Wake states and frequency selection of a streamwise oscillating cylinder

This paper presents the results of an in-depth study of the flow past a streamwise oscillating cylinder, examining the impact of varying the amplitude and frequency of the oscillation, and the Reynolds number of the incoming flow. These findings are presented in a framework that shows that the relationship between the frequency of vortex shedding fs and the amplitude of oscillation A* is governed by two primary factors: the first is a reduction of fs proportional to a series in A*2 over a wide range of driving frequencies and Reynolds numbers; the second is nonlinear synchronization when this adjusted fs is in the vicinity of N = (1 - fs/fd)-1, where N is an integer. Typically, the influence of higher-order terms is small, and truncation to the first term of the series (A*2) well represents the overall trend of vortex shedding frequency as a function of amplitude. However, discontinuous steps are overlaid on this trend due to the nonlinear synchronization. When fs is normalized by the Strouhal frequency fSt (the frequency of vortex shedding from an unperturbed cylinder), the rate at which fs/fSt decreases with amplitude, at least for fd/fSt = 1, shows a linear dependence on the Reynolds number. For a fixed Re = 175, the truncated series shows that the rate of decrease of fs/fSt with amplitude varies as (2 - fd/fSt)-1/2 for 1 < or egal fd/fSt < or egal 2, but is essentially independent of fd/fSt for fd/fSt < 1. These trends of the rate of decrease of fs with respect to amplitude are also used to predict the amplitudes of oscillation around which synchronization occurs. These predicted amplitudes are shown to fall in regions of the parameter space where synchronized modes occur. Further, for the case of varying fd/fSt, a very reasonable prediction of the amplitude of oscillation required for the onset of synchronization to the mode where fs = 0.5fd is given. In a similar manner, amplitudes at which fs = 0 are calculated, predicting where the natural vortex shedding is completely supplanted by the forcing. These amplitudes are found to coincide approximately with those at which the onset of a symmetric vortex shedding mode is observed. This result is interpreted as meaning that the symmetric shedding mode occurs when the dynamics crosses over from being dominated by the vortex shedding to being dominated by the forcing

A numerical study of an inline oscillating cylinder in a free stream

Simulations of a cylinder undergoing externally controlled sinusoidal oscillations in the free stream direction have been performed. The frequency of oscillation was kept equal to the vortex shedding frequency from a fixed cylinder, while the amplitude of oscillation was varied, and the response of the flow measured. With varying amplitude, a rich series of dynamic responses was recorded. With increasing amplitude, these states included wakes similar to the Kármán vortex street, quasiperiodic oscillations interleaved with regions of synchronized periodicity (periodic on multiple oscillation cycles), a period-doubled state and chaotic oscillations. It is hypothesized that, for low to moderate amplitudes, the wake dynamics are controlled by vortex shedding at a global frequency, modified by the oscillation. This vortex shedding is frequency modulated by the driven oscillation and amplitude modulated by vortex interaction. Data are presented to support this hypothesis

Streamwise forced oscillations of circular and square cylinders

The modification of a cylinder wake by streamwise oscillation of the cylinder at the vortex shedding frequency of the unperturbed cylinder is reported. Recent numerical simulations [J. S. Leontini, D. Lo Jacono, and M. C. Thompson, “A numerical study of an inline oscillating cylinder in a free stream,” J. Fluid Mech. 688, 551–568 (2011)] showed that this forcing results in the primary frequency decreasing proportionally to the square of the forcing amplitude, before locking to a subharmonic at higher amplitudes. The experimental results presented here show that this behavior continues at higher Reynolds numbers, although the flow is three-dimensional. In addition, it is shown that this behavior persists when the body is a square cross section, and when the frequency of forcing is detuned from the unperturbed cylinder shedding frequency. The similarity of the results across Reynolds number, geometry, and frequency suggests that the physical mechanism is applicable to periodic forcing of the classic von Ka ́rma ́n vortex street, regardless of the details of the body which forms the street

Modification of three-dimensional transition in the wake of a rotationally oscillating cylinder

A study of the flow past an oscillatory rotating cylinder has been conducted, where the frequency of oscillation has been matched to the natural frequency of the vortex street generated in the wake of a stationary cylinder, at Reynolds number 300. The focus is on the wake transition to three-dimensional flow and, in particular, the changes induced in this transition by the addition of the oscillatory rotation. Using Floquet stability analysis, it is found that the fine-scale three-dimensional mode that typically dominates the wake at a Reynolds number beyond that at the second transition to three-dimensional flow (referred to as mode B) is suppressed for amplitudes of rotation beyond a critical amplitude, in agreement with past studies. However, the rotation does not suppress the development of three-dimensionality completely, as other modes are discovered that would lead to three-dimensional flow. In particular, the longer-wavelength mode that leads the three-dimensional transition in the wake of a stationary cylinder (referred to as mode A) is left essentially unaffected at low amplitudes of rotation. At higher amplitudes of oscillation, mode A is also suppressed as the two-dimensional near wake changes in character from a single- to a double- row wake; however, another mode is predicted to render the flow three-dimensional, dubbed mode D (for double row). This mode has the same spatio-temporal symmetries as mode A

