This paper describes a method of modelling time-varying flow in hydraulic pipelines which may be incorporated into time domain simulations of hydraulic systems operating with variable time steps. A previously reported finite element method is extended. New approximations to frequency-dependent friction for laminar and turbulent flow are presented. These are applicable to this finite element method as well as the method of characteristics and finite difference methods. Simulation results are compared against theory and excellent agreement is found.
JohnstonD. N.LongmoreD.K.DrewJ. E.A technique for the measurement of the transfer matrix characteristics of two-port hydraulic components. In ASME Winter Annual Meeting, Chicago, Illinois, November 1994 (American Society of Mechanical Engineers, New York).
2.
SanadaK.RichardsC. W.LongmoreD. K.JohnstonD. N.BurrowsC. R.Practical requirements for modelling the dynamics of hydraulic pipelines. In Second JHPS International Symposium onFluid Power, Tokyo, September 1993, pp. 657–664 (Chapman and Hall, London).
3.
WattonJ.TadmoriM. J.A comparison of techniques for the analysis of transmission line dynamics in electrohydraulic control systems. Appl. Math. Modelling, October 1988, 12 (5), 457–466.
4.
HsueC. Y.-YHullenderD. A.Modal approximations for the fluid dynamics of hydraulic and pneumatic transmission lines. In Proceedings of ASME Winter Annual Meeting on Fluid Transmission Line Dynamics, Boston, Massachusetts, November 1983, pp. 51–77 (American Society of Mechanical Engineers, New York).
5.
SteckiJ. S.DavisD. C.Fluid transmission lines-distributed parameter models. Part 1: A review of the state of the art. Proc. Instn Mech. Engrs, 1986, 200 (A4), 215–228.
6.
RichardsC. W.TilleyD. G.TomlinsonS. P.BurrowsC. R.Type insensitive codes for the simulation of fluid power systems. In Proceedings of ASME Winter Annual Meeting, Texas, November 1990, 90WA FPST6 (American Society of Mechanical Engineers, New York).
7.
LongmoreD. K.StammersC. W.Combined longitudinal and lateral vibration of a curved reinforced hose containing fluid. In International Conference onRecent Advances in Structural Dynamics, Southampton, 1980, pp. 521–532.
8.
LongmoreD. K.SchlesingerA.Transmission of vibration and pressure fluctuations through hydraulic hoses. Proc. Instn Mech. Engrs, Part I, 1991, 205 (12), 97–104.
9.
SanadaK.RichardsC. W.LongmoreD. K.JohnstonD. N.A finite element model of hydraulic pipelines using an optimized interlacing grid system. Proc. Instn Mech. Engrs, Part I, 1993, 207 (14), 213–222.
10.
MichelM.An Introduction to Genetic Algorithms, 1996 (The MIT Press, Cambridge, Massachusetts).
11.
ZielkeW.Frequency-dependent friction in transient pipe flow. Trans. ASME, J. Basic Engng, March 1968, Ser. D, 90, 109–114.
12.
TrikhaA. K.An efficient method for simulating frequency-dependent friction in transient liquid flow. Trans. ASME, J. Fluids Engng, March 1975, Ser. I, 97, 97–105.
13.
HarrisF. J.On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE, January 1978, 66 (1), 51–83.
14.
VardyA. E.BrownJ. M.B.Kuo-LunH.A weighting function model of transient turbulent pipe friction. J. Hydraul. Res., 1993, 31 (4), 533–548.
15.
BrownF. T.MargolisD. L.ShahR. P.Small-amplitude frequency behaviour of fluid lines with turbulent flow. Trans. ASME, J. Basic Engng, December 1969, Ser. D, 91, 678–693.
16.
TaylorS. E. M.JohnstonD. N.LongmoreD. K.Experimental validation of pipeline models for laminar and turbulent transient flow. In Proceedings of ASME International Mechanical Engineering Congress and Exposition, Dallas, Texas, November 1997, FPST-Vol. 4, pp. 99–104 (American Society of Mechanical Engineers, New York).
