The Flow Past a Thin Wing with an Oscillating Jet Flap

Abstract

An exact solution is obtained for the linearized flow past a thin two-dimensional wing of chord c at zero incidence in an incompressible stream of density p and undisturbed velocity U, with a thin jet of momentum-flux 2pU^2cμ emerging from its trailing edge at an oscillating deflexion-angle r exp (iwUt/c). The motion is governed by a singular third-order integro-differential equation, which becomes tractable when μ is small: solutions in this 'weak-jet' limit depend on a single parameter v = μw, and are found to exist only when v ≤ 2. The possible significance of this critical frequency is discussed. Computations of jet shape and lift force for a range of values of v are presented, and the solutions for periodic plunging and pitching motions of the wing are derived from that for deflexion. The formulation follows that of an earlier paper (Spence 1961 b), in which, however, an unsound approximation was made to the governing equations.

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