The Study of Kinematics and Dynamics of Oscillating Laminar Flow About a Cylinder

In this paper, the oscillating two-dimensional laminar flow about a cylinder and the oscillation of a cylinder in still water are studied. A finite volume method is applied to solve the Navier Stokes equations using SIMPLEC algorithm on a body fitted co-located O-type grid. In this study, the non-dimensional flow numbers, Keulegan-Carpenter and Stokes’ numbers are chosen over a range where different laminar flow regimes are normally three-dimensional. The results of this simulation and comparison with numerical and experimental works indicate the good capability of this two-dimensional model in showing the various regimes of flow patterns and vortex shedding. Considering the forces exerted on the cylinder, this study shows that in cases where the flow is of a regular type, there is a good match between longitudinal force presented by this work and the one calculated through Morrison’s equation. But for irregular flows where the flow pattern changes in each cycle, there is less overlap and the accuracy of Morrison’s equation is reduced. Studying the time variation of the transversal force gives accurate information about the vortex shedding and its frequency in each cycle and mode changing. Since the flow mode changes continuously with time, the average of transversal and longitudinal forces on consecutive cycles is not a good representation of the force exerted on the cylinder. On the other hand, the model has satisfactorily reproduced the time variation of the tranversal and longitudinal forces of a pure mode, matching the experimental results. Keywords: Oscillating flow, Laminar flow about a cylinder, Numerical solution