Numerical Studies On Acoustic Damping Performance Of Coupled Helmholtz Resonators With A Sharable Sidewall In The Presence Of Grazing Flow

To absorb noise and suppress combustion instabilities,Helmholtz resonators are widely used in propulsion systems such as aeroengines,gas turbines and turbojet thrust enhancers.Helmholtz resonator has good noise damping performance but smaller effective frequency bandwidth.The use of multiple Helmholtz resonators can increase the frequency bandwidth of sound attenuation.However,the space available for applying such resonators is limited in the propulsion system.To effectively use the space,reduce the noise of the propulsion system and broaden the damping frequency range in this paper,acoustic damping performance of coupled Helmholtz resonators with a sharable sidewall in the presence of grazing flow are tested.The sharable sidewall may be a rigid thin wall or a porous thin wall.For this,3D numerical model is developed via solving linearized Navier-Stokes equations in frequency domain.The numerical model in the presence of grazing flow is validated by comparing with the experimental data available in the literature and theoretical data via caculation.After achieving good agreement,this model was used to study the coupled Helmholtz resonators with a sharable sidewall.The classical theoretical formula fails in predicting the resonant frequencies of the mechanical coupled resonators in presence of the grazing flow.Therefore,the numerical simulation method is used in this paper to conduct a systematic study.First of all,for a sharable perforated single sidewall,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 D_x/D_r,Ma and the flow direction in terms of the magnitude and the resonant frequencies.Furthermore,increasing D_x/D_r leads to the secondary peak being shifted to the right.However,increasing the grazing flow Mach number gives rise to deteriorated noise damping performance in terms of the local maximum transmission losses decrease.Then,for a sharable multiple perforated single sidewall,it is found that the local transmission peaks depend strongly on Ma and the hole shapes in terms of the magnitude and the resonant frequencies.Furthermore,compared with circular holes,decreasing the number of holes or for a given number of holes,increasing the perforation rate S_x/S_rfor square hole leads to improving acoustic damping performance of the coupled resonators.And the noise damping performance of the resonator can be improved by rationally designing the perforation rate S_x/S_r and the number of holes.Finally,for a sharable multiple perforated double sidewall,it is found that the local transmission peaks depend strongly on the perforation rate S_x/S_r,the number of holes in the first sharable sidewall,the number of sharable sidewall and holes in terms of the magnitude and the resonant frequencies.Furthermore,compared with a sharable single sidewall,acoustic damping performance under a sharable double sidewall is more stable.In addition,incresing the perforation rate S_x/S_rleads to improving the resonant frequencies.And the noise damping performance of the resonator can be improved by rationally designing the distribution of holes.