Optimal duct length of ducted fans for minimizing first blade-passing frequency noise

Fans generate tone noise and broadband noise. The first blade-passing frequency noise is a tone noise and is the most dominant; attaching a duct and a stator can reduce this noise. However, there has been no theoretical development in using structural characteristics to reduce the noise generated by ducted fans. In this study, noise predictions using Lighthill's equation and Green's function were performed to determine the optimal duct length for a ducted fan's noise reduction. New formulations for predicting the length were derived using a modal noise analysis. Noise sources were obtained from computational fluid dynamics data and wall pressure spectra. The formulations deduce a linear relationship between a duct's radius and length and can be used as a tool to indicate fan size at the design stage under space and weight constraints without high computational costs.