Shedding Modes Research Articles

On wave–current interaction with a horizontal cylinder: Load characteristics and vortex pattern

This study performed a two-dimensional experiment to reveal the load characteristics of a submerged horizontal cylinder with vortex patterns in the wake region under wave–current flows. Wave–current conditions were tested with both following and opposing currents. Instantaneous representations of the velocity field, streamline topology, and vorticity patterns, obtained using particle image velocimetry, provided insight into the origin of the unsteady loading of the cylinder. The spatiotemporal characteristics of the pressure distribution on the cylinder were analyzed using Fourier series expansion across the circumference of the cylinder. The results demonstrate that, unlike the action of current only, the presence of waves modifies the frequency and position of vortex shedding, resulting in three distinct modes in the frequency domain of the vertical force on the cylinder, where each mode exhibits a distinct mode of vortex shedding. The variation in frequency domain of Fourier coefficients of pressure around the cylinder is consistent with the force corresponding to different modes. Moreover, velocity rate β and the frequency relationship between the wave and current-induced vortex shedding play important roles in the frequency characteristics of the vertical force.

Vortex induced vibration for mixed convective flow past a square cylinder

In this work, a comprehensive numerical investigation of the combined effect of buoyancy and flow approach angle (α) on vortex-induced vibration of an elastically mounted square cylinder at a fixed Reynolds number, Re = 100, Prandtl number (Pr = 7.1) and mass ratio (Mred) of 2 is conducted. Extensive numerical experiments were carried out for different flow approach angles (α = 0°-90°) and for various reduced velocities (Ured = 3–25) at Richardson number, Ri = 0, 0.25 and 0.50. The Arbitrary Lagrangian-Euler (ALE) approach models the solid-fluid interaction. The coupled fluid-structure interaction problem in two-degree-of-freedom (2-DOF) was solved using a high-fidelity finite difference-based solver. The Lock-in regime was found to be fixed, between Ured = 5 and 6, for all flow approach angles irrespective of Ri. For all flows other than transverse flow, the reduced frequency is found to be equal in both directions (fx=fy) but in the transverse situation, (α=90°), reduced frequency in the x-direction is twice that of the y-direction for all reduced velocities (Ured). Different vortex shedding modes 2S, 2S*, P + S and 2P are also observed in the study. The average coefficient of drag (C¯D) and Nusselt number (N¯u) was found to peak at α = 45° for all Ured. It was also found that as α is increased, C¯DandN¯u increases due to larger heated surface area exposure to the fluid particles. When Ri increases, C¯DandN¯u increases at a α due to the higher heat transfer rate. Highest value of N¯u is observed for Ured = 6, α = 45° at Ri = 0.5.

Numerical Investigation of Vortex Shedding from a 5:1 Rectangular Cylinder at Different Angles of Attack

Although flow around a 5:1 rectangular cylinder at small angles of attack (AoA) has been extensively studied, when the AoA becomes larger, the research is rare. Therefore, this study performs Unsteady Reynolds-Averaged Navier-Stokes simulations (URANS) using the k-ω SST turbulence model for unsteady flow around a two-dimensional 5:1 rectangular cylinder at different AoAs up to 45°. A strong dependence of the flow characteristics on AoA is observed through the analysis of the time-averaged lift coefficient, drag coefficient, and Strouhal number. The peak of lift and drag coefficient is observed to be correlated, respectively, to the leading- and trailing-edge vortex based on the analysis of the flow. The x′-directional length of the main recirculation bubble on the top side and the distance from the bubble center to the leading edge of the cylinder both reach the maximum when α = 15°. In addition, the standard deviation σx′ of the time-averaged velocity U¯x′ along the cylinder shows a trend of increasing at first and then decreasing, and that σy′ also shows the same trend at α = 20°~45°; it fluctuates within a range of 0.05~0.2 at α = 0°~20°. Finally, two principal modes of vortex shedding are observed with α = 15° being their turning point, (i) “1 + 1” mode: in one vortex shedding period, two major vortices shed off from the top and bottom sides of the cylinder at α ≤ 15°; (ii) “2 + 2” mode, four vortices shed off from the top and bottom sides of the cylinder at α > 15° in one vortex shedding period.

