Direct numerical simulation of vortex synchronization due to small perturbations

Abstract

Direct numerical simulation (DNS) is performed to investigate the vortex synchronization phenomena in the wake behind a circular cylinder at the Reynolds numbers, Re = 220 (mode-A regime) and 360 (mode-B regime). To generate vortex synchronization, a sinusoidal streamwise velocity perturbation, the frequency of which is about twice the natural shedding frequency, is superimposed on the free stream velocity. At Re = 360, vortex synchronization occurs when the perturbation frequency is exactly twice the natural shedding frequency. However, at Re = 220, it does not occur when the same perturbation frequency condition is imposed. Instead, it occurs when the perturbation frequency is near twice the hypothetical two-dimensional laminar vortex shedding frequency as if there were no wake transition at Re = 220. It is elucidated that, as a result of vortex synchronization, the trajectory of the Karman vortices and the vortex structure are changed. The Karman vortices are formed along the mean separating streamline slightly inside the mean wake bubble at Re = 220, but slightly outside at Re = 360. Thus, the Reynolds shear stress force has different contribution to the streamwise force balance of the mean wake bubble depending on the Reynolds numbers: its magnitude is negligible at Re = 220, compared to other force components, while it reverses its sign at Re = 360. More importantly, at Re = 220, the mode-A instability is suppressed into two-dimensional laminar flow with strong Karman vortices. At Re = 360, the dominant instability mode changes from mode B to mode A.