Including Wall Effects in Analytical Leading Edge Noise Predictions

Abstract

An analytical solution to leading-edge noise produced by a translating two-dimensional flat plate ingesting turbulence in proximity to a hard-wall is presented. This is a relevant problem to calculate the installation noise of open rotors and un-ducted fans. The analytical solution to the problem is given by using Amiet’s flat plate theory in conjunction with the Method Of Images (MOI) to include the effects of the wall. The low frequency, low Mach number limit of the analytical solution is investigated and it is shown that the flat plate in this limit behaves like a compact vertical dipole. The analytical solution is verified by a Computational AeroAcoustic (CAA) simulation that also uses the MOI to simulate a wall. While the MOI gives an approximation of the wall, it does not model all of the effects, such as diffraction from the edges of the flat plate and acoustic shielding due to the presence of the flat plate. These effects, which are ignored in the MOI are quantified using a CAA simulation that models the wall using a hard-slip-wall boundary condition. It is found that the analytical predictions and the CAA simulations using the MOI compare well. However, when the MOI is compared to the CAA simulation using a hard-slip-wall boundary condition, it is found that the MOI does not capture the effect of the shadow zone that is created due to the shielding effect of the aerofoil. The extent of the shadow zone is modified by changing the height of the aerofoil from the wall, and it shown that as the height of the aerofoil from the wall is increased, the shielding effect decreases.