Aeroacoustic Instability Analysis of Helmholtz Resonators Through High-Order Unsteady Reynolds-Averaged Navier-Stokes Simulations

This paper presents a numerical analysis of the aeroacoustic instabilities in a slit-type Helmholtz resonator subjected to a low Mach number grazing flow. This configuration can be susceptible to nonlinear feedback phenomena due to the mutual coupling between the aerodynamic and acoustic fields in the proximity of the slit. The aeroacoustic flowfield is simulated through a direct approach by solving the unsteady compressible Reynolds-averaged Navier-Stokes equations using a high-order discontinuous Galerkin discretization. The response of the Helmholtz resonator to an incident acoustic field is analyzed using a two-port characterization technique. The onset of the aeroacoustic instabilities is investigated by applying an acoustic energy criterion based on the scattering matrix formulation. The Nyquist stability diagram is studied to determine the system stability and identify the whistling occurrence. The two- and three-dimensional numerical results are compared to experimental data obtained from a dedicated measurement campaign. The comparison between the numerical and experimental data demonstrates a very good agreement, highlighting the potential of the applied numerical approach for the investigation of the aeroacoustic instabilities. This allows a deep description of the aeroacoustic feedback mechanisms leading to the whistling onset, proposing a valid engineering tool for the early design stage.