High Acoustic Pressure Near Resonance in an Oscillating Tube

Abstract

When a piston located at one end of a closed pipe excites an interior medium at a resonance frequency, a shock wave is often generated and propagates periodically back and forth in the pipe. This nonlinear phenomenon has been extensively investigated in many works([1]~[3]) theoretically and experimentally. Recent studies([4], [5]) performed at MacroSonix Corp. have focused attention on inducing high acoustic pressure without shock formation in an oscillating axisymmetric tube. The results revealed that the waveform of acoustic pressure is strongly related to the shape of the tube. However, while acoustic losses were considered by allowing viscous damping, an isentropic process was also assumed at all positions to simplify the governing equation. This contrary proposition may yield undesirable results for a viscous gas because the viscous damping strongly affects the motion of the gas near a resonance frequency. Therefore, it is necessary to study the motion of a fluid for obtaining more meaningful results at a resonance frequency. In this paper, we have studied the fundamentals of nonlinear acoustic phenomena such as shocks and macrosonic waves caused by the oscillation of an entire tube. Firstly, we derived a general governing equation including viscous effects. In contrast to the previous studies, an isentropic process was assumed only at both ends of the tube. A numerical code was developed to solve the nonlinear governing equation by using a finite difference scheme. In order to see the damping effects on the shock formation in the cylindrical and conical tubes, numerical simulations were performed with changing the magnitude of viscosity. In addition, we investigated a pressurizing performance for various conical tubes with the same volume and length. Experiments were accomplished for the cylindrical and conical tubes, too.