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TECHNICAL PAPERS

Fluid Transmission Line Modeling Using a Variational Method

[+] Author and Article Information
Jari Mäkinen

Department of Mathematics, Tampere University of Technology, Fin-33101, Tampere, Finlande-mail: jari@mohr.me.tut.fi

Robert Piché

Department of Mathematics, Tampere University of Technology, Fin-33101, Tampere, Finland

Asko Ellman

Institute of Hydraulics and Automation, Tampere University of Technology, Fin-33101, Tampere, Finland

J. Dyn. Sys., Meas., Control 122(1), 153-162 (Nov 04, 1998) (10 pages) doi:10.1115/1.482449 History: Received November 04, 1998
Copyright © 2000 by ASME
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References

Stecki,  J., and Davis,  D., 1986, “Fluid Transmission Lines-Distributed Parameter Models, Part 1: A Review of the State of the Art,” Proc. Inst. Mech. Eng., Part A, 200, pp. 215–228.
Stecki,  J., and Davis,  D., 1986, “Fluid Transmission Lines-Distributed Parameter Models, Part 2: Comparison of Models,” Proc. Inst. Mech. Eng., Part A, 200, pp. 229–236.
Wylie, E., Streeter, V., and Suo, L., 1993, Fluid Transients in Systems, Prentice-Hall.
Hsue, C., and Hullender, D., 1983, “Modal Approximations for the Fluid Dynamics of Hydraulic and Pneumatic Transmission Lines,” Fluid Transmission Line Dynamics, M. Franke and T. Drzewiecki, eds. ASME, pp. 51–77.
Hullender, D., Woods, R., and Hsu, C., 1983, “Time Domain Simulation of Fluid Transmission Lines using Minimum Order State Variable Models,” Fluid Transmission Line Dynamics, M. Franke and T. Drzewiecki, eds., ASME, pp. 78–97.
Watton,  J., and Tadmori,  M., 1988, “A Comparison of Techniques for the Analysis of Transmission Line Dynamics in Electrohydraulic Control Systems,” Appl. Math. Modelling, 12, pp. 457–466.
Piché, R., and Ellman, A., 1995, “A Fluid Transmission Line Model for Use with ODE Simulators,” The Eighth Bath International Fluid Power Workshop.
Brown,  F., 1962, “The Transient Response of Fluid Lines,” ASME J. Basic Eng., 84, pp. 547–553.
D’Souza,  A., and Oldenberger,  R., 1964, “Dynamic Response of Fluid Lines,” ASME J. Basic Eng., 86, pp. 589–598.
Goodson,  R., and Leonard,  R., 1972, “A Survey of Modeling Techniques for Fluid Line Transients,” ASME J. Basic Eng., 94, pp. 474–482.
Reddy, J., 1987, Applied Functional Analysis and Variational Methods in Engineering, McGraw-Hill.
Trikha,  A., 1975, “An Efficient Method for Simulating Frequency Dependent Friction in Transient Liquid Flow,” ASME J. Basic Eng., 97, pp. 97–105.
Taylor,  S., Johnston,  D., and Longmore,  D., 1997, “Modelling of Transient Flow in Hydraulic Pipelines,” Proc. Inst. Mech. Eng., Part I, 211, pp. 447–456.
Woods, R., 1983, “A First-Order Square-Root Approximation for Fluid Transmission Lines,” Fluid Transmission Line Dynamics, M. Franke and T. Drzewiecki, eds., ASME, pp. 37–49.
Yang,  W., and Tobler,  W., 1991, “Dissipative Modal Approximation of Fluid Transmission Lines Using Linear Friction Model,” ASME J. Dyn. Syst., Meas., Control, 113, pp. 152–162.
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Harris,  F., 1978, “On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform,” Proc. IEEE, 66, pp. 51–83.
Piché,  R., and Ellman,  A., 1994, “Numerical Integration of Fluid Power Circuit Models using Semi-Implicit Two-Stage Runge-Kutta Methods,” Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci., 208, pp. 167–175.
Ellman, A., and Piché, R., 1996, “A Modified Orifice Flow Formula for Numerical Simulation,” 1996 ASME International Mechanical Engineering Congress and Exposition, Atlanta, GA.
Holmboe,  E., and Rouleau,  W., 1967, “The Effect of Viscous Shear on Transients in Liquid Lines,” ASME J. Basic Eng., 89, pp. 174–180.
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Mäkinen, J., et al., 1997, “Dynamic Simulations of Flexible Hydraulic-Driven Multibody Systems using Finite Strain Theory,” Fifth Scandinavian International Conference on Fluid Power, Linköping.

Figures

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Imaginary part of the propagation operator Γ2(s̄=iωT) and its approximations, when friction coefficient ε=1/10
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A pipe system with Q-pipe models. Pipes are connected by the orifice that simply calculates flow rate through it when pressure drop is known.
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SIMULINK realization of the Q-model with 4 modes
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A pipe system with P-pipe models. Pipes are connected to the volume that is modeled by an integrator. More than two pipes may be connected to a single volume.
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Single pipe example, pressure response at beginning of line
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Single pipe example, comparing dissipative (2D viscous) and linear friction (1D viscous) models of pressure response at beginning of line
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Water hammer example pressure response at valve for first cycle of water hammer in high-viscosity oil
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Nonlinear (turbulent) flow example pressure response at beginning of line

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