Vortex-induced vibrations of a rectangular cylinder

Vortex-induced vibrations of three tandem cylinders in laminar cross-flow: Vibration response and galloping mechanism

A numerical simulation study is conducted to investigate the effect of the mass ratio (m* = 3, 10, and 20) on vortex-induced vibration (VIV) of two tandem square cylinders at Re = 150. In this study, we mainly focus on the mass ratio effect on the vibration response, force characteristics, wake mode pattern, and fluid–structure-interaction (FSI) mechanism. The results show that mass ratio plays an important role in the VIV response of the two cylinders. With increasing reduced velocity, both the upstream cylinder (UC) and downstream cylinder (DC) at m* = 3 exhibit the soft-lock-in phenomenon (at a lock-in frequency ratio of fy/fn < 1) instead of the typical lock-in phenomenon (at a lock-in frequency ratio of fy/fn ≈ 1). With increase in the mass ratio to m* = 10 and 20, the soft-lock-in phenomenon disappears, while the DC exhibits the typical lock-in phenomenon. The maximum amplitudes of the two cylinders notably decrease with increasing mass ratio. Furthermore, the mass ratio exerts a major impact on the distance between the two cylinders, which may change the flow pattern. The distance sharply decreases in the synchronization region at m* = 3 but remains almost constant at m* = 10 and 20. In addition, the wake mode and FSI mechanism are more diverse at a low mass ratio (m* = 3).

The effect of the mutative side ratio (D/B) on the vortex-induced vibration (VIV) characteristic, aerodynamic characteristics, and the surrounding time-averaged and transient flow field of a rectangular cross section model were simulated numerically. Based on Fluent 19.0 platform, overset grid technology and the fourth-order Runge–Kutta method were used at Re 22 000. First, a rectangular cross section model with D/B = 0.25 was selected, and the simulation method and parameter settings were validated against previous literatures. The subsequent analysis compared and evaluated the effect of side ratio on the VIV response by focusing on statistical values of aerodynamic force coefficients, self-spectra, amplitude ratio, motion trajectory, and phase transition changes for stream-wise and cross-flow directions. Moreover, the study examined the influence of different models at different reduced velocities (Ur) on wake vortex-shedding. The findings suggest that, within a fixed cross-sectional area, a smaller side ratio leads to a weaker VIV characteristic and notably lower aerodynamic performance compared to a larger side ratio. The vortex-shedding mode of the rectangular cross section, particularly with a large side ratio, is less sensitive to changes in Ur compared to the standard square cylinder. An examination of the Reynolds number (Re) effect on the minimum and maximum side ratio models reveals that it has a more pronounced impact on the aerodynamic performance and VIV of the cross-flow when compared to in-line flow. In general, it is noted that larger side ratio model exhibits a stronger sensitivity to the variation of Re.

This work presents a two-dimensional (2D) numerical study on the flow-induced vibrations (FIV) of elastically mounted rectangular cylinders without and with barrier walls in a wide range of reduced velocities U*=1–200 and Scruton numbers Sc=0–64 at the Reynolds number of 1000. It reveals that a slender rectangular cylinder of aspect ratio 5:1 without barrier walls may experience vortex-induced vibration (VIV), while the one with barrier walls can have both VIV and soft galloping motions. The VIV motions of both cylinders occur at relatively small reduced velocities U*≤20, and their maximum amplitudes are gradually reduced with the increase in the Scruton number. The galloping motions of the cylinder with barrier walls take place at higher reduced velocities U*>30 with smaller frequencies and larger oscillation amplitudes. Quantitative analysis on the amplitude, displacement, and frequency of oscillation for both cylinders is carried out. Two phase diagrams of the vortex-shedding flow patterns are presented to illustrate the flow characteristics in VIV and galloping modes. Meanwhile, the dynamic mode decomposition analysis indicates the difference between the dominant mode of the dynamic flow field in the VIV and galloping motions. With the quasi-steady theory, it further shows that the occurrence of the soft galloping motion of the cylinder with barrier walls is caused by the negative slope of the lift coefficient at the angle of attack zero. These results may shed new light onto deeper understanding of the FIV phenomenon and provide some inspirations to engineering applications in the design of civil and offshore structures.

