The boundary layer on an impulsively started rotating and translating cylinder

Abstract

The time-dependent boundary-layer flow past an impulsively started translating and rotating circular cylinder is investigated. Two different solution methods are used to calculate the initial flow development; these are an expansion of the solution in a power series in time after the impulsive start and a fully numerical integration of the governing equations. Both solution methods are in excellent agreement during the initial stages of the motion. Calculations are carried out for various rotational speeds of the cylinder and in the boundary-layer limit of infinitely large Reynolds number. The results show a wide variety of unusual and complex boundary layer separation flow patterns; it is demonstrated how separation is affected by increasing rotation rates and further how it is ultimately completely suppressed by the rotation. This problem involves both an upstream and downstream moving wall for the boundary layer flow and consequently is of interest in connection with the Moore–Rott–Sears criterion for unsteady separation; the present results suggest the criterion for both the upstream moving wall and the downstream moving wall will be achieved in these flows.