A new simulation technique called the system modal approximation method (SMA) for fluid transients in complex pipeline systems has been proposed. The superiority of this technique compared to other existing methods has been verified. Thus far, however, detailed considerations have been limited to pipelines having elementary boundary conditions. In the present paper, for the generalization of the SMA method, calculation methods are newly proposed for the case in which the boundary conditions are given by the time-variant nonlinear relationship between pressure and flow rate, such as the conditions in a safety valve, and its usefulness is verified by comparison to experimental measurements.

1.
Wylie
,
E. B.
, and
Streeter
,
V. L.
, 1978,
Fluid Transients
,
MacGraw-Hill
, New York.
2.
Zielke
,
W.
, 1968, “
Frequency-Dependent Friction in Transient Pipe Flow
,”
ASME J. Basic Eng.
0021-9223,
90
(
1
), pp.
109
115
.
3.
Brown
,
F. T.
, 1969, “
A Quasi Method of Characteristics With Application to Fluid Lines With Frequency Dependent Wall Shear and Heat Transfer
,”
ASME J. Basic Eng.
0021-9223,
91
, pp.
217
227
.
4.
Hullender
,
D. A.
, and
Healey
,
A. J.
, 1981, “
Rational Polynominal Approximations for Fluid Transmission Line Models
,” Fluid Transmission Line Dynamics, Special Publication for the ASME Winter Annual Meeting, Washington DC, pp.
33
55
.
5.
Hsue
,
C. Y.
, and
Hullender
,
D. A.
, 1983, “
Modal Approximations for the Fluid Dynamics of Hydraulic and Pneumatic Transmission Lines
,” Fluid Transmission Line Dynamics, Special Publication for the ASME Winter Annual Meeting, Boston, pp.
51
77
.
6.
Watton
,
J.
, 1988, “
Modelling of Electrohydraulic Systems With Transmission Lines Using Modal Approximations
,”
Proc. Inst. Mech. Engr.
,
202
(
3
), pp.
153
163
.
7.
Zhao
,
T.
,
Peng
,
G.
, and
Xu
,
Y.
, 1989., “
A Study on Basic Methods of Time Domain Simulation of Fluid Transmission Lines
,”
Proccedings of the First JHPS International Symposium on Fluid Power
, Tokyo, Japan.
8.
Yang
,
W. C.
,
Glidewell
,
J. M.
,
Tobler
,
W. E.
, and
Chui
,
G. K.
, 1991, “
Dynamic Modeling and Analysis of Automotive Multi-Port Electronic Fuel Delivery System
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
113
, pp.
143
151
.
9.
Yang
,
W. C.
, and
Tobler
,
W. E.
, 1991, “
Dissipative Modal Approximation of Fluid Transmission Lines Using Linear Friction Model
,”
ASME J. Dyn. Syst., Meas., Control
0022-0434,
113
, pp.
152
162
.
10.
Muto
,
T.
,
Kayukawa
,
H.
, and
Kato
,
H.
, 1993, “
Fast and Convenient Method for Simulation of Hydraulic Transmission Lines
,”
Trans. Jpn. Soc. Mech. Eng., Ser. C
0387-5024,
59
(
568
), pp.
3773
3777
.
11.
Piche
,
R.
, and
Ellmann
,
A.
, 1995, “
A Standard Hydraulic Fluid Transmission Line Model for Use With ODE Simulators
,” Eighth Bath International Fluid Power Workshop, University of Bath, UK.
12.
Seko
,
A.
,
Muto
,
T.
,
,
H.
, and
Tanaka
,
K.
, 1999, “
Development of Simulation Program for Hydraulic Systems
,”
Journal of the Japan Fluid Power System Society
(in Japanese),
30
(
2
), pp.
42
47
.
13.
Kojima
,
E.
,
,
M.
, and
Yu
,
J.
, 2002, “
Development of Accurate and Practical Simulation Technique Based on the Modal Approximations for Fluid Transients in Compound Fluid-Line System (1st Report: Establishment of fundamental calculation algorithm and basic considerations for verification of its availability)
,”
Int. J. Fluid Power
1439-9776,
3
(
2
), pp.
5
15
.
14.
Kojima
,
E.
, and
,
M.
, 2003, “
Development of Accurate and Practical Simulation Technique Based on the Modal Approximations for Fluid Transients in Compound Fluid-Line System (2nd Report: Enhancement of analytical functions for generalization)
,”
Int. J. Fluid Power
1439-9776,
4
(
3
), pp.
35
45
.
15.
Kojima
,
E.
, and
Edge
,
K. E.
, 1994, “
Experimental Determination of Hydraulic Silencer Transfer Matrices and Assessment of the Method for Use as a Standard Test Procedure
,” Seventh Bath International Fluid Power Workshop, University of Bath, UK.
16.
Kojima
,
E.
, 1992, “
A New Method for the Experimental Determination of Pump Fluid-Borne Noise Characteristics
,” Fifth Bath International Fluid Power Workshop, University of Bath, UK.