Theoretical, Computational and Experimental Investigation of Helmholtz Resonators: One-Dimensional versus Multi-Dimensional Approach

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. It is shown that individual volume dimensions may have a considerable effect on resonator performance, particularly in reducing the primary resonance frequency compared to the classical result. The second computational approach investigates the effects of multi-dimensional physics by solving the three-dimensional wave equation with a boundary element method and comparing the results with those of the one-dimensional treatments.