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

A numerical investigation on nonlinear oscillations of gas in an axisymmetr ic closed tube is presented. When the tube is oscillated at a resonant freq uency of the interior acoustic field, it is well known that acoustic variab les such as density, velocity, smd pressure undergo very large perturbation , often described as nonlinear oscillation. One-dimensional nonlinear gover ning equations, which explicitly include attenuation terms related to visco sity, were derived. Then, the equations were solved numerically by using th e higher-order finite difference scheme, which divided into two parts of sp atial differentiation and time evolution. Numerical simulations were accomp lished 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 th e same volume and length, were investigated. Results show that the resonant frequency and patterns of pressure waves strongly depend on not only the t ube shape but also the amplitude of driving acceleration. The degree of non linearity of wave patterns was also measured by the newly defined nonlinear energy ratio of the pressure signals. It was found that the 1/2 cosine-sha pe tube is more suitable to induce high compression ratio than other shapes . (C) 2000 Acoustical Society of America. [S0001-4966(00)01511-3].