Effects of an opening on pressure wave propagation in a tube

Abstract

This paper focuses on the effects of an opening placed along a tube on the propagation of a pressure wavefront. Such a configuration has been chosen for its relevance to many of the countermeasures envisaged in reducing strong pressure transients in tunnels due to the entry of high-speed trains (this installation includes a perforated entrance hood and ventilation shaft). We will start by establishing that when a compression wavefront passes through an opening, the front is split into an infinite number of smaller pressure steps, with their amplitude expressed as the terms of a mathematical series. The main parameter of the series is a transmission coefficient of the opening. The shape of each of the smaller pressure steps is driven by the transmission–reflection process that takes place at the opening. Both experimental and numerical studies have been carried out to carefully estimate both the transmission coefficient and the shape of the transmitted and reflected pressure waves. Three major parameters are identified: the relative surface area of the opening to the tube cross-section, the ratio of the incident front length to the longitudinal opening length, and the incident front amplitude.

It will be shown that the transmission coefficient decreases exponentially with the relative surface area of the opening and is significantly influenced by the incident front amplitude. Both the length and shape of the transmitted front are similar to those of the incident front. The reflected front length, however, increases linearly with the incident front length as well as with the longitudinal opening length. The shape of the reflected front is greatly influenced by the incident front length. A linear analysis has been conducted and shows that the transmission coefficient can be predicted in a straightforward manner. These results are deemed to be of help not only in the design of countermeasures for the train/tunnel entry problem, but also for technological applications involving transient pressure pulses in branched pipe flows (e.g. pulsed flow in exhaust pipes).