The sound of an elastic airfoil in the wake of a vortex generator

The acoustic signature of an acoustically-compact tandem airfoil setup in uniform high-Reynolds number flow is investigated. The upstream airfoil is considered rigid, and is actuated at its leading edge with small-amplitude harmonic pitching motion. The downstream airfoil is taken passive and elastic, with its motion forced by the vortex-street excitation of the upstream airfoil. The non-linear near-field description is obtained via potential thin-airfoil theory. It is then applied as a source term into the Powell-Howe acoustic analogy, to yield the far-field dipole radiation of the system. To assess the effect of downstream-airfoil elasticity, results are compared with counterpart calculations for a non-elastic setup, where the downstream airfoil is rigid and stationary. Depending on separation distance between airfoils, airfoil-motion and airfoil-wake dynamics shift between in-phase (synchronized) and counter-phase behaviors. Consequently, downstream-airfoil elasticity may act to amplify or suppress sound, through the direct contribution of elastic-airfoil motion to the total signal. Resonance-type motion of the elastic airfoil is found when the upstream airfoil is actuated at the least stable eigenfrequency of the downstream structure. This, again, results in system sound amplification or suppression, depending on separation distance between airfoils. With increasing actuation frequency, the acoustic signal becomes dominated by the direct contribution of upstream airfoil motion, whereas the relative contribution of the elastic airfoil to the total signature turns negligible.