Transient motion of finite amplitude standing waves in acoustic resonators

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-onedimensionalmodel based on the compressibleNavier–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. © 2014 Elsevier B.V. All rights reserved.