Eigenfrequency Shift Mechanism due to an Interior Blockage in a Pipe

Abstract

The presence of blockages in water supply systems wastes energy, decreases system performance, and may pose safety concerns. Previous research showing that blockages induce a shift in the resonant frequencies (eigenfrequencies) of the pipe system made use of that shift information to develop improved inverse problem solution techniques for blockage detection. This paper studies in more detail the eigenfrequency shift mechanism itself that arises from an interior blockage in a pipe system, and shows that more information could be obtained from understanding the nature and physical basis for the shift mechanism. This improved understanding can improve the computational efficiency of current blockage detection solution techniques. This paper explains the mechanism causing positive, negative, and zero eigenfrequency shifts, and shows how these shifts vary with blockage location, size, and resonant modes. Zero shift occurs if the midlength of the blockage is located at a position where the pressure head and flow harmonics are equal in magnitude, whereas maximum (or significant) shifts occur if the midlength of the blockage is located at either a pressure node (if the shift is negative) or a stagnation point (if the shift is positive), where pressure node and stagnation points are where the pressure and flow harmonics’ magnitudes are zero. It is also shown that the Bragg resonance phenomenon directly influences the direction and magnitude of the observed eigenfrequency under different resonant modes.