Analysis of Elliptical-Jet Acoustic Directivity and Efficiency Using a Vortex-Sheet-Based Wave-Packet Model

Abstract

The hydrodynamic characteristics and associated far-field acoustics of installed elliptical jets were studied using linear models based on the Navier–Stokes equations. A compressible elliptical vortex-sheet model predicted that the growth rates of the varicose [Formula: see text] and wagging [Formula: see text] modes decreased with the aspect ratio, whereas the growth rate of the flapping [Formula: see text] mode increased, which was consistent with previous studies using finite-thickness stability models. Using a propagation model adapted from the Lighthill acoustic analogy, it was found that the acoustic efficiency of the “varicose” [Formula: see text] mode is significantly higher than the “flapping” [Formula: see text] and “wagging” [Formula: see text] modes for both free- and installed jets. Increasing the aspect ratio of the elliptical jet produces a slight reduction in sound for the [Formula: see text] mode, a significant decrease in the [Formula: see text] mode, and a significant increase for the [Formula: see text] mode. A similar trend was observed for the installed case. An exponential relationship between the jet–plate distance and scattered sound was found for elliptical jets, as observed for circular jets. Other geometric parameters such as the orientation angle of the ellipse were also analyzed.