Acoustic damping performance of coupled Helmholtz resonators with a sharable perforated sidewall in the presence of grazing flow

Helmholtz resonators are widely used in gas turbines and aeroengines, because of its simple structure and high noise damping. To broaden its effective frequency range, two or more Helmholtz resonators could be applied. In this work, systematic studies are conducted to evaluate the aeroacoustic damping performance of two coupled Helmholtz resonators with a sharable perforated sidewall in the presence of a grazing flow. For this, 2D numerical model of a duct with two Helmholtz resonators implemented is developed via solving linearized Navier-Stokes equations in frequency domain. The model is validated first by comparing with the experimental data available in the literature. It is then modified to examine the effects of 1) the perforated orifice width Dx with respect to the back-cavity width Dr, 2) the mean grazing flow Mach number Ma, 3) the flow direction: forward and reverse. It is found that unlike conventional uncoupled Helmholtz resonators, the coupled ones are associated with three or more damping peaks. The local transmission peaks depend strongly on Dx/Dr, Ma and the flow direction in terms of the magnitude and the resonant frequencies. Furthermore, increasing Dx/Dr leads to the secondary peak being shifted to a higher frequency by approximately 100 Hz. However, increasing the grazing flow Mach number gives rise to deteriorated noise damping performance in terms of the local maximum transmission losses by about 10 dB. Finally, the classical theoretical formula ω2=c2S/VLeff fails in predicting the resonant frequencies of the coupled resonators in presence of the grazing flow. The present study help on optimizing the design of coupled multiple Helmholtz resonators in application.