Numerical studies of transmission loss performances of asymmetric Helmholtz resonators in the presence of a grazing flow

As a typical noise-attenuating device, Helmholtz resonators are widely implemented in aero-engines and gas turbines to decrease the transmission of acoustic noise. However, an asymmetric Helmholtz resonator could be designed and implemented due to the limited space available in the engines. To examine and optimize the noise-attenuating performances of the asymmetric resonator, comparison studies are performed. For this, a two-dimensional frequency-domain model of a cylindrical duct with a grazing flow is developed. An asymmetric Helmholtz resonator is attached as a side branch. The model containing the linearized Navier-Stokes equations is validated first by comparing the predicted results with the experimental ones available in the literature. Further validation is conducted by comparing the results of an asymmetric resonator with the analytical ones available in the literature. The effects of (1) neck offset distance from the center of the resonator cavity denoted by ec/as and (2) the grazing flow Mach number Mu are evaluated. It is shown that as the grazing flow Mach number is increased, the resonant frequencies and the maximum transmission losses are dramatically varied for a given ec/as. As ec/as is increased from 0 to 0.5 and Mu >= 0.1, the resonant frequencies and the maximum transmission losses are increased. However, when Mu is lower than 0.07, i.e. Mu <= 0.07, the transmission loss performances are almost unchanged with ec/as increased. The optimum design of the asymmetric resonator is shown to give rise to the resonant frequency being shifted by 10% and 2-5 dB more transmission loss at higher Mach number. Finally, visualization of vortex shedding formed at the neck of the asymmetric resonator confirms that acoustical energy is transformed into kinetic energy and absorbed by the surrounding air. This study opens up a numerical design approach to optimize an asymmetric resonator.