Wave-Leak Interaction in a Simple Pipe System

Abstract

In previous work, the authors have found that blockage-wave interaction relates to Bragg resonance effect, which is governed by the ratio of the wavelength to the length of the blockage. A direct extension of this work for the case of wave-leak interaction has led to a total failure. This is because, unlike blockages, a leak has a vanishingly small length (generally modeled as a point), and according to the blockage results, this would require an infinitesimal wavelength (i.e., infinite frequency). Yet, leak-imposed patterns are known to occur for finite wavelengths. Therefore, the motive of this work was to seek a novel mechanism that is responsible for leak-induced Bragg resonance. It was discovered that what matters in this case is the position of the leak point in relation to the node and antinode of the modes. It is shown that a leak located at an antinode of a given mode will induce Bragg-type resonance of maximum reflection, and the corresponding peak amplitude in the frequency response function (FRF) is a minimum. On the other hand, if a leak is located at a node of a given mode, it experiences Bragg-type resonance of maximum transmission, and the peak amplitude in the FRF is a maximum. The pattern induced by a leak on the FRF, used in many leak detection schemes, is attributable to the leak interaction with different modes. In fact, the closer the leak to a node is, the higher is the amplitude of the corresponding resonant peak, and vice versa for leaks closer to antinodes. A number of leak detection methods are discussed in light of the Bragg resonance mechanism. These insights are exploited for several distinguished leak detection methods showing how a leak-induced pattern is explained from a new point of view.