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 L10: Instability: General II |
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Chair: Outi Tammisola, University of Cambridge Room: 334 |
Monday, November 25, 2013 3:35PM - 3:48PM |
L10.00001: Oscillations in Power and Structure During the Transition to Defect Turbulence Marcus Daum, Zrinka Greguric Ferencek, John Cressman Electroconvecting liquid crystals support a wide range of dynamics from ordered rolls to highly chaotic states characterized by the creation, interactions, and dissipation of defects. In addition to visual observations these systems also allow the direct measurement of the electrical power injected into them. Here we report on a remarkable phenomenon that occurs when a sample is abruptly driven from an ordered steady state to a complex driven state. During such transitions the system transiently maintains its ordered structure beyond the transition to defect dynamics. The order enables the system to absorb more and then less power than in the steady state. By simultaneously imaging the system and measuring the power injected into the system, we are able to investigate the relationship between defect dynamics, conductivity, and power injection in this system. [Preview Abstract] |
Monday, November 25, 2013 3:48PM - 4:01PM |
L10.00002: Numerical Simulation of Liquid Sheet Instability in a Multiphase Flow Domain Chatterjee Souvick, Soumik Mahapatra, Achintya Mukhopadhyay, Swarnendu Sen Instability of a liquid sheet leading to the formation of droplets is a classical problem finding a wide range of multi-scale applications like gas turbine engines and inkjet printers. Numerical simulation of such a phenomenon is crucial because of its cost and time effective nature. In this work, the hydrodynamics in a custom designed nozzle is analyzed using Volume of Fluid method in Ansys Fluent. This innovative nozzle design includes an annular liquid sheet sandwiched between two air streams such that the inner air channel is recessed to a certain length. Such a recession leads to interaction between the two multiphase streams inside the atomizer resulting to an increased shear layer instability which augments the disintegration process. The numerical technique employed in this work couples Navier Stokes equation with VoF surface tracking technique. A parametric study with the hydrodynamic parameters involved in the problem, as well as the recession length, is performed while monitoring the axial and tangential exit velocities along with the spray cone angle. Comparison between the full 3D model and two different equivalent 2D axisymmetric models have been shown. The two axisymmetric models vary based on conserving different physical parameters between the 2D and 3D cases. [Preview Abstract] |
Monday, November 25, 2013 4:01PM - 4:14PM |
L10.00003: A novel numerical approach and stability analysis of thermo-acoustic phenomenon in the Rijke tube problem Taraneh Sayadi, Vincent Le Chenadec, Peter Schmid, Franck Richecoeur, Marc Massot The modeling of thermo-acoustic coupling in reactive flows represents a challenging task. In this study, we focus on the Rijke tube problem, which includes relevant features such as a compact acoustic source, an empirical modeling of the heat source, and non-linearities. This thermo-acoustic system features a complex dynamical behavior, which renders the characterization of the different encountered flow regimes difficult. In order to synthesize accurate time series, we tackle this problem from a numerical point-of-view, and start by proposing a dedicated solver designed for dealing with the underlying stiffness, in particular, the retarded time and the discontinuity at the location of the heat source. Convergence and parametric studies are carried out to assess the accuracy of the discretization, hence laying a foundation for a stability analysis of the semi-discrete system. This stability analysis is performed by means of the projection method proposed by Jarlebring [1], which alleviates the linearization of the retarded term, and is used to validate the numerical results. Finally, the focus is set on the application of the dynamic mode decomposition [2] technique to study bifurcations.\\[4pt] [1] Jarlebring, E., Thesis, 2008\\[0pt] [2] Schmid P., JFM, 2010 [Preview Abstract] |
Monday, November 25, 2013 4:14PM - 4:27PM |
