Airfoil synchronous surging and pitching

Combined surging and pitching of an airfoil at the identical frequency (i.e. synchronously), at four different phase differences, was investigated theoretically and experimentally. The most general unsteady theoretical formulation was adopted to calculate the lift coefficient, and then extended to explicitly compute the unsteady bound vortex sheet. This was used for comparison with experiments and facilitated the computation of both Joukowsky and impulsive-pressure lift contributions. Experiments were performed using a symmetric 18 % thick airfoil in an unsteady wind tunnel at an average Reynolds number of $3.0\times 10^5$ , with a free-stream oscillation amplitude of 51 %, an angle-of-attack range of $2^\circ \pm 2^\circ$ and a reduced frequency of 0.097. In general, excellent correspondence was observed between theory and experiment, representing the first direct experimental validation of the general theory. It was shown, both theoretically and experimentally, that the lift coefficient was not accurately represented by independent superposition of surging and pitching effects, due to variations in the instantaneous effective reduced frequency not accounted for during pure pitching. Deviations from theory, observed at angle-of-attack phase leads of $90^\circ$ and $180^\circ$ , were attributed to bursting of separation bubbles during the early stages of the acceleration phase. The largest deviations occurred when the impulsive-pressure lift contribution was small relative to the Joukowsky contribution, because the latter was most affected by bubble bursting. Bubble bursting resulted in large form-drag oscillations that occurred at identical phase angles within the oscillation cycle, irrespective of the phase difference between surging and pitching, as well as in the absence of pitching.