Timing Of Vortex Shedding Research Articles

Lagrangian particle tracking velocimetry investigation of vortex shedding topology for oscillating heavy spherical pendulums underwater

The vortex shedding topology of a heavy pendulum oscillating in a dense fluid is investigated using time-resolved three-dimensional particle tracking velocimetry (tr-3-D-PTV). A series of experiments with eight different solid to fluid mass ratios $m^*$ in the range $[1.14, 14.95]$ and corresponding Reynolds numbers of up to $Re \sim O(10^4)$ was conducted. The period of oscillation depends heavily on $m^*$ . The relation between amplitude decay and oscillation frequency is non-monotonic, having a damping optimum at $m^* \approx 2.50$ . Moreover, a novel digital object tracking (DOT) method using vorticity-magnitude iso-surfaces is implemented to analyse vortical structures. A similar vortex shedding topology is observed for various mass ratios $m^*$ . Our observations show that first, a vortex ring in the pendulum's wake is formed. Soon after, the initial ring breaks down to two clearly distinguishable structures of similar size. One of the two vortices remains on the circular path of the pendulum, while the other detaches, propagates downwards, and eventually dissipates. The time when the first vortex is shed, and its initial propagation velocity, depend on $m^*$ and the momentum imparted by the spherical bob. The findings further show good agreement between the experimentally determined vortex shedding frequency and the theoretical vortex shedding time scale based on the Strouhal number.

Asymmetric wake, origin, generation, and suppression behind asymmetrically pitching hydrofoil

The wakes behind a symmetrically and a quasi-symmetrically pitching hydrofoil are numerically studied. To understand the generation mechanism of the asymmetric wake behind a symmetrically pitching hydrofoil, we shed light on the timing of vortex shedding and convection velocity of vortices in the wake. The centers of the vortices in the wake are tracked using a method based on the critical point theory. The tracks of the vortex centers reveal crucial insights into the dependence of the vortex convection velocity on pitching frequency and pitching amplitude. The vortex strength and the spatial separation between the vortices embody the wake deflection. We find the inherent inability of the shear-layer rolling up at par with the pitching motion results in an uneven temporal separation (Δtʹ) between two consecutive vortices, which dictates the spatial separation between the vortices. The uneven temporal separation facilitates formation of vortex dipoles, which gives rise to the asymmetric wake formation. To substantiate the hypothesis of the uneven temporal generation of vortices, we used quasi-symmetric pitching of the hydrofoil, which can even the timing of vortex shedding and can metamorphose the asymmetric wake into a symmetric wake. On the contrary, relaxing the shear-layer roll-up can transmute a symmetric wake to an asymmetric wake. The detailed analysis of symmetrically pitching hydrofoil, quasi-symmetrically pitching hydrofoil, flexible hydrofoil, and asymmetrically pitching hydrofoil reveals that Δtʹ = 0.5, Δtʹ < 0.5 and Δtʹ > 0.5 correspond to a symmetric wake, an upward deflected wake and a downward deflected wake, respectively.

Numerical simulation of surface roughness effects on the vortex-induced vibration of a circular cylinder at a subcritical Reynolds number

The Vortex-Induced Vibration (VIV) of a circular cylinder with different surface roughness is numerically simulated at a subcritical Reynolds number of 3900. The effects of surface roughness on the vibration response amplitude, hydrodynamic coefficients and wake vortex are analyzed. The results show that as surface roughness increases, four branches (initial, upper, super-upper and lower branches) appear in the VIV response for a smooth cylinder, and for a cylinder with a small surface roughness of K S / D = 2.5 × 10 − 3 , this response changes to three branches (initial, upper and lower branches). The vortex shedding for the initial and lower branches is 2S mode, and that for the upper and super-upper branches (lock-in range) is P + S − , P+S + and 2P modes. With increasing surface roughness, the maximum amplitude has little difference, and the width of the lock-in range increases. A large jump in the vortex phase at the transition of the initial and upper branches and a large jump in the total lift phase at the transition of the upper and lower branches are found, and these jumps are associated with a switch in the timing of vortex shedding (jump of the vortex phase: 2S mode to P + S − mode; jump of the lift phase: other modes to 2S mode). The results are significant for the development of flow and vibration control technology.

