Pipes are widely used in hydraulic and pneumatic subsystems for transferring energy or signals. Accurate prediction of pressure transients is very important in the drive and control circuits of complex fluid-line systems. Based on the approximation of Navier-Stokes equations for one-dimensional flow, a mathematical model of the pneumatic pipe with lumped parameters was developed using ordinary differential equations, which can be easily implemented in most computer programs for the simulation of complex heterogeneous engineering systems. Implemented in Matlab-Simulink software, the computer model of the pipe makes it possible to determine the influence of capacitance, inertance, resistance and heat exchange on the dynamic characteristics of the control and power circuits of pneumatic systems. An advantage of the model is that various functions can be selected to describe linear resistances and local resistances are taken into account, particularly at the inlet and outlet. Such resistances largely affect flow resistances in short tubes (up to 10 m) that can be found, e.g., in pneumatic brake systems of road vehicles. Confirmed by Kolmogorov-Smirnov test results, the consistency of the pressure curves obtained in experimental and simulation tests proves the implemented tube model to be useful for the calculations of pneumatic system dynamics.

References

References
1.
Reeßing
,
M.
,
Döring
,
U.
, and
Brix
,
T.
, 2007, “
Modeling of Heterogeneous Systems in Early Design Phases
,”
The Future of Product Development: Proceedings of the 17th CIRP Design Conference
, Springer, Berlin, Heidelberg, pp.
247
258
.
2.
Brown
,
F. T.
, 1962, “
The Transient Response of Fluid Lines
,”
ASME J. Basic Eng. Ser. D
,
84
(
4
), pp.
547
553
.
3.
Currie
,
I. G.
, 1993,
Fundamental Mechanics of Fluids
,
2nd Ed.
,
McGraw-Hill
,
New York
.
4.
Goodson
,
R. E.
, and
Leonard
,
R. G.
, 1972, “
A Survey of Modeling Techniques for Fluid Line Transients
,”
ASME J. Basic Eng.
,
94
(
2
), pp.
474
482
.
5.
Soumelidis
,
M. I.
,
Johnston
,
D. N.
,
Edge
,
K. A.
, and
Tilley
D. G.
, 2005, “
A Comparative Study of Modelling Techniques for Laminar Flow Transients in Hydraulic Pipelines
,”
Proceedings of the 6th JFPS International Symposium on Fluid Power
, Tskuba, November 7–10, pp.
100
105
.
6.
Bisgaard
,
C.
,
Sørensen
,
H. H.
, and
Spangenberg
,
S.
, 1987, “
A Finite Element Method for Transient Compressible Flow in Pipelines
,”
Int. J. Numer. Methods Fluids
,
7
(
3
), pp.
291
303
.
7.
Chen
,
Y.
,
Gao
,
F.
,
Zhang
,
Z.
,
Wang
,
H.
, and
Cai
,
G.
, 2008, “
Finite Volume Model for Quasi One-dimensional Compressible Transient Pipe Flow, (I) Finite Volume Model of Flow Field
,”
J. Aerosp. Power
,
23
(
2
), pp.
311
316
.
8.
Manning
,
J. R.
, 1968, “
Computerized Method of Characteristics Calculations for Unsteady Pneumatic Line Flows
,”
ASME J. Basic Eng., Ser. D
,
90
(
2
), pp.
231
240
.
9.
Krus
,
P.
,
Weddfeld
,
K.
, and
Palmberg
,
J. O.
, 1994, “
Fast Pipeline Models for Simulation of Hydraulic Systems
,”
ASME J. Dyn. Syst., Meas., Control
,
116
(
1
), pp.
132
136
.
10.
Krus
,
P.
, 1999, “
Distributed Modelling for Simulation of Pneumatic Systems
,”
4th JHPS International Symposium
, Tokyo, pp.
443
452
.
11.
Franco
,
W.
, and
Sorli
M.
, 2004, “
Time-domain Models for Pneumatic Transmission Lines
,”
Bath Workshop on Power Transmission & Motion Control, PTMC 2004
,
C. R.
Burrows
,
K. A.
Edge
, and
D. N.
Johnston
, eds., pp.
257
269
.
12.
Almondo
,
A.
, and
Sorli
,
M.
, 2006, “
The Time Domain Fluid Transmission Line Modelling Using a Passivity Preserving Rational Approximation of Frequency Dependent Transfer Matrix
,”
Int. J. Fluid Power
,
7
(
1
), pp.
41
50
.
13.
Hsue
,
C.
, and
Hullender
,
D.
, 1983, “
Modal Approximations for the Fluid Dynamics of Hydraulic and Pneumatic Transmission Lines
,”
Proceedings of ASME Winter Annual Meeting on Fluid Transmission Line Dynamics
,
M.
Franke
and
T. M.
Drzewiecki
, eds., pp.
51
77
.
14.
Mäkinen
,
J.
,
Piché
,
R.
, and
Ellman
,
A.
, 2000, “
Fluid Transmission Line Modeling Using a Variational Method
,”
ASME J. Dyn. Syst., Meas., Control
,
122
(
1
), pp.
153
162
.
15.
Anderson
,
J. D.
, 1995,
Computational Fluid Dynamics — The Basics With Applications
,
McGraw-Hill International Editions
.
16.
Brower
,
W. B.
Jr.
, 1999,
A Primer in Fluid Mechanics. Dynamics of Flows on One Space Dimension
,
CRC Press
,
Boca Raton, FL
.
17.
Elmqvist
,
H.
,
Tummescheit
,
H.
, and
Otter
,
M.
, 2003, “
Object-Oriented Modeling of Thermo-Fluid Systems
,”
Proceedings of the 3rd International Modelica Conference
,
P.
Fritzson
, ed., Linköping, November 3–4, pp.
269
286
.
18.
Sjöstedt
,
C.-J.
, and
Persson
,
J.-G.
, 2005, “
The Design of Modular Dynamical Fluid Simulation Systems
,”
Proceedings from OST 05 Conference
, Oulu, October 2005, pp.
1
12
.
19.
Beater
,
P.
, 2007,
Pneumatic Drives. System Design, Modelling and Control
,
Springer-Verlag
,
Berlin, Heidelberg
.
20.
Wylie
,
E. B.
,
Streeter
,
V. L.
, and
Suo
,
L.
, 1993,
Fluid Transients in Systems
,
Prentice-Hall Inc.
,
Englewood Cliffs, NJ
.
21.
Weigand
,
B.
, 2004,
Analytical Methods for Heat Transfer and Fluid Flow Problems
,
Springer-Verlag
,
Berlin, Heidelberg
.
22.
Giorgi
,
R.
,
Kobbi
,
N.
,
Sesmat
,
S.
, and
Bideaux
E.
, 2008, “
Thermal Model of a Tank for Simulation and Mass Flow Rate Characterization Purposes
,”
Proceedings of the 7th JFPS International Symposium on Fluid Power
, Toyama, September 15–18, pp.
225
230
.
23.
Kagawa
,
T.
, and
Shimizu
,
M.
, 1988, “
Non Dimensional Pressure Responses of Pneumatic RC Circuit Considering Heat Transfer
,” Proceedings of Hydraulics and Pneumatics,
19
(
4
), pp.
306
311
.
24.
Junke
,
G.
, and
Pierrey
,
J.
, 2003, “
Modified Log-Wake Law for Turbulent Flow in Smooth Pipes
,”
J. Hydraul. Res.
,
41
(
5
), pp.
493
501
.
You do not currently have access to this content.