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Two-dimensional numerical computations are carried out for two rigidly connected cylinders of unequal sizes undergoing vortex-induced vibrations (VIV) perpendicular to the free stream. Results are examined for Re = 250 and a fixed diameter ratio of d / D = 0.2. The VIV response of the system is investigated for various positions of the small cylinder, covering a fine grid of wide radial (r) and azimuthal (θ) ranges, relative to the origin of the main cylinder. It is shown that the structural dynamics and hydrodynamic forces are strongly dependent on the arrangements. Regions of VIV reduction and amplification are distinguished, and the highest and lowest oscillation amplitudes are, respectively, acquired at configurations of (r , θ) = (0.7 D , 90 °) and (r , θ) = (0.88 D , 130 °). A deeper analysis in terms of the wake topology and surface pressure is then provided for these two extreme cases, to figure out the underlying mechanisms that lead to such markedly distinct responses. For the former case, the shear layers from two cylinders intensely interact and amalgamate during the oscillation, setting off subsequent processes of shear layer reattachment and downflow that are responsible for the observed high-amplitude response, while for the latter case, the shear layers from the small cylinder are highly stretched and absent from direct interaction with that from the large cylinder, which is favorable for stabilizing the wake and maintaining the low-amplitude response. Proper orthogonal decomposition (POD) is further utilized to correlate the key features of the wake with the dominant coherent structures in the flow. [ABSTRACT FROM AUTHOR]

Three-dimensional numerical computations are carried out for a cylinder undergoing controlled sinusoidal oscillation perpendicular to the free stream. The results are examined for Re = 500 and an oscillation amplitude of A / D = 0.25 , to allow comparison with the two-dimensional study by Blackburn and Henderson [J. Fluid Mech. 385, 255–286 (1999)]. The dynamic response of the flow is investigated over a wide oscillation frequency range from 0.5fo to 1.5fo, with fo being the natural shedding frequency of the fixed cylinder. As the oscillation frequency passes through fo, the ubiquitous abrupt shift in the phase of vortex shedding is again observed. On either side of this shift, the wakes exhibit Kármán mode of shedding, in the absence of the mode switch. The hypothesis for the mechanism of phase shift proposed by Blackburn and Henderson [J. Fluid Mech. 385, 255–286 (1999)] is further examined by quantitatively measuring the flux of vorticity generated on the base of the cylinder. Unlike in two-dimensional flow, where hysteresis is found to be associated with four branches, in three-dimensional flow only two longer branches K1 and K2 are identified, which bring out a remarkably simplified bifurcation structure. Dynamic mode decomposition (DMD) and its sparsity-promoting variant are used to characterize the coherent modes that govern the dynamics of the flow, as well as their corresponding frequencies. For the non-synchronized case, a multitude of DMD modes must be retained to accurately approximate the original flow, while for the synchronized case, only four DMD modes suffice to guarantee a same performance loss. In addition, the DMD modes that have the most profound impact on the hysteresis of lift and drag fluctuations are identified by DMD reconstruction. [ABSTRACT FROM AUTHOR]

Floquet stability analysis has been employed to identify modes of three-dimensional (3D) instability in the flow over a circular cylinder of diameter D above a moving wall at a gap height of G = 0.2D, beyond the onset of two-dimensional vortex shedding. Two subharmonic modes (mode C1 and mode C2) and one long-wavelength quasi-periodic mode (mode QPL) are revealed. The characteristics of these 3D modes are discussed in detail. The results of 3D direct simulations show that it is the intensively nonlinear modal interactions that lead to a chaotic final flow state at higher Reynolds numbers, rather than the interference of the shear layer caused by the no-slip moving wall. [ABSTRACT FROM AUTHOR]

The flow-induced vibrations of an infinite long flexible cable with a triangular cross section allowed to oscillate in the transverse direction are numerically investigated at a subcritical Reynolds number of 3900. The aim of the present investigation is to reveal the underlying mechanisms of galloping of a triangular cable via a highly resolved direct numerical simulation employing a high-order spectral/hp element method. Based on our previous results [Zhu et al., Phys. Fluids 31, 057101 (2019)], only one angle of attack in which one of the sides is facing the incoming flow, α = 60°, is studied in the present simulation. A tensioned beam model is employed to govern the dynamics of the triangular cable, and a tension value is selected to trigger a single wave along the cable. The numerical results show that the response amplitude of the triangular cable is significantly larger than that of a circular cable at the same conditions, i.e., the triangular cable vibration is more vigorous. Besides, the motion of the triangular cable can be divided into two independent types: the low frequency related to galloping and the high frequency related to vortex shedding. The first- and second-order turbulence statistics are also resolved to investigate the wake characteristics of a flexible body in a turbulent regime. The numerical results indicate that, as compared to the circular cable at the same conditions, more kinetic energy is transferred from the fluid to the triangular cable, which, in turn, is responsible for a lower turbulence intensity in the near wake (x/D < 10.0) of the cable. [ABSTRACT FROM AUTHOR]

