Session HE: Instability: Jets and Wakes II

Experimental Test of the Fluctuation Theorem in a Driven System

In systems that are far from equilibrium it is possible that the entropy fluctuations of the system are smaller than zero. This behavior is theoretically predicted by several fluctuation theorems. In our work we studied the motion of a falling disk in a gravity driven system. On average the fluid exerts a dissipative drag on the falling body. However, these forces are dynamic and lead to fluctuations in the kinetic energy of the disk. The resulting power fluctuations are of the same magnitude as the mean power dissipated by the fluid and can be large enough to cause the disk to move upward against the force of gravity. To test the influence of the Reynolds Number on the fluctuations we used disks of the same geometry but different densities. The relative probability of negative to positive entropy production rates is compared to theoretical predictions.   

Flow instabilities in the wake of a thin disk

Instabilities of the flow behind a thin disk were investigated. We are presenting systematic experiments with flow visualisation and PIV measurements in order to measure the velocity field in the wake of a disk in a water channel. The measurements were performed in the range of Reynolds numbers from 20 to 400, where stationary and oscillatory instabilities appear. From these experimental data, we are studying the azimuthally modal decomposition of the streamwise vorticity in an instationnary case, which allow us to describe the evolution of perturbations and obtain the bifurcation branches of the instabilities. In addition, some results were obtained from measurements of the transversal vorticity which allow to compare the evolution of the circulation. Finally, we are comparing these results with similar ones obtained in previous studies of the flow behind spheres.   

Experimental investigation of the influence of inlet conditions to a bluff body wake

Wind tunnel experiments have been performed in a bluff body wake with varying inlet conditions in order to enhance the physical understanding of the wake flow instability, which may lead to successful flow control and in turn reduced aerodynamic drag. The geometry consists of a rectangular-based forebody with permeable surfaces, an elliptic leading edge and a blunt trailing edge. Length, width and base height of the forebody is 2.3, 0.5 and 0.04 meters, respectively. Applying continuous suction or blowing, of different levels, through the permeable surfaces along the forebody, varies the wall-normal trailing edge velocity profile in a systematic way and hence the inlet condition to the wake. The streamwise velocity component has been measured both throughout the boundary layer and in the wake behind the body using hot-wire anemometry. High-speed stereo PIV has been used in the wake in order to collect statistics of vortical structures in the wake. The influence of boundary layer parameters on the wake flow characteristics, such as vortex shedding frequency and base pressure, will be presented.   

Parametric study of the transition in the wake of oblate spheroids and flat cylinders

Recently, the wake of a flat disk has regained the interest of researchers.\footnote{Fabre, Auguste and Magnaudet Physics of Fluids 20, 051702 (2008); Meliga, Chomaz and Sipp, J. Fluid Mech. 633, 159 (2009)} Simultaneously, some numerical simulations were concerned with cylindrical bodies of finite thickness and showed\footnote{Auguste, Fabre and Magnaudet, Theor. Comput. Fluid Dyn. 24, 305 (2010)} that the wakes of such bodies present a different scenario from that of a flat disk and that of a sphere (which is widely known and accepted\footnote{Bouchet, Mebarek and Du\v{s}ek, Eur. J. Mech. B/Fluids 25, 321 (2006)}). A systematic study covering the whole range of cylinders of aspect ratio (diameter/thickness) between one and infinity as well as a study concerning oblate spheroids which establishes the link between the wake of a sphere and that of an infinitely flat disk, which until now was missing, will be the topic of this communication. The state diagram obtained for oblate spheroids illustrating the transition between the scenario of a sphere wake and that of a flat disk will be presented and discussed.   

Stability effects of a base cavity on the wake of axisymmetric bluff bodies

We extend our previous research on the instability properties of the laminar incompressible flow around a cylindrical body with a rounded nose and length-to-diameter ratio $L/D=2$, at zero angle of attack, by analyzing the effects of a cylindrical base cavity of length $h$ and diameter $D_c$. We combine experiments, three-dimensional direct numerical simulations and a global linear stability analysis. The direct numerical simulations and the global stability results accurately predict the stabilizing effect of the cavity on the stationary, three-dimensional bifurcation in the wake as $h/D$ increases. In fact, it is shown that, for a given value of $D_c/D$, the critical Reynolds number for the steady bifurcation, $Re_ {cs}$, increases monotonically as $h/D$ increases, reaching an asymptotic value, that depends on $D_c/D$, at $h/D\approx$ 0.7. On the other hand, for a fixed value of $h/D$, $Re_{cs}$ exhibits a maximum at $D_c/D\approx$ 0.8. Similar behavior has been observed experimentally and numerically for the second, oscillatory bifurcation, and its associated critical Reynolds number, $Re_ {co}$.   

