Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session BG: Instability: Jets and Wakes II |
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Chair: Mathew Juniper, University of Cambridge Room: Salt Palace Convention Center 250 A |
Sunday, November 18, 2007 10:34AM - 10:47AM |
BG.00001: Experiments on the global instability of confined axisymmetric dense wakes. Larry Li, Matthew Juniper Recent theoretical studies [M. Juniper, J. Fluid Mech. \textbf{565}, 171-195 (2006); M. Juniper and S. Candel, J. Fluid Mech. \textbf{482}, 257-269 (2003)] predict that confinement increases the hydrodynamic instability of wakes by causing the transition from convective to absolute instability to occur at lower values of shear. Experimental evidence supporting this prediction is presented here for a confined, axisymmetric wake at density ratios, $S \quad \equiv $ \textit{$\rho $}$_{1 }/$\textit{$\rho $}$_{2} \quad >$ 1 (i.e. dense wake). The wake was produced by a pair of convergent nozzles mounted concentrically, one within the other, in a low-turbulence wind tunnel facility. Variations in $S$ were achieved by employing two high density gases ($S$ = 1.53 and 5.11) in the inner flow with air in the outer flow. For a fixed $S$, there existed a critical value of shear above which dominant peaks appeared abruptly in the near-wake velocity spectra, as quantified by hot-wire anemometry. Corresponding high-speed video sequences revealed large-scale, sinuous wake motions. Results on the confined wake's response to externally-applied, acoustic forcing are also presented. The presence of discrete spectral peaks and coordinated instability oscillations suggests the emergence of a self-sustained, global mode. [Preview Abstract] |
Sunday, November 18, 2007 10:47AM - 11:00AM |
BG.00002: The effect of confinement on the absolute/convective stability of viscous jets and wakes Simon Rees, Matthew Juniper It has been shown recently that inviscid jets and wakes become more unstable when confined within a duct. This numerical study examines the effect of confinement on viscous jets and wakes. The numerical codes use polynomial spectral methods to solve for the equations of motion at a low computation cost, making investigation over a large range of parameter space feasible. Criteria for absolute or convective instability are found as a function of the Reynolds number, shear, shear layer thickness and confinement. The results at high Reynolds number match the inviscid case. As expected, decreasing the Reynolds number or increasing the shear layer thickness stabilizes the flow. It is not clear from previous studies whether confinement should have a stabilizing or destabilizing effect on viscous flows. However, this study shows conclusively that confinement enhances the absolute instability of viscous flows, as well as inviscid flows. [Preview Abstract] |
Sunday, November 18, 2007 11:00AM - 11:13AM |
BG.00003: Effect of viscosity on the stability of confined plane wakes Outi Tammisola, L. Daniel Soderberg, Fredrik Lundell Modern papermaking machines often separates different layers of fibres by vanes in the headbox. The wakes behind the vanes may introduce instabilities and thereby unwanted mixing between the layers. To be able to control such mixing the stability of confined two-dimensional streamwise developing wakes has been analysed. The analysis has been performed numerically using an ansatz assuming two-dimensional temporal global modes. Initially the results are compared to results found in literature that are based on an inviscid local analysis assuming uniform velocity layers. In the present work viscosity is taken into account both through its influence on the base- flow as well as in the stability analysis. This gives a Reynolds number as a third parameter in addition to the shear ratio and confinement relation that controls the inviscid problem. The viscous effects are found to be considerable and it is shown that the global stability is a function of Reynolds number. The most obvious reason seems to be the base flow development. The results also indicate that the effects of confinement can be both stabilizing and destabilizing depending on the Reynolds number. In addition, the development of the most unstable mode with Reynolds number for confined wakes is shown to be clearly different from that of unconfined wakes. [Preview Abstract] |
Sunday, November 18, 2007 11:13AM - 11:26AM |
BG.00004: Bifurcations and symmetry breakings in the wake of a disk David Fabre, Franck Auguste, Jacques Magnaudet We investigate by means of numerical simulations the wake of a circular flat disk. As for the related problem of a solid sphere, the flow experiences two successive bifurcations as the Reynolds number is increased. The first of these occurs for $Re \approx 115.5$ and breaks the axial symmetry, leading to a steady state with only a reflexional symmetry, characterised by the presence of a pair of counterrotating vortices and by the appearance of a constant lift force on the body. The second bifurcation occurs for $Re\approx 121.5$ and breaks the time invariance, leading to a periodic state. However, in contrast with the case of a sphere, this second bifurcation breaks the reflexional symmetry. The resulting state is fully three-dimensional, and the lift force exerted on the body oscillates in both amplitude and direction around a nonzero mean value. Then, a third bifurcation is observed for $Re \approx 139.5$, where the wake recovers a reflexional symmetry. In the resulting state the lift force oscillates around zero along a fixed direction. A model based on the normal form describing the interaction of a steady-state bifurcation and a Hopf bifurcation in presence of $O(2)$ symmetry is presented. This model allows us to reproduce the three successive bifurcations observed numerically, and to explain the differences with the case of a solid sphere. The application of this model to other cases of fixed or moving axisymmetric bodies will also be discussed. [Preview Abstract] |
