THE DIGITAL COMPUTATION OF PRESSURES IN HYDRAULIC PIPES WITH SMALL VOLUME USING AN ITERATIVE TECHNIQUE

This paper describes a mathematical stiffness problem encountered in the digital simulation of hydraulic pipe systems and an iterative technique that may be employed to avoid it. Mathematical stiffness often arises in systems where the compliance of one or more elements is much smaller than the compliance of the majority of elements in the system. In hydraulic systems, pipes are usually described by first-order differential equations, but if the pipe volume for one or more of the pipes is small, the simulation of this equation by digital computer techniques will necessitate the use of very small computer time steps and simulation times may be very long. However, under these conditions, pressure changes are usually very rapid, and for practical purposes can be considered to instantaneously follow the forcing function, that is, behave as though no compliance existed. A very similar set of circumstances arises in the simulation of orifices at start-up of flow or when flow is reversed. In this paper iterative models are proposed for such cases and their effectiveness is demonstrated in simulating two types of system. © 1990, Institution of Mechanical Engineers. All rights reserved.