Response of a circular cylinder wake to rotary oscillation

Abstract

A numerical study is made of flow behind a circular cylinder in a uniform flow, where the cylinder is rotationally oscillated in time. The temporal behavior of vortex formation is scrutinized over broad ranges of the two externally specified parameters, i.e., the dimensionless rotary oscillating frequency ($.110≤S_f≤.220$) and the maximum angular amplitude of rotation ($θ_max$=15˚, 30˚ and 60˚). The Reynolds number ($Re=U_{∞}D/υ$) is fixed at $Re=110$. A fractional-step method is utilized to solve the Navier-Stokes equations with a generalized coordinate system. The main emphasis is placed on the initial vortex formations by varying $S_f$ and $θ_max$. Instantaneous streamlines and pressure distributions are displayed to show the vortex formation patterns. The oscillatory forcing is in the vicinity of the lock-on range, which can be applied to flow feedback control afterwards. The vortex formation modes and relevant phase changes are characterized by measuring the lift coefficient ($C_L$) and the time of negative maximum $C_L(t_{-C_{L_{max}}})$ with variable forcing conditions. Next, an numerical analysis is performed for the quasi-periodicity in the wake where a circular cylinder is rotationally oscillated in time. The main emphasis is placed on the identification of frequency selections subjected to the controlled perturbations in the vicinity of lock-on. The frequency responses are scrutinized by measuring the lift coefficient ($C_L$). A direct numerical simulation is made to portray the unsteady dynamics of wake flows at $Re=110$. It is found that, after the shedding frequency is bifurcated at the boundary of lock-on, one frequency follows the forcing frequency and the other gradually converges to the natural shedding frequency. The asymptotic convergence phenomena are observed by solving the Van der Pol equation and the circle map. A new frequency selection formula is proposed. The quasi-periodic states are interpreted in terms of the forcing frequency, sh...