Self-propulsion of oscillatory airfoils. An analytic approach
by
Adrian Carabineanu
University of Bucharest, Faculty of Mathematics and Computer Science
Coauthors: Stelian Gradinaru, "Spiru Haret" University, Bucharest,Romania

In this paper we show that the oscillatory motion of an airfoil (wing)

in a fluid can determine the apparition of a propulsive force (thrust).

In the framework of the linearized perturbation theory, the pressure

jump over the oscillating wing is the solution of a two-dimensional

hypersingular integral equation. Performing an asymptotic expansion

with respect to the aspect ratio and keeping the leading terms, we

reduce the integral equation to a one-dimensional one and we obtain a

simplified form of the lifting surface integral equation for a

class of thin wings of low aspect ratio with straight trailing edges.

The one-dimensional integral equation is solved analytically for the oscillatory

motion of a delta wing and the pressure field and the drag force are

calculated. One shows that for certain oscillatory motions, if the

reduced frequency surpasses a critical value, the average drag force

takes negative values, i.e. there appears a propulsion force.

Date received: March 10, 2008