On the acoustic optimality of leading-edge serration profiles

Leading-edge serrations are studied extensively as a way of reducing leading-edge noise and have been shown to be able to reduce leading-edge noise significantly. Previous experiments showed that different serration geometries have different noise reduction capabilities. However, the optimal serration geometry has not been known. Consequently, there are no guides that can be used at the design stage of serrations. In this paper, by performing an asymptotic analysis, we show that in order to achieve greater noise reduction in the high frequency regime (k1h ≫ 1, where k1 denotes the dimensionless streamwise hydrodynamic wavenumber and h half of the dimensionless root-to-tip amplitude of serrations), the serration profile cannot have stationary points. Therefore, piecewise smooth profiles free of stationary points are more desirable. Moreover, we show that greater noise can be achieved in the high frequency regime by using serrations that are sharper around the non-smooth points. The underlying physical mechanisms of these findings are discussed. Based on these findings, a new type of serration profile is proposed, and analytical model evaluations confirm its improved acoustic performance in the frequency range of interest. At low frequencies, a slight deterioration may be expected, but this is often negligible. To verify the conclusion drawn from the analysis, we perform an experimental study to investigate the acoustic performance of this new serration design. The results show that it is indeed superior than conventional sawtooth serrations. For example, a remarkable 7 dB additional noise reduction is observed in the intermediate frequency range with no perceivable noise increase elsewhere. The trends predicted by the analysis are well validated by the experiment. It is expected that these findings can serve as an essential guide for designing serrations, and lead to more acoustically optimized serration geometries.