Numerical simulation of the vortex-induced vibrations of a 4:1 rectangular cylinder subjected to yaw uniform currents

Flow-induced vibrations of elastically-mounted C- and D-section cylinders

Aerodynamic interaction between galloping instability and vortices in corner-cut rectangular cylinders

It has been well known that the shear layers behind a prism at subcritical Reynolds number (Re) remain persistently stable. However, potential response of an elastically mounted non-circular prism at subcritical Re is still open. In this study, we numerically investigate the flow-induced vibrations of an equilateral triangular prism at subcritical laminar flow using the immersed boundary method. The prism is allowed to vibrate only in the transverse direction. It is found that the prism vibration could be excited and sustained at subcritical Re due to the instability triggered by the prism's movability. Within angles of attack α = 0°–60°, the triangular prism experiences three responses: i.e., vortex-induced vibration (VIV) at α = 0°–30°, large-amplitude vibration at α = 37.5°–46.5°, and galloping at α = 47.5°–60°. The characteristics of vibration amplitude, frequency, and dependence of fluid forces on reduced velocity and α are investigated. Eight different wake modes exist behind the prism, i.e., one stable mode, two shear layer modes, and five vortex shedding modes. In the VIV regime, the 2S mode (2 single vortices per vibration cycle) is the only vortex shedding mode, while the vortex shedding mode with more than two vortices is unique in the other two regimes. In the end, we discuss (i) the influences of Re and mass ratio and (ii) prediction of the galloping instability using quasi-steady analysis. It is found that three different response regimes are noticed, although their characteristics are strongly affected by the two factors. Quasi-steady approach could provide a reasonable prediction of the emergence of galloping instability for non-circular prism.

The effect of the mass of a 2D elastically-mounted circular cylinder in cross-flow on its vortex-induced vibrations and on the related vortex shedding lift forces is analyzed via a single-degree-of-freedom multi-frequency model (sdof-mf). The mechanical system in question is characterized by low mass ratio, low structural damping and Reynolds number of order $$10^4$$. The proposed sdof-mf model relies on the decomposition of the total hydrodynamic force in a inertia/drag force, conventionally associated with the cylinder motion in still fluid, and an additional lift force associated to pure vortex shedding. The lift force is assumed to be composed by not-Fourier-dependent harmonics; this constitutes the key point of the proposed sdof-mf model. The parameters of this model are determined via a parameter identification method based, in this case, on VIV data obtained via CFD. The simulations are carried out changing systematically the values of the mass ratio, within the range of engineering practice, and covering a wide range of flow regimes including lock-in conditions. The results from the application of the sdof-mf model highlight the large influence of the mass ratio on the response of the cylinder and on the vortex shedding lift force. The effects are clearly visible on the maximum amplitude at lock-in, on the range of incident flow velocity over which synchronization occurs, on ultra/sub harmonic behavior and phase lag of the cylinder motion, and finally on the magnitude and harmonic content of the lift force induced by pure vortex shedding.

Effect of side ratio on fluid flow and heat transfer from rectangular cylinders using the PANS method

