Lumped-parameter representation of fluid-system transients

Abstract

Flow and pressure transients in closed pipes are described by non-linear hyperbolic partial differential equations. In many control applications a discrete-space lumped-parameter ordinary differential equation model is required. With such representations, care is needed to ensure that they retain essential physical characteristics of the phenomena described. Intentionally or otherwise, most of these fluid-system models are related to the numerical discretisation technique known as the Method of Lines. Aspects of implementing this are investigated, including the form of the basic equations and variables, representation of pipe friction, choice of interpolating polynomials in space and method of integration in time. These are compared with the standard Method of Characteristics solution for the original partial differential equations to eliminate any potential numerical instabilities, parasitic transient solutions or inconsistencies between steady and transient states which might influence adversely system control or stability studies. The Method of Lines is most appropriate for parabolic problems, and many existing applications to fluid transients are found to be satisfactory only where changes are gradual and continuous. The preferred formulation is free from this restriction, and applied to a stability investigation (prediction of compressor surging) is shown to perform reliably.