Fluid Transmission Lines—Distributed Parameter Models Part 1: A Review of the State of the Art

Abstract

This paper presents a hierarchical class$cation of linear, distributed parameter models which have been used in the study of rigid, uniform juid transmission lines. The development of the models from the fundamental equations of..Puid dynamics is discussed, and the assumptions necessary in obtaining each model are shown. The solutions to the models are presented in general Laplace forms, and the terms that appear in the solutions are discussed with reference to the initial and subsequent assumptions. The existence qfseuett distinct forms of models was identtfied and verified by comparison with a vast number of apparently different models quoted in over three hundred research papers covering various engineering, medical, and biological applications. Significant contributions by various researchers over the last eighty years to the development of distributed parameter models offluid transmission lines are reviewed. The application ofthe various models based upon comparisons made in the literature is deali with, and the eflect of the initial assumptions on each model's accuracy is discussed. The aim of the paper is to assist in the identtjication of areas of research where future efforts should he directed and hopefully to prevent needless duplication of research effort. NOTATION parameter constants of integration speed of sound in fluid-filled transmission line body force 2/-1

A distributed parameter systems view of control problems in drilling

“…However at conditions of unsteady flow, this simple relation understates the actual viscous dissipation due to the 2-dimensional effects in the flow, usually referred to as the Richardson annular effect. Specifically, unsteady friction should be considered when the shear wave number r 0 (ω/ν 0 ) 1/2 is greater than 5 [Stecki and Davis, 1986].…”

Frequency-Domain Modeling of Transients in Pipe Networks with Compound Nodes Using a Laplace-Domain Admittance Matrix

“…Both these methods have their origins in Laplace-domain transmission line theory, where pipes are described by their wave propagation characteristics [Brown and Nelson, 1965;Stecki and Davis, 1986] . Within the impedance method, a pipe network is characterised by the distribution of hydraulic impedance throughout the network and impedance relationships are derived to relate the hydraulic impedance values across an element (note that Hydraulic impedance refers to the ratio of transformed pressure to transformed flow).…”

“…Zielke [1968]; Brown [2003, 2004]),τ j exactly captures the unsteady effects as a convolution is a linear operation (see Stecki and Davis [1986] for more detail). Note that in the case of nonhomogeneous initial conditions, P j and Q j are taken as the Laplace transform of the transient fluctuations about these initial conditions.…”

Head- and Flow-Based Formulations for Frequency Domain Analysis of Fluid Transients in Arbitrary Pipe Networks

“…The analysis of pipelines in the frequency domain (which also includes Laplace domain analysis) began in the 1950s (summarised in Goodson andLeonard 1972, Stecki andDavis 1986). This work was typically limited to a single pipeline.…”