Nonlinear pressure wave analysis by concentrated mass model (2nd report, modeling and validity verification of branch 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 a branched junction is proposed. The model at the branched junction consists of masses, nonlinear pressure elements, base support dampers, and nonlinear dampers. The nonlinear damper is derived from pressure loss at the branched junction. To confirm the validity of the proposed branch model, the numerical result obtained by the concentrated mass model is compared with the theoretical value of the transmission loss of a branch pipe. Additionally, an experiment on a sound tube with a branch pipe is performed and the experimental result is compared with the numerical result. All numerical computational results agree very well with the theoretical value and the experimental results. Therefore, it is concluded that the proposed branch model is valid for the numerical analysis of nonlinear pressure wave problem in a tube with a branch pipe.