Forces and Moments in Incompressible Quasi-Potential Flows

An exact formulation, based on the Trefftz-plane pproach, for the evaluation of aerodynamic loads acting on bodies having arbitrary motion, is presented for incompressible flows that are quasi-potential (i.e., potential everywhere except for the points of a zero- thickness wake surface). The resulting expressions, obtained without using simplifying assumptions, give an exact representation for forces and moments in terms of (i) the velocity potential over the body surface, (ii) the velocity potential and its normal derivative over an arbitrary plane that intersects the wake (Trefftz plane), and (iii) the potential discontinuity over the portion of the wake limited downstream by such a plane. It is shown that the present formulation includes, as particular cases, some classical results by Prandtl, Trefftz and Lamb, for the evaluation of forces and moments in incompressible quasi-potential flows. A convergence analysis is presented in order to assess the accuracy of the present formulation in comparison with the evaluation of forces and moments by direct integration of the pressure distribution over the body surface. Numerical results concerning lift, drag and moments acting on isolated wings in steady and unsteady flows are included.