abstract] |
Tuesday, November 26, 2013 8:52AM - 9:05AM |
M30.00005: Geometric scaling of purely elastic instability in viscoelastic Taylor-Couette flow Christof Schaefer, Alexander Morozov, Christian Wagner The behavior of viscoelastic Taylor-Couette flow, the flow of, e.g., a polymeric fluid between two concentric, rotating cylinders, has been extensively investigated for many years in experiments as well as in theory. In the most simple case of an outer beaker at rest and a rotating inner cylinder with radii $R_2$ and $R_1$, respectively, even at negligible Taylor number $Ta=2 \mathrm{Re}^2(R_2-R_1)/R_1$, the circular Couette (base) flow gets linearly unstable at a critical Weissenberg number $Wi_c=\lambda \dot\gamma$, the product of the characteristic polymer relaxation time $\lambda$ and the (critical) shear rate $\dot\gamma_c$. This non-inertial transition to complex flow patterns is purely elastic by nature and the dimensionless criterion by P. Pakdel and G.H. McKinley (JNNFM 67 (1996)) gives a simple, critical condition for its onset. It pictures the competition between viscous shear and elastic normal stresses as well as the influence of polymer relaxation length and curvature of the streamlines. We present a comparative study of the explicit curvature scaling of the onset of elastic instability in the Taylor-Couette flow, including experimental data as well as linear stability analyses and theoretical examinations. [Preview Abstract] |
Tuesday, November 26, 2013 9:05AM - 9:18AM |
M30.00006: ABSTRACT WITHDRAWN |
Tuesday, November 26, 2013 9:18AM - 9:31AM |
M30.00007: ABSTRACT WITHDRAWN |
Tuesday, November 26, 2013 9:31AM - 9:44AM |
M30.00008: Transition to turbulence in pulsating pipe flow Bjorn Hof, Sascha Warnecke, Duo Xu We report an experimental study of the transition to turbulence in a pulsating pipe flow the most important example of pulsating flows is the cardiovascular system where the onset of fluctuations and turbulence can be a possible cause for various diseases such as the formation of aneurysms. The present study is limited to a straight rigid pipe, sinusoidal modulation of the flow rate and a Newtonian fluid. The dimensionless parameters (Womersley and Reynolds numbers) were chosen to include the parameter range encountered in larger arteries. We observe that at large frequencies the critical point for the onset of turbulence remains completely unaffected by pulsation for all amplitudes investigated (up to 40{\%}). However for smaller frequencies (Womersley numbers below 10) the critical point considerably increases. Furthermore we investigate how the transition scenario is affected for a fixed frequency and increasing amplitudes (approaching oscillatory flow). [Preview Abstract] |
Tuesday, November 26, 2013 9:44AM - 9:57AM |
M30.00009: Linear stability analysis of pipe Poiseuille flow for an Oldroyd-B fluid Armandojanni Petrucci Orefice, Gennaro Coppola, Luigi de Luca The effects of viscoelasticity on the linear evolution of disturbances on pipe Poiseuille flow are numerically investigated. The viscoelastic fluid is described by the Oldroyd-B model and the work primarily focuses on high Reynolds numbers flows of diluted solutions. The equations governing both flow and elastic variables are written in polar coordinates and are discretized by an accurate Chebyshev pseudospectral code. Both linear modal and non modal stability properties of infinitesimal disturbances are considered. The eigenvalue spectrum of the governing operator and linear transient growth of three dimensional perturbations are determined and the results are compared to analogous classical results for pipe Poiseuille flow. Non modal analysis reveals that elasticity is generally active in reducing the transient growth at high values of streamwise wave number. [Preview Abstract] |
Tuesday, November 26, 2013 9:57AM - 10:10AM |
M30.00010: A Theoretical and Numerical Study of Flexible Flapping Dynamics in a Uniform Flow Rajeev Jaiman, Pardha Gurugubelli, Jie Liu This work presents a numerical and theoretical study of fluid-elastic instability exhibited by a linear elastic plate immersed in a mean flow. Using the Euler-Bernoulli model for the plate and a 2D viscous potential flow model, a generalized closed-form expression of added-mass force has been derived for a flexible plate oscillating in fluid. We present an analytical formulation for predicting critical velocity for the onset of flapping instability. In the second part, a high-order finite element one-field scheme is employed for simulating flapping motion of a thin flexible body in a uniform flow with strong added-mass effects. Through our direct fluid-structure simulations, we study flapping results for a wide range of mass ratios and varying Reynolds numbers while maintaining relatively low bending rigidity. As a function of mass ratio, the flapping dynamics reveals three distinct regimes: fixed-point stability, limit-cycle flapping, and chaotic flapping. The changes associated with regime transition with increasing mass ratio are analyzed by vortex wake patterns, tip displacements, and force coefficients. Dependencies of stability predicated by the theoretical analysis are confirmed by the nonlinear fluid-structure simulations. [Preview Abstract] |
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