Vortex Shedding Modes Research Articles

Analysis of coherence in turbulent stratified wakes using spectral proper orthogonal decomposition

We use spectral proper orthogonal decomposition (SPOD) to extract and analyse coherent structures in the turbulent wake of a disk at Reynolds number $ {\textit {Re}} = 5 \times 10^{4}$ and Froude numbers $ {\textit {Fr}} = 2$ , 10. We find that the SPOD eigenspectra of both wakes exhibit a low-rank behaviour and the relative contribution of low-rank modes to total fluctuation energy increases with $x/D$ . The vortex shedding (VS) mechanism, which corresponds to $ {\textit {St}} \approx 0.11 - 0.13$ in both wakes, is active and dominant throughout the domain in both wakes. The continual downstream decay of the SPOD eigenspectrum peak at the VS mode, which is a prominent feature of the unstratified wake, is inhibited by buoyancy, particularly for $ {\textit {Fr}} = 2$ . The energy at and near the VS frequency is found to appear in the outer region of the wake when the downstream distance exceeds $Nt = Nx/U = 6 - 8$ . Visualizations show that unsteady internal gravity waves (IGWs) emerge at the same $Nt = 6 - 8$ . A causal link between the VS mechanism and the unsteady IGW generation is also established using the SPOD-based reconstruction and analysis of the pressure transport term. These IGWs are also picked up in SPOD analysis as a structural change in the shape of the leading SPOD eigenmode. The $ {\textit {Fr}} = 2$ wake shows layering in the wake core at $Nt > 15$ which is captured by the leading SPOD eigenmodes of the VS frequency at downstream locations $x/D > 30$ . The VS mode of the $ {\textit {Fr}} = 2$ wake is streamwise coherent, consisting of $V$ -shaped structures at $x/D \gtrsim 30$ . Overall, we find that the coherence of wakes, initiated by the VS mode at the body, is prolonged by buoyancy to far downstream. Also, this coherence is spatially modified by buoyancy into horizontal layers and IGWs. Low-order truncations of SPOD modes are shown to efficiently reconstruct important second-order statistics.

Mode transformations of vortex shedding behind a sphere with the effect of Lorentz force

In this paper, the modes of vortex shedding in the wake of a stationary sphere with the Lorentz force, which can be generated by the actuators in weakly conductive fluids and is parallel to the sphere surface, are numerically investigated at Re = 300. The relations among the wake structures, the vorticity distribution, and the motions of the rear stagnation point and the separation point are discussed before and after the application of Lorentz force. From this, the mechanism of mode transformations in the sphere wake is revealed. The results indicate that the fluid near the sphere surface is accelerated with the application of Lorentz force. The rear stagnation point and the separation point move rearward and become steady. Therefore, the vorticity on the rear surface of the sphere gradually decays and becomes steady, which leads to the periodic shedding mode of hairpin vortex replaced by the steady double-thread wake structure. Moreover, the wake structure varies with the interaction parameter N of the Lorentz force. When the Lorentz force is relatively small (N = 0.04), the vibration amplitude of hairpin vortex is weakened, and the vortex heads disappear with vortex legs and necks left. The wake is still periodic due to the hairpin vortex shedding. As N increases to 0.08, the hairpin vortex is suppressed completely, while the double-thread wake appears. The wake is steady due to the suppression of the hairpin vortex shedding. As N further increases to 0.20, a spanwise vortex ring is formed around the double-thread wake.

Study on energy extraction of Kármán gait hydrofoils from passing vortices

How swimming fish extract energy from environmental vortices is still an open question. In this work, fish swimming in unsteady flow is numerically investigated by using the immersed boundary lattice Boltzmann method. The swimming fish is modeled as a forced Kármán gait hydrofoil, and the vortical flow is generated by a stationary circular cylinder. We calculate the Fourier spectra of hydrodynamic forces on the hydrofoil surface and found that there is a coupling between lateral force and drag, which results from a nonlinear wave interaction. The Kármán gait hydrofoil adjusts the lateral force by applying lateral excitation to the vortical flow and improves the drag/thrust through nonlinear wave interaction. We find that suppressing the harmonic energy of the viscous mode is the key ingredient to extract energy from the passing vortex. In turn, the downstream distance LN and foil-vortex phase φ determine whether the viscous harmonic energy can be suppressed. If the viscous mode harmonic is strong, the interaction between the vortex shedding mode and the viscous mode leads to a series of combined modes, which extract energy from the fundamental mode. These combined modes that appear in the fluid force spectra reduce the efficiency of energy extraction.

