Nonlinear pressure wave analysis by concentrated mass model (3rd report, modeling of enlargement and contraction element)

A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effect of the fluid it is traveling through. The purpose of this study is to establish a practical analytical model to analyze this phenomenon. In the first report, a concentrated mass model was proposed to analyze a nonlinear pressure wave phenomenon in a straight cylindrical tube. In this paper, the modeling of an enlargement and a contraction is proposed. The model at the enlargement and the contraction consists of masses, nonlinear pressure elements, base support dampers, and nonlinear dampers. The nonlinear damper is derived from pressure loss at the enlargement and the contraction. To confirm the validity of the proposed model, an experiment on a sound tube with an expansion-chamber muffler is performed and the experimental result is compared with the numerical result obtained by the concentrated mass model. The numerical computational result agrees very well with the experimental result. Therefore, it is concluded that the proposed enlargement and contraction model is valid for the numerical analysis of nonlinear pressure wave problem in a tube with an expansion-chamber muffler.