L10.00004: Nonlinear optimization of multiple perturbations and stochastic forcing of subcritical ODE systems Daniel Lecoanet, Rich Kerswell Subcritical transition between states has been proposed to explain a variety of phenomena, including transition to turbulence in shear flows, and the generation of a magnetic dynamo in accretion discs. These systems feature an easily specified linearly stable ``laminar'' equilibrium state, along with at least one other stable ``turbulent'' state. We present simple 2D ODE model systems with these features, and study how the systems react to different types perturbations. First, we extend variational techniques used to study transition to turbulence in shear flows (e.g. Pringle \& Kerswell 2010, Rabin et al 2012) to find the optimal (that is, closest to the ``turbulent'' state at late time) set of multiple perturbations, each occurring at a different time, that will cause a transition to the ``turbulent'' state. We find that some systems transition to the ``turbulent'' state much more easily with multiple perturbations than with a single perturbation. Second, we introduced random noise into the model systems, and determined the mean exit time from the attractor of the ``laminar'' state. We find that systems in which ``turbulence'' is more easily triggered by multiple perturbations have shorter mean exit times when subjected to noise. [Preview Abstract] |
Monday, November 25, 2013 4:27PM - 4:40PM |
L10.00005: Second-order sensitivity of eigenvalues: large or spanwise wavy perturbations Outi Tammisola, Flavio Giannetti, Vincenzo Citro, Matthew Juniper Sensitivity maps can be used to determine how the stability of a flow changes with control (by for example a control cylinder), or changes in the flow parameters. However, being linear with respect to the control parameter, the sensitivities can only represent the influence of small-amplitude control. More importantly, the sensitivities vanish for some important classes of perturbations, such as spanwise wavy base flow modifications. Spanwise wavy modifications can appear in a flow due to inflow asymmetry or streakiness. In flow control, spanwise wavy steady blowing and suction has been shown to suppress vortex shedding behind a cylinder in computations at Re=140 (Kim \& Choi, PoF 2005, 17, 033103). Sensitivities can be derived from a standard perturbation analysis. In this study, we generalize the sensitivities by considering the second-order term in the perturbation expansion. We derive some general insights about the effects of large and wavy base-flow modifications from an expansion in the eigenmode basis. As an example of the ``second-order sensitivity,'' we consider the effect of steady streakiness on the global instability of a backwards-facing step. [Preview Abstract] |
Monday, November 25, 2013 4:40PM - 4:53PM |
L10.00006: Unsteady engulfment regime in a three dimensional T-mixer: stability and sensitivity analyses Simone Camarri, Andrea Fani, Maria Vittoria Salvetti Micro T-mixers are important devices in microfluidics; for instance, they are often used as junction elements in complex micro-systems. Most of the studies in the literature focused their attention on the steady engulfment regime, characterized by a loss of the flow symmetries in the outflow channel which in turn leads to a considerable increase of the mixing efficiency. It has been recently observed that if the Reynolds number is increased beyond the steady engulfment critical value, the flow may become unsteady with a periodic pulsating behavior and this regime corresponds to a significant further increase of mixing compared to the steady one. We consider a given T-mixer geometry and we combine direct numerical simulations with fully 3D linear stability and sensitivity analyses to characterize the unsteady engulfment regime in terms of critical Reynolds number, characteristic time frequencies and flow dynamics. The unsteadiness seems to be triggered by a critical value for the intensity and orientation of vortices at the confluence in the mixing channel; the instability core is indeed located in the center of these vortices. The sensitivity to a generic modification of the base-flow is investigated, to obtain indications on possible control strategies. [Preview Abstract] |
Monday, November 25, 2013 4:53PM - 5:06PM |
