Flow-induced vibrations of a pair of in-line square cylinders

Flow-induced bidirectional vibrations of two in-line square cylinders of same size and mass ratio (=10) are analyzed at Reynolds number, Re = 100. The cylinders are located in the co-shedding regime, i.e., they are separated by a normalized center-to-center spacing of 5. The reduced speed, U*, is varied from 3 to 15 keeping Re constant. The upstream and downstream cylinders display identical frequency characteristics with U*. Accordingly, the cylinders share identical decomposition of dynamic response. The response is composed of the desynchronization regimes and lower branch; an initial branch does not exist. The vibrations are hysteretic at the lock-in boundaries whereas for a single square oscillator, hysteresis is identified only near the onset of lock-in. Hysteresis in the solutions for U*=7 within the lower branch is reflected in the wake mode of the rear cylinder whereas for the upstream cylinder, wake mode remains identical. The vortex-induced vibration (VIV) of the upstream cylinder is qualitatively similar to that of an isolated square oscillator. Despite the range of lock-in of the cylinders being identical, the VIV of the downstream cylinder departs significantly from its upstream counterpart. The shear layers separated from the front cylinder impinge on the rear cylinder and alter its flow field. The rear cylinder executes high amplitude VIV over the entire lower branch. The symmetry of the drag-lift phase diagrams does not necessarily translate to symmetric phase plots of in-line and cross-stream response. The drag and in-line response of the cylinders are out of phase throughout.