A variational method is used to derive numerical models for transient flow simulation in fluid transmission lines. These are generalizations of models derived using the more traditional modal method. Three different transient compressible laminar pipe flow models are considered (inviscous, one-dimensional linear viscous, and two-dimensional dissipative viscous flow), and a model for transient turbulent pipe flow is given. The (model) equations in the laminar case are given in the form of a set of constant coefficient ordinary differential equations, and for the turbulent case (model) in the form of a set of nonlinear ordinary differential equations. Explicit equations are given for various end conditions. Attenuation factors, similar to the window functions used in spectral analysis, are used to attenuate Gibbs phenomenon oscillations. [S0022-0434(00)03201-9]

Issue Section:
Technical Papers
Keywords:
fluidic devices, transmission lines, flow simulation, transients, pipe flow, variational techniques, Rayleigh-Ritz methods, hydraulic systems
Topics:
Approximation, Flow (Dynamics), Fluids, Pressure, Transmission lines, Variational techniques, Transfer functions, Modeling, Friction, Pipes, Boundary-value problems, Steady state
1.
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
.
2.
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
.
3.
Wylie, E., Streeter, V., and Suo, L., 1993, Fluid Transients in Systems, Prentice-Hall.
4.
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.
5.
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.
6.
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
.
7.
Piche´, R., and Ellman, A., 1995, “A Fluid Transmission Line Model for Use with ODE Simulators,” The Eighth Bath International Fluid Power Workshop.
8.
Brown
,
F.
,
1962
, “
The Transient Response of Fluid Lines
,”
ASME J. Basic Eng.
,
84
, pp.
547
–
553
.
9.
D’Souza
,
A.
, and
Oldenberger
,
R.
,
1964
, “
Dynamic Response of Fluid Lines
,”
ASME J. Basic Eng.
,
86
, pp.
589
–
598
.
10.
Goodson
,
R.
, and
Leonard
,
R.
,
1972
, “
A Survey of Modeling Techniques for Fluid Line Transients
,”
ASME J. Basic Eng.
,
94
, pp.
474
–
482
.
11.
Reddy, J., 1987, Applied Functional Analysis and Variational Methods in Engineering, McGraw-Hill.
12.
Trikha
,
A.
,
1975
, “
An Efficient Method for Simulating Frequency Dependent Friction in Transient Liquid Flow
,”
ASME J. Basic Eng.
,
97
, pp.
97
–
105
.
13.
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
.
14.
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.
15.
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
.
16.
Lanczos, C., 1956, Applied Analysis, Prentice Hall.
17.
Harris
,
F.
,
1978
, “
On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform
,”
Proc. IEEE
,
66
, pp.
51
–
83
.
18.
Piche´
,
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
.
19.
Ellman, A., and Piche´, R., 1996, “A Modified Orifice Flow Formula for Numerical Simulation,” 1996 ASME International Mechanical Engineering Congress and Exposition, Atlanta, GA.
20.
Holmboe
,
E.
, and
Rouleau
,
W.
,
1967
, “
The Effect of Viscous Shear on Transients in Liquid Lines
,”
ASME J. Basic Eng.
,
89
, pp.
174
–
180
.
21.
Gottlieb, D., and Orszag, S., 1977, Numerical Analysis of Spectral Methods, Vol. 26, SIAM, Philadelphia.
22.
Ma¨kinen, J., et al., 1997, “Dynamic Simulations of Flexible Hydraulic-Driven Multibody Systems using Finite Strain Theory,” Fifth Scandinavian International Conference on Fluid Power, Linko¨ping.
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