Numerical simulation of finite amplitude standing waves in acoustic resonators using finite volume method

Abstract

Finite amplitude standing waves in acoustic resonators are simulated. The fluid is initially at rest and excited by a harmonic motion of the entire resonator. The unsteady compressible Navier–Stokes equations and the state equation for an ideal gas are employed. This study extends the traditional pressure based finite volume SIMPLEC scheme for solving the equations without any predefined standing waves. The pressure waveforms are computed in three different closed resonators and two opened resonators. The studied shapes of resonators include cylinder, cone and exponential horn. The numerical results obtained from the proposed finite volume method in the study are in agreement with those obtained with the Galerkin method and the finite difference method. We also investigate the velocity waveforms in the three different kinds of resonators, and finds that the sharp velocity spikes appear at the ends of the resonator when the pressure has a shock-like waveform. The velocity in the closed conical resonator displays a smooth harmonic waveform. Finally, the pressure waveforms in opened resonators are simulated and analyzed. The results show that the decrease in the ratio of the maximum to the minimum pressure at the small end of the exponential resonator is less than that of cylindrical resonators when the flow velocity at the opened end (relative to the resonator) is the same.