On the interaction of Tollmien-Schlichting waves with a wall-embedded Helmholtz resonator

Abstract

The influence of a wall-embedded Helmholtz resonator on the development and stability of Tollmien-Schlichting (TS) waves is investigated numerically and experimentally for a range of frequencies extending from below to above resonance. Interactions are found to be limited in the near-wall region and toward the trailing edge of the resonator orifice while at the same time being linear nature. The dynamic response of the flow-excited resonator is shown to have a fixed phase relation with respect to the TS-waves, indicating that only amplification of the latter can be achieved. The same resonant behavior is maintained regardless of whether the resonator is flow-excited or acoustically excited. Thus, it is suggested that pressure perturbations propagate perpendicularly and acoustically within the resonator throat and cavity. The amplification observed in the vicinity of the resonator displays features typical of TS-wave scattering; however, it is confirmed that this is not solely the result of mean flow distortion due to the geometry and recirculation region. Instead, the results indicate that the phenomenology is a consequence of the combination of scattering, localized non-modal growth, and wall-forcing in the wall-normal direction due to resonance.