Energy losses in an acoustical resonator.

A one-dimensional model has recently been developed for the analysis of nonlinear standing waves in an acoustical resonator. This model is modified to include energy losses in the boundary layer along the resonator wall. An investigation of the influence of the boundary layer on the acoustical field in the resonator and on the energy dissipation in the resonator is conducted. The effect of the boundary layer is taken into account by introducing an additional term into the continuity equation to describe the flow from the boundary layer to the volume. A linear approximation is used in the development of the boundary layer model. In addition to the viscous attenuation in the boundary layer, the effect of acoustically generated turbulence is modeled by an eddy viscosity formulation. Calculatons of energy losses and a quality factor of a resonator are included into the numerical code. Results are presented for resonators of three different geometries: a cylinder, a horn cone, and a bulb-type resonator. A comparison of measured and predicted dissipation shows good agreement.