Analysis of jet oscillations with acoustic radiation in the recorder by direct aeroacoustic simulations.

Abstract

To elucidate the selection mechanism of a predominant mode in acoustic radiation from the recorder, the jet oscillations predicted by direct aeroacoustic simulations are analyzed based on a proposed formula for hydrodynamic and acoustic jet displacements. The displacements are well represented by the formula, taking into account the non-zero initial amplitude around the windway exit and variations of oscillation center with streamwise position for jet displacement. The analysis is applied to the jet oscillations in two different recorders with a straight- and an arch-shaped windway, where the shift of the predominant mode from the first to the second mode occurs for the straight-shaped recorder at a lower jet velocity compared to the arch-shaped recorder. The analytical results present the influence of the recorder shape on the amplification rate of the hydrodynamic jet displacement, the acoustic feedback effects and the phase relation between the hydrodynamic jet displacement and acoustic pressure in the resonator, along with the jet offset to the edge. Compared to the arch-shaped recorder, the convex curve of the amplification rate with the non-dimensional frequency based on the windway height for the straight-shaped recorder is located in the higher-frequency region, which contributes to the predominance of the higher mode.