Boundary-layer effects on performance of surface-mounted actuators for active noise control

A theoretical analysis is developed for the effects of the viscous boundary-layer on the acoustic field produced by surface-mounted actuators. The analysis is based on linearization about a two-dimensional compressible subsonic mean flow. Asymptotic solutions are developed for the unsteady boundary-layer flow over an acoustically-compact actuator that is 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 acousticallythin 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. The boundary-layer analysis is applied to a model problem for active control of gust-airfoil interaction noise using actuators mounted near the leading-edge of the airfoil.