Studying Sound Production in the Hole-Tone Configuration Using Compressible and Incompressible Global Stability Analyses

Abstract

We study the jet passing through two successive circular holes, also known as hole-tone configuration. Such flow is relevant to many applications like human whistling, wind instruments and tea kettles. Recently, Fabre et al. [1] investigated this flow configuration adopting a global stability approach, showing that the whistling is linked to a purely incompressible instability of the jet between the two holes. In this work, we focus our attention on a little different and more realistic geometry, known as birdcall configuration, consisting into two successive holes in curved thick plates. Although the whistle is related to compressible phenomena, the incompressible approach can provide some useful information, at least in the region near the hole, where, in some conditions, the flow can be considered incompressible. We thus initially perform a purely incompressible stability approach. We identify the critical conditions, the global frequencies and discuss the structure of the resulting global eigenmodes. In order to reintroduce and evaluate compressible effects, which can be relevant into the cavity between the two holes, we model the cavity as a Helmholtz resonator and couple it to the incompressible simulation. Finally, a full compressible stability analysis is performed in order to check the accuracy of these simplified approaches in term of critical conditions, global frequencies and structure of the modes.