NONLINEAR RESONANCE AND VISCOUS DISSIPATION IN AN ACOUSTIC CHAMBER

The nonlinear resonance of an air-filled acoustic chamber with rigid endwalls is studied numerically using the fully nonlinear Lagrangian wave equation. The effects of bulk viscous dissipation and external excitation are included. It has been found that at large excitation, the sound amplitude and the quality factor Q of the chamber are independent of viscosity, and are inversely proportional to each other. The highlight of this work is the interpretation of these results in simple physical terms. These results are consistent with those from a previously developed analytical theory, although in the latter they have been overshadowed by algebra and have not been properly interpreted. It has been deduced that the free decay rate of a large-amplitude wave due to bulk dissipation is proportional to its acoustic Mach number, and is also independent of viscosity. Also considered was viscous dissipation on the side walls, but it was found that it is much less important than bulk dissipation at high nonlinearity, considering the typical dimension and boundary layer thickness in this type of system. The wave profiles excited at slightly off-resonance frequencies have also been calculated, and found to be similar to those in a piston-driven resonant tube.