Numerical analysis for nonlinear resonant oscillations of gas in axisymmetric closed tubes

Abstract

A numerical investigation on nonlinear oscillations of gas in an axisymmetric closed tube is presented. When the tube is oscillated at a resonant frequency of the interior acoustic field, it is well known that acoustic variables such as density, velocity, and pressure undergo very large perturbation, often described as nonlinear oscillation. One-dimensional nonlinear governing equations, which explicitly include attenuation terms related to viscosity, were derived. Then, the equations were solved numerically by using the higher-order finite difference scheme, which divided into two parts of spatial differentiation and time evolution. Numerical simulations were accomplished to study the effect of the tube shape on the maximum pressure we can obtain. The tubes of cylindrical, conical, and cosine shape, which have the same volume and length, were investigated. Results show that the resonant frequency and patterns of pressure waves strongly depend on not only the tube shape but also the amplitude of driving acceleration. The degree of nonlinearity of wave patterns was also measured by the newly defined nonlinear energy ratio of the pressure signals. It was found that the 12 cosine-shape tube is more suitable to induce high compression ratio than other shapes.