Bragg-Type Resonance in Blocked Pipe System and Its Effect on the Eigenfrequency Shift

Abstract

Recent studies of measured transient pressure signals showed that eigenfrequencies shift with changes in cross-sectional area of the conduit and used this fact to develop blockage-detection algorithms. However, an understanding of the physical basis for eigenfrequency shift-based algorithms is currently lacking. This paper shows heuristically, analytically, and numerically that a blockage in either unbounded or bounded pipe systems interacts strongly with waves at specific frequencies. These specific interacting frequencies conform precisely to Bragg’s resonance condition. The frequency interval between consecutive Bragg frequencies is proportional to the wave speed divided by the blockage length. In addition, it is found that pipe blockage imposes a distinct signature through Bragg resonance phenomena on the unbounded and bounded pipe systems in exactly the same manner (i.e., they exhibit the same variation pattern). It is further shown that the eigenfrequency shift, currently used without physical basis or explanation in many published papers as a basis for blockage detection methods, is because of the Bragg resonance effect. Examples are used to show how this physical insight into the nature and cause of the eigenfrequency shifts can be advantageously used to design direct blockage detection techniques.