Mode classification for vortex shedding from an oscillating wind turbine using machine learning

This study presents an effective strategy that applies machine learning methods to classify vortex shedding modes produced by the oscillating cylinder of a bladeless wind turbine. A 2-dimensional computational fluid dynamic (CFD) simulation using OpenFOAMv2006 was developed to simulate a bladeless wind turbines vortex shedding behavior. The simulations were conducted at two wake modes (2S, 2P) and a transition mode (2PO). The local flow measurements were recorded using four sensors: vorticity, flow speed, stream-wise and transverse stream-wise velocity components. The time-series data was transformed into the frequency domain to generate a reduced feature vector. A variety of supervised machine learning models were quantitatively compared based on classification accuracy. The best performing models were then reevaluated based on the effects of artificial noisy experimental data on the models’ performance. The velocity sensors orientated transverse to the pre-dominant flow (u y ) achieved improved testing accuracy of 15% compared to the next best sensor. The random forest and k-nearest neighbor models, using u y , achieved 99.3% and 99.8% classification accuracy, respectively. The feature noise analysis conducted reduced classification accuracy by 11.7% and 21.2% at the highest noise level for the respective models. The random forest algorithm trained using the transverse stream-wise component of the velocity vector provided the best balance of testing accuracy and robustness to data corruption. The results highlight the proposed methods’ ability to accurately identify vortex structures in the wake of an oscillating cylinder using feature extraction.

Attenuation of vortex street by suction through the structured porous surface

We experimentally investigated the attenuation of the von Kármán vortex street behind a circular cylinder by the use of active suction through a structured porous surface in wind tunnel tests. The Reynolds number Re, based on the outer diameter of the cylinder D, is set to be 1.0×104. The structured porous surface of the test model is made of resin by the three-dimensional printing technique to obtain well-organized porous structures. The active suction control effectiveness is quantified by a non-dimensional suction coefficient CQ, which is determined by the suction flow rate Q, the porous structure of the cylinder's surface, and the free stream velocity U∞. A high-speed particle image velocimetry measurement system is utilized to acquire global and detailed wake flows behind the baseline and controlled cylinders. In addition to directly perceived time-averaged characteristics, flow analysis methods including proper orthogonal decomposition, spectral analysis, and linear stability analysis are employed to study the underlying nature of cylinder wakes with and without distributed suction control. Experimental results show that multi-scale coherent structures in the cylinder wake are homogenized and the near wake is regularized under the control of suction. With a proper CQ, the alternating vortex street behind the circular cylinder is found to be greatly attenuated and the vortex shedding mode completely switched.

Secondary vortex, laminar separation bubble and vortex shedding in flow past a low aspect ratio circular cylinder

Large eddy simulation of flow past a circular cylinder of low aspect ratio ( $AR=1$ and $3$ ), spanning subcritical, critical and supercritical regimes, is carried out for $2\times 10^3 \le Re \le 4\times 10^5$ . The end walls restrict three-dimensionality of the flow. The critical $Re$ for the onset of the critical regime is significantly lower for small aspect ratio cylinders. The evolution of secondary vortex (SV), laminar separation bubble (LSB) and the related transition of boundary layer with $Re$ is investigated. The plateau in the surface pressure due to LSB is modified by the presence of SV. Proper orthogonal decomposition of surface pressure reveals that although the vortex shedding mode is most dominant throughout the $Re$ regime studied, significant energy of the flow lies in a symmetric mode that corresponds to expansion–contraction of the vortex formation region and is responsible for bursts of weak vortex shedding. A triple decomposition of the time signals comprising of contributions from shear layer vortices, von Kármán vortex shedding and low frequency modulation due to the symmetric mode of flow is proposed. A moving average, with appropriate size of window, is utilized to estimate the component due to vortex shedding. It is used to assess the variation, with $Re$ , of strength of vortex shedding as well as its coherence along the span. Weakening of vortex shedding in the high subcritical and critical regime is followed by its rejuvenation in the supercritical regime. Its spanwise correlation is high in the subcritical regime, decreases in the critical regime and improves again in the supercritical regime.

