CAA Study of Helmholtz Resonator Application on Edge-Tone Noise Suppression

This paper reports a numerical study of low-frequency acoustics on a modern open-jet wind tunnel design. The study simulates the acoustic response inside the wind tunnel which is subjected to a simulated edge-tone emission without a moving flow. The effects of a Helmholtz resonator installed at different locations along the wind tunnel circuit are investigated with the aim to attenuate the resonance effect of the edge-tone noise. The simulation assumes that the frequency of the edge tone is equal to the natural frequency of the resonator and the corresponding wavelength is the same as the total longitudinal length (~ 72.4 m) along the wind tunnel circuit centerline. Due to the long wavelength, the study excludes the relatively small length-scale components, including corner turning vanes, main fan, and main fan hub, from the wind tunnel geometry. The computational aeroacoustics study is performed using a solver JUSTUS which is based on a time-accurate local-time-stepping space-time conservation element and solution element method in which the full (instead of linearized) Euler equations are solved. All solutions are obtained using unstructured tetrahedral meshes with local mesh refinements, which are required for accurate geometry representation. The design of the unstructured meshes results in a very large disparity between the minimum and maximum local time step sizes whose ratio is more than three orders in magnitude. The study starts with a demonstration problem of a standalone resonator on a straight duct, and the prediction is compared to a lumped-parameter theory. Resulting in agreeable solution to the theory, the similar mesh design for the standalone resonator is then applied to the application study for the wind tunnel. The study shows that, without a resonator, an acoustic resonance occurs in the wind tunnel circuit where the response pressure magnitudes are higher than the source strength. Two acoustic nodes (of locally lowest pressure magnitudes) are predicted in the baseline wind tunnel, and this result is shown to agree to a 1D theory which is developed in the study. The pattern and response amplitude of the resonance are modified with a resonator. It is found that, among the resonator cases, the resonator atop the test section creates the broadest area of constant-level attenuation. Different resonator locations result in different levels of attenuation along the wind tunnel circuit. It is surprising to find that the case of a resonator on corner 3 increases, albeit incrementally, the response magnitudes in comparison to the baseline condition. The results suggest that a resonator may be strategically located to produce one acoustic node at or near the nozzle exit plane where the initial jet shear-layer is most susceptible to acoustic excitations. It is expected that the lowest excitation would minimize the tendency of the jet instability to become coherently amplified and develop into an edge-tone feedback intensification. The resonator location may effectively attenuate the edge-tone feedback phenomenon in the test section and thus diminish the resulting strength of resonance with the circuit. As an initial effort, the current acoustic study neglects the effects of the moving mean flow and assumes the low-frequency noise to emit at fixed locations and be statistically stationary. A more accurate description of the acoustics, influenced by convection effect and flow-sound coupling, is to allow the physical aeroacoustics to take place in the wind tunnel with the moving mean flow. This will be a continuous effort of the computational study.