Assessment of sensitivity and accuracy of BEM-based aeroelastic models on wind turbine load predictions

The general goal of the work reported in this paper is to gain more confidence when performing blade element momentum (BEM)-based aeroelastic simulations, especially when setting-up sub-models and their parameters. Due to limited or no information, the set-up of these methods is often highly uncertain. To achieve this objective, we have developed and used methodologies to perform the analysis of model uncertainty in wind turbine aeroelastic simulations, while assessing their accuracy. This paper presents an example where these methodologies have been applied to a) the different aerodynamic models used in BEM-based aeroelastic tools to account for unsteady airfoil aerodynamics (UAA) and b) key parameters used in one of these models (Beddoes-Leishman). The accuracy of the simulations is assessed by comparing the simulated unsteady loads with measurements from the DAN-AERO MW experiments. One of the main achievements of this work is the ability to assess the uncertainty in load predictions that derives from the uncertainty related to the UAA models and their constants. The study on the sensitivity of the parameters was performed using Sobol indices and showed that for the case under study the normal force standard deviation at outboard blade locations is mostly sensitive to the Beddoes-Leishman model’s vortex shedding time constant.

Lock-in phenomenon of vortex shedding in oscillatory flows: an analytical investigation pertaining to combustors

An analytical investigation is performed to understand the lock-in phenomenon, observed in vortex shedding combustors. Several aeroengine afterburners and ramjets use a bluff body to stabilize the flame. The bluff body sheds vortices. During the occurrence of high-amplitude combustion instability, the frequency of vortex shedding locks in to the frequency of the chamber acoustic field. This phenomenon is termed vortex-acoustic lock-in. In general, there is a two-way coupling between the vortex shedding process and the acoustic field, making analytical investigation difficult. Since the frequency of the latter remains largely unaltered, performing an investigation to study the response of vortex shedding to external excitation not only allows one to gain insights, but also make the problem analytically tractable. We begin with a lower-order model available in the literature to describe the vortex shedding process in non-reacting flows, arising from sharp corners in the presence of upstream velocity excitation. The continuous time domain model is transformed to a discrete map, which connects the time instances of two successive vortex shedding events. The frequency and amplitude of excitation are varied to study the instantaneous vortex shedding time period, as the response of the system. In the absence of forcing, the iterates of the map form a period-1 solution with the frequency equalling the natural vortex shedding frequency. On increasing the amplitude of excitation, quasi-periodic behaviour of the iterates is observed, followed by a period-1 lock-in solution, where vortex shedding occurs at the excitation frequency. On further increasing the amplitude, de-lock-in occurs. From the map, an analytical solution is extracted, which represents the lock-in state. The condition and thereby the region in the frequency–amplitude parameter space where a general$p:1$lock-in occurs is then identified. Several important analytical expressions, such as for (1) critical threshold frequency above which lock-in occurs, (2) boundary of lock-in region in the parameter space, that are of direct importance to the design of quieter combustors are obtained. The study also identifies the transition of higher-order$p:1$to$1:1$lock-in state, through a series of lock-in and de-lock-in steps, whose occurrence could be verified from future experiments.

Vortex dynamics in the wake of a pivoted cylinder undergoing vortex-induced vibrations with elliptic trajectories

Vortex-induced vibrations of a pivoted cylinder are investigated experimentally at a fixed Reynolds number of 3100, a mass ratio of 10.8, and a range of reduced velocities, $$4.42 \le U^* \le 9.05$$ . For these conditions, the cylinder traces elliptic trajectories, with the experimental conditions producing three out of four possible combinations of orbiting direction and primary axis alignment relative to the incoming flow. The study focuses on the quantitative analysis of wake topology and its relation to this type of structural response. Velocity fields were measured using time-resolved, two-component particle image velocimetry (TR-PIV). These results show that phase-averaged wake topology generally agrees with the Morse and Williamson (J Fluids Struct 25(4):697–712, 2009) shedding map for one-degree-of-freedom vortex-induced vibrations, with 2S, $$2{\hbox {P}}_{\mathrm{o}}$$ , and 2P shedding patterns observed within the range of reduced velocities studied here. Vortex tracking and vortex strength quantification are used to analyze the vortex shedding process and how it relates to cylinder response. In the case of 2S vortex shedding, vortices are shed when the cylinder is approaching the maximum transverse displacement and reaches the streamwise equilibrium. 2P vortices are shed approximately half a period earlier in the cylinder’s elliptic trajectory. Leading vortices shed immediately after the peak in transverse oscillation and trailing vortices shed near the equilibrium of transverse oscillation. The orientation and direction of the cylinder’s elliptic trajectory are shown to influence the timing of vortex shedding, inducing changes in the 2P wake topology.

