“Added-Mass” Vortex-Sheet Development in an Accelerating Incident Flow

Abstract

The time-variation of unsteady flow around flapping wings [1] or during wing gust encounters [2] significantly complicates the aerodynamics involved [3] and can make it especially difficult to correctly identify the force response. One possible approach to compute this unsteady force is the impulse method proposed by [4]. He extended principles first developed by [5], and showed that the relative motion and change in strength of vorticity within the flow field can be related to a force. Moreover, in a bid to more easily model these complex unsteady phenomena, the flow field is often described using potential flow theory. Here, a true viscous flow field is modelled by superposing individual flow elements, where free vorticity is represented by point vortices and the boundary layer vorticity is modelled as an infinitely thin vortex sheet located on the object's surface [6]. The strength of this vortex sheet matches the vorticity distribution of the original viscous boundary layer and simultaneously enforces the no-through flow condition along its length, thereby itself becoming a streamline. Alternatively, the vortex sheet can be associated with the slip velocity along an object's surface [7].