Modelling of Acoustic Resonators Using the Linearized Navier Stokes Equations

To tune the acoustics of intake systems resonators are often used. A problem with this solution is that the performance of these resonators can be affected a lot by flow. First, for low frequencies (Strouhal-numbers) the acoustic induced vorticity across a resonator inlet opening will create damping, which can reduce the efficiency. Secondly, the vorticity across the opening can also change the end-correction (added mass) for the resonator, which can modify the resonance frequency. However, the largest problem that can occur is whistling. This happens since the vortex-sound interaction across a resonator opening for certain Strouhal-numbers will amplify incoming sound waves. A whistling can then be created if this amplified sound forms a feedback loop, e.g., via reflections from system boundaries or the resonator. To analyse this kind of problem it is necessary to have a model that allows for both sound and vorticity and their interaction. This means using a convected wave equation type of model is not sufficient. A better approach is to apply the linearized Navier Stokes equations, which will give a full model of the vortex-sound effects. In this paper an effort to apply this approach on a set of generic resonators is described. Besides the numerical results comparisons with experiments are also presented.