Effect of near-wake jet on the lock-in of a freely vibrating square cylinder

Abstract

We present a numerical study of a freely vibrating square cylinder with steady bleeding at its base side. In particular, we focus on the suppression of vortex-induced vibration (VIV) and the reduction of drag force for the elastically mounted square cylinder at a laminar flow condition via near-wake jet. We examine the base bleeding mechanism in the near-wake region of a square cylinder and its influence over the flow dynamics and the wake characteristics for both stationary (nonlock-in) and freely vibrating (lock-in) conditions. We consider the near-wake jet parameter as a function of the bleed coefficient (C_q), which is the ratio of near-wake jet flow velocity to the freestream velocity and depends on the Reynolds number (Re) based on the diameter of the cylinder. Investigations of the hydrodynamic coefficients and the flow features are carried out for the laminar Re range, namely, Re = 40, 60, 100, and 150. A single dominant frequency peak is observed in the lift coefficient spectrum plot for all the Reynolds numbers considered, but two peaks are observed for Re = 150 at C_q = 0.175 and 0.2. Higher C_q values behave like a splitter plate thereby preventing the interaction of alternating shear layers. The variation of the mean drag is associated with the pressure distribution around the cylinder surface and along the streamwise locations. This leads to a thinner wake width, weaker vortices, and higher vortex shedding frequency as observed earlier in the literature. The sharp spikes of pressure coefficient at the base side of the cylinder are observed for Re ∈ [40, 150] due to the near-wake jet, accounting for the fluctuations of drag force coefficient. We demonstrate the formation of multiple vortices at the wake region due to the near-wake jet from our detailed qualitative analysis. We observe counter-rotating pair of recirculating fluids flanking at the near-wake jet location and examine the recovery of base pressure due to the jet flow. We demonstrate the splitting of big circulation fluid bubble into many smaller counter-rotating fluids due to high-velocity jet flow, resulting into the stabilization of flow profiles in the wake region. We extend this investigation to quantify the effect of the near-wake jet on the two-degree-of-freedom cylinder system at the representative Reynolds number Re = 100 and three mass ratios $m^{*}$ = 1, 2, and 3. We demonstrate the reduction of peak transverse VIV amplitude by 90% in comparison to the plain cylinder counterpart.