Nonlinear Pressure Wave Analysis by Concentrated Mass Model  (1st Report, Suggestion and Validity Verification of Analytic Model)

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 previous reports, a concentrated mass model was proposed to analyze nonlinear pressure wave phenomena in a straight cylindrical tube. In this paper, the modeling of a branched junction is proposed. The model of the branched junction consists of masses, nonlinear pressure elements, base support dampers, and nonlinear dampers. The nonlinear damper is derived from the pressure loss at the branched junction. To confirm the validity of the proposed branch model, the numerical results obtained from the concentrated mass model are 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 results are compared with the numerical result. All 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. method which considers the pressure loss by using an iterative calculation. Chae et al. (8) proposed a treatment of a branch element in a difference method to perform a nonlinear pressure wave analysis.In the present paper, we propose a treatment of a branch element using the concentrated mass model. First, we propose a model of a branch element in which the nonlinear dampers are derived from the pressure loss at a branched junction. Next, we compare the numerical results from the concentrated mass model with the transmission loss (9) to confirm the validity of the branch model in a linear region. Then, we consider an experiment on a sound tube with a branch pipe to confirm the validity of the branch model in a nonlinear region. Furthermore, we investigate the reduction effect of a branch pipe on a standing pressure wave. This effect has not been studied before.

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Nonlinear Pressure Wave Analysis by Concentrated Mass Model

Ishikawa

Kondou

Matsuzaki

2010

JSDD

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Nonlinear Pressure Wave Analysis by Concentrated Mass Model (4th Report, Modeling of Elastic Pipe Element)

Ishikawa

Kondou

Matsuzaki

et al. 2011

JSDD

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A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effects in the propagation medium. The purpose of this study is to establish a practical analytical model of this phenomenon. In previous reports, a concentrated mass model was proposed to analyze nonlinear pressure wave phenomena in a rigid straight cylindrical pipe. In this paper, we apply the model to an elastic pipe. The model of the elastic pipe consists of masses, nonlinear connecting springs, base support dampers, base support springs, and connecting dampers. The effect that the cross-sectional area of the elastic pipe changes is taken into account through the nonlinear connecting spring. To confirm the validity of the proposed elastic pipe model, we perform experiments on a silicone pipe, and the experimental results are compared with the numerical results obtained by the concentrated mass model. The numerical computational results agree well with the experimental results. Therefore, it is concluded that the proposed elastic pipe model is valid for the numerical analysis of nonlinear pressure wave problems in an elastic pipe.

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