Nonlinear pressure wave analysis by concentrated mass model (1st report, suggestion and validity verification of analytic model)

Satoshi Ishikawa, Takahiro Kondou, Kenichiro Matsuzaki

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Pressure wave propagating in a tube often changes to shock wave because of nonlinear effect of fluid. Analyzing this phenomenon by the finite difference method requires high computation cost. In order to overcome the problem of computation cost, a concentrated mass model is proposed. This model consists of masses, connecting nonlinear springs, connecting dampers, and base support dampers. The characteristic of connecting nonlinear spring is derived from the condition of adiabatic change of fluid, and the equivalent mass and the equivalent damping coefficient of the base support damper are derived from the equation of motion of fluid in cylindrical tube. Pressure waves generated in a hydraulic oil tube, in a sound tube and in a plane-wave tube are analyzed numerically by using the proposed model in order to confirm the validity of the model. All numerical computational results agree very well with the experimental results carried out by Okamura, Saenger and Kamakura. Especially, the phenomena that the pressure wave with large amplitude propagating in the sound tube and in the plane tube change to shock wave are numerically reproduced. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear pressure wave problem.

Original languageEnglish
Pages (from-to)1436-1443
Number of pages8
JournalNihon Kikai Gakkai Ronbunshu, C Hen/Transactions of the Japan Society of Mechanical Engineers, Part C
Volume75
Issue number753
DOIs
Publication statusPublished - Jan 1 2009

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Shock waves
Fluids
Acoustic waves
Finite difference method
Equations of motion
Costs
Numerical analysis
Damping
Hydraulics
Oils

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering

Cite this

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abstract = "Pressure wave propagating in a tube often changes to shock wave because of nonlinear effect of fluid. Analyzing this phenomenon by the finite difference method requires high computation cost. In order to overcome the problem of computation cost, a concentrated mass model is proposed. This model consists of masses, connecting nonlinear springs, connecting dampers, and base support dampers. The characteristic of connecting nonlinear spring is derived from the condition of adiabatic change of fluid, and the equivalent mass and the equivalent damping coefficient of the base support damper are derived from the equation of motion of fluid in cylindrical tube. Pressure waves generated in a hydraulic oil tube, in a sound tube and in a plane-wave tube are analyzed numerically by using the proposed model in order to confirm the validity of the model. All numerical computational results agree very well with the experimental results carried out by Okamura, Saenger and Kamakura. Especially, the phenomena that the pressure wave with large amplitude propagating in the sound tube and in the plane tube change to shock wave are numerically reproduced. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear pressure wave problem.",
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AU - Kondou, Takahiro

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AB - Pressure wave propagating in a tube often changes to shock wave because of nonlinear effect of fluid. Analyzing this phenomenon by the finite difference method requires high computation cost. In order to overcome the problem of computation cost, a concentrated mass model is proposed. This model consists of masses, connecting nonlinear springs, connecting dampers, and base support dampers. The characteristic of connecting nonlinear spring is derived from the condition of adiabatic change of fluid, and the equivalent mass and the equivalent damping coefficient of the base support damper are derived from the equation of motion of fluid in cylindrical tube. Pressure waves generated in a hydraulic oil tube, in a sound tube and in a plane-wave tube are analyzed numerically by using the proposed model in order to confirm the validity of the model. All numerical computational results agree very well with the experimental results carried out by Okamura, Saenger and Kamakura. Especially, the phenomena that the pressure wave with large amplitude propagating in the sound tube and in the plane tube change to shock wave are numerically reproduced. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear pressure wave problem.

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