Vortex-induced vibration of a circular cylinder with nonlinear restoring forces at low-Reynolds number

The numerical simulation of two-dimensional flows around an elastically-mounted circular cylinder on a linear/quadratic spring configuration at low-Reynolds number (Re) is conducted in order to study the vortex-induced vibration (VIV) of the system. The extent of Re used in this study range from 50 to 150 inclusive. The data obtained from the numerical simulations are used to investigate the impact of the nonlinearity in the spring configuration on the VIV response of the dynamical system. The equivalent natural frequency for a circular cylinder supported elastically on a linear/quadratic spring is derived and found to depend on the square root of the maximum amplitude of the transverse displacement. The range of Re associated with the initial branch of the response is increased (extended) and the upper and lower branches are suppressed (almost disappearing when the hardening nonlinearity is sufficiently strong) for an elastically-mounted cylinder on a linear/quadratic spring configuration compared to that for the same cylinder supported elastically on a linear spring. The detailed characteristics (e.g., vortex shedding modes, amplitude and oscillation frequency of the transverse displacement, etc.) of the lock-in range and the transition out of this range for the VIV system as a function of increasing Re is studied using power spectrum, phase portrait and dynamical mode decomposition analysis. The information obtained from the analysis is synthesized in order to investigate the different physical mechanisms and phenomena appearing in the VIV system and how these are linked to the underlying vortex shedding and amplitude response regimes (initial branch, upper branch, desynchronization branch) of the dynamics of the fixed (stationary) and elastically-mounted cylinder.

Vortex-induced vibration of a two degree-of-freedom flexibly mounted circular cylinder in the crossflow direction

Vortex-induced vibration (VIV) of a two degree-of-freedom (DOF) circular cylinder, placed in the test section of a recirculating water tunnel and free to oscillate in its first two vibrational modes in the crossflow direction, is studied experimentally. The dynamic response of the cylinder is studied for a reduced velocity range of $U^*=4\unicode{x2013}30$ for eigenfrequency ratios in the range of 1.3–3.0. For the two DOF system, while the onset of the VIV response followed a similar lock-in region as those observed for a classical VIV response of a single DOF system, by increasing the reduced velocity a secondary lock-in region was observed over which the oscillations of the cylinder were locked into the system's second mode. In addition, there existed an intermediate range of reduced velocity over which the VIV response consisted of oscillations at a combination of the first two natural modes of the system. As the eigenfrequency ratio between the first two modes increased, the secondary lock-in range was extended to higher reduced velocities and the reduced velocity range over which multi-modal oscillations were observed was decreased. A full map of vortex dynamics in the wake of the cylinder was developed qualitatively and quantitatively using hydrogen bubble flow visualization and time-resolved volumetric particle tracking velocimetry techniques, respectively. A Q-criterion analysis revealed the existence of highly three-dimensional vortex structures in the wake of the cylinder. The spatiotemporal mode analysis using the proper orthogonal decomposition technique revealed strong coupling between the vortex shedding modes in the wake of the cylinder and the structural vibration modes.

Numerical simulation of vortex-induced vibrations of inclined flexible risers subjected to uniform current

The vortex-induced vibrations (VIVs) of a flexible riser at four different inclination angles (θ) subjected to a uniform current were numerically simulated by using three-dimensional Large-Eddy-Simulation (LES). A weak coupling method was adopted for addressing the fluid-structure interaction, where the fluid domain was calculated by the commercial code ANSYS Fluent, while the structural response was calculated by the mode superposition method. The sensitivity of the vibration to grid refinement was checked, and the numerical simulation accuracy was validated by comparison to experimental results. The effects of the θ on the VIV of the flexible cylinder were investigated. The cross-flow vibration is found to decrease with increasing θ, while the in-line vibration does not show the same variation. Figure-eight shaped orbital trajectories are observed in four different θ cases. If θ attains a specific value, the vortex shedding separates into two different modes (i.e., straight vortex and hairpin vortex) along the flexible cylinder. With increasing θ, the hairpin vortex tubes gradually become the dominant vortex shedding mode.

