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 M10: Instability: General III - Stratified and Planar Flow, Cavity Flow and Periodic Orbits |
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Chair: Rama Govindarajan, Tata Institute of Fundamental Research Room: 334 |
Tuesday, November 26, 2013 8:00AM - 8:13AM |
M10.00001: Self-Sustained Oscillations of Flow Past Sequential Cavities: Effects of Gravity Wave Coupling Burak A. Tuna, Donald Rockwell Shallow flow past successive cavities can lead to highly coherent oscillations, due to coupling between: the inherent instability of the separated shear layer along the opening of each cavity; and a gravity standing wave mode within the cavity. As the flow velocity is varied, this coupling is associated with different orientations of the gravity standing wave, i.e., it can occur in either the transverse or the streamwise direction. The flow structure along the separated shear layer and within the cavity is, in turn, a strong function of the orientation and phase of the standing wave. When the oscillation amplitude of the coupled instability- cavity mode becomes large, as indicated by the amplitude of deflection of the free-surface, enhanced coherence and scale of the phase-averaged vortex formation occurs in the separated shear layer along the opening of the cavity. This coherent vortex formation results in a large increase in the magnitude of the turbulent shear stresses in the separated shear layer and, as a consequence, an increase of the time-averaged exchange velocity and mass exchange coefficient along the opening of the cavity. Furthermore, the flow structure and mass exchange along each of the sequential cavities may be either substantially different or very similar, depending on the orientation and phase of the gravity standing wave within the cavity, that is, a streamwise-oriented versus a transverse-oriented gravity standing wave, as well as the phase shift of the oscillations occurring in adjacent (sequential) cavities. [Preview Abstract] |
Tuesday, November 26, 2013 8:13AM - 8:26AM |
M10.00002: Fast and slow transition to turbulence in plane Poiseuille flow Bruno Eckhardt, Stefan Zammert Plane Poiseuille flow has two paths to turbulence: a slow one connected with a linear instability to Tollmien-Schlichting waves at Reynolds numbers above 5772, and a fast one through a by-pass transition at much lower Reynolds numbers. We explore the conditions for the two transition scenarios and their connections in the state space of the system by tracking the time evolution of different perturbations, i.e. we use the edge tracking algorithm for the identification of edge states (PRL 96, 174101 (2006)). We identify the two travelling waves that govern the transition process and study their subcritical bifurcations. The fast transition is realized for a large set of initial conditions as soon as it appears. The slow transition process first appears in a very thin slice that grows with Reynolds number but becomes noticeable only shortly before the linear instability. Both transition paths are shown to converge to the same turbulent state. [Preview Abstract] |
Tuesday, November 26, 2013 8:26AM - 8:39AM |
M10.00003: Stability Analysis of High-Speed Cavity Flow Yiyang Sun, Kunihiko Taira, Louis Cattafesta, Guillaume Bres, Lawrence Ukeiley Stability analysis is conducted to uncover the inherent instabilities in subsonic to supersonic open cavity flows. Two- and three-dimensional direct numerical simulations of spanwise periodic cavity flows are performed with the high-fidelity compressible flow solver ``Charles'' developed at Cascade Technologies. Two-dimensional nonlinear computations are carried out to characterize the flow stability over a wide range of Mach numbers and Reynolds numbers, and to extract a base flow for three-dimensional linear stability analysis. Selective frequency damping method is used to solve for the steady state for cases where the flow is found to be unstable. Both stable and unstable two-dimensional steady state can then be used as base state to examine, in the linear limit, how instabilities grow in space and over time. The present study forms a foundation to pursue three-dimensional flow control in which the spanwise instability will be exploited to redistribute kinetic energy from large spanwise vortices to reduce load fluctuations within the cavity. [Preview Abstract] |
Tuesday, November 26, 2013 8:39AM - 8:52AM |
M10.00004: Unstable periodic orbits in a homogeneous shear flow Atsushi Sekimoto, Siwei Dong, Javier Jim\'enez Unstable periodic orbits (UPOs) are numerically obtained by a Newton-Krylov method in a homogeneous shear flow. The two classes of UPOs have a box-time period synchronized with that of the boundary condition, which is shear-periodic between shifting points of the upper and bottom boundaries of the computational box. The first one is characterized by the shift-reflection symmetry, and by staggered streamwise-inclined vortex pairs, as in Nagata's Couette equilibrium solution ({\it JFM} 217, 519-527 (1990)). The second is characterized by the mirror symmetry in the spanwise direction, similar to Townsend's sketch of a inclined double-roller eddy ({\it JFM} 41, 13-46 (1970)). It is revealed that the lower branch of the mirror-symmetric UPO has an important role in the transition to turbulence, and is an ``edge-state'' on the basin boundary between laminar and turbulent states, whose two unstable directions lead to direct laminarization and to turbulence bursting. We also present subharmonic UPOs, whose periods are longer than the periodicity of the boundary condition. The dynamic UPO represents the breakdown and regeneration of streaks, associating with the streamwise-inclined vortices, which is similar to the self-sustaining process in wall-bounded flows. [Preview Abstract] |
Tuesday, November 26, 2013 8:52AM - 9:05AM |
M10.00005: Experimental Investigation of Fluid-Structure Interactions in Compressible Cavity Flows Justin Wagner, Katya Casper, Steven Beresh, Patrick Hunter, Russell Spillers, John Henfling, Randall Mayes Experiments were performed to understand the complex fluid-structure interactions that occur during internal store carriage. A cylindrical store was installed in a cavity having a length-to-depth ratio of 3.33 and a length-to-width ratio of 1. The Mach number ranged from 0.6 -- 2.5 and the incoming turbulent boundary layer thickness was about 30-40{\%} of the cavity depth. Fast-response pressure measurements provided aeroacoustic loading in the cavity, while triaxial accelerometers and laser Doppler vibrometry provided simultaneous store response. Despite occupying only 6{\%} of the cavity volume, the store significantly altered the cavity acoustics. The store responded to the cavity flow at its natural structural frequencies, as previously determined with modal hammer tests, and it exhibited a directional dependence to cavity resonance. Specifically, cavity tones excited the store in the streamwise and wall-normal directions consistently, while a spanwise response was observed only occasionally. The streamwise and wall-normal responses were attributed to the known pressure gradients in these directions. Furthermore, spanwise vibrations were greater at the downstream end of the cavity, attributable to decreased levels of flow coherence near the aft-wall. [Preview Abstract] |