Sunday, November 18, 2007 11:26AM - 11:39AM |
BG.00005: Linear Stability Analysis of a Variable-Density Jet Gregory Rodebaugh, Lester Su We investigate the instability properties of an incompressible, variable-density, axisymmetric jet. While there has been considerable interest in the role of density on stability properties, prior analyses typically rely on the Boussinesq approximation. Our study is not restricted by the use of this approximation, thereby allowing a full range of density profiles to be examined. Retaining density effects in the inertial terms allows consideration of realistic density profiles, incorporating large density variations, such as might occur in reacting flow systems. The jets in question here are nominally momentum-driven, and the imposed disturbances are spatially developing. Initial results show that the modification of the linear stability properties of the flow due to the density variations primarily arises in the inertial terms, rather than the buoyancy terms. We also make qualitative comparisons of the instability properties of the flow, determined numerically, with flow visualization results in the near-field of uniform-density and variable-density jets in the laboratory. [Preview Abstract] |
Sunday, November 18, 2007 11:39AM - 11:52AM |
BG.00006: Structural sensitivity of the finite-amplitude vortex shedding behind a circular cylinder Paolo Luchini, Flavio Giannetti, Jan Pralits Recirculating flows such as mixing layers, wakes and jets, may sustain synchronised periodic oscillations in a suitable parameter range. Under these conditions the whole flow field behaves like a global oscillator (``global mode''). A theoretical approach to this class of problems, in the context of weakly nonparallel quasi-onedimensional flows, was formulated by Chomaz, Huerre \& Redekopp (1991), Monkewitz, Huerre \& Chomaz (1993) and Le Diz\`es {\it et al.} (1996) who introduced the idea of a {\it wavemaker}. In the context of a fully twodimensional linear mode analysis of the wake behind a cylinder, a spatial visualisation of the {\it wavemaker} was obtained by Giannetti \& Luchini (2007), who determined the regions where the sensitivity of the frequency of oscillation to a localized feedback from velocity to force is maximal. In this contribution we apply a similar approach to nonlinear, finite-amplitude vortex shedding, in order to assess how unsteadiness and saturation modify the numerical results and how these compare to the predictions of the nonlinear weakly nonparallel theory. [Preview Abstract] |
Sunday, November 18, 2007 11:52AM - 12:05PM |
BG.00007: A Symmetric breaking hysteresis in a plane wake Guiren Wang, Hong Jiang We have observed a new phenomenon called symmetric breaking hysteresis. The flow is a confined plane wake in a pipe, i.e. the inlet of the pipe is a plane wake with adjustable initial mean flow velocity U$_{1}$ and U$_{2}$ respectively on each side of the splitter plate. When the forcing level is sufficiently high at low frequency, the wake becomes asymmetric to the trailing edge. Randomly one side has much higher turbulence than the other. When U$_{1}$ is at the side with lower turbulence and is gradually increased up to a critical value (thus the flow is no more a wake, but mixing layer), there is a sudden switch of the asymmetric flow: the side with lower turbulence and higher mean velocity now has higher turbulence than the other side (i.e. U$_{2})$. If U$_{1}$ is now reduced to the same value as U$_{2}$, no change in the flow can be observed. However, when U$_{1}$ is reduced to a critical value lower than U$_{2}$, the asymmetric flow suddenly switches again. In the whole process, no symmetric wake can be observed. This phenomenon of symmetric breaking hysteresis becomes weaker with the increase of the Reynolds number of the wake. Quantitative scalar measurement confirmed the visualization. [Preview Abstract] |
Sunday, November 18, 2007 12:05PM - 12:18PM |
BG.00008: Wake Behind a Sphere Second Bifurcation Konrad Gumowski, Jan Miedzik, Sophie Goujon-Durand, Patrice Jenffer, Gilles Bouchet, Jose-Euardo Wesfreid The objective was to study second transition phenomenon and to make transition between second and third regimes better known. We present in this communication very controlled experiments concerning second instabilities in the wake of the sphere. We discuss the first transition from homogenous flow to a stationary instability and we present original results about peristaltic instability preceeding the hairpins shedding. From our results we proposed now a new insight on the generation of hairpins-vortex shedding phenomena. We obtained a new scenario ``precursor'' of the hairpin vortex shedding, with a peristaltic instability of oscillations of the two parallel counter-rotating vortices behind a sphere. [Preview Abstract] |
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