Laminar flow-induced vibration of a three-degree-of-freedom circular cylinder with an attached splitter plate

Splitter plates are widely used for drag reduction and vibration control or enhancement of circular cylinders. The effects of a splitter plate on the vertical flow-induced vibrations of a circular cylinder have been well studied. However, its effects on the vertical-torsional coupled vibrations require further investigation. In this paper, the three-degree-of-freedom (TDoF) flow-induced vibrations of a circular cylinder with an attached splitter plate are numerically investigated at a Reynolds number of 100. The ratio between the torsional and vertical natural frequencies is varied within fθ,0/fh,0 = 6, 4, 3, 2, and 1. Numerical results show that the flow-induced vibrations of a TDoF cylinder-plate assembly, depending on the frequency ratio, may differ significantly from those of a single-degree-of-freedom (SDoF) vertical or torsional assembly. For cylinder-plate assemblies with fθ,0/fh,0 = 6–2, the vibrations can be divided into a vertical vibration-dominated branch (V branch), a torsional vibration-dominated branch (T branch), and a coupled vibration-dominated branch (C branch). The V branch vibration of a TDoF assembly is similar to that of an SDoF vertical assembly at the same reduced flow velocity, while the difference increases with decreasing the frequency ratio. The T branch vibration of a TDoF assembly is almost identical to the vibration of an SDoF torsional assembly at the same reduced flow velocity. The ratio between the torsional and vertical vibration amplitudes increases with decreasing the frequency ratio in the C branch. For the assembly with fθ,0/fh,0 = 1, vertical-torsional coupled vortex-induced vibrations are observed with the largest torsional amplitude as high as 46.3°. The vibrations of TDoF assemblies with all considered frequency ratios may be more severe than those of SDoF vertical and torsional assemblies within specific ranges of reduced flow velocities. The mean drag coefficients for the fθ,0/fh,0 = 6–2 assemblies are lower than a stationary circular cylinder but often higher than a stationary cylinder-plate assembly. The mean drag coefficients for the fθ,0/fh,0 = 1 assembly in the lock-in range are considerably larger than that of a stationary circular cylinder. For TDoF assemblies with fθ,0/fh,0 = 6–2, the V branch and C branch vibrations are mainly driven by the interaction between the assembly and the shear layers, while the T branch vibrations are excited by the typical 2S mode of vortex shedding. The 2S vortex shedding mode is also observed in the lock-in range of the fθ,0/fh,0 = 1 assembly.

Numerical study on vortex-induced vibration of circular cylinder with two-degree-of-freedom and geometrical nonlinear system

The vortex-induced vibration (VIV) of circular cylinder in uniform flow with two-degree-of-freedom (2DOF) and geometrical nonlinear system is investigated numerically using the combined sliding and layering dynamic meshes. The characteristics of vibration amplitude, fluid force coefficients, branching behaviour, vibration trajectory, energy transfer and flow pattern of circular cylinder in VIV are studied with two-dimensional shear stress transfer (SST) k-ω turbulence model and three-dimensional large eddy simulation (LES). It is found that in the simulation with LES model the predicted vibration amplitude and fluid force coefficients show good agreement with the experimental data, while in the simulation with SST k-ω model these parameters are significantly underestimated. The two triplets (2T) vortex shedding mode happens in the super upper branch of circular cylinder with 2DOF linear system and leads the large-magnitude positive energy transferring from fluid to cylinder, which causes the maximum vibration amplitude. For the circular cylinder with 2DOF nonlinear system, the vibration simulated by LES model shows a galloping-like phenomenon that the amplitude keeps increasing with the reduced velocity Ur. The crescent-shaped trajectory and the 2T vortex shedding mode happen upon the critical Ur, which is similar to that in the super upper branch of circular cylinder with 2DOF linear system. This phenomenon is caused by the amplitude-dependent stiffness of nonlinear system and the modified reduced velocity U∗ reveals the universality of vibration amplitude for the circular cylinders with linear and nonlinear systems.