Special Section on Data-Driven Mechanics and Digital Twins for Ocean Engineering

Abstract This special issue focuses on the topic of Data-Driven Mechanics and Digital Twins for Ocean Engineering. Two categories of papers are included in this issue; they deal with: (i) reduced-order modeling and data analytics; and (ii) data-driven computing and digital twins. In the first category, Yin et al. present the modal analysis of hydrodynamic forces in flow-induced vibrations using dynamic mode decomposition (DMD). Using snapshots of the flow field, spatio-temporal evolution characteristics of the wake patterns are analyzed. The dominant DMD modes with their corresponding frequencies are identified and used to reconstruct the flow fields. In another paper in this category, Janocha et al. presented a 3D large-eddy simulation and data-driven analysis of the flow around a flexibly mounted cylinder via proper orthogonal decomposition (POD) analysis. The POD-based modal extractions are performed on slices in the wake to identify the coherent structure in the flow. Vortex shedding modes are analyzed and classified by examining three-dimensional wake flow structures. Such a body of work is useful for building reduced-order (surrogate) models that can be considered for multi-query analysis, design optimization, and feedback control. However, these POD/DMD studies are restricted to linear physics as well as to idealized canonical geometries. There is a need for further extension to large-scale marine and offshore structures (e.g., offshore wind turbines, marine risers and pipelines). Moreover, projection-based POD/DMD techniques generally face difficulties to scale for highly nonlinear turbulent flow. Nonlinear model reduction and deep neural networks (e.g., convolutional autoencoders) are possible alternatives to be explored for advanced reduced-order modeling.

Three-Dimensional Large Eddy Simulations and Proper Orthogonal Decomposition Analysis of Flow Around a Flexibly Supported Circular Cylinder

Abstract Three-dimensional (3D) numerical simulations of the flow around a cylinder undergoing vortex-induced vibration (VIV) at Re = 3900 (defined as Re = U∞D/ν, where U∞ is the inlet flow velocity, D is the diameter of the cylinder, and ν is the fluid kinematic viscosity) are performed using large eddy simulations (LES). Detailed mesh and time-step convergence studies are carried out for the flow past a stationary cylinder to obtain the optimal mesh and time-step. The validation studies are performed by comparing the present results with the previous published experimental data and numerical results to confirm feasibility of the present numerical model for predicting the wake characteristics. The numerical model is then applied to investigate the flow around a self-excited cylinder vibrating in the cross-flow direction at three different reduced velocities. The effects of the reduced velocity are analyzed based on the cross-flow vibration amplitudes, the power spectral densities of lift and drag coefficients, and the wake flow coherent structures. Different vortex shedding modes are identified and categorized using the iso-surfaces of the pressure coefficient and the Q-criterion. The dominant 3D wake flow features are extracted and discussed by carrying out the proper orthogonal decomposition (POD) for flow velocities on multiple two-dimensional (2D) sampling planes in the wake region. The modes on the XY planes display a traveling-wave behavior and the modes on the XZ planes show cells of streamwise vortices, which display the three-dimensionality of the wake flow.

The space effect on WIV interference between a fixed and oscillating diamond cylinder at a low Reynolds number of 100

To clarify the space effect on wake-induced vibration (WIV) of twin tandem diamond cylinders, the fixed upstream cylinder and the downstream cylinder freely oscillating in both in-line and transverse directions have been numerically investigated. The nondimensional center-to-center spacing ratio L* is varied in the range of 2–6, the Reynolds number Re is 100, the reduced velocity Ur is 3–20, and the mass ratio m* is 3. According to the wake modes and dynamic responses, the mechanism for the wake excitation of twin diamond cylinders with different spacing is further discussed. At a smaller spacing (L* = 2 and 3), the reattachment and co-shedding regimes appear with the increasing Ur, but when it comes to a larger spacing (L* = 4–6), only the co-shedding one occurs. The downstream cylinder shares a similar lock-in region at each spacing, while the corresponding flow patterns are not the same. The vortex shedding mode of the downstream cylinder within the lock-in region is 2S at L* = 2, while it is 2P at L* = 3–6. Additionally, the downstream diamond cylinder displays significant in-line and transverse oscillations at each spacing ratio, with the largest amplitude appearing at L* = 3.

