Separation and reattachment near the leading edge of a thin oscillating airfoil

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Abstract
The evolution of unsteady boundary layers in the vicinity of the leading edge of a thin oscillating airfoil has been examined with a novel numerical method which is able to deal with the movement of the stagnation point and with regions of reverse and separated flow. Solutions to the unsteady boundary-layer equations, with a prescribed pressure distribution which causes flow reversal and separation, demonstrate the importance of numerical steps in distance and time and that a requirement similar to the stability criterion of Courant, Friedrichs and Lewy must be satisfied to avoid numerical errors. At the lower reduced frequencies of the investigation, solutions could not be obtained with this procedure and it was necessary to introduce interaction between the viscous and inviscid flows. The solutions obtained with the interactive method were increasingly different from those without interaction as the reduced frequency was decreased towards zero and, for some combinations of Reynolds number and frequency, exhibited behaviour consistent with the instability of separation bubbles.

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