Analysis of elliptical-jet acoustic directivity and efficiency using a vortex-sheet-based wave-packet model

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 ce₀ and wagging ce₁ modes decreased with the aspect ratio, whereas the growth rate of the flapping se₁ 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” ce₀ mode is significantly higher than the “flapping” se₁ and “wagging” ce₁ modes for both free- and installed jets. Increasing the aspect ratio of the elliptical jet produces a slight reduction in sound for the ce₀ mode, a significant decrease in the se₁ mode, and a significant increase for the ce₁ 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.