Helmholtz Resonator: A Multidimensional Analytical, Computational, and Experimental Study

Helmholtz resonators are widely used for noise reduction in vehicle induction and exhaust systems. This study investigates the effect of specific cavity dimensions of these resonators theoretically, computationaly, and experimentally. An analytical model is developed for circular concentric resonators to account for the multidimensional wave propagation in both the neck and the cavity. Driving this model with an oscillating piston isolates the interface between the neck and the resonator volume, thereby allowing, at this location, for an accurate evaluation of the empirical end correction, which is often used with the classical lumped approach in an attempt to incorporate the effect of multidimensional behavior at the transitions. The analytical method developed in the study is then compared with a similar one-dimensional analytical model that also allows for wave propagation in the neck and cavity. By using these two approaches, it is shown that the resonance frequency predictions obtained from the end correction given by Ingard are in close agreement with the results of the multidimensional model for resonator volumes with a length to diameter ratio greater than about 0.5. The results from the analytical methods are also compared with the numerical predictions from a three-dimensional boundary element method and with experiments.