Plunging Motion Research Articles

Non-Linear Theory for Slender Wings in Sudden Plunging Motion

SummaryA theoretical treatment is considered for the flow past slender wings in sudden plunging motion when leading-edge vortices are present. A form of slender-wing theory is used and, although the basis of the theory involves no restriction on compressibility, it has proved possible to make calculations only for an incompressible fluid.Use is made of an analogy between the unsteady flow and related steady flows. In the incompressible case, an extension of the theory of Brown and Michael is given to determine the strength of the vortex and its path from the leading edge to the final steady-state position. A qualitative comparison with experiment is made of the instantaneous position of the vortex. In a typical case the lift is calculated to remain within one per cent of its final value after the vortex strength has reached 55 per cent of its final value.

The flow past a thin wing with an oscillating jet flap

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.