Modal simulation of unidirectional fluid dynamics (water hammer)

Abstract

This paper presents a general approach to analog simulation of "water-hammer" type phenomena. In brief, the simulation approach consists of obtaining a general Fourier-series time solution in terms of boundary variables (pressures or flowrates), retaining a finite number of terms in this series solution, and then obtaining the ordinary differential equations to which the terms correspond. One customarily "winces" when contemplating a series solution of any form, particularly when informed that the solu tion is to be subsequently approximated by retaining only a finite number of terms. Although the mathe matical manipulations contained in the paper may appear forbidding, they need be developed but once, and the final differential equations which result are quite simple. Truncation of the Fourier series solu tions happily results only in a truncation of the valid frequency range. Within this valid frequency range there is little or no loss in accuracy. These and other advantageous characteristics of the modal simula tion technique are developed by various analytical and numerical examples.