Three-dimensional flow past a symmetrically curved circular cylinder with the free stream parallel to the plane of curvature is numerically investigated by high-order spectral element method. The axial line of the cylinder is described in Cartesian coordinates as y = A [ c o s h (x ∕ A) − 1 ] with A being a catenary coefficient used to scale its span ratio. In this geometry configuration, the deformed cylinder can be divided into two half segments, respectively of the convex segment in the upstream and the concave segment in the downstream. Different span ratios are investigated with respect to A = 0. 5 ∼ 10. It is found that four wake topologies, namely of single body, bi-stable, vortex impingement and steady wakes, are successively appeared with the increase of the span ratio. By examining the flow field quantities including mean and fluctuation of velocities and pressure along the axial line, some important characteristics of axial flow dynamics are intensively revealed. Most interestingly, the generation of axial flow along the curved surface of the cylinder is strongly influenced by not only the curvature ratio but also the wake interference effects. [ABSTRACT FROM AUTHOR]

Three-dimensional numerical simulation for the three circular cylinders at Re = 3900 is carried out by using the large eddy simulation (LES) in this paper. The present numerical model and parameters are verified by solving single cylinder and two cylinders cases. Then, the parameters consisted of spacing ratio (L / D) and incidence angle (α) are checked in three circular cylinders array. The fluid force and near-wake behavior of the two- and three-cylinder systems are analyzed with emphasis. Under a tight arrangement, there are three flow patterns: reattachment flow pattern, large-incidence-angle flow pattern, and biased flow pattern, corresponding to cases with incidence angles of 0, 45, and 90 degrees, respectively. The Strouhal number (St) of the three cylinders is essentially overlapping at α = 0° and α = 90°, the distinctive secondary peaks can be observed at the small spacing ratio in power spectral density (PSD). The mean pressure coefficient of midstream cylinder (MC) influenced by the number of cylinders is negative in the tandem arrangement at the stagnation point, accompanied by reattachment phenomenon the upstream surface of MC with L/D = 1.5. Placing the third cylinder between the two cylinders in a tandem arrangement significantly suppresses their lift oscillations. The phase difference (φ um) between the fluctuating lift of the upstream two cylinders is highly sensitive to the incidence angle of the system. [ABSTRACT FROM AUTHOR]

The wake of wavy cylinder has been shown to exhibit bistability. Depending on the initial condition, the final state of the wake can either develop into steady flow (state I), or periodic shedding (state II). In this paper, we perform numerical simulations to reveal the Reynolds number effects (R e = 30 – 300) on these two wake states. With increasing Reynolds number, the steady vortical structures in state I wake sways back and forth in the spanwise direction, resulting in low-frequency fluctuations in drag forces, but not in lift. For state II, the increase in Reynolds number is associated with the emergence of another spectral peak in the lift coefficient. The secondary frequency is associated with highly three-dimensional vortical structures in the wake. For both states, the wakes transition to turbulent flows at higher Reynolds numbers, with the development of small-scale vortices. We further study the streamwise gust flows over the wavy cylinder. The time-varying inflow velocity results in a wide range of instantaneous Reynolds number spanning from the absolutely unstable flow regime to the bistable regime. Depending on the period of the inflow velocity variation, the wake perturbations grown at the absolutely unstable flow regime can be damped out in state I wake, or grow large enough to trigger the transition to state II, resulting in loss of flow control efficacy. The above analyses reveal novel flow physics of the bistable states at unexplored Reynolds numbers, and showcase the complex transition behavior between the two states in unsteady flows. The insights gained from this study improve the understanding of the wake dynamics of the wavy cylinder. • The Reynolds number effects on the bistable states in the wake of a wavy cylinder are revealed. • A novel unsteady flow which only induces variations in drag but not in lift is discovered. • Complex transition behaviors between the two wake states in streamwise gust flow is unveiled. [ABSTRACT FROM AUTHOR]