Wake instability modes for forced transverse oscillation of a sphere

The present numerical study aims to identify the instability modes in the wake behind a transversely oscillating sphere with amplitude A=0.5 at Reynolds number Re=300. The governing equations are solved in the non-inertial frame using the immersed boundary method. The longitudinal thread-like structure is accompanied by asymmetric shedding before the onset of a “lock-in” regime. The wake is found to exhibit symmetric vortex shedding and organized chain like structures in the synchronized regime. Lesser flow inertia at a relatively low Re is dominated by the externally applied motion of the sphere resulting in negative energy transfer by the fluid to the sphere. In the synchronous regime different timing of vortex shedding and phases of coefficient of vortex with sphere motion demarcate two wake modes which have close resemblance with the modes found in induced vibration of a sphere.

Dynamic response of a turbulent cylinder wake to sinusoidal inflow perturbations across the vortex lock-on range

Large-eddy simulations are employed to investigate the dynamic response of the turbulent wake of a circular cylinder to sinusoidal perturbations in the inflow velocity superposed on a mean component. The perturbation frequency is varied across the vortex lock-on range at a constant amplitude of 5% of the mean velocity corresponding to a Reynolds number of 2580. The effect on the instantaneous, time-averaged and phase-averaged characteristics of the near-wake flow and fluid forces on the cylinder is reported. Comparisons of the present simulations to experimental realizations show that the physics of the unsteady three-dimensional separated flow are well reproduced. The simulations capture the modification of the wake structure including the shrinking of the recirculation bubble and vortex-formation region and the enhancement of the wake fluctuations and vortex strength in the lock-on regime. These wake effects are accompanied by an increase in the steady and unsteady drag and the unsteady lift acting on the cylinder. An empirical formula for the amplification of the mean drag coefficient due to inflow perturbations and equivalent oscillations of the cylinder in a steady flow is provided from compilation of available data. Particular attention is given to the change in the timing of vortex shedding with respect to the imposed perturbation across the lock-on range in order to reveal the link between the vortex dynamics and the fluid-induced forces on the cylinder. It is shown that the phase at which vortices are shed from the cylinder shifts monotonically as a function of the perturbation frequency resulting in corresponding changes in the phase of the unsteady forces. It is further shown that the phase of the lift is directly linked to that of vortex shedding but the phase of the drag is biased by inertial forces due to added mass and induced pressure waves. Decomposition of the total in-line force to inviscid “potential-flow” and viscous “vortex-drag” components indicates that the latter exhibits a behavior which is not physically consistent. The stochastic character of vortex synchronization in turbulent wakes and the implications of the present findings for vortex-induced free in-line vibrations are also discussed.

The timing of vortex shedding in a cylinder wake imposed by periodic inflow perturbations

The interaction of vortex shedding from a circular cylinder with an inflow which has low-amplitude periodic velocity oscillations (perturbations) superimposed upon it, was investigated experimentally by means of particle image velocimetry. The experiments were made at three perturbation frequencies across the lock-on range in which the vortex shedding frequency is synchronized with the subharmonic of the imposed frequency. The basic wake pattern in this range is antisymmetric vortex shedding, i.e. the familiar 2S mode. The timing of vortex shedding is defined with respect to the cross-flow oscillation of the wake which is found to play a critical role. Quantitative analysis of the phase-referenced patterns of vorticity distribution in the wake shows that a vortex is actually shed from the cylinder when the cross-flow oscillation of the wake is strongest, marked by a sudden drop in the computed vortex strength. At the middle of the lock-on range, shedding occurs near the minimum inflow velocity in the cycle or, equivalently, during the forward stroke of a cylinder oscillating in-line with the flow. It is argued that the imposed timing of vortex shedding relative to the cylinder motion induces a negative excitation from the fluid, which might explain why the in-line response of a freely vibrating cylinder exhibits two positive excitation regions separated by the lock-on region found in forced oscillations.

