Flow Transient Near the Leading Edge of a Flat Plate Moving Through a Viscous Fluid

Abstract

An investigation is made of the unsteady flow in the leading-edge region of a semi-infinite plate impulsively started from rest. Based entirely on the vorticity concepts outlined by Lighthill, numerical results are obtained for the complete two-dimensional flow field by solving the single vorticity transport equation. An essential input to the calculations is the distribution of vorticity production at the plate surface. This is determined at each instant of time from the no-slip condition at the plate and represents a departure from conventional numerical analyses of viscous flows. Departing further from conventional approaches, the velocity field is computed from the law of induced velocities (Biot-Savart law) rather than the stream function. Because of vorticity diffusion well ahead of the plate, a significant disturbance propagates upstream, thereby destroying the uniformity of the approaching flow. Calculations are carried sufficiently forward in time for an approximately steady state to be reached at a distance downstream of the leading edge equal to the thickness of the viscous layer. As viewed by an observer moving with the plate, the flow transient exhibits a velocity overshoot relative to the apparent free-stream velocity. This effect was unexpected for a semi-infinite plate and represents a novel aspect of the flow not found in transient analyses based on the boundary-layer approximations.