Previous studies have revealed that fluid induced forces and wake structure of a cylinder can be significantly modified by varying the cross-section size along its axis. However, the fluid dynamic characteristics behavior of a flexible cable with a sinusoidal wavy surface remains unclear. The current study endeavors to present a systematic investigation of flow-induced vibrations (FIV) of an infinitely long wavy cable with different wave amplitude (A = 0. 1 D to 0. 3 D) and a constant spanwise wavelength λ = 4 π , by using a highly resolved direct numerical simulation employing a high-order spectral/ h p element method at a Reynolds number of 100, corresponding to laminar flow state. A tensioned beam model with a tension value can trigger a single wave is selected to govern the dynamics of the wavy cables. In addition, the structural dynamics are initialized from a standing wave. The present study focuses on the effects of the wave amplitude on the cable wake and the structural dynamic response, including the transverse displacement, wake pattern, vortex formation length, energy transfer, vortex shedding frequency and flow separation angle. Two completely different vibration modes are identified from the numerical cases studied, and hence the wavy cable are divided into control failure (A < 0. 2 D) and optimal wavy cable (0. 2 D ⩽ A ⩽ 0. 3 D) classes, respectively. It is also revealed that the counter-rotating vortices observed in the optimal wavy cables play an important role in stabilizing the shear layer and elongating the vortex formation length. Furthermore, the three-dimensional wake patterns of the wavy cable are mainly caused by the variations of flow separation angle along its spanwise direction. For the optimal wavy cables, the separation point is almost fixed along its spanwise direction while is variable for the control failure cases. [ABSTRACT FROM AUTHOR]

Three-dimensional large-eddy simulations are carried out for flow past a cylinder beneath a deformable free surface at a fixed Reynolds number of Re = 7550. The results are examined for two Froude numbers of F r = 0.2 and 0.6 and a gap ratio of 0.4, to investigate the effects of the distortion of the free surface on the flow fields and hydrodynamics. At the low Froude number of F r = 0.2 , the deformation of the free surface is small with little influence on the wake characteristics, and an alternative vortex shedding modulated by the free surface is detected in the wake. As the Froude number increases to 0.6, intense interface distortion occurs, which can be divided into three different regions: a hydraulic jump in the region of overtopping, a well-defined long-wavelength wave generation region in the large-scale recirculation zone near the free surface, and a water level recovery slope further downstream. The sudden change in flow regime from locally supercritical to subcritical allows the occurrence of the hydraulic jump. The induced surface waves behind the cylinder are ascribed to the shedding process of three shear layers, two of which are separated from the cylinder surface and one from the free surface. In addition, a jet-like flow originated from the gap between the free surface and the top of the cylinder occurs, exerting a downward thrust on the cylinder and pushing the wake away from the free surface. The Kármán vortex shedding in the wake is suppressed due to the interruption of the jet-like flow. The fluctuations of the wake turbulence and hydrodynamic forces are also suppressed to a low level. [ABSTRACT FROM AUTHOR]

This paper presents two-dimensional unsteady Reynolds-Averaged-Navier–Stokes simulations of flow past a circular cylinder beneath a free surface at a Reynolds number of 4. 96 × 1 0 4 . The effects of the free surface on the wake dynamics and hydrodynamics are systematically examined over a parameter space consisting of the Froude number (0.2–0.8) and the gap ratio (0.1–2.0). For high Froude numbers, it is easier to agitate the water to produce violent surface distortion compared to low Froude numbers. Three surface deformation patterns are identified and the underlying mechanisms are proposed. The wake type transition from the wake featured a jet flow, to the one-sided vortex shedding, to the free-surface modulated Kármán vortex shedding, and to the pure Kármán vortex shedding is discussed in detail. The strength hierarchy between the three shear layers present in the wake plays a decisive role in the transition of the wake types. An extra recirculation zone appears near the free surface due to the blocking effect of the front blunt body. The proximity to the free surface exerts a modulation effect on the temporal and spectral characteristics of hydrodynamics. Relatively large mean drag force with substantial fluctuations can be induced when (unilateral or bilateral) vortex shedding process occurs. When a jet dominates the wake, the mean drag force stays at a low level and the hydrodynamic fluctuations are suppressed. The circular cylinder is always subjected to a downward thrust which increases as the cylinder approaches the free surface. The critical range of parameter combinations is provided when the wake dynamics and hydrodynamics are not influenced by the free surface. • Three surface distortion patterns are identified, featuring hydraulic jump and wave. • Five wake types are identified, underlying mechanisms are proposed. • Blockage of the cylinder induces an extra recirculation zone near the free surface. • The free surface exerts temporal and spectral modulations on the hydrodynamics. • Critical parameters are provided when the flow is not affected by the free surface. [ABSTRACT FROM AUTHOR]

