Nonlinear Resonant Gas Oscillations in Resonators with Variable Cross-section

Abstract

In a number of studies, it has been shown that the geometry of an acoustic resonator strongly affects its resonant frequencies, as well as the nonlinear shape of the standing pressure waves generated inside the cavity. In this paper, we consider three resonators with different wall shapes (cone, exponential and bulb-shaped resonators) in which gas vibrations are formed due to an external periodic force. The acoustic field in the resonators is generated by the vibration of the left wall of the enclosure. The oscillation frequency of this wall is chosen so that the lowest acoustic mode can propagate along the resonator. The fully compressible form of the Navier–Stokes equations is used, and the explicit time-stepping algorithm is employed for modeling the motion of acoustic waves. The structure of acoustic flows of the second order, resulting from the interaction between the wave field and viscous effects on the walls, leads to the formation of flow patterns. These patterns can be revealed by averaging solutions over a specific period of time. To evaluate the performance of resonators, the pressure amplitude gain factor is used. This is defined as the ratio of pressure amplitude at the small end of the resonator to the pressure amplitude at its large end. It has been found that the best performance is observed in a flask-shaped resonator.