Operational fluid modal analysis of full-scale pressure and wake flow measurements on the Gjemnessund Bridge

The present paper is dealing with observations of vortex shedding on the wedge-shaped Gjemnessund Bridge Box girder in the period from August 2019 to February 2020. Wake flow oscillations are identified using operational fluid modal analysis with correlation functions of surface point pressures near the trailing edge, flow velocities upstream and in the wake measured in full-scale. Even though vortex shedding is barely observed in the lift and response spectra, operational fluid modal analysis is able to identify evidence from vortex shedding. A characteristic vortex shedding fluid mode shape is recognized for 179 ten-minutes records at Reynolds numbers ranging from 500,000 to 2,000,000. The Strouhal numbers from the full-scale measurements are identified simultaneously with the vortex shedding fluid mode shapes. A comparison with wind tunnel tests of a 1:30 scaled section model indicates a Reynolds number dependency of the Strouhal number.

Bifurcation scenario for a two-dimensional static airfoil exhibiting trailing edge stall

We numerically investigate stalling flow around a static airfoil at high Reynolds numbers using the Reynolds-averaged Navier–Stokes equations (RANS) closed with the Spalart–Allmaras turbulence model. An arclength continuation method allows to identify three branches of steady solutions, which form a characteristic inverted S-shaped curve as the angle of attack is varied. Global stability analyses of these steady solutions reveal the existence of two unstable modes: a low-frequency mode, which is unstable for angles of attack in the stall region, and a high-frequency vortex shedding mode, which is unstable at larger angles of attack. The low-frequency stall mode bifurcates several times along the three steady solutions: there are two Hopf bifurcations, two solutions with a two-fold degenerate eigenvalue and two saddle-node bifurcations. This low-frequency mode induces a cyclic flow separation and reattachment along the airfoil. Unsteady simulations of the RANS equations confirm the existence of large-amplitude low-frequency periodic solutions that oscillate around the three steady solutions in phase space. An analysis of the periodic solutions in the phase space shows that, when decreasing the angle of attack, the low-frequency periodic solution collides with the unstable steady middle-branch solution and thus disappears via a homoclinic bifurcation of periodic orbits. Finally, a one-equation nonlinear stall model is introduced to reveal that the disappearance of the limit cycle, when increasing the angle of attack, is due to a saddle-node bifurcation of periodic orbits.

Spectral proper orthogonal decomposition of compressor tip leakage flow

To identify the spatiotemporal coherent structure of compressor tip leakage flow, spectral proper orthogonal decomposition (SPOD) is performed on the near-tip flow field and the blade surface pressure of a low-speed compressor rotor. The data used for the SPOD analysis are obtained by delayed-detached eddy simulation, which is validated against the experimental data. The investigated rotor near-tip flow field is governed by two tip leakage vortices (TLV), and the near-tip compressor passage can be divided into four zones: the formation of main TLV (Zone I), the main TLV breakdown (Zone II), the formation of tip blockage cell (Zone III), and the formation of secondary TLV (Zone IV). Modal analysis from SPOD shows that a major part of total disturbance energy comes from the main TLV oscillating mode in Zone I and the main TLV vortex shedding mode in Zone III, both of which are low-frequency and low-rank; on the contrary, modal components in Zones II and IV are broadband and non-low-rank. Unsteady blade forces are mainly generated by the impingement of the main TLV on the blade pressure surface in Zone III, rather than the detachment of the secondary TLV from the blade suction surface in Zone IV. These identified coherent structures provide valuable knowledge for the aerodynamic/aeroelastic effects, turbulence modeling, and reduced-order modeling of compressor tip leakage flow.

A particle image velocimetry measurement of flow over a highly confined circular cylinder at 60% blockage ratio

In this study, a Particle Image Velocimetry (PIV) measurement is carried out to investigate the flow past a highly confined circular cylinder at a fixed blockage ratio of 60%. The Reynolds number (Re) in terms of the cylinder diameter and the mean incoming flow velocity is varied from 318 to 1431. It is observed that the characteristic frequency of the separated shear layers is amplified through a so-called frequency-filtering process. The instability of the separated shear layers causes two different vortex shedding modes including alternating and symmetric shedding modes, which are observed at Re = 927–1242. An intermittent switch between the two shedding modes is also observed. The theory of mixing layers is applied with modification to predict the characteristics of the separated shear layers, and the prediction shows a good agreement with the experimental data. It is found that the vortex roll-up and merging locations can be estimated by calculating the energy contents of individual frequency modes.

