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 and undisturbed velocity U , with a thin jet of momentum-flux emerging from its trailing edge at an oscillating deflexion-angle exp.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 = and are found to exist only when . 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.