Digital Distributed Parameter Model for Analysis of Unsteady Flow in Liquid-Filled Lines

A distributed parameter model for computing unsteady flow conditions in liquid systems is presented. The model is adapted for use in conjunction with a digital computer. The analytical method employed is essentially a solution synthesized from the effects of incremental step pressure pulses. The pressure pulses are generated because of incremental flow-rate changes that originate in a fluid system from a variety of sources, including the mechanical motion of the system structure. The pressure pulses propagate throughout the system at sonic velocity and are partially transmitted and reflected at each discontinuity. The velocity change caused by each pressure pulse is obtained from the relation for the characteristic acoustic impedance. Pressure and velocity time histories at any point in the system are obtained by a timewise summation of the contributions of the incremental pressure pulses passing that point. The analysis is presented in a form general enough to be applied to a variety of liquid-filled fluid systems. To illustrate the application of the method to a specific system, the response of a long, straight propellant line to a sinusoidal inlet flow and pressure perturbation is computed. Both a constant-cross-section line and a tapered line are analyzed in the example.