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

Abstract

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.

Real-time implementation of Kalman filter for unsteady flow measurement in a pipe

“…Using the interlacing grid system shown in Figure 2, in which pressure grid points and flow rate grid points are located interlaced, finite approximation of the equation of motion [equation (1)] and the continuity equation [equation (2)] leads to (Sanada et al, 1993;Sanada, 1994):…”

“…Kalman filter theory is applied to a one-dimensional uncompressible unsteady laminar fluid flow model, that is, the optimised finite element model of pipeline dynamics (Sanada et al, 1993;Sanada and Kitagawa, 1994). In this technique, only pressure signals are measured, and flow rate is estimated according to the Kalman filter.…”

A Study on Order Reduction of Optimized Finite Element Model of Pipeline Dynamics

“…For more sophisticated simulation, adaptive time step is used. For this purpose, the author proposed an optimized finite element model of pipeline dynamics (OFEM) 2) . Treatment of friction in the OFEM has been investigated for expanding the usage of the OFEM 3) .…”

“…(33) Equation (33) is the reduced-order system in which the state vector 2 x having small Hankel singular value is eliminated from the original system of Eq. (29) and Eq.…”

The management of intelligence-assisted finite element analysis technology

“…Neural Network and Genetic Algorithm implementations have been to a much more limited extent within FEA and FEMG and have mostly been confined to evolutionary growth of an FE mesh and associated shape optimisation( [1], [3], [14], [17], [38], [60], [71]). Each paradigm has its advantages and limitations and so any future FEA package/design tool that wishes to achieve the ideals of a perfect FE implementation [10] should try to take into account the feasibility of incorporating such methods based on their limitations rather than their advantages [32].…”