An experimental investigation of vortex-induced vibration of a curved flexible cylinder

Vortex-induced vibration of a curved flexible cylinder placed in the test section of a recirculating water tunnel and fixed at both ends is studied experimentally. Both the concave and the convex orientations (with respect to the incoming flow direction) are considered. The cylinder was hung by its own weight with a dimensionless radius of curvature of $R/D=66$ , and a low mass ratio of $m^{*} = 3.6$ . A high-speed imaging technique was employed to record the oscillations of the cylinder in the cross-flow direction for a reduced velocity range of $U^{*} = 3.7 - 48.4$ , corresponding to a Reynolds number range of $Re= 165 - 2146$ . Mono- and multi-frequency responses as well as transition from low-mode-number to high-mode-number oscillations were observed. Regardless of the type of curvature, both odd and even mode shapes were excited in the cross-flow directions. However, the response of the system, in terms of the excited modes, amplitudes and frequencies of the oscillations, was observed to be sensitive to the direction of the curvature (i.e. concave vs convex), in particular at higher reduced velocities, where mode transition occurred. Hydrogen bubble flow visualization exhibited highly three-dimensional vortex shedding patterns in the wake of the cylinder, where there existed spatial and temporal evolution of the vortex shedding modes along the length of the cylinder. The time-varying intermittent vortex shedding in the wake of the cylinder was linked to the spanwise travelling wave behaviour of the vortex-induced vibration response. The observed spatially altering wake corresponded to the multi-modal excitation and mode transition along the length of the cylinder.

Vortex shedding induced vibration of thin strip in confined rectangular channel

To study the basic behavior of vortex shedding of spacer grids, both experiments and numerical simulations of a single flat plate with a high chord-to-thickness ratio in a confined rectangular channel were performed. Frequencies of vortex-induced vibrations were obtained through a laser Doppler vibrometer (LDV), and the upstream velocity distribution was acquired by particle image velocimetry (PIV). Two-dimensional large eddy simulations (LES) were conducted, with the PIV results being used as the inlet boundary conditions. Dynamic mode decomposition (DMD) was applied to the numerical results to identify the vortex shedding modes for a number of cases. The numerical results showed good agreement with the experiments in terms of the vortex shedding frequencies. From the simulations, three vortex shedding modes were obtained: trailing edge shedding without the leading edge–vortices coupling (Type I), weak leading edge–vortices coupled shedding (Type II), and strong leading edge–vortices coupled shedding (Type III). The leading edge vortices showed different types of characteristics, namely those that diffused before reaching the trailing edge (Type I), those that stayed close to the plate surface until they reached the trailing edge (Type II), and those that got detached from the plate surface in the transverse direction, and then moved back (Type III). The results showed that both the Reynolds number based on the plate thickness (Red) and dimensionless width of the channel (h/d) could affect the vortex shedding. A higher Red or lower h/d led to stronger leading edge vortices. Moreover, stronger leading edge vortices led to a smaller dimensionless boundary layer thickness (δ/d) at the trailing edge. Finally, the Strouhal number based on the separation distances between similarly shed rotational vortices (Stλ) and the thickness of the plate together with the boundary layer (Std+2δ) were more robust than that based on the thickness of the plate (Std).

Effect of an upstream cylinder on the wake dynamics of two tandem cylinders with different diameters at low Reynolds numbers

This paper presents a systematic numerical study on the fluid dynamics and flow structures around a cylinder with diameter D placed in the wake of another cylinder with a smaller diameter d. Reynolds numbers of Re = 100 and 150 (based on D) are considered so the flow is physically two-dimensional. The ratios d/D and L/D vary in the ranges of 0.4–1.0 and 1.0–8.0, respectively, where L is the distance from the center of the upstream cylinder to the forward stagnation point of the downstream cylinder. The analysis focuses on how d/D and L/D influence the Strouhal number St, wake topology, and fluid forces on the downstream cylinder and links them with the flow physics. The flow is classified into the reattachment and co-shedding flow regimes, with the latter being further subdivided into the prime vortex shedding, two-layer vortex shedding, and secondary vortex shedding (SVS) modes, and the detailed aspects of the three modes are discussed based on the time-averaged flow fields. The two vortex frequencies of the downstream cylinder can be detected only in the SVS mode, and in addition to the fundamental vortex frequency f1, the shedding of the secondary vortex further results in the subharmonic frequency f2. Only when the secondary shedding length Ls* is <10 does f2 affect the downstream cylinder and lead to a pattern of alternating high- and low-amplitude peaks in the time history of the lift coefficient. A novel mechanism of secondary vortex formation is identified, and the critical spacing and the modulation of lift by f2 are also discussed.

