Aerodynamic sound generated by a slotted trailing edge

Abstract

This paper discusses the theory of the generation of sound by turbulent flow over a trailing-edge flap of an airfoil or guidevane. A narrow slot separates the flap from the airfoil, and the configuration is modelled analytically by a semi-infinite rigid plate that contains a slot at an arbitrary, finite distance from the edge. The aerodynamic sound problem is formulated in terms of a singular integral equation which can be solved in closed form when the width of the slot is small compared with both the acoustic wavelength and the chord of the flap. The theory is applied to examine (i) the influence of the slot on the noise generated as a result of boundary-layer separation close to the trailing edge of the flap, and (ii) the generation of sound by boundary-layer turbulence in the immediate vicinity of the slot. At low, subsonic mean flow Mach numbers the presence of the slot is shown to reduce the level of the radiated noise in case (i) provided that kd < 10, where k is the characteristic acoustic wavenumber and is the chord of the flap. Boundary-layer noise is predicted to be significantly enhanced by the slot in the range 0.1 < kd 10.