On the flow over a rotationally oscillating flat plate: A numerical study

The characteristics of the flow in the wake of a plate that is normal to the free stream in its neutral position undergoing rotational oscillation has been investigated. The governing equations based on stream-function/vorticity formulation are solved numerically to determine the two-dimensional flow field structure. The numerical simulations are performed in a rotating reference frame attached to the plate. The simulations focus on the lock-on phenomenon of vortex shedding for frequency ratios of forcing Strouhal number to natural shedding Strouhal number Ste/Stn=0.96-1.04 at a Reynolds number Re=100. The time histories of drag coefficient as well as surface vorticity of the plate show amplitude modulation when the vortex shedding is not-locked-on to the plate oscillation at smaller forcing amplitude. The modulation disappears once lock-on occurs where the vortex shedding is synchronized with the plate oscillation at larger amplitude. The limits of lock-on regime bounded by the forcing frequency and amplitude are found in good agreement with the experiments conducted at higher Reynolds numbers (Re=3600-9800). For the approach to lock-on from a lower frequency (Ste/Stn=0.96) and an upper frequency (Ste/Stn=1.04), the numerical simulations demonstrate significant differences in lock-on behavior, including the structure of vortices, fluctuation amplitudes of drag coefficient and surface vorticity, and route leading to lock-on.