We present an effective reduced-order model (ROM) technique to couple an incompressible flow with a transversely vibrating bluff body in a state-space format. The ROM of the unsteady wake flow is based on the Navier–Stokes equations and is constructed by means of an eigensystem realization algorithm (ERA). We investigate the underlying mechanism of vortex-induced vibration (VIV) of a circular cylinder at low Reynolds number via linear stability analysis. To understand the frequency lock-in mechanism and self-sustained VIV phenomenon, a systematic analysis is performed by examining the eigenvalue trajectories of the ERA-based ROM for a range of reduced oscillation frequency $(F_{s})$, while maintaining fixed values of the Reynolds number ($Re$) and mass ratio ($m^{\ast }$). The effects of the Reynolds number $Re$, the mass ratio $m^{\ast }$ and the rounding of a square cylinder are examined to generalize the proposed ERA-based ROM for the VIV lock-in analysis. The considered cylinder configurations are a basic square with sharp corners, a circle and three intermediate rounded squares, which are created by varying a single rounding parameter. The results show that the two frequency lock-in regimes, the so-called resonance and flutter, only exist when certain conditions are satisfied, and the regimes have a strong dependence on the shape of the bluff body, the Reynolds number and the mass ratio. In addition, the frequency lock-in during VIV of a square cylinder is found to be dominated by the resonance regime, without any coupled-mode flutter at low Reynolds number. To further discern the influence of geometry on the VIV lock-in mechanism, we consider the smooth curve geometry of an ellipse and two sharp corner geometries of forward triangle and diamond-shaped bluff bodies. While the ellipse and diamond geometries exhibit the flutter and mixed resonance–flutter regimes, the forward triangle undergoes only the flutter-induced lock-in for $30\leqslant Re\leqslant 100$ at $m^{\ast }=10$. In the case of the forward triangle configuration, the ERA-based ROM accurately predicts the low-frequency galloping instability. We observe a kink in the amplitude response associated with 1:3 synchronization, whereby the forward triangular body oscillates at a single dominant frequency but the lift force has a frequency component at three times the body oscillation frequency. Finally, we present a stability phase diagram to summarize the VIV lock-in regimes of the five smooth-curve- and sharp-corner-based bluff bodies. These findings attempt to generalize our understanding of the VIV lock-in mechanism for bluff bodies at low Reynolds number. The proposed ERA-based ROM is found to be accurate, efficient and easy to use for the linear stability analysis of VIV, and it can have a profound impact on the development of control strategies for nonlinear vortex shedding and VIV.

Effects of end condition and aspect ratio on vortex-induced vibration of a 5:1 rectangular cylinder

Although there are a great many papers dedicated to the problem of a cylinder vibrating transverse to a fluid flow ($Y$-motion), there are almost no papers on the more practical case of vortex-induced vibration in two degrees of freedom ($X,Y$ motion) where the mass and natural frequencies are precisely the same in both $X$- and $Y$-directions. We have designed the present pendulum apparatus to achieve both of these criteria. Even down to the low mass ratios, where $m^*\,{=}\,6$, it is remarkable that the freedom to oscillate in-line with the flow affects the transverse vibration surprisingly little. The same response branches, peak amplitudes, and vortex wake modes are found for both $Y$-only and $X,Y$ motion. There is, however, a dramatic change in the fluid–structure interactions when mass ratios are reduced below $m^*\,{=}\,6$. A new amplitude response branch with significant streamwise motion appears, in what we call the ‘super-upper’ branch, yielding massive amplitudes of 3 diameters peak-to-peak ($A^*_Y \,{\sim}\, 1.5$). We discover a corresponding periodic vortex wake mode, comprising a triplet of vortices being formed in each half-cycle, in what we define as a ‘2T’ mode. We qualitatively interpret the principal vortex dynamics and vortex forces which yield a positive rate of energy transfer ($\dot{e}_V$) causing the body vibration, using the following simple equation: \[\dot{e}_V = 2 {\Gamma}^* U^*_V \skew3\dot{Y}\] where $\Gamma^*$ is vortex strength, $U^*_V$ is the speed downstream of the dominant near-wake vorticity, and $\skew3\dot{Y}$ is the transverse velocity of the body. This simple approach suggests that the massive amplitude of vibration for the 2T mode is principally attributed to the energy transfer from the ‘third’ vortex of each triplet, which is not present in the lower-amplitude 2P mode. We also find two low-speed streamwise vibration modes, which is not unexpected, since they correspond to the first and second excitation modes of vibration for flexible cantilevers. By considering equations of motion for the two degrees of freedom, we find a critical mass, $m^*_{\hbox{\scriptsize\it crit}} \,{=}\, 0.52$, similar to recent $Y$-only studies, below which the large-amplitude vibrations persist to infinite flow velocity. We show that the critical mass $m^*_{\hbox{\scriptsize\it crit}}$ is the same for the $X$- and $Y$-directions, which ensures that the shapes of $X, Y$ trajectories can retain their form as the velocity becomes large. The extensive studies of vortex-induced vibration for $Y$-only body motions, built up over the last 35 years, remain of strong relevance to the case of two degrees of freedom, for $m^* \,{>}\, 6$. It is only for ‘small’ mass ratios, $m^* \,{<}\, 6$, that one observes a rather dramatic departure from previous results, which would suggest a possible modification to offshore design codes.

