Modelling of wake-induced vibrations of tandem cylinders with a nonlinear wake-deficit oscillator

Abstract

For a pair of elastically mounted circular cylinders in a tandem configuration, the downstream cylinder may experience the wake-induced vibration (WIV) due to the hydrodynamic excitation associated with the wake behind the upstream cylinder. In addition to WIV, the downstream cylinder may also be simultaneously subject to the vortex-induced vibration (VIV) due to the vortex shedding in its own wake. This nonlinear coupled wake-vortex interaction can result in a sustained large-amplitude response depending on the cylinder spacing. In this study, a new nonlinear wake-deficit oscillator model for predicting the combined WIV-VIV responses in the cross-flow direction of the downstream cylinder is presented. While the upstream stationary or oscillating cylinder is placed in a uniform steady flow, the downstream cylinder is subject to a non-uniform unsteady flow with a space–time varying velocity being modified by the wake deficit or shielding effect. The total cross-flow hydrodynamic force on the downstream cylinder is modelled as a combination of the wake-induced transverse force and the combined vortex-induced lift and drag forces. The wake-induced force is approximated using a wake deficit theory based on a linearised boundary layer equation. The vortex-induced force is modelled using the van der Pol oscillator which incorporates the wake-deficit flow velocity, relative flow-cylinder velocities and dynamically staggered positions between the two interfering cylinders. These empirical hydrodynamic force equations are nonlinearly coupled, simulating the wake-vortex interaction leading to the combined WIV-VIV responses depending on the fluid–structure parameters. By focusing on the wake interference regime, the wake profiles and hydrodynamic forces are calibrated and validated, introducing new empirical coefficients and functions. The downstream cylinder responses and oscillation frequencies are predicted and compared with relevant experimental data by accounting for the important effects of cylinder spacing ratio, reduced flow velocity and Reynolds number in a subcritical flow regime. The wake stiffness characterisation is also presented, providing an analytical formulation related to the dynamic wake profile. Several key features associated with WIV response amplitudes and frequencies are highlighted and discussed using the calibrated wake-deficit oscillator. The present concept and model can be further improved to account for the effects of in-line response and arbitrarily staggered arrangement as well as the application of multiple long flexible cylinders with multi modal responses.