Three-dimensional effects for flow past a wavy cylinder at low Reynolds numbers

The three-dimensional (3D) flow characteristics affected by the structural heterogeneity of a wavy cylinder varied sinusoidally along the spanwise direction at a low Reynolds number (50∼350), are studied using numerical simulations. Compared with a uniform cylinder, the transition routes and vortex shedding modes of a wavy cylinder can be revealed based on the Strouhal number–Reynolds number relationship, with new vortex structures features discovered in each mode. Unsynchronized transitions between several 3D shedding modes and the resulting hysteresis-like phenomenon attributed to different initial conditions. The extrinsic 3D effects caused by the structural wavy perturbations afford the inhomogeneous spanwise variations in flow physical quantities, such as the pressure coefficient, time-averaged separation angles, and vortex formation lengths. The effects of the Reynolds number on the wake quantities of the wavy cylinder are compared with those of a uniform cylinder, which is described by a single function form in the laminar regime and irregular features in the 3D wake-transition regime. In addition, the deviations of the time-averaged separation angles between the two-dimensional (2D) and 3D results are adopted to reveal the strengthened three-dimensionality of the flow for a wavy cylinder and its variations with shedding mode transitions.

Applicability of two-dimensional numerical simulation associated with vortex-induced vibration response of the circular cylinder

ABSTRACT The VIV responses of the circular cylinder at low and moderate Reynolds numbers are calculated according to two-dimensional numerical simulation and the fourth-order Runge–Kutta algorithm. The first part of the study is focused on the applicability of 2D numerical simulation between the response of 2D numerical simulation and the actual response, which can guide the preliminary engineering studies by vortex shedding. The reasonable vortex shedding mode of each branch, and the change process of the trajectory from the ‘8’ type to the ‘droplet’ type, are discussed in the second part of the study. And independent calculations under different speed reduction conditions are employed to suit practical application scenarios. The comparison shows the applicability of the 2D numerical simulations at low Reynolds numbers. Although the amplitude calculation results at moderate Reynolds numbers are inconsistent with the experimental results, the two-dimensional numerical simulation has good reliability in the trailing vortex capture.

Effect of angle of attack on flow past a partially-burrowed, isolated freshwater mussel

Though freshwater mussels in rivers tend to be aligned with the flow, the angle of attack can increase significantly during periods when the stage and discharge vary rapidly (e.g., floods). As the near-bed flow changes, mussels can experience larger drag forces before they reorient themselves parallel to the flow and/or increase their level of burial into the substrate to avoid dislocation. The present paper used a previously validated eddy-resolving numerical model to study the changes in the structure of the near-wake flow, horseshoe vortex system, drag forces acting on the exposed part of the mussel shell, sediment entrainment mechanisms and dilution of the jet of filtered water originating in the excurrent siphon with the increase in the magnitude of the angle of attack, |θ|, for an isolated mussel placed in an open channel with incoming fully-developed, turbulent flow. Given that the mussel may modify its mean volumetric discharge through the two siphons and level of mussel burial as θ changes, simulations are performed with and without active filtering and with two heights of the exposed part of the mussel, h. The raise in |θ| increases the total drag force acting on the exposed part of the shell, the entrainment into the excurrent-siphon jet containing filtered water, the circulation of the horseshoe vortices, the strength of the anti-symmetric wake shedding mode and the circulation of the main streamwise-oriented (base) vortex forming behind the mussel. Results show that, for all angles of attack, the downflow induced by the primary base vortex generates a large region where the bed shear stresses are strongly amplified. So, particulate deposition is expected to be low and significant local scour may occur in the near wake of a partially burrowed mussel.

Refined production simulation and operation cost evaluation for power system with high proportion of renewable energy

The change of energy structure brings new challenges to the operation and planning of the power system, which requires the support of refined production simulation and evaluation techniques. Firstly, a scenario set generation method based on clustering coupling is proposed to generate typical operating scenarios of the power grid. Secondly, this paper proposes a power system operating cost evaluation index, considering line power flow constraints, energy storage constraints, system reserve cost, carbon emission cost, and cost per kWh. Furthermore, the calculation method of the system operation cost under the uncertainty scenario is given. In addition, the operation mode of wind and solar load shedding participating in reserve capacity scheduling is adopted, and the validity of the model is verified by the IEEE-30 node system as an example.