This paper identifies and characterizes modes of the three-dimensional instability of the flow over a circular cylinder of diameter D near a plane moving wall with a gap height of G = 0. 1 D beyond the onset of vortex shedding through the Floquet stability analysis. The associated effects of the transitions on the hydrodynamic forces of the cylinder are examined by performing direct numerical simulations. Six distinct three-dimensional modes are identified and their characteristics are discussed in detail. It is found that the physical mechanism responsible for the synchronous mode 1 appears to be associated to an elliptic instability. The quasi-periodic mode 4 is observed to transform to a synchronous mode (mode 6) on increasing the Reynolds number, indicating that they are likely to be resulted from the same physical mechanism. For mode 6, its physical nature seems to be a hyperbolic instability. Fully three-dimensional simulations show that the wake undergoes a rapid transition to complex chaotic flow state after the most dominant mode starts to saturate, due to the strongly nonlinear interactions of many modes with different spanwise wavelengths. • The presence of a plane moving wall in close proximity to a circular cylinder fundamentally alters the dynamics and the 3D wake transitions. • Six distinct modes of 3D instability are identified, their characteristics are discussed and the underlying physical mechanisms are proposed. • The three-dimensionality of the flow is triggered by different 3D instabilities as the Reynolds number is varied beyond the onset of vortex shedding. • The wake undergoes a rapid transition to complex chaotic flow state after the most dominant instability mode starts to saturate. [ABSTRACT FROM AUTHOR]

This paper presents numerical investigations of the flow-induced vibration of an elastically mounted elliptical cylinder with different aspect ratios. The cylinder is constrained to vibrate only in the cross-flow direction, with the major axis being perpendicular to the uniform flow. The Reynolds number, based on the free stream velocity and the major axis width, is fixed as 100. The aspect ratio (AR) is based on the minor axis width over the major axis width. By specifying AR = 0.1, 0.25, 0.5, 0.75 and 1, with a fixed mass ratio of 10, the fluid–cylinder interactions are simulated using a high-order Spectral/ hp element method to characterize the vibration responses, oscillation frequencies, fluctuating drag and lift coefficients, lock-in regimes and vorticity contours, with the variation of reduced velocities. A synchronization regime is found to be directly correlated with AR. For the lowest AR = 0.1, the elliptical cylinder response is found to be greater, as much as twice, than the circular cylinder response, by also exhibiting an earlier onset of the lock-in. The lack of the cylinder afterbody has a significant effect on the lower-branch response, resulting in a beating phenomenon and a rapid reduction in the response with decreasing AR. The effect of varying mass ratios is also investigated for low AR cases. The vortex shedding modes for all the response branches are found to be 2S with wake variants. A parallel vortex-shedding mode is noticed in a lower AR case with a large-amplitude oscillation whereas the C(2S) mode is observed in a higher AR case. • VIV of elliptical cylinders is investigated using Spectral/ hp element method. • Transverse responses and hydrodynamic features are simulated at Re =100. • Results highlight a significant effect of aspect ratio and cylinder afterbody. • Components of pressure versus viscous lift force fluctuations are described. • Variants of 2S vortex wake mode are observed behind elliptical cylinders. [ABSTRACT FROM AUTHOR]

Abstract In order to shed some light upon the mechanism for the free vibrations of the wavy cylinder reported previously (Zhang et al., 2017), we numerically investigate the effect of external forcing on the flow around a wavy cylinder at R e = 5000. The forcing takes the form of sinusoidal transverse motion with the amplitude fixed at A e / D m = 0.2 and the frequency spanning from f e D m / U ∞ = 0.1 to 0.3. Even though the wavy cylinder is optimally designed to annihilate the Kármán vortex shedding in the fixed configuration, the Strouhal frequency is found to resurrect in the forced vibration cases, leading to very similar responses between the normal and wavy cylinders, especially at high forcing frequencies. By sectional analysis it is revealed that the sectional distribution of the force coefficients undergoes significant changes with the increase of the forcing frequency. Statistical tools such as the correlation and coherence reveals further spanwise features of the force coefficients. In addition, the instantaneous three-dimensional vortical structures are visualized by the spanwise voriticity isosurfaces to collaborate the previous discussions. The cessation of the flow control efficacy in the forced vibration is explained by the recession of the mean streamwise vorticity contours. The results presented in the work imply that the vortex-induced vibration of the wavy cylinder might be ascribed to the typical wake-structure interaction as the normal cylinder, although the mechanism for the initial growth of the oscillations still warrants further investigations. Highlights • The forced vibration of a wavy cylinder is systematically studied. • The concealed Karman vortex shedding resurrect in the forced vibration, and may serve as the mechanism for VIV. • The response curves of the drag and lift coefficients, the vortex shedding patterns of the wavy cylinder resemble that of the normal cylinder. [ABSTRACT FROM AUTHOR]