A theoretical study of leading-edge devices for active and passive control of wake-airfoil interaction noise

A theoretical analysis is developed for control of wake-airfoil interaction noise by the use of actuators on the airfoil surfaces near the leading edge. The objective is to eliminate the sound radiation by canceling the wake-airfoil noise near its source (the leading edge). Actuators are mounted on the upper and lower surfaces of the airfoil and driven out of phase to match the antisymmetric nature of the wake-airfoil noise field. The analysis is based on linearization about a two-dimensional compressible subsonic mean flow past a semi-infinite flat-plate airfoil. Asymptotic solutions are developed for the unsteady boundary-layer flow over surface-mounted actuators which are long compared to the triple-deck scale. The analysis shows that boundary layer effects play a significant role in determining the acoustic field, and that traditional approaches used to account for acoustically thin boundary layers are not always adequate. In addition to the acoustic monopole field associated with the actuator volume flux, acoustic monopole and dipole fields are produced at leading order by deflection of the boundary layer into the oncoming free stream. For a specified actuator size and location (relative to the leading edge), the analysis determines the actuator amplitude and phase which minimizes the total sound radiation. The cancellation is most effective when the directivity pattern for the control field closely matches that for the wake-airfoil noise field. At low Mach numbers, this is achieved by mounting the actuators sufficiently close to the leading edge. At high subsonic Mach numbers, the sound cancellation that can be achieved with a single actuator on each surface is limited by mismatch in the directivity patterns. However, a match in directivity patterns can be recovered in part by using two actuators on each surface. The use of passive treatment in the leading-edge region to locally control wake-airfoil interaction noise is also discussed