Effect of Variation in the Mass Ratio on Vortex-Induced Vibration of a Circular Cylinder in Crossflow Direction at Reynold Number = 104: A Numerical Study Using RANS Model

This study reports on the numerical analysis of the impact of mass ratio on the Vortex-Induced Vibration (VIV) phenomenon of an elastically rigid cylinder, oscillating freely in a crossflow direction. Reynolds-averaged Navier–Stokes (RANS) equations with (k-ω SST) model were used to analyze the flow behavior, amplitude ratio and vortex shedding patterns. The study was performed at constant Reynold number (Re) = 104 with reduced velocity (Ur) ranging from 2 to 14 and mass ratio (m*) of 2.4 and 11. The mass ratio was defined as the ratio between mass of the vibrating cylinder and mass of the fluid displaced. It was found that increasing the mass ratio from 2.4 to 11 resulted in decrease in amplitude response by 80%, 71% and 31% at initial branch, upper to lower transition region and lower branch, respectively. However, the amplitude in the upper branch decreased only 8% at high mass ratio. The peak amplitude observed in the present study was lower than previous experimental and DES results. However, the RANS k-ω SST well captured the vortex shedding modes of 2S, 2P, P + S, and 2T. In 2S mode, two single pairs of vortices were formed, whereas in 2P mode two pairs were generated in single oscillation. Similarly, P + S meant one pair and one individual vortex; whereas 2T mode meant two triplets of vortices generated in one oscillation. The study concluded that increase in mass ratio results in shortening of the lock-in region and decrease in amplitude response.

Nucleation effects on cloud cavitation about a hydrofoil

The dynamics of cloud cavitation about a three-dimensional hydrofoil are investigated experimentally in a cavitation tunnel with depleted, sparse and abundant free-stream nuclei populations. A rectangular planform, NACA 0015 hydrofoil was tested at a Reynolds number of $1.4\times 10^{6}$ , an incidence of $6^{\circ }$ and a range of cavitation numbers from single-phase flow to supercavitation. High-speed photographs of cavitation shedding phenomena were acquired simultaneously with unsteady force measurement to enable identification of cavity shedding modes corresponding to force spectral peaks. The shedding modes were analysed through spectral decomposition of the high-speed movies, revealing different shedding instabilities according to the nuclei content. With no active nuclei, the fundamental shedding mode occurs at a Strouhal number of 0.28 and is defined by large-scale re-entrant jet formation during the growth phase, but shockwave propagation for the collapse phase of the cycle. Harmonic and subharmonic modes also occur due to local tip shedding. For the abundant case, the fundamental shedding is again large-scale but with a much slower growth phase resulting in a frequency of $St=0.15$ . A harmonic mode forms in this case due to the propagation of two shockwaves; an initial slow propagating wave followed by a second faster wave. The passage of the first wave causes partial condensation leading to lower void fraction and consequent increase in the speed of the second wave along with larger-scale condensation. For a sparsely seeded flow, coherent fluctuations are reduced due to intermittent, disperse nuclei activation and cavity breakup resulting in an optimal condition with maximum reduction in unsteady lift.

Analysis of the dynamics of subharmonic flow structures via the harmonic resolvent: Application to vortex pairing in an axisymmetric jet

We demonstrate the use of the harmonic resolvent to study the physics of subharmonic flow structures in the proximity of time-periodic solutions of the Navier-Stokes equation. As an illustrative example, we study the vortex pairing phenomenon in a periodically forced axisymmetric jet. While it is well-known that vortex pairing in jets and mixing layers arises from the interaction between subharmonic perturbations and the fundamental vortex shedding mode, here we provide additional insight. In particular, we uncover the nature of the strong cross-frequency interactions in the flow, and we compute the spatiotemporal mode that drives the pairing mechanism.

