A new analytical model is developed for the prediction of noise from serrated trailing edges. The model generalizes Amiet's trailing-edge noise theory to sawtooth trailing edges, resulting in a complicated partial differential equation. The equation is then solved by means of a Fourier expansion technique combined With an iterative procedure. The solution is validated through comparison with the finite element method for a variety of serrations at different Mach numbers. The results obtained using the new model predict noise reduction of up to 10 dB at 90 degrees above the trailing edge, which is more realistic than predictions based on Howe's model and also more consistent with experimental observations. A thorough analytical and numerical analysis of the physical mechanism is carried out and suggests that the noise reduction due to serration originates primarily from interference effects near the trailing edge. A closer inspection of the proposed mathematical model has led to the development of two criteria for the effectiveness of the trailing-edge serrations, consistent but more general than those proposed by Howe. While experimental investigations often focus on noise reduction at 90 degrees above the trailing edge, the new analytical model shows that the destructive interference scattering effects due to the serrations cause significant noise reduction at large polar angles, near the leading edge. It has also been observed that serrations can significantly change the directivity characteristics of the aerofoil at high frequencies and even lead to noise increase at high Mach numbers.
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