A linearized potential flow theory for airfoils with spoilers

Abstract

Linearized two-dimensional potential flow theory is applied to an airfoil with an upper surface spoiler. The spoiler wake is modelled as a cavity of empirically given constant pressure, and a sequence of conformal transformations maps the linearized physical plane, with a slit on the real axis representing the airfoil plus cavity, onto the upper half of the plane exterior to the unit circle. The complex acceleration potential is used, and its real part is specified on the real axis, repre- senting the cavity boundary, while its imaginary part is specified on the unit semicircle, representing the wetted surface of the airfoil and spoiler. Solutions are found for both the steady-state lift and the transient lift after spoiler actuation for airfoils of arbitrary camber, thickness and incidence, with and without a simple flap, and with spoilers of arbitrary position, height and angle. The empirical cavity pressure is arbitrary for the steady-state solution, but is assumed to have the free-stream value for the transient solutions. Comparisons are made with the results of wind-tunnel experiments, and, for the steady-state solutions, with predictions of an earlier theory. The agreement of the present theoretical predictions with the experimental results is generally good, and is in most cases somewhat better than that of the earlier theory.