A nonlinear time-domain simulation model for predicting two-dimensional vortex-induced vibration (VIV) of a flexibly mounted circular cylinder in planar and oscillatory flow is presented. This model is based on the utilization of van der Pol wake oscillators, being unconventional since wake oscillators have typically been applied to steady flow VIV predictions. The time-varying relative flow-cylinder velocities and accelerations are accounted for in deriving the coupled hydrodynamic lift, drag and inertia forces leading to the cylinder cross-flow and in-line oscillations. The system fluid-structure interaction equations explicitly contain the time-dependent and hybrid trigonometric terms. Depending on the Keulegan-Carpenter number (KC) incorporating the flow maximum velocity and excitation frequency, the model calibration is performed, entailing a set of empirical coefficients and expressions as a function of KC and mass ratio. Parametric investigations in the case of varying KC, reduced flow velocity, cylinder-to-flow frequency ratio and mass ratio are carried out, capturing some qualitative features of oscillatory flow VIV and exploring the effects of system parameters on response prediction characteristics. The model dependence of hydrodynamic coefficients on the Reynolds number is studied. Discrepancies and limitations versus advantages of the present model with different feasible solution scenarios are illuminated to inform the implementation of wake oscillators as a computationally efficient prediction model for VIV in oscillatory flows.

Phenomenological wake-cylinder oscillators have been extensively implemented for vortex-induced vibration (VIV) predictions. Although such models capture fundamental VIV phenomena, the maximum response estimations and comparisons with different experimental data reveal some quantitative discrepancies due to the model empiricism embedding some uncertainties through system variables. This vital issue has not been well addressed in the literature of VIV modelling. This paper presents a new comprehensive investigation into the sensitivity to empirical input variables of nonlinear wake-cylinder oscillators simulating the twodimensionally coupled cross-flow/in-line VIV and amplified mean displacements of a flexibly mounted circular cylinder in uniform flows. The fluid-structure coupling terms are advanced by accounting for the higher-order nonlinear effects of fluctuating lift-drag forces and steady-drag dynamic magnifications, depending on the relative flow-cylinder velocities. A random sampling and variance-based sensitivity studies are carried out using Monte Carlo simulations which are computationally efficient based on the reduced-order model. This enables a large series of parametric examinations. Individual contribution, relative importance,coupling and interdependence of multiple input variables affecting output uncertainties are qualitatively and quantitatively evaluated. The Reynolds number dependence is also captured by correlating the wake and hydrodynamic coefficients with experimental data. Parametric studies highlight greater variations in the predicted amplitudes and mean displacements of the cylinder two-degree-of-freedom VIV with a lower mass ratio. Numerical findings allow for the identification of a few most influential variables to be treated as the empirically tuned coefficients. The improved understanding of model versatility and sensitivity enhances the calibration confidence and the response predictability with a reduced computational effort.Highlights  Monte Carlo-based sensitivity analyses of nonlinear wake-cylinder oscillators are presented. Contribution, relative importance, coupling and interdependence of empirical variables are studied. Reynolds number dependence of empirical wake and hydrodynamic coefficients is accounted for. Most influential variables correspond to lift force wake oscillator governing cross-flow/in-line VIV. Input sensitivities and output uncertainties depend on system parameters and response amplitudes.

This paper presents a numerical phenomenological model for a two-degree-of-freedom VIV of a flexibly mounted circular rigid cylinder subject to sinusoidal oscillatory flows. This prediction model is based on the use of double Duffing-van der Pol (structure-wake) oscillators which capture the structural geometrical coupling and fluid-solid interaction effects through system cubic-quadratic nonlinearities. Empirical coefficients are calibrated based on computational fluid dynamics results in the literature for the Keulegan-Carpenter numbers (KC) of 10, 20 and 40, satisfying a reasonable correspondence in amplitude and frequency responses. For KC = 10, the cross-flow vibrations present a single-frequency response. For KC = 20 and 40, cross-flow vibrations have multi-frequency responses. The primary frequency of the response in the cross-flow direction decreases with increasing reduced velocity, except for small values of the reduced velocities. In all KC cases, the in-line vibrations exhibit mostly a single frequency. Overall, parametric studies capture the dependence of response characteristics on the KC, reduced velocity, mass ratio, frequency ratios and empirical coefficients.

