Energy analysis of transient frequency shift pattern induced by non-uniform blockages in water pipelines

Blockages are commonly formed in water pipelines due to various factors such as chemical corrosion, biofilm accumulation, and sediment deposition. Existence of blockages in water pipeline systems may cause different critical problems of water supply quality and security as well as water and energy resources wastage. Although many methods such as transient-based analysis method have been developed for the identification and detection of such blockages, the applications of these methods so far are largely limited to very idealized blockage cases (discrete inline valve or uniform section) and simple pipeline systems. This is mainly because of the inefficient understanding of mechanism and process of the transient wave-flow-blockage interactions for further developing and extending such methods. This paper aims to investigate the transient wave-blockage interactions from the perspective of energy analysis, so that the mechanism and physics of their interactions could be better understood and utilized. For this purpose, the non-uniform blockages with linearly varying diameters are adopted for the analysis. The energy transmission coefficient (TC) of an unbounded pipeline system containing non-uniform blockages is firstly obtained by analytical derivations, which is then applied to analyze the influences of non-uniform properties on TC for different blockage cases. It is found that the higher the incident wave frequency, the more energy would transmit through the non-uniform blockages. This result indicates that the non-uniform blockages may have less influence on the propagation of high frequency incident waves; and thus, the frequency shifts induced by the non-uniform blockages in a bounded pipeline system become less evident for relatively high frequency wave inspection.