Far-field condition of vortex methods on an impulsively started two-dimensional circular cylinder with rotation

Abstract

The far-field condition in the problem of the steady two-dimensional flow past a rotating circular cylinder is well known, but this condition is not clear in the problem of the two-dimensional unsteady flow past a rotating circular cylinder which is impulsively started. In the latter problem, the circulation around a contour of sufficient large radius surrounding the cylinder is dependent on initial conditions: (1) The circular cylinder is impulsively started with rotation from rest and (2) the rotating cylinder is impulsively started. The hybrid vortex method combined with a panel method is used for the flow of a slightly viscous, incompressible fluid around the rotating circular cylinder in the two initial conditions mentioned above. The numerical accuracy of this hybrid method is tested on the flow around an impulsively started cylinder without rotation. The detailed results of the flow around the rotating cylinder with a constant clockwise angular velocity show: (1) The initial shedding vortex is anticlockwise in the former initial case, but it is clockwise in the latter initial case. (2) The growth of the wake depends on the initial condition. (3) The time history of the aerodynamic force is dependent on the initial condition at the early stages of the development but it is almost independent of the initial condition after the early stages.