A Finite Element Model of Hydraulic Pipelines using an Optimized Interlacing Grid System

Simulation of flow and pressure variations in fluid pipelines using finite difference and finite element models can give unrealistic results, corresponding to errors in natural frequencies. A novel finite element model of hydraulic pipelines has been developed, using an interlacing grid system. The grid spacing is non-uniform and is optimized, using a genetic algorithm, to make some or all of the undamped natural frequencies of the model as close as possible to exact theoretical ones for a uniform pipe with the extreme boundary conditions of either constant pressure or no flow. Inaccuracies in the highest natural frequencies may be acceptable because of the effect of frequency-dependent friction and limited system frequency response. The optimized model gives accurate results in time domain simulation, and it allows variable properties and a variable integration step to be readily accommodated.

[1]  F. T. Brown,et al.  The Transient Response of Fluid Lines , 1962 .

[2]  F. T. Brown,et al.  Step Responses of Liquid Lines With Frequency-Dependent Effects of Viscosity , 1965 .

[3]  W. Zielke.  Frequency dependent friction in transient pipe flow , 1968 .

[4]  R. E. Goodson,et al.  A Survey of Modeling Techniques for Fluid Line Transients , 1972 .

[5]  J. T. Karam.  A Simple but Complete Solution for the Step Response of a Semi-Infinite, Circular Fluid Transmission Line , 1972 .

[6]  R. G. Leonard,et al.  A Simple Yet Theoretically Based Time Domain Model for Fluid Transmission Line Systems , 1973 .

[7]  A. J. Healey,et al.  Rational polynomial approximations for fluid transmission line models , 1981 .

[8]  D. A. Hullender,et al.  Modal approximations for the fluid dynamics of hydraulic and pneumatic transmission lines , 1983 .

[9]  Donald Margolis,et al.  Bond Graph Models for Fluid Networks Using Modal Approximation , 1985 .

[10]  R. F. Boucher,et al.  Transmission Line Modelling of a Hydraulic Position Control System , 1986 .

[11]  J Watton.  Modelling of Electrohydraulic Systems with Transmission Lines using Modal Approximations , 1988 .

[12]  John Watton.  Fluid Power Systems: Modeling, Simulation, Analog and Microcomputer Control , 1989 .

[13]  W. E. Tobler,et al.  Dissipative Modal Approximation of Fluid Transmission Lines Using Linear Friction Model , 1991 .

[14]  D N Johnston,et al.  Practical requirements for modelling the dynamics of hydraulic pipelines , 1993 .