Numerical Simulation of Nonlinear Resonant Oscillations in an Elliptical Cylinder

Abstract

A resonant gas oscillation generated in a cylinder with elliptical cross section is numerically studied. Resonant gas oscillations in circular cylinder have distinctive features such as shock free oscillation and periodic amplitude modulation. These phenomena are from the nature of the geometry of the sound field (dispersive effect). In contrast to the cylindrical wave, the resonance of the plane wave always emanates a shock wave if the dissipation effect of the gas is sufficiently small. Resonance of cylindrical and plane wave are one dimensional phenomena. On the other hand, the wave propagation in elliptical cylinder is essentially two dimensional problem and the geometry of the ellipse is defined by the eccentricity. Thus the resonant gas oscillation in elliptical cylinder shows interesting natures due to the two dimensionality of the system, such as the presence of even and odd oscillation mode. This study shows the dependence of the behavior of resonant oscillation on the eccentricity, and nonlinear effect including shock wave.