Sound radiation from semi-infinite elliptical ducts with uniform subsonic jets: An analytical approach

Abstract

This paper presents an analytical method for modeling the acoustic field radiation from a semi-infinite elliptical duct with a uniform subsonic jet. Elliptical ducts are often used as inlets for turbofan engines to take full advantage of the pre-compression effect of the fuselage and improve the stealth performance of the aircraft. The method accounts for the instability wave inside the vortex sheet induced by the shearing of jet and ambient flow and its effect to sound radiation. The method uses Mathieu functions to describe the incident and scattered sound in the elliptic cylindrical coordinates. A semi-analytical Wiener-Hopf approach with low computational cost is applied to obtain the near and far field solutions. The near field is illustrated by acoustic pressure maps at different modes and circumferential angles. The far field is shown by directivity patterns at single tones. Numerical simulations based on a finite element method are conducted to validate the accuracy of the analytical method. The results show good agreement between the analytical and numerical solutions. The proposed method can be used to analyze the acoustic characteristics of elliptical ducts with jets, which are relevant for noise control and optimization of turbofan engine inlets.