Synchronization of vortex shedding from a cylinder under rotary oscillation

A numerical study is made of the unsteady two-dimensional, incompressible flow past a circular cylinder under rotary oscillation. Our aim is to simulate the synchronization or phase-locking phenomena via an explicit time-marching algorithm for the governing equations. Associated with the stream function (psi)-vorticity(omega) formulation of the Navier-Stokes equations, the Poisson equation for psi is solved by a Fourier-finite-analytic, separation-of-variable approach. This approach offers an improvement in treating both the no-slip and the far-field boundary conditions. As for the vorticity transport equation, spatial discretization is performed by means of finite-difference in which the convection terms are improved by an ENO (essentially non-oscillatory)-like data reconstruction process. The interior vorticity is then updated by an explicit, second-order Runge-Kutta method. Present computations relate to flow at a Reynolds number R = 1000. It is shown that the scenes of synchronization are comparable with those relating to cross-flow and in-line oscillations at a Reynolds number R less than or equal to 1300. In addition, the efficacy of reducing drag by means of rotary oscillation is addressed. (C) 1997 Elsevier Science Ltd.