Effect of the angle of attack on the transient lift during the interaction of a vortex with a flat plate. Potential theory and experimental results

Abstract

The dynamics of a two-dimensional vortex interacting with a flat plate at different angles of attack α is analysed using potential flow theory based on conformal mapping varying the nondimensional separation distance h∕c of the upstream incoming vortex to the plate (c is the chord length of the plate) and the vortex intensity Γl. Transient lift forces measured in a wind tunnel are also compared with the potential theory results for a given Γl and several values of h∕c and α. For the Reynolds number considered in the experiments (about 25 000) it is found that the potential theory predicts reasonably well the transient fluctuation in the lift force provided that the separation distance is not too close to the critical one h∗∕c at which the vortex trajectory given by the potential theory bifurcates. We find that the separation distance generating the highest induced lift is around this critical value h∗∕c, which, according to the potential theory, is displaced about −2.3(1−0.07|Γl|1∕2)α in relation to the zero angle of attack for the same Γl. Potential theory also predicts that the maximum peak of the lift fluctuation depends on α only through the relative separation |h−h∗|∕c, and that the maximum lift is substantially larger when a clockwise vortex passes below the plate than when it passes above the plate, for the same vortex intensity Γl and relative separation distance. The opposite happens for a counter-clockwise vortex. This asymmetry in the maximum lift fluctuation increases slightly with |Γl|, approaching a ratio of almost two for large |Γl|.