Influences of upstream extensions on flow around a curved cylinder

In simulations of flow around a concave curved cylinder, i.e. free-stream aligned with the plane of curvature and directed towards the inner face of the curvature, one cannot avoid interactions between the cylinder and the inlet boundary. To get rid of the effects brought about by this interaction, we consider different lengths of upstream straight extensions at the lower end of the curved cylinder (0D, 5D and 10D, where D is the cylinder diameter), referred to as horizontal extensions. In this study, we directly solve the time-dependent three-dimensional Navier-Stokes equations. Results reveal that the appended horizontal extension allows the boundary layer to develop, so that the velocity profile at the curved cylinder inception is significantly different from the case where no horizontal extension is considered. The laminar boundary layer is thinner than that in the flat plate flow, which is given by Blasius' solution. The results from 5D and 10D extensions show a clear convergent tendency. We therefore suggest that a horizontal extension is essential for concave curved cylinder flow simulation, and 10D would be a preferred choice.