Self-sustained whistling in long-cavity Helmholtz resonators with bias flow

Abstract

This study examines the hydrodynamic-acoustic feedback mechanisms responsible for whistling in double-neck Helmholtz resonators under bias flow, with emphasis on long-cavity configurations representative of human whistling. Combined flow and acoustic experiments were performed using particle image velocimetry and pressure measurements to characterize vortex dynamics, sound generation, and oscillation regimes across a range of Reynolds numbers and geometric parameters. Within the self-sustained oscillation regime, sound pressure levels scale consistently with the Strouhal number, exhibiting a peak near St=0.32. Experimental data collapse is achieved using a modified Reynolds number that incorporates cavity-length effects. Moreover, two-point coherence and cross-spectral analyses show that acoustic generation occurs predominantly inside the resonator chamber, with maximum sound production located approximately 2.3 diameters downstream of the upstream neck. Flow visualization reveals that vortices dissipate before reaching the downstream neck, indicating a feedback mechanism distinct from classical hole-tone and Rossiter-type oscillations. To interpret these findings, an empirical model was developed, consisting of a two-degree-of-freedom lumped acoustic system coupled to a nonlinear oscillator representing vortex shedding. The model reproduces the onset, lock-in, saturation, and abrupt extinction of self-sustained oscillations, capturing the essential coupling that transfers energy from the mean flow to the acoustic field. These results provide new insight into long-cavity whistles and offer a predictive framework for Helmholtz-type resonators under bias flow.