This paper presents new laboratory experiments of two-degree-of-freedom vortex-induced vibration of a flexibly mounted vertical circular cylinder in regular waves. A new experimental model has been developed and tested in the Wind, Wave & Current Tank at Newcastle University. The system mass ratio is close to 3 and the cylinder aspect ratio based on its submerged length is close to 27. The Stokes first-order wave theory is considered to describe the depth-dependent, horizontal velocity amplitude of the wave flow in the circulating water tank. This wave theory is satisfactorily validated by the wave probe measurement. The effects of cylinder stiffness affecting system natural frequencies are also investigated by using a combination of different spring setups in in-line and cross-flow directions. For each set of springs, VIV tests are performed in regular waves, with flow frequency ranging from 0.4 to 1 Hz and amplitude from 0.01 to 0.09 m. The associated Reynolds number at the water surface is in a range of 1.7 × 103–1.5 × 104. The surface Keulegan-Carpenter number (KC) is in the range of 2 < KC < 28 while the surface reduced velocity (Vr) is in the range of 0.5 < Vr < 16 depending on the implemented spring stiffness. Combined in-line/cross-flow oscillations of the cylinder are measured using two non-intrusive Qualisys cameras and the associated data acquisition system. The spring forces are also acquired using four load cells. Results reveal that, depending on KC and Vr, the cylinder primarily oscillates at the flow frequency in the in-line direction and at an integer (mainly 2, 3 and 4) multiple of the flow frequency in the cross-flow direction. Such occurrence of multi frequencies corroborates other experimental and numerical results in the literature. Several peculiar trajectories are observed, including infinity, butterfly, S and V shapes. The present experimental data of vibration amplitudes and oscillation frequencies in in-line/cross-flow directions as well as response patterns provide new results and improved understanding of VIV in oscillatory flows. These will be useful for the development of an industrial tool in predicting offshore structural responses in waves.

This paper presents the experimental investigation of vortex-induced vibrations (VIV) of a flexibly mounted circular cylinder in combined current and wave flows. The same experimental setup has previously been used in our previous study (OMAE2020-18161) on VIV in regular waves. The system comprises a pendulum-type vertical cylinder mounted on two-dimensional springs with equal stiffness in in-line and cross-flow directions. The mass ratio of the system is close to 3, the aspect ratio of the tested cylinder based on its submerged length is close to 27, and the damping in still water is around 3.4%. Three current velocities are considered in this study, namely 0.21 m/s, 0.29 m/s and 0.37 m/s, in combination with the generated regular waves. The cylinder motion is recorded using targets and two Qualisys cameras, and the water elevation is measured utilizing a wave probe. The covered ranges of Keulegan-Carpenter number KC are [9.6–35.4], [12.8–40.9] and [16.3–47.8], and the corresponding ranges of reduced velocity Vr are [8–16.3], [10.6–18.4] and [14–20.5] for the cases with current velocity of 0.21 m/s, 0.29 m/s and 0.37 m/s, respectively. The cylinder response amplitudes, trajectories and vibration frequencies are extracted from the recorded motion signals. In all cases the cylinder oscillates primarily at the flow frequency in the in-line direction, and the in-line VIV component additionally appears for the intermediate (0.29 m/s) and high (0.37 m/s) current velocities. The cross-flow oscillation frequency is principally at two or three times the flow frequency in the low current case, similar to what is observed in pure regular waves. For higher current velocities, the cross-flow frequency tends to lock-in with the system natural frequency, as in the steady flow case. The inline and cross-flow cylinder response amplitudes of the combined current and regular wave flow cases are eventually compared with the amplitudes from the pure current and pure regular wave flow cases.