Three-Dimensional Transition in the Wake of an Ellipse

The transition to three-dimensional flow from the nominally two-dimensional Ka ́rma ́n vortex street in the wake of bluff bodies is a problem of fundamental importance as it marks the first step on the path towards fully developed turbulence. Here, this transition is studied in the wake of an elliptical cross-section using Floquet stability analysis. A number of modes of instability are identified as a function of the aspect ratio of the ellipse. Three-dimensional simulations confirm the importance of the identified instability modes

The flow around stationary and elastically-mounted circular cylinders in tandem and staggered arrangements

A numerical study is presented of the flow around two circular cylinders in tandem and staggered arrangements in a freestream, examining the fluid forces and vortex-shedding behaviour, as well as the oscillation of both cylinders when allowed to move and vibrate in response to the flow. The streamwise distance between the cylinder centres is 1.5 diameters, while the cross-stream offset is varied from 0.0 to 5.0. The Reynolds number, based on cylinder diameter, D, and freestream velocity, U, is 200. Reduced velocity, U∗ = U , where fN is the fND spring natural frequency, is varied from 0.0 to 14.0. Results are obtained using a sharp-interface immersed boundary finite- difference method. For the stationary cylinders a range of be- haviours are observed over the cylinder offset range, includ- ing a difference in primary vortex-shedding frequency when the crossstream offset is greater than 1.5D. For the elastic- mounting, in contrast to existing results in the literature, three modes of vortex-shedding and oscillation are observed over the U∗ range for the tandem arrangement. These modes are dis- tinct in the phase difference between the front and rear cylinder oscillation, as well as the number of vortices shed from each cylinder

Passive heaving of elliptical cylinders with active pitching – From cylinders towards flapping foils

This paper presents a study of the flow past elastically mounted cylinders with prescribed rotational oscillation about the cylinder centre, which are free to heave, or oscillate transverse to the flow. The configuration serves as an idealized model of a flapping-foil energy harvester. A range of geometries are tested, from the circular cylinder with an aspect ratio of 1.0 to elliptical cylinders up to aspect ratio of 6.0 approaching a flat plate. The driving frequency of the rotational oscillation is varied, while the amplitude of rotation is fixed at π/2, meaning both axes of the geometries present fully to the oncoming flow each cycle. The Reynolds number is 200. The natural frequency of the elastic-mounting is set to the Strouhal frequency for a circular cylinder. The ratio of the mass of the cylinder to the mass of the equivalent volume of displaced fluid is set to 5.0. Configurations with zero-damping reveal a rich parameter space, with increasing cross-stream oscillation with increasing geometry aspect ratio. Driving frequencies for peak oscillation amplitude are grouped around a driving frequency of 0.9 times the natural frequency of the elastic structure. The variation of the power input to actuate the rotational oscillation of the cylinder is also analysed. The fluid structure interaction is analysed for energy harvesting potential; power output is modelled by linear damping on the heave. Increasing the damping on the structure leads to optimal values of driving frequency and damping for each aspect ratio tested. For each aspect ratio, comparisons are drawn and similarities found between these optimal cases for power output and the undamped cases for maximum oscillation amplitude and velocity. The study of the parameter space serves as a useful starting point for further study of the many parameters affecting the performance of flapping-foil energy harvesting

Chaotic vortex induced vibrations

This study investigates the nature of the dynamic response of an elastically mounted cylinder immersed in a free stream. A novel method is utilized, where the motion of the body during a free vibration experiment is accurately recorded, and then a second experiment is conducted where the cylinder is externally forced to follow this recorded trajectory. Generally, the flow response during both experiments is identical. However, particular regimes exist where the flow response is significantly different. This is taken as evidence of chaos in these regimes

The flow-induced vibration of an elliptical cross-section at varying angles of attack

This paper presents a study of the flow-induced vibration of an elliptical cross section at various angles of attack immersed in a free stream. The body is elastically-mounted and constrained to move only in the cross-stream direction. Two-dimensional direct numerical simulations are used to study the system response as a function of the spring stiffness and the angle of attack. The elliptical cross section used has an aspect ratio Γ = 1.5. This aspect ratio is large enough so that the deformation from a circular cylinder is obvious, but not so large that the geometry is not related to the cylinder. Because of this, the impact of the symmetry of the system on the flow-induced vibration is studied without also introducing other complexities such as sharp corners or fixed separation points. The body is light with a mass ratio (body mass to displaced fluid mass) of one. The results show a surprisingly wide range of different flow regimes. For small angles (where the body is slightly streamlined) the flow behaviour is similar to that of a cylinder. However, for large angles, where the body is far from symmetric with respect to the wake centreline, the flow can be markedly different with distinct asymmetric modes, including one which is period-doubled. For angles where the body regains its symmetry (aligned across the flow and slightly bluff), an asymmetric mode continues to exist, apparently the result of a spontaneous symmetry breaking that is dependent on Reynolds number. Large- amplitude oscillations persist for very low stiffness or high reduced velocity, and this is explained in terms of the dependence of a critical mass on the angle of attack