Illuminating the complex role of the added mass during vortex induced vibration

The role of the added mass coefficient in vortex induced vibration (VIV) of the bluff body is complex and elusive. It is certain that decoding the relationship between the added mass and the vibration pattern will benefit the prediction and prevention of VIV. We present a study on VIV of a long flexible cylinder and forced vibration of a rigid cylinder, in a combination of experimental optical measurements and high-fidelity numerical simulation. We focus on uniform flow over a uniform cylinder at a fixed Reynolds number, Red = 900, but systematically varied the motion amplitude in the in-line (Axd) and cross-flow direction (Ayd), as well as the phase angle (θ) between the motions. We show that θ∈[π2,3π2] is associated with negative added mass coefficients in the cross-flow direction (Cmy < 0), and there is a strong correlation between the vortex shedding mode of “2P” or “P+S” and Cmy < 0.

Numerical investigation into the effect of spacing on the flow-induced vibrations of two tandem circular cylinders at subcritical Reynolds numbers

Two-degree-of-freedom (2DOF) flow-induced vibrations (FIV) for a pair of elastically mounted circular cylinders in tandem arrangement with varying centre-to-centre spacings (Sx) are numerically studied. The Reynolds number range Re=1470–10320 belongs to the subcritical flow regime. Two identical cylinders with a mass ratio of m∗=2.6 and a mass-damping parameter of m∗+Caζ=0.013 are considered in the simulation. Four spacing ratios (Sx∕D, where D is the identical diameter) ranging from 3.0 to 8.0 are employed to investigate the effect of Sx∕D on the FIV responses, hydrodynamic characteristics and wake patterns of the two cylinders. It is found that the effect of the downstream cylinder on the FIV of the upstream one becomes insignificant when Sx∕D≥4.0. Due to the unsteady wake-cylinder interactions, multi-peak responses are observed for the downstream cylinder. Dual resonance with the 2:1 in-line to cross-flow oscillation frequency ratio and figure-eight orbital trajectories is found to occur for the upstream cylinder. In contrast, the trajectories of the downstream cylinder are rather irregular because of the low frequency components in the in-line response at high reduced velocity (Vr). Both shear flow and vortex shedding may appear in the gap region depending on Sx∕D and the relative motion of the two cylinders. In general, the vortex shedding modes of the upstream cylinder are similar to those of a single cylinder. Whereas, the analyses on the wake patterns suggest that the interactions of the upstream wake with the downstream cylinder and its own wake contribute to the unsteady fluid dynamics, which is crucial to maintaining the large-amplitude vibrations of the downstream cylinder at high Vr.

Torsional vibration of a circular cylinder with an attached splitter plate in laminar flow

