Vortex-induced vibration of an elastically mounted cylinder subject to planar inflow shear

Abstract

We have numerically investigated the effect of planar inflow shear on the vortex-induced vibration of a three-dimensional circular cylinder mounted on elastic supports in streamwise and cross-stream directions. At a Reynolds number Re=300, the reduced velocity (U∗) is varied in the range U∗=2−12 for a fixed mass ratio m∗=2. The effect of inflow shear is brought about by varying the shear parameter βy=0,0.05,0.1. We have observed four distinct branches in the structural response curve: Initial Branch (IB), High Amplitude Branch-1 (HAB1), High Amplitude Branch-2 (HAB2), and Desynchronization Branch (DS). The response of the cylinder is locked in with the near wake during IB, HAB1, and HAB2, where the inline oscillation amplitude of the cylinder triggers for increasing βy. The cylinder oscillates with a tilt against the high-velocity side at larger βy for HAB1 and HAB2 responses. During IB response at βy=0, the near wake shows the formation of vortex filaments clustered through the spanwise extent. However, in the HAB1 and HAB2 regimes, the propagation of secondary instability yields random occurrences of vortex splits in the wake. Similar consequences of vortex splits are found at βy=0.1 for IB, HAB1, and HAB2 regimes, where we observe fragmented vortex filaments wrapping around the vortex rings. For βy=0, we have found mode B-type wake instability in the IB response at a plane x=2, where the vortex structures form a staggered array with a spatial periodicity λ≈D. At z=0 plane, the vortex shedding mode is “2S” for the IB response at βy=0.05, while the “P+S” mode is at βy=0.1. The vortex strands experience stretching in the DS branch, where no specific shedding mode is discerned. The cross-stream evolution of time-averaged streamwise velocity shows a data collapse with an asymmetric localization above the cylinder for increasing βy. The streamwise and spanwise velocity fluctuations at βy=0.1 are insignificant compared to the cross-stream. However, for the IB and DS regimes, the growth of the rms velocities reveals spanwise invariance. In contrast, we found small-scale fluctuations of cross-stream velocities about the mean in the HAB1 regime. The temporal growth of the sectional drag coefficients (CDs) along the span shows a negative value in the IB regime for βy=0,0.5. However, we observe the quasiperiodic behavior of CDs along the span for the HAB1 regime at βy=0. The spanwise growth of CDs for the DS regimes shows intermittent transitions via the positive, zero, and negative values for different βy. For both IB and DS regimes at βy=0, the time evolution of sectional lift coefficients (CLs) is asymmetric along the span and represents a helical pattern. However, for increasing βy, the growth of CLs for HAB1 and HAB2 regimes is intermittent. An increase in βy triggers the magnitudes of CLs in the DS branch, where the spanwise evolution shows symmetric periodic bands of sectional lift coefficients.