Experimental and numerical modelling of vortex-induced and wake-induced vibrations of clusters of subsea cylindrical structures

Abstract

The Fluid-Structure Interaction phenomenon of Wake-Induced Vibrations (WIV) of groups of cylinders is studied herein. This is particularly a problem for subsea pipelines, riser systems, and other structures that may be installed in clusters. Currently, a realistic and computationally efficient model to predict WIV is lacking and, therefore, the present research focuses on the analytical and experimental modelling of VortexInduced Vibrations (VIV) and WIV. Modelling of the wake flow deficit through classical boundary layer theory permits the derivation of steady wake-induced hydrodynamic forces and a computationally efficient modelling framework is introduced based on the wake oscillator concept. The model is validated with experimental results from the literature as well as experimental measurements conducted in the Wind, Wave and Current Tank at Newcastle University, for a pair of identical cylinders in the co-shedding regime, with low mass and damping ratios, and immersed in water. The experimental cylinders were attached to pendulum systems and supported by linear extension springs. Configurations tested included tandem and staggered cylinders, with a stationary or oscillating front cylinder, for a wide range of streamwise and transverse spacings. Both the model and experimental outputs illustrate the main features of WIV that are well known from literature. Nonetheless, novelties of the work include: the proposal of an analytical model for WIV of tandem and staggered cylinder couples based on a higher order hydrodynamic force theory; derivation of the nonlinear wake stiffness concept; mapping of the response of the downstream cylinder with respect to the mechanisms of VIV and WIV for a given reduced velocity and spacing; providing measurements for the wake flow behaviour and cylinder response after a static or freely vibrating upstream cylinder; investigation of the critical effect of the mean drag force on WIV; and the effect of the inline degree-of-freedom for tandem and staggered cylinders. The response of the downstream cylinder has been shown to be independent of the variation of d for the reduced velocity regime known as the first VIV regime; in the present study this is approximately Ur ≤ 5, i.e. the second cylinder behaves as a single cylinder undergoing VIV. This is one of the main features of this study and has been observed for all configurations and systems tested, whether these are for a 1DOF or 2DOF, fixed-free or free-free, tandem or staggered arrangement and from experimental or numerical results. For Ur > 5, investigation of time series, amplitudes of vibration and oscillation frequencies led to the conclusion that, depending on d, the

second cylinder could behave within three regimes: WIV, classical VIV or a transition from WIV to VIV. Three distinct oscillation frequency branches have been observed in the 1DOF response of the second cylinder. These are associated with three different concepts: the first cylinder vortex shedding frequency through the free-stream Strouhal law; the wake stiffness equivalent natural frequencies [12]; a wake-reduced vortex shedding frequency based on the Strouhal law which is computed using the steady wake flow velocity. They have been correlated to the mechanisms of VIV of the upstream cylinder, WIV and VIV of the downstream cylinder respectively. However, these frequency branches, although still observed, are less evident when the cylinders are also allowed to vibrate in the inline direction, as for the 2DOF numerical or experimental results