Tuesday, November 26, 2013 9:05AM - 9:18AM |
M10.00006: The genesis of streamwise-localized solutions from globally periodic travelling waves in pipe flow Matthew Chantry, Ashley Willis, Rich Kerswell At intermediate Reynolds numbers, pipe flow exhibits spatio-temporal turbulence, where localized patches of turbulence may spread, split or decay. To construct a dynamical systems framework for this behaviour requires streamwise-localized solutions embedded within the turbulent dynamics. To date a single localized periodic orbit has been found, in contrast to the large number of known downstream-periodic solutions. Here we find the origin of this localized solution in a symmetry-breaking Hopf bifurcation from a known downstream periodic travelling wave. This bifurcation structure is found in a second symmetry subspace leading to new localized solutions. Our results indicate that localized versions of every downstream-periodic travelling wave should be expected. [Preview Abstract] |
Tuesday, November 26, 2013 9:18AM - 9:31AM |
M10.00007: Transient growth of 3D perturbations in a stratified mixing layer flow Helena Vitoshkin Three-dimensional non-modal disturbances growth in a stably stratified viscous mixing layer flow is studies. The research is performed in the framework of linearized equations using two indepndent approaches and then is verified by computational modeling of evolution of the optimal perturbations found via numerical solution of fully non-linear time-dependent Boussinesq equations. We examined the effect of stratification on linearly stable three-dimensional disturbance, which attains the largest non-modal amplification in the non-isothermal case. The transient strong amplification could be reached at short times by a 3D optimal perturbation, whose amplitude grows larger than those computed in the 2D case, even in cases of very strong stable stratification. This non-modal growth is governed mainly by the Holmboe modes, and does not necessarily weaken with increase of the Richardson number. [Preview Abstract] |
Tuesday, November 26, 2013 9:31AM - 9:44AM |
M10.00008: Linear optimal perturbations of a stratified shear layer Alexis Kaminski, John Taylor Stratified shear flows are ubiquitous features of the ocean and atmosphere, and a large literature is devoted to describing their stability and mixing properties. A classical example is the Kelvin-Helmholtz instability that is possible when the gradient Richardson number is less than $1/4$ somewhere in the flow. Here, we use numerical simulations to seek the three-dimensional ``optimal perturbations'' which maximize the growth of perturbation energy over a finite time interval $T$. In the limit of a long time interval, we expect to recover the fastest growing linear normal mode. However, for shorter time intervals, enhanced transient growth is possible due to the non-normality of the governing equations. The Reynolds, Richardson, and Prandtl numbers of the flow are varied in our analysis, and the resulting optimal perturbations compared to predictions from theory and past work. Enhanced growth rates are observed for short times in both the linearly stable (i.e. $\mathrm{Ri}>1/4$) and unstable cases, and the optimal perturbations found have more structure than the most unstable mode predicted by normal-mode stability theory. [Preview Abstract] |
Tuesday, November 26, 2013 9:44AM - 9:57AM |
M10.00009: Instability in viscosity-stratified free shear layer Kirti Sahu, Rama Govindarajan The stability of a mixing layer made up of two miscible fluids, with a viscosity-stratified layer between them, is studied. The two fluids are of the same density. It is shown that unlike other viscosity stratified shear flows, where species diffusivity is a dominant factor determining stability, species diffusivity variations over orders of magnitude do not change the answer to any noticeable degree in this case. Viscosity stratification, however, does matter, and can stabilize or destabilize the flow, depending on whether the layer of varying velocity is located within the less or more viscous fluid. This flow is a thus a prototype for a situation where viscosity stratification acts on the stability by an inviscid mechanism. This is confirmed by making an inviscid model flow with a slope change across the ``viscosity" interface. The absolute instability of the flow can also be significantly altered by viscosity stratification. [Preview Abstract] |
Tuesday, November 26, 2013 9:57AM - 10:10AM |
M10.00010: Absolute instability in viscoelastic mixing layers Prasun Ray, Tamer A. Zaki The linear stability of viscoelastic planar mixing layers is investigated. The influence of viscoelasticity in dilute polymer solutions is modeled with the Oldroyd-B and FENE-P constitutive equations, and we examine how flow and viscoelastic parameters influence the onset of local absolute instability. With the Oldroyd-B model, the influence of the polymer is destabilizing, and this effect is almost fully captured by an elasticity parameter. Results obtained with the FENE-P model exhibit a rich variety of behavior. At large values of the maximum polymer extensibility, L, results are similar to those for the Oldroyd-B fluid as expected. However, when L is reduced to more realistic values, one must consider the ratio We/L (where We is the Weissenberg number), in addition to the elasticity. When We/L is large, the base-state polymer stress obtained by the FENE-P model is reduced relative to the Oldroyd-B stress. As a result, the overall influence of viscoelasticity on stability is reduced. Additionally, elasticity exhibits a stabilizing effect. As We/L is reduced, the FENE-P base-state polymer stress increases towards the Oldroyd-B value, and the destabilizing influence of elasticity observed with the Oldroyd-B model is again present. [Preview Abstract] |
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