Blockage detection in pressurized water-filled pipe using high frequency acoustic waves

Abstract

This paper presents a method for detecting small blockages (i.e., blockages whose radial length scale LR is significantly smaller than the pipe diameter D) in water supply lines. A blockage that develops in the inside wall of a pressurised pipe makes its presence felt to transient waves through drag and inertial forces. The blockage-induced wave scattering by the drag force becomes negligible in comparison to that of the inertial force when LR/D ≪ 1. This paper shows theoretically and experimentally that the detectability of small blockages is made possible by operating in the regime where the Helmholtz number (ratio of blockage longitudinal length scale LL to probing wavelength λ) is of order 1 or larger. In particular, wave scattering by a blockage with length scales LR and LL is obtained by solving the system of governing equations (multi-dimensional wave equation for the fluid and general impedance equation for the pipe wall) using the Neumann series. An efficient robust high resolution technique for detecting small blockages is developed on the basis of Maximum Likelihood Estimation (MLE). The proposed method, which requires a single measurement point only, is tested successfully through both numerical and laboratory experiments. The method is shown to be robust against noise where the error in blockage dimension estimation is of the order of 1% even for signal-to-noise ratio (SNR) as low as −5 dB. The proposed methodology allows the detection of blockages at an early enough stage of their development and provides the opportunity to deal with these defects so as to prevent their growth into severe operational problems and notable damages.