Effects of Tube Shape on Nonlinear Resonant Oscillations of Interior Gas

Abstract

An investigation is conducted to get an outline of designing the tube shape for a sonic compressor with high efficiency. When a closed tube oscillates with its resonant frequency, the interior acoustic properties such as density, velocity, and pressure undergo very large perturbation with nonlinear patterns. In order to analyze the nonlinear acoustic phenomena such as harmonic generation, shock formation, and resonant frequency shift, two-dimensional axisymmetric governing equations are derived and solved numerically. Numerical simulations are performed to investigate the effect of the tube shape that gives us maximum possible pressure. 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 pressure signals is measured by the newly defined nonlinear energy ratio of the signals. The nonlinear energy ratio well describes not only the energy transfer to higher harmonics but also the compression efficiency, so that it can be a good measure for designing tube shape.