A Simple Yet Theoretically Based Time Domain Model for Fluid Transmission Line Systems

Abstract

A simple, theoretically based time domain model for the propagation of small, arbitrary signals in a finite, circular, fluid transmission line is developed. A recent simple theoretical solution for the step response at a downstream point in a semi-infinite fluid line is combined with a two-port representation of a finite line. The major feature of this finite line model is two “filters” which represent a convolution of their arbitrary inputs with the unit impulse response at the equivalent location in a semi-infinite line. Experimental tests are reported which further verify the simple semi-infinite line solution and verify the response of several example systems containing finite lines. The models developed herein show good agreement with experiment. The major anomaly noted was an amplitude dependence in the experimental response for signals larger than one percent of the bulk modulus of the fluid. Since the theory represents a linearized, small perturbation model, such disagreement might have been anticipated and is viewed as a limitation, rather than invalidation, of the model. Finally, quantitative comparisons are made between the proposed model and those in current use.

An enhanced transmission line method for modelling laminar flow of liquid in pipelines

“…[7][8][9][10] The TLM has been shown to be a very effective method for modelling unsteady flow and pressure in pipelines. It can model sudden transients, such as those caused by sudden closure of a valve, clearly and precisely, retaining the sharp wavefronts without the unrealistic oscillations or excessive smoothing that may occur with other methods such as the FEM or LEM.…”

“…Several techniques for dynamic modelling of flow and pressure of liquids in pipelines are available, ranging from simple lumped element methods (LEMs), 1 to the method of characteristics (MOC), 2,3 the finite element method (FEM), 4 various modal approximation (MA) methods 5,6 and the transmission line method (TLM). 7–10 The TLM has been shown to be a very effective method for modelling unsteady flow and pressure in pipelines. It can model sudden transients, such as those caused by sudden closure of a valve, clearly and precisely, retaining the sharp wavefronts without the unrealistic oscillations or excessive smoothing that may occur with other methods such as the FEM or LEM.…”

The transmission line method for modelling laminar flow of liquid in pipelines

“…These include the method of characteristics (MOC), 1,2 the lumped-element method (LEM), 3 the finite-element method (FEM), 4 various modal approximation (MA) methods 5,6 and the transmission line method (TLM). [7][8][9] In the simulation of many fluid systems, the dynamics of the flow in pipelines is not important, and simpler models can be used, resulting in simpler, faster and often more reliable simulations. However, for some systems involving rapid dynamics or long pipelines, wave transmission effects become significant, and more sophisticated models need to be used.…”

“…The TLM is a very efficient technique for modelling transmission line problems. [7][8][9] It makes use of the inherent delay in transmission of pressure and flow from one end of the line to the other. In some respects, the method is very similar to the MOC; in the MOC, the line is split up into short elements, and pressure and flow values propagate from one node to the next over one time step.…”

About Inverse Laplace Transform of a Dynamic Viscosity Function

“…On the other hand, Zielke presented an inverse Laplace transform of the weighting function suitable for the numerical modeling of the wall shear stress, but he did not work on a complete analytical solution. In the 1970s, an interesting solution was presented by Karam [37,38]. This theoretical solution was limited to the step response at a downstream end in a semi-infinite fluid line, combined with a two-port representation of a finite line.…”