It is well known that fairing devices are better alternatives than helical strakes due to their low-drag performance while suppressing vortex-induced vibration (VIV). Our objective is to present a systematic numerical study to understand the hydrodynamic performance and physical mechanism of fairing configurations and then propose a new device for suppressing VIV and reducing drag force. In this work, we simplify our investigation by allowing the cylinder-fairing system to oscillate in cross-flow direction without rotation. Firstly, we present a set of simulations of vortex-induced vibration for Short Crab Claw (SCC) fairings [1] with different nondimensional length (Lf/D), where Lf is the length of fairing and D denotes the diameter of cylinder. To establish the relation between the length of fairing and the performance with respect to VIV suppression and drag reduction, we consider the length ratio Lf/D = 1.25, 1.50, 2.00. The underlying VIV suppression mechanism is investigated with the aid of force and amplitude variations, wake flow structures and frequency ratios. Our results show that the SCC fairing with longer length performs better by suppressing the amplitude up to 84% and reduces the drag coefficient by 40%. This finding implies that by offsetting the vortices shed away from the main cylinder, it lowers the influence of vortex interactions, which leads to the suppression of VIV and net reduction in the drag force generation. Based on this mechanism, we propose a new design of fairing, namely the “Hinged C-shaped”, which consists of a thin splitter plate (connected at the base of main cylinder) bifurcating into a C-shaped geometry after a certain distance. Through our numerical study on its hydrodynamic performance, it is shown to be efficient with respect to VIV suppression and drag reduction. To understand the VIV suppression physics, the numerical study is conducted in two-dimension for the cylinder-fairing mounted elastically with mass ratio m* = 2.6 and the damping ξ = 0.001 at low Reynolds number. We further demonstrate the performance of the new fairing device in three-dimension at sub-critical Reynolds number.

In this study, we investigate the critical mass phenomenon in vortex-induced vibration over a wide range of Reynolds numbers (Re=4000–30 000). We consider an elastically mounted cylinder that is able to vibrate transverse to a fluid flow. If we remove the restoring spring (k=0), then above a certain critical mass ratio (m∗ is oscillating body mass/displaced fluid mass), the cylinder will experience almost no motion, despite its unrestrained freedom to move transverse to the flow. However, when the mass ratio is decreased below a special critical value, without altering anything else in the system, we see a catastrophic increase in amplitude, and the body settles into a large amplitude periodic vibration. This corresponds to a change from a desynchronized wake to a 2P mode of vortex formation, where two pairs of vortices are formed per cycle of motion. Since a system with no restoring force represents a case of infinite normalized velocity (U∗→∞), the observation of high amplitude motion indicates that the regime of U∗ giving resonant vibration extends to infinity, for sufficiently small mass ratio. In this work, we measure the critical mass directly from experiments with no spring stiffness, and we show also how the critical mass may be accurately predicted from force measurements from controlled vibration experiments, or from free vibration measurements of elastically mounted cylinders. Critical mass gradually increases with Reynolds number from a value of 0.36 to 0.54, over the regime Re=4000–30 000. The fact that the critical mass is a function of Reynolds numbers should be expected because it depends on the vortex-induced forces, which are influenced by gradual changes in vortex formation as Re increases. The evaluation of critical mass in this configuration, and indeed in other diverse vortex-induced vibration (VIV) systems, is important because it can predict the regime of normalized velocities that will yield large amplitude vibration, and which one may wish to avoid in practice. The fact that critical mass, at moderate Reynolds numbers, in several diverse VIV systems, including cylinders in one or two degrees of freedom, pivoted bodies, cantilevers, and tethered spheres, are all within a small range 0.36–0.6, remains an interesting question.