Numerical Prediction of 3-D Vortex-Induced Vibration of Catenary Riser In Planar and Non-Planar Flows

Vortex-induced vibration (VIV) is one of the most critical issues in deepwater developments due to its resultant fatigue damage to subsea structures such as risers, pipelines and jumpers. Although VIV effects on slender bodies have been comprehensively studied over decades, very few studies have dealt with VIV modelling and prediction of catenary risers in current flows with varying directions leading to complex fluid-structure interactions. This study advances a numerical model to simulate and predict 3-D VIV responses of a catenary riser in three flow orientations, relative to the riser curvature plane, including concave/convex (planar) and perpendicular (non-planar) flows. The model is described by equations of cross-flow and in-line responses of the catenary riser coupled with the hydrodynamic forces modelled by the distributed nonlinear wake oscillators. A finite difference method is applied to solve the coupled fluid-structure dynamic system. To consider the approaching flow in different directions, the vortex-induced lift and drag forces are formulated by accounting for the effect of flow angle of attack and the riser-flow relative velocities. Results show VIV features of a long catenary riser exhibiting a standing and travelling wave response pattern. VIV response amplitudes and oscillation frequencies are predicted and compared with experimental results in the literature for both straight and catenary risers. Overall results highlight the model capability in capturing the effect of approaching flow direction on 3-D VIV of the curved inclined flexible riser.

Capturing Wake Stiffness in Wake-Induced Vibration of Tandem Cylinders

When a downstream circular cylinder is in the vicinity of the disturbed wake flow which is originated from the presence of an upstream cylinder, fluid-structure interactions due to vortex- and wake-induced vibrations may coexist. Their combined effects are of practical concern for offshore structures deployed in an array or proximity such as marine risers, pipelines and mooring lines. The wake flow deficit law and wake-induced drag and lift hydrodynamic forces are modelled based on the boundary layer theory, which is modified to account for the oscillation of the upstream cylinder. Unsteady drag and lift forces associated with the vortex-induced vibration (VIV) and wake-induced vibration (WIV) are represented dynamically by van der Pol-type wake oscillators. The present paper proposes a new modelling concept and framework capable of evaluating the combined WIV-VIV of tandem circular cylinders in comparison with experimental data, capturing a key feature of the wake stiffness associated with WIV. An equivalent natural frequency based on the wake stiffness mechanism behaves equivalently to the WIV frequency. Numerical studies show that the downstream cylinder may respond in a multi-frequency scenario at specific reduced velocities. The prediction model captures the wake stiffness trend similar to the experimental observation. The correlation to the wake stiffness concept allows the identification of situations for which the downstream cylinder is mainly governed by the WIV mechanism resulting in largest vibration amplitudes.

Phenomenological Modelling of Cylinder VIV With Contributions From Oscillatory Flows

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.

Manifestation of additional frequencies in vortex induced vibrations in the presence of noise

In this study, we examine the effect of random input fluctuations in the mean flow to a circular cylinder undergoing transverse oscillations. A Duffng-Van der pol combined system has been used to model the structure and wake oscillators in the VIV system. We observe that the addition of noise brings in major qualitative and quantitative changes on the structural response of the system compared to the deterministic cases. It has been observed that the stochastic system is always influenced by the presence of structural frequency. In contrast, the system under mean flow condition aligns with the structural frequency, only in the lock-in range. This feature is seen as noise exciting multiple frequencies in the response of the cylinder in the pre lock-in and post lock-in regimes.

Combined FIV and VIV Effects on a Cantilevered Pipe Discharging Fluid in Deep Waters

To avoid or mitigate global warming, several ocean carbon capture and storage concepts have been proposed. One of the recent approaches is to dispose carbon dioxide via a fixed vertical cantilevered pipe onto the seabed in deep waters. Due to a high aspect ratio and flexibility of such long pipe conveying fluid with fixed-free end conditions and external hydrodynamic loading caused by currents, the pipe may experience large-amplitude 3-D vibrations leading to structural failure. Hence, it is essential to understand and investigate the pipe nonlinear dynamic behaviors subject to combined flow-induced vibration (FIV) and vortex-induced vibration (VIV). In this study, the 3-D nonlinear equations of a cantilevered pipe discharging fluid in the sea are analyzed using a Galerkin-based multi modal approach combined with a finite difference Houbolt’s integration scheme. Particular attention is paid to the combined effects of FIV and VIV on the dynamic response of the cantilevered pipe in water. To model the fluctuating lift and drag forces associated with VIV, the two dimensional wake oscillators distributed along the pipe are adopted. Numerical simulations in the FIV case of a pipe discharging fluid in the air are first validated with experimental results in the literature to justify the mathematical models and numerical approaches. Modal convergence analysis is also performed. Results in the combined FIV and VIV cases are then highlighted in order to show the effects of cross-flow and in-line VIV when compared with the pure FIV case. The effects of geometric nonlinearities, the coupling/interaction of multi modes and the space-time modifications of pipe responses and trajectories are highlighted. It is hoped that the numerical observations and findings obtained from this study could be verified by experimental studies which are presently lacking in the literature.

Experimental Investigation of Two-Degree-of-Freedom VIV of Circular Cylinder With Low Equivalent Mass and Variable Natural Frequency Ratio

This paper presents an experimental investigation and validation of numerical prediction model for a 2-DOF VIV of a flexibly mounted circular cylinder by also accounting for the effect of geometrically nonlinear displacement coupling. A mechanical spring-cylinder system, achieving a low equivalent mass ratio in both in-line and cross-flow directions, is tested in a water towing tank and subject to a uniform steady flow in a sub-critical Reynolds number range of about 2000–50000. A generalized numerical model is based on double Duffing-van der Pol (structure-wake) oscillators which can capture the structural geometrical coupling and fluid-structure interaction effects through system cubic and quadratic nonlinearities. Experimental results are compared with numerical predictions in terms of response amplitudes, lock-in ranges and time-varying trajectories of cross-flow/in-line motions. Some good qualitative and quantitative agreements are found which encourage the use of the proposed numerical model subject to calibration and tuning of empirical coefficients. Various features of figure-of-eight orbital motions due to dual resonances are observed experimentally as well as numerically, depending on the natural frequency ratio of the oscillating cylinder.

Wake-Induced Transverse Vibration of Two Interfering Cylinders in Tandem Arrangement: Modelling and Analysis

A considerable number of numerical and experimental studies have been performed on the problem of vortex induced vibration (VIV) of an isolated circular cylinder. A very few studies have considered a practical situation where cylinders are deployed in clusters. This study presents a mathematical fluid-structure interaction modelling and analysis of two flexibly-mounted circular cylinders arranged in tandem and subject to fluid cross flows. The hydrodynamic lift forces and their time variations are approximated by two different semi-empirical wake oscillator models based on the van der Pol and Rayleigh equations. These nonlinear wake oscillators are coupled with linear structural oscillators through the acceleration and velocity coupling terms, respectively. A direct numerical time integration approach is used to predict the response amplitude behaviors and parametrically investigate the vortex- and wake-induced vibration transverse response of the two interfering upstream and downstream cylinders. Some empirical coefficients are calibrated against available, although very limited, computational fluid dynamics results. Preliminary parametric studies are conducted with the case of varying reduced flow velocity, and some insightful aspects on the effect of mass and damping ratio are highlighted. Depending on system parameters, numerical prediction results based on the van der Pol and Rayleigh equations are compared, and a combination of the two wake oscillators is suggested as a new model for predicting the vortex and wake-induced of the two interfering cylinders.