Abstract
This paper investigates the impacts of non-uniformities of pipe diameter (i.e., an inhomogeneous cross-sectional area along pipelines) on transient wave behavior and propagation in water supply pipelines. The multi-scale wave perturbation method is firstly used to derive analytical solutions for the amplitude evolution of transient pressure wave propagation in pipelines, considering regular and random variations of cross-sectional area, respectively. The analytical analysis is based on the one-dimensional (1D) transient wave equation for pipe flow. Both derived results show that transient waves can be attenuated and scattered significantly along the longitudinal direction of the pipeline due to the regular and random non-uniformities of pipe diameter. The obtained analytical results are then validated by extensive 1D numerical simulations under different incident wave and non-uniform pipe conditions. The comparative results indicate that the derived analytical solutions are applicable and useful to describe the wave scattering effect in complex pipeline systems. Finally, the practical implications and influence of wave scattering effects on transient flow analysis and transient-based leak detection in urban water supply systems are discussed in the paper.
Highlights
Wave scattering has been commonly studied in shallow water fields where the water waves propagate through the channel bottom with randomly varying bars, as depicted in Figure 1 [1]
By applying the multi-scale perturbation method in Equation (9) to the transient wave equation in Equation (6), the analytical results of wave scattering with regard to the pressure wave envelopment and evolution can be obtained for both the regular case in Figure 4b and the random case in Figure 4a of pipe diameter variations
The analytical expressions for transient wave evolution in water pipelines with different non-uniformities were derived in this paper by using the multi-scale wave perturbation method, which was validated and examined through extensive 1D numerical simulations
Summary
Wave scattering has been commonly studied in shallow water fields where the water waves propagate through the channel bottom with randomly varying bars, as depicted in Figure 1 [1]. Experimental results for such cases together with some theoretical considerations are investigated and discussed in [2,3]. Many factors can attribute to the random non-uniformities of pipe cross-sectional area, for example, bio-film build up, corrosion, and deposition in water supply pipes, drainage pipes, crude oil pipes, and arterial systems.
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