A refinement of asymptotic predictions and full numerical solution of helicopter rotor noise in the far field

The asymptotic analysis of Parry and Crighton [1] for propeller noise in the far field, which is based on Hanson's formulation [2] of the FW-H equation, is refined to second order by Laplace's method [3] for evaluating integrals, accounting for second order contributions near the blade tip for loading and thickness noise. The full numerical solution of Hanson's integrals for both thickness and loading noise is also presented. In particular, the theory is applied to a four-bladed helicopter rotor with tip Mach numbers ranging between 0.5 and 0.7. The aerodynamic loading in this case is obtained using a 3D compressible code based on finite volume method with intensified grid density near the blade tip. The far field angular SPL noise distributions of a helicopter rotor in hover show that the present second order asymptotic formula is in better agreement with full numerical computations than that of the first order formula, especially for thickness noise.