Numerical Study of Forced Nonlinear Acoustic Gas Oscillations in a Tube under the Action of Two Pistons with Phase Shift

Abstract

Nonlinear acoustic oscillations of large amplitude created in a gas-filled tube under the action of two pistons located at the ends of the pipe are numerically investigated. The pistons oscillate according to the harmonic law at one of the natural frequencies and with different values of phase shift. The movement of the gas is described by mathematical equations of conservation for the main determining relations for the flow, which are estimated by applying the finite volume method based on OpenFOAM package. The non-stationary forced oscillatory motion of a gas inside an axisymmetric tube from a state of rest to a periodic steady motion is investigated. The features of nonlinear acoustic fluctuations of gas in cylindrical duct under the action of two pistons are found. The effect of the phase shift value has a strong effect on the oscillation amplitude of gas, when pistons oscillating at equal natural frequencies, in turn, when the pistons oscillate at different natural frequencies, the effect is very small. In particular, resonant oscillations are detected when the pistons vibrate at the same frequency values equal to odd values of their own higher harmonics in the absence of a phase shift value. In the case when the frequency values are equal to even values of the natural harmonics, resonant oscillations occur when the pistons move in anti-phase. The numerical method appears to work well and would be hoped for practical computations of different resonators.

Keywords

• closed acoustic resonator
• nonlinear standing wave
• finite volume method
• weak shock wave
• navier-stokes equations