Trailing edge noise at low Mach numbers

A review is made of the diffraction theory of the trailing edge noise gener ated by a flat-plate airfoil of zero-thickness and non-compact chord, accor ding to which the sound is attributed to the scattering of a "frozen" patte rn of turbulence wall pressure swept over the edge in the mean flow. Extens ion is made to determine the sound produced by very low Mach number flow ov er the edge of an airfoil of finite thickness. In applications it is desira ble to represent the noise in terms of a surface integral over the airfoil involving a Green's function and a metric of the edge flow that can be calc ulated locally using the equations of motion of an incompressible fluid. It is argued that the appropriate metric for a rigid airfoil is the incompres sible "upwash" velocity (determined by the Biot-Savart induction formula ap plied to the boundary layer vorticity outside the viscous sublayer), and no t the surface pressure. Formulae for calculating the noise are given when t he airfoil thickness is acoustically compact, and for both three- and two-d imensional edge flows. The theory is illustrated by a detailed discussion of a two-dimensional vor tex flow over an airfoil with a rounded trailing edge. The problem is simpl e enough to be treated analytically, yet is also suitable for validating co mputational edge noise schemes. (C) 1999 Academic Press.