Investigation Of 3D Effects And Free-Surface Proximity Influence On The Flow Around A Hydrofoil Using PIV Measurements

An Eppler 817 (E817) hydrofoil was studied experimentally using two dimensions two components Particles Image Velocimetry (PIV) measurements. Both statistical and time-resolved series were used to study the effect of Reynolds number and angle of attack on the flow topologies and dynamics. Vortex shedding modes were observed over a range of low chord-based Reynolds numbers 400 ≤ Rec ≤ 20000 and four angles of attack ( α = 2◦, 6◦, 12◦ and 30◦). Those Reynolds numbers are scarce documented on such hydrofoil as they are far from usual operating conditions. However, those low Reynolds numbers allowed us to observe Reynolds number based transitions of the vortex shedding modes at a given angle of attack. The data were acquired on both an extruded 2D hydrofoil and a 3D "T-shaped" hydrofoil, composed of a vertical shaft (e.g. rudder on a boat) holding the horizontal lifting surface. The latter was used to investigate the influence of both the 3D shape and surface proximity on the hydrofoil’s behaviour through three different depths, ranging from 3.5 to 0.875 chords. Additional measurements from a 6-axis loads sensor were used to characterize the loss of performance due to the free-surface proximity.

Vortex shedding modes of a vibrating cylinder colliding with a rigid wall

We have conducted two-dimensional computations of vortex-induced vibration of an elastically mounted circular cylinder colliding with a rigid wall at a Reynolds number of 300. For wide ranges of reduced velocities, we have identified C (chaotic), P (periodic), and QP (quasi-periodic) vortex shedding modes at two gap and mass ratios. The deflected gap flow induced by the wall shear layer during the descending motion of the cylinder cause stretching of the vortex strands, while both the P and QP modes show the “S”-type shedding signature. The pathlines for the C-mode yield unstable hyperbolic behavior, whereas twisted knots and spirals are seen for the P-mode. Criss-cross interactions with the swirling pathlines are observed in the QP-mode.

Attenuation of the unsteady loading on a high-rise building using feedback control

The unsteady wind loading on high-rise buildings has the potential to influence strongly their structural performance in terms of serviceability, habitability and occupant comfort. This paper investigates numerically the flow structures around a canonical high-rise building immersed in an atmospheric boundary layer, using wall-resolved large eddy simulations. The switching between two vortex shedding modes is explored, and the influence of the atmospheric boundary layer on suppressing symmetric vortex shedding is identified. It is shown that the antisymmetric vortex shedding mode is prevalent in the near wake behind the building, with strong coherence between the periodic fluctuations of the building side force and the antisymmetric vortex shedding mode demonstrated. Two feedback control strategies, exploiting this idea, are designed to alleviate the aerodynamic side-force fluctuations, using pressure sensing on just a single building wall. The sensor response to synthetic jet actuation along the two ‘leading edges’ of the building is characterised using system identification. Both the designed linear controller and the least mean square adaptive controller attenuate successfully the side-force fluctuations when implemented in simulations. The linear controller exhibits a better performance, and its effect on the flow field is to delay the formation of dominant vortices and increase the extent of the recirculation region. Feedback control that requires a smaller sensing area is then explored, with a comparable control effect achieved in the attenuation of the unsteady loading. This study could motivate future attempts to understand and control the unsteady loading of a high-rise building exposed to oncoming wind variations.

Energy exchanges in the flow past a cylinder with a leeward control rod

We study the energy exchanges between coherent structures and the mean flow in the wake of a cylinder in the presence of a leeward control rod using particle image velocimetry data at Reynolds number ( $Re$ ) $20\times 10^3$ . The shedding of the control rod depends on the oncoming shear layer and hence the downstream interaction of the main cylinder's and control rod's wake strongly depends on the control rod's setting angle ( $\theta$ ). In this work we study this interaction between the shedding modes from the cylinder and control rod at different $\theta$ . New secondary coherent motions with distinct characteristic frequencies appear in the flow field aside from the frequencies associated with the sheddings of the control rod, the main cylinder and its harmonics. A multiscale triple decomposition method is applied to extract the coherent modes associated with each of these frequencies, and the dynamics of the modes are studied using kinetic energy budget equations. The primary shedding modes of the control rod and main cylinder, as well as the harmonics of the main cylinder's shedding modes, are found to be primarily energised by the mean flow at this $Re$ , while the secondary modes are almost entirely energised by the primary modes, similar to the findings of Baj & Buxton (Phys. Rev. Fluids, vol. 2, issue 11, 2017, 114607) for a different multiscale flow configuration. The remarkable similarity in the energy exchange process forming the secondary coherent modes, observed in two different studies, hints at a possible universality in the formation process of these secondary structures in a multiscale flow.