Simulation of Fluid Network Dynamics by Transmission Line Modelling

Abstract

The classical solution to the acoustic wave equation reveals decoupled left- and right-going waves carrying pressure and flow. Using a variant of these waves representing power, it is shown that such decoupled waves permit fluid transmission lines in circuits to be modelled simply as pure time delays. It is also demonstrated that lumped inertance and capacitance may be modelled as transmission line stubs. Thus all dynamic elements in a circuit are represented as pure time delays and the only computations required are of wave scattering at junctions. Linear resistance is most easily admitted, especially if it is concentrated at the junctions. Computations on simple circuits are presented and shown to compare favourably with classical ‘lumped’ analyses. The significance of various approximations made is discussed. The method may be applied to fluid circuits of arbitrary size and complexity, and to circuits of other wave-propagating elements.