  An analytical model is developed for the prediction of noise radiated by an
aerofoil with leading edge serration in a subsonic turbulent stream. The model
makes use of the Fourier Expansion and Schwarzschild techniques in order to
solve a set of coupled differential equations iteratively and express the
far-field sound power spectral density in terms of the statistics of incoming
turbulent upwash velocity. The model has shown that the primary noise reduction
mechanism is due to the destructive interference of the scattered pressure
induced by the leading edge serrations. It has also shown that in order to
achieve significant sound reduction, the serration must satisfy two geometrical
criteria related to the serration sharpness and hydrodynamic properties of the
turbulence. A parametric study has been carried out and it is shown that
serrations can reduce the overall sound pressure level at most radiation
angles, particularly at downstream angles close to the aerofoil surface. The
sound directivity results have also shown that the use of leading edge
serration does not particularity change the dipolar pattern of the far-field
noise at low frequencies, but it changes the cardioid directivity pattern
associated with radiation from straight-edge scattering at high frequencies to
a tilted dipolar pattern.