Splitter plates have been recognized as useful passive devices to reduce drag, mitigate flow-induced vibration, and enhance heat transfer efficiency of a circular cylinder. However, undesired torsional flow-induced vibrations due to splitter plate attachment require further investigation. This paper numerically studies the flow-induced torsional vibrations of an elastically mounted circular cylinder with an attached splitter plate in laminar flow with a Reynolds number of 100. A finite volume formulation is utilized to solve the incompressible two-dimensional fluid governing equations. Torsional vortex-induced vibrations (VIVs) are observed at lower reduced flow velocities, while a symmetry-breaking bifurcation occurs as the reduced flow velocity increases, after which the cylinder-plate assembly vibrates around a nonzero equilibrium angle. The numerical results show that the synchronization range of VIV extends, the peak VIV amplitude increases, and the critical reduced flow velocity for the bifurcation decreases with decreasing the moment of inertia. The symmetry-breaking bifurcation is due to a combined effect of the structural restoring moment and the flow-induced moment. The critical reduced velocity of the bifurcation and the nonzero equilibrium angle at any reduced velocity can be calculated based on the mean moment coefficients of the cylinder-plate assembly. The flow-induced moment is mainly induced by the pressure difference between the splitter plate's upper and lower surfaces. The phase difference between the torsional moment and displacement is 0° at lower reduced velocities, while the phase difference jumps to 180° at a reduced velocity of approximately 6.5. The mean drag coefficient of the vibrating cylinder-plate assembly is lower than the mean drag coefficient of a stationary circular cylinder but often higher than that of a stationary cylinder-plate assembly. The dominant frequency of the drag force is twice the vibration frequency before the symmetry-breaking bifurcation, while the dominant frequency becomes consistent with the vibration frequency after the bifurcation. The typical 2S mode of vortex shedding is identified for all considered moments of inertia and reduced flow velocities. However, the timing of a non-shedding vortex changes at the critical flow velocities for the phase jump and symmetry-breaking bifurcation. The observed torsional vibrations suggest that circular cylinders with splitter plate attachments may be competitive candidates for VIV-based energy harvesting, while they may not be good choices for heat exchangers.

Active feedback VIV control of sprung circular cylinder using TDE-iPID control strategy at moderate Reynolds numbers

The efficacy of active control of flow-induced vibrations in the turbulent flow around a sprung cylinder using time delay estimation based intelligent proportional-integral-derivative (TDE-iPID) controller is studied in this article. Two-dimensional incompressible unsteady Reynolds-averaged Navier-Stokes (URANS) equations are solved using the finite volume approach . The two-equation k-ω-SST model is employed for turbulence modeling, and fluid-structure interaction (FSI) simulations are conducted for a low mass damping ratio (m*ζ = 0.013) over the Reynolds number range of 1700–13000 which corresponds to the reduced velocities of 2–14.9. To validate the employed numerical procedure, the obtained findings for the cylinder cross-flow oscillations at different reduced velocities are compared with other empirical and numerical data, indicating a generally excellent agreement. In view of the numerical simulations, the utilized active control system can perfectly (up to almost 100%) attenuate the cross-flow and streamwise vibrations at the reduced velocity of 5 (Re ≈ 4200) that matches the maximum displacement in the lock-in region. Deploying the active controller disrupts the vortical structure especially in the far wake region, gradually transforming the vortex-shedding mode for the controller in the predefined green region from C(2S) to 2S where the vortices resemble the classical von Kármán vortex street. Moreover, the controller performance is evaluated at the maximum vibration amplitude of the cylinder. The findings substantiate the success of an active control system in mitigating flow-induced vibrations immediately after switching the TDE-iPID controller on.

Flow-induced vibrations of circular cylinder in tandem arrangement with D-section cylinder at low Reynolds number

Elastically mounted circular cylinder in a fluid flow undergoes vortex-induced vibrations (VIV) and exhibits high amplitudes, however in a limited range of reduced velocity (UR). Studies have shown an introduction of asymmetry in the flow around the cylinder may lead to galloping, characterized by large amplitudes over a wide range of UR. Here, flow-induced vibrations of tandem arrangement of a D-section and a circular cylinder of equal diameter and density are studied computationally. The circular cylinder is placed in the wake-interference region. An in-house sharp-interface immersed boundary method has been used to solve for the fluid flow, while the rigid body dynamics of the cylinders are modeled through a linear spring-mass model. Over the range of UR considered (1≤UR≤15), the D-section cylinder shows both VIV and soft-galloping response characteristics. The excitation of galloping instability in the D-section is attributed to wake disruption by the circular cylinder. Oscillation frequencies of both cylinders are found to be in synchronization with the natural frequency of the structure once lock-in is attained. The circular cylinder's oscillations attain high amplitudes only when a transition in vortex shedding mode of the D-section cylinder is observed. The spectral characteristics of the forces and oscillations of the cylinders are studied, and overlapping VIV and galloping characteristics have been observed for both D-section and circular cylinders. In context of relevant literature, the wake-induced response of the cylinder is classified as galloping. The vorticity dynamics associated with the different regimes of response have been investigated.