Unsteady Flow Structure and Surface Pressure Due To Translation of a Cylinder Past An Elliptical Leading-Edge

Abstract

Translation of a cylinder past an elliptical leading-edge induces three basic classes of flow structure: a jet-like injection between the cylinder and the edge, which inhibits large-scale vortex formation; formation of a large-scale vortical structure that translates along the surface of the edge; and formation of small-scale vortices from the cylinder in the absence of either of the two types of previous patterns. These three classes of flow structure occur at successively higher values of translations velocity of the cylinder. There are two principal contributions to the unsteady surface pressure. The first is that arising from the cylinder-induced distortion of the flow. This inviscid distortion corresponds to a pressure wave along the surface of the edge having infinite propagation speed. The second is associated with the vortical disturbances arising from the cylinder-edge interaction; the corresponding pressure wave has a propagation speed of the speed of the order of the free-stream velocity. At low translational velocities of the cylinder, the latter type of pressure disturbance dominates, while at higher values of cylinder velocity, the former contribution becomes relatively large. In this case, the minimum pressure amplitude occurs neither at the tip of the edge nor at large distances downstream of it. Rather, it occurs in an intermediate region downstream of the tip where the inviscid distortion effect becomes small and the contribution from the vortical disturbance is still small due to the incomplete concentration of vorticity in the developing vortical structure along the surface of the edge.