The scenario of two-dimensional instabilities of the cylinder wake under EHD forcing: A linear stability analysis

We propose to study the stability properties of an air flow wake forced by a dielectric barrier discharge (DBD) actuator, which is a type of electrohydrodynamic (EHD) actuator. These actuators add momentum to the flow around a cylinder in regions close to the wall and, in our case, are symmetrically disposed near the boundary layer separation point. Since the forcing frequencies, typical of DBD, are much higher than the natural shedding frequency of the flow, we will be considering the forcing actuation as stationary. In the first part, the flow around a circular cylinder modified by EHD actuators will be experimentally studied by means of particle image velocimetry (PIV). In the second part, the EHD actuators have been numerically implemented as a boundary condition on the cylinder surface. Using this boundary condition, the computationally obtained base flow is then compared with the experimental one in order to relate the control parameters from both methodologies. After validating the obtained agreement, we study the Hopf bifurcation that appears once the flow starts the vortex shedding through experimental and computational approaches. For the base flow derived from experimentally obtained snapshots, we monitor the evolution of the velocity amplitude oscillations. As to the computationally obtained base flow, its stability is analyzed by solving a global eigenvalue problem obtained from the linearized Navier–Stokes equations. Finally, the critical parameters obtained from both approaches are compared

A systematic numerical study of the tidal instability in a rotating triaxial ellipsoid

The full non-linear evolution of the tidal instability is studied numerically in an ellipsoidal fluid domain relevant for planetary cores applications. Our numerical model, based on a finite element method, is first validated by reproducing some known analytical results. This model is then used to address open questions that were up to now inaccessible using theoretical and experimental approaches. Growth rates and mode selection of the instability are systematically studied as a function of the aspect ratio of the ellipsoid and as a function of the inclination of the rotation axis compared to the deformation plane. We also quantify the saturation amplitude of the flow driven by the instability and calculate the viscous dissipation that it causes. This tidal dissipation can be of major importance for some geophysical situations and we thus derive general scaling laws which are applied to typical planetary cores

Frequency selection in time-dependent open flows

This paper studies the process by which open flows select a global frequency of oscillation. Two model systems are presented: the canonical flow past a circular cylinder; and the flow over an open rectangular cavity. The method used is a global linear stability analysis of the time-mean flow. For both the model systems, this method is shown to very accurately capture the saturated global frequency of the flow, even at Reynolds numbers far beyond that at which the flow becomes unsteady. Additionally, the time-mean flow in both systems is shown to be close marginally stable over a wide range of Reynolds numbers, an important finding in the effort to understand the nonlinear saturation process

Active control of flow-induced vibration from bluff-body wakes: the response of an elastically-mounted cylinder to rotational forcing

This paper investigates the flow past an elastically-mounted cylinder, constrained to oscillate in the cross-stream direction, which is then externally forced to perform rotational oscillations. The motivation for this study is the enhancement of crossstream oscillations of the body. These oscillations can be used to drive a generator, and therefore used as a renewable energy technology. More generally, this forcing is treated as an openloop control strategy of the wake and the resulting cylinder oscillations. The system tested is such that its natural structural frequency, fn, is close to the vortex shedding frequency from a stationary cylinder. This means that with no forcing, the cylinder oscillations, and the periodic vortex shedding that characterizes the wake, are synchronized. Numerical simulations have been conducted for a range of forcing frequencies fn/2leqslant fd 6 2 fn, and the effect of the forcing on this base, synchronized case determined. It is shown that the forcing can significantly increase the peak oscillation amplitude, and that the wake and cylinder cross-stream oscillation remains synchronized to the rotational driving over a significant range of driving frequencies. Outside of this synchronized range, the flow is shown to be typically quasiperiodic, with modulated oscillations around the system natural structural frequency

Modelling vortex-induced vibration with driven oscillation

Two-dimensional simulations of flow past an elastically mounted cylinder, and flow past an externally driven oscillating cylinder were performed at a Reynolds number of 200. The results of both are compared to see if the driven oscillation could model the coupled fluid-structure flow of the elastically mounted cylinder. The driven system could model the elastically mounted system, but was very sensitive to input parameters. We argue that this sensitivity could cause experimental discrepancies between the two systems

Cylinder wake destabilisation due to elastic mounting

Abstract not availabl

The beginning of branching behaviour of vortex-induced vibration during two-dimensional flow

To date, the majority of studies of vortex-induced vibration (VIV) of a cylinder constrained to oscillate transverse to the freestream have been experimental, and at a Reynolds number, Re, where the flow is inherently three-dimensional. At these higher Re, an upper and lower branch of response are observed. Mostly, these branches have not previously been investigated at lower Re where the flow is two-dimensional. Therefore, two-dimensional simulations have been performed at Re = 200 to thoroughly investigate the response of a cylinder to VIV. It was found that two regimes of response were present, similar in nature to the upper and lower branch at higher Re. While some differences were present, it was found that the genesis of the higher-Re flow behaviour was present in the low-Re two-dimensional flow, with evidence for this found in the amplitude, frequency and phase response of the cylinder

A numerical study of global frequency selection in the time-mean wake of a circular cylinder

A series of direct numerical simulations, both in two- and three-dimensions, of the flow past a circular cylinder for Reynolds numbers Re <= 600 has been conducted. From these simulations, the time-mean (and, for the three-dimensional simulations, the spanwise spatial-mean) flow has been calculated. A global linear stability analysis has been conducted on these mean flows, showing that the mean cylinder wake for Re <= 600 is marginally stable and the eigenfrequency of the leading global mode closely predicts the eventual saturated vortex shedding frequency. A local stability analysis has also been conducted. For this, a series of streamwise velocity profiles has been extracted from the mean wake and the stability of these profiles has been analysed using the Rayleigh stability equation. The real and imaginary instability frequencies gained from these profiles have then been used to find the global frequency selected by the flow using a saddle-point criterion. The results confirm the success of the saddle-point criterion when the mean flow is quasi-parallel in the vicinity of the saddle point; however, the limitations of the method when the mean flow exhibits higher curvature are also elucidated