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.