Transient wave behavior in water pipes with non-uniform blockages

Abstract

In urban water supply systems, partial blockages are commonly formed in water pipes from various complicated physical, chemical, and biological processes (e.g., sediment deposition, corrosion, and biofilm accumulation); thus, their cross-sectional areas usually constrict randomly and non-uniformly along their lengths (termed as non-uniform blockages). In recent years, the transient-based method, which utilizes the physical information collected by transient waves, has been developed and applied for blockage detection in water pipes. However, the current transient-based method for blockage detection is largely based on blockages with idealized uniform constriction along their lengths (termed as uniform blockages), which are equivalent to multiple pipes with different diameters connected in series. As a result, inaccuracy and invalidity of the current transient-based method have been widely observed in the applications for non-uniform blockage detection. This is mainly due to the incapability of the current transient-based theory for describing the interaction between transient waves and non-uniform blockages. Therefore, a physical understanding of transient wave behavior in water pipes with non-uniform blockages is necessary to enhance the theoretical development and practical applications of the transient-based method for real blockage detection. In this thesis, the transient wave behavior in water pipes with non-uniform blockages is investigated in both the time and frequency domains by a combined methodology of theoretical analysis and numerical simulation. First, the transfer matrix method is adopted to understand and analyze the effect of properties of a non-uniform blockage in water pipes on the system frequency responses. Second, the physical mechanisms of the interaction between transient waves and non-uniform blockages are explained from an energy perspective. Afterwards, the frequency range of validity of the developed theory is investigated and quantified numerically by a full two-dimensional (2D) water hammer model. Finally, the developed theory and gained findings are validated through advanced numerical investigations with the aid of the computational fluid dynamics (CFD) model coupled with user-defined functions (UDFs). The obtained results indicate that the resonant frequency shifts induced by non-uniform blockages have very different patterns from that of uniform blockages presented in the literature. Specifically, the frequency shifts induced by non-uniform blockages become less evident for higher harmonics of the incident waves. This is because the impedance of non-uniform blockages is highly frequency dependent, which becomes smaller for higher frequency incident waves. That means non-uniform blockages have a less blocking effect on the propagation of higher frequency incident waves; thus, the frequency shifts induced by non-uniform blockages become less evident. This understanding and theory is developed based on the 1D wave equation, where the plane wave assumption is imposed. Therefore, to satisfy the developed theory, the incident wave frequency (i.e., the frequency range of validity) must be lower than the cut-off frequency of the radial mode 1 (M1). This result has been confirmed by preliminary experiments in the literature as well as numerical results from the full 2D model and CFD tools. The physical understanding gained in this thesis may contribute to narrow the gap between transient-based theory and practical applications of non-uniform blockage detection, which is crucial and necessary for developing smart urban water supply systems. Based on the results and achievements of this thesis, essential and useful recommendations are also made for future work.