Transient motion of finite amplitude standing waves in acoustic resonators

• The transient motion of gases within oscillating resonators is simulated.
• The effects of physical parameters on the transient motion are investigated.
• The numerical results are in good agreement with existing physical experiments.
• Two-peak pressure waveform at the small end of horn-cone resonator is found.

Extraordinarily high maximum-to-minimum gas pressure ratios appear in an oscillating closed resonator at its resonance frequency for certain resonator shapes. Using a quasi-one-dimensional model based on the compressible Navier–Stokes equations and a finite volume method, we investigate the transient motion of a fluid inside oscillating axisymmetric tubes, from the quiescent condition to the periodic steady motion. We find that the amplitude of the fast oscillations in pressure increases monotonically to the value of its steady state for a cylindrical tube of constant cross-section, while the amplitude undergoes a spiral toward the final steady state value for conical or horn-cone resonators. We discuss the effects of fluid properties on the transient motions. In addition, we compare our numerical results with available experimental results and find good agreement. In particular, for horn-cone resonators driven by large amplitude force, we find a secondary lower peak in pressure waveform within one period of oscillation at the small end of the cavity, matching the findings of the existing experimental result.