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Helmholtz resonators are widely used for the noise reduction in vehicle induction and exhaust systems. This study investigates the effect of specific cavity dimensions of these resonators theoretically, computationally and experimentally. By considering one-dimensional wave propagation through distributed masses in the connector and cavity, a closed-form expression for the transmission loss of axisymmetric configurations is presented, thereby partially eliminating the limitations of a lumped-parameter analysis. Eight resonators of fixed neck geometry and cavity volume with length-to-diameter ratios of the volume varying from 0.32 to 23.92 are studied both computationally and experimentally. The first of the two computational approaches employed in the study implements a finite difference time domain technique to solve the nonlinear governing equations of one-dimensional compressible flow.

The coupling of shear layer instabilities with the acoustic resonances at the interface of two ducts, a main duct and a connecting sidebranch, leads to whistle noise. The present study investigates experimentally the mechanism of such pure tone noise. A generic sidebranch adapter is fabricated to allow for: (1) the ability to mount downstream of the throttle body in the induction system of a production engine; (2) the adjustment of sidebranch length; and (3) the changes in the diameter of the branch duct. Experiments are conducted both in a flow facility and an engine dynamometer facility for the same set of flow rates. The correlation of the whistle noise between these two facilities is examined in terms of frequency and the dimensionless numbers, including Strouhal and Mach.