The influence of shear layer thickness in the stability of confined 2D wakes

The goal of this communication is to understand how the presence of a finite shear layer thickness in a confined wake modifies the stability properties of the flow. Two different approaches are used to illustrate its influence: a local stability analysis of a family of wakes introduced by Monkewitz (1988)\footnote{{\it Phys. Fluids}, {\bf 31}, 999-1006} and a nonlinear global analysis on several confined spatially evolving 2D wakes conducted by means of a spectral DNS code. Concerning the spatio-temporal analysis, we show that there exists, for any given confinement, an optimal value of the shear layer thickness for which the absolute instability is maximal. Using the DNS to compute the base flow, the local streamwise velocity distributions as well as the local value of shear layer thickness can be extracted as a function of the streamwise direction. The deduced local stability predictions are compared with the nonlinear stability properties of the flow for two values of the Reynolds number. Furthermore, the Strouhal numbers obtained from the DNS are compared to those predicted by the local analysis.   

Numerical and experimental analysis of the near wake flow over a square cylinder

The flow that develops behind a cylinder is very complex because it is fully three-dimensional, unsteady, including transition regions to turbulence as well as flow separations along the sidewall. The formation of a vortex street is generally considered to be the result of a coupling between KelvinHelmholtz instabilities within the separated shear layers and the Karman instability in the near wake. In the present paper we propose a joint experimental / numerical study in order to investigate the flow features in the near wall region of a square cylinder at Re = 21400 (ERCOFTAC benchmark). The interaction between KH vortical structures in the separating shear layer and Karman vortex shedding in the near wake will be discussed based on both visualisations and frequency analysis. In particular, the dependency with Reynolds number of the ratio from the shear layer frequency to the fundamental Karman frequency by Bloor (1964) will be investigated for the square cylinder. The controversial resulting square root law discussed by Rajagopalan and Antonia (2005) will be focused for the square cylinder case as well.   

Design of an End Plate to Promote Quasi-Two-Dimensionality in the Near-Wake of a Circular Cylinder

To design an end plate that attains nearly parallel vortex shedding from a circular cylinder with an aspect ratio of L/D = 12.3 at $Re_D =10,000$, effect of a rectangular end plate on spanwise flow uniformity is investigated experimentally. Experiments are carried out in a free-surface re-circulating water channel. At one end, the cylinder is bounded by the end plate; and at the other end, by the free surface. Leading edge distance of the end plate from the cylinder axis is varied from 0.5D to 7.0D by the repositioning of the cylinder. The spanwise flow structure on the plane of symmetry of the cylinder, coincident with its centerline, is determined via Particle Image Velocimetry (PIV). Spanwise distributions of streamwise and spanwise velocity contours on this plane are used for the quantitative determination of the degree of spanwise two-dimensionality. Our results indicate that the flow uniformity in the near-wake is highly dependent on the leading/trailing edge distances of the end plate from the cylinder centerline, and a leading edge distance of about 2.5D promotes the best distribution in terms of flow uniformity.   

Low-Reynolds numbers vortex-induced vibrations by means of asymptotic methods

We investigate the onset of vortex-induced vibrations in the wake of a spring-mounted circular cylinder by means of stability analyses and asymptotic methods. We carry out an expansion of the coupled flow-structure system, assuming that the Reynolds number departs from criticality at second order. The flow is forced by a third-order cylinder displacement under the form of an equivalent resonant blowing and suction velocity, applied at the wall of a virtually fixed cylinder. This imposes the classical compatibility conditions to be modified so as to encompass the effect of a resonant boundary condition. By analyzing the nonlinear dynamics of the associated limit cycles, we will show that the present model allows to recover the main phenomenology of vortex-induced vibrations, including subcritical vortex-shedding, lock-in and hysteretical behaviours. We will also use this model to assess the influence of the structural damping on the amount of energy that can be extracted from the flow and dissipated by the structure.   

Energy extraction from a low Reynolds-number-flow using vortex-induced vibrations and optimal control

The present work investigates the dynamics of a spring-mounted circular cylinder by focusing on the amount of energy that can be extracted from the flow when an appropriate forcing is applied, which is of practical interest when vortex-induced vibrations are thought to be used for energy production. The analysis relies on an asymptotic model developed at low Reynolds numbers, herein extended to encompass the effect of the forcing. In practice, we consider the case of an actuator prescribing a small, periodical blowing and suction velocity at the cylinder wall. We vary the structural damping and natural frequency of the cylinder, and characterize the dynamics of the forced, nonlinear limit cycles. We then evidence that the magnitude of extracted energy can be maximized using the framework of the optimal control theory, which relies on an iterative algorithm based on the repeated computation of adjoint fields. A physical interpretation for the optimal control will also be proposed, in terms of the cylinder displacement, velocity and acceleration.