Flow development in the vicinity of the sharp trailing edge on bodies impulsively set into motion

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Abstract
The initial development of the viscous flow in the vicinity of the sharp trailing edge of a symmetrical body, impulsively set into motion is studied within the framework of boundary-layer theory. For a blunt trailing edge there exists a similarity solution for the inviscid outer flow as has been pointed out by Proudman & Johnson (1961). The present work shows that for sharp trailing edges, however, no such solution exists.For small or moderate trailing-edge angles, a moving singularity occurs in the solution fairly early in the flow development. The flow in the vicinity of this singularity exhibits the characteristics of unsteady separation. For large trailing-edge angles, the boundary layer becomes so thick that solutions must be terminated before there is any evidence of a singularity. For a cusped trailing edge, the solution is arbitrarily terminated to avoid large computational times and with the realization that the trailing edge flow must eventually be influenced by the leading edge at which time the present solutions cease to have meaning.

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