NUMERICAL STUDY OF THE FLOW PAST A CYLINDER EXCITED TRANSVERSELY TO THE INCIDENT STREAM. PART 2: TIMING OF VORTEX SHEDDING, APERIODIC PHENOMENA AND WAKE PARAMETERS

In Part 1 of the present study, it was found that the phase angle between the transverse force and the motion of a cylinder subjected to oscillations in the cross-flow direction, is strongly dependent on the parameters of the cylinder excitation. Since the phase angle is associated with the timing of vortex shedding, i.e., the phase of vortex formation with respect to the cylinder motion, the alteration of the phase angle at different conditions of forced excitation suggests a change in timing. For the investigation of timing at different excitation conditions, a detailed numerical visualization in the near-wake was conducted, by superimposing the vorticity contours on the streamlines when the cylinder displacement had reached the uppermost position. Flow visualization during a half-cycle for characteristic cases of the cylinder excitation was also performed, in an attempt to explain the alterations induced in the vortex spacing by the cylinder motion, which were also observed in Part 1. The numerical solution revealed a switch in timing when the excitation frequency is increased over the natural shedding frequency, which is accompanied by an instability in the near-wake which renders the wake aperiodic. Various examples of aperiodic flows are illustrated, and an explanation for the initiation of aperiodicity is provided. Finally, a balance between the circulation shed into the wake per oscillation cycle and that surviving in the vortices is conducted, while the distribution ofu ′rmsalong the wake centreline and the base pressure on the cylinder for various excitation conditions are also presented.

Modification of Vortex Shedding in the Synchronization Range

One aspect of the synchronization phenomenon, which has attracted little attention so far, is the timing of vortex shedding in relation to the displacement of a bluff body. Systematic analysis of flow visualization within the synchronization range revealed that the jump in fluctuating forces had a simple fluid mechanics origin. The oscillating cylinder imposed not only its frequency to the wake behind it but also the timing of the vortex shedding. In the lower region of the synchronization range, the vortex formed on one side of the cylinder was shed when the cylinder was near to the maximum amplitude on the opposite side. This timing changed suddenly in the upper synchronization range where the vortex of the same circulation as before was shed when the cylinder reached the maximum amplitude on the same side.

On the Existence of Atmospheric Vortices Downwind of Hawaii during the HAMEC Project

Abstract Aircraft observations west of the island of Hawaii in June 1980 during the Hawaii Mesoscale Energy and Climate (HAMEC) Project have provided the first in situ measurements of airflow within atmospheric vortices downwind of a tall island. A band of low-level westerly winds was observed to extend more than 150 km west of the island along the axis line separating cyclonic vortices to the north of that line from anticyclonic vortices to the south. The theoretical downstream propagation speed of those vortices is obtained from the solution to a quadratic equation, and while previous satellite studies of atmospheric vortices used the larger root (i.e., ∼80% of the ambient flow), the present data are consistent with the smaller root ∼20%). The turbulent Reynolds number for the flow is 140, and the corresponding vortex shedding time is 32 h.

Vortex simulation of the pressure field for a jet

Variations of the pressure field of a jet are simulated numerically by axisymmetric vortex rings with viscous cores submerged in an inviscid uniform stream. The results are compared with the experimental data measured near a jet. The intervals of shedding time between successive vortex rings are first matched with time intervals between successive pressure peaks of the experiments. and then generated by a numerical program to simulate the randomness of the pressure distribution in the acoustic field. This numerical program randomly generates shedding time intervals with the same probability distribution as that given by those measured in the experiments. Statistical comparisons between numerical and experimental results including probability distributions of shedding periods between successive peaks and variations of peak time period of vortex shedding along the cone of measurement are made up to six diameters downstream of the jet. The role played by the axisymmetric model in the pressure field is also discussed.