L10.00007: Short-wave analysis of 3D and 2D instabilities in a driven cavity Paolo Luchini, Flavio Giannetti, Vincenzo Citro The short-wave asymptotic approximation of inviscid instabilities proposed by Bayly (\textit{Phys. Fluids} \textbf{31}, 1988) and Lifschitz \& Hameiri (\textit{Phys. Fluids A} \textbf{3}, 1991) is here applied to the dominant (three-dimensional) instability of two-dimensional flow in either an open or a closed driven cavity, and compared to the structural sensitivity obtained by direct-adjoint computation. The comparison shows that the structural sensitivity of the eigenmode is indeed localized around the critical streamline identified by short-wave asymptotics, and that the latter provides a reasonably good expression of even the first unstable eigenvalue at critical Reynolds number. Curiously enough, the same approximation appears also to apply with success to the two-dimensional instability of the same flow, despite the absence of a large spanwise wavenumber to be used as an expansion parameter. The theoretical justification of this extension, and the importance of phase quantization along the trajectory, will be discussed. [Preview Abstract] |
Monday, November 25, 2013 5:06PM - 5:19PM |
L10.00008: Effect of an axial flow on three-dimensional instabilities in Stuart vortices Manikandan Mathur, Sabine Ortiz, Thomas Dubos, Jean-Marc Chomaz In this talk, we present a stability analysis of the Stuart vortices in the presence of an axial flow by numerically solving the local stability equations derived by Lifschitz \& Haimeri (1991). Deriving the criteria for wave vectors to be periodic upon their evolution around flow trajectories that are periodic in a plane perpendicular to the axial direction, we integrate the amplitude equations around periodic trajectories for periodic wave vectors. The elliptic and hyperbolic instabilites, which are present without the axial velocity, disappear beyond a threshold value for the axial velocity strength. Furthermore, a threshold axial velocity strength, above which a new centrifugal instability branch is present, is identified. A heuristic novel criterion, which reduces to the Leibovich \& Stewartson (1983) criterion in the limit of an axisymmetric vortex, for centrifugal instability in a non-axisymmetric vortex with an axial flow is then proposed and validated. [Preview Abstract] |
Monday, November 25, 2013 5:19PM - 5:32PM |
L10.00009: The rich life of light rising spheres Jacques Magnaudet, Alice Lieu, Franck Auguste The straight path of spheres falling or rising in a weakly viscous fluid is known to become unstable beyond a critical value of the so-called Archimedes number Ar, a Reynolds number built on the gravitational velocity scale. Various styles of non-vertical paths have been reported so far: steady or oscillating oblique, planar zigzags, three-dimensional chaotic, etc. However despite careful computations and experiments, there is currently no consensus as regards the possible critical density ratio m* below which significant departures from straight (vertical or oblique) path are observed. To revisit this question, we carry out a detailed DNS study focused on rising spheres (m*\textless 1) in the range 150 $\le $ Ar $\le $ 350. Non-straight paths with significant horizontal excursions are observed throughout the whole range of m*. In addition to the various aforementioned types of paths we also identify other styles such as intermittent zigzagging/oblique paths and find that very light spheres describe highly nonlinear zigzags and have drag coefficients up to 15{\%} beyond standard values. [Preview Abstract] |
Monday, November 25, 2013 5:32PM - 5:45PM |
L10.00010: Stability of Resting Cylinders Cunjing Lu, Christophe Clanet, David Quere The capillary instability of a cylinder is a classical topic in the field of fluid interface. As experimentally found by Plateau, the instability happens if the ratio of the wavelength of an axisymmetric fluctuation to the initial diameter of the cylinder is larger than 3.14. We discuss how the fact that the cylinder rests on a superhydrophobic surface (which avoids stabilizing) pining effects modifies this picture. By employing a finite element method, we mainly conclude that: (1) the ratio of the wavelength to the width of the liquid cylinder increases as the liquid cylinders grow; (2) above a critical value $D_{\mathrm{c}}$ of the cylinder diameter, the instability disappears; (3) conversely, decreasing the cylinder diameter restores the instability, yet at a wavelength larger than the Plateau value. This is attributed to the loss of axisymmetry, and discussed more generally by considering the effect of confinement around the cylinder. [Preview Abstract] |
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