This note proposes a new quasi-two-dimensional (quasi-2D) numerical scheme for simulating a water hammer that significantly reduces the computational burden compared to two existing quasi-2D schemes, as numerically demonstrated in this note by application to a reservoir-pipe-valve system. Computational cost is decreased through using one-dimensional (1D), rather than two-dimensional equations for pressure head and discharge and using a staggered grid with half of the computational nodes compared to a rectangular grid. It is valid to use the proposed 1D characteristic equations for the pressure head and discharge, as it is proved that these yield identical results to explicit quasi-2D solution procedures previously introduced in the literature.

Water temperature affects the peak pressure damping of transient flows in viscoelastic pipes. Owing to the viscoelastic properties of pipes, the accuracy of peak pressure damping simulations hinges on both viscoelastic and frictional factors. In simulations, the influence of both factors on peak pressure damping at different water temperatures is unclear. In this study, the Kelvin–Voigt model with both a quasi-steady friction model and modified Brunone model was employed. Based on experimental data, the accuracy of simulated peak pressure damping was verified at four different water temperatures (13.8, 25, 31, and 38.5 °C). From the perspective of energy transfer and dissipation, the influence of viscoelastic and frictional factors on peak pressure damping were clarified, and the applicability of different friction models was determined based on the contributions of viscoelastic and frictional factors to peak pressure damping. The numerical results indicate that the viscoelastic properties of pipes have a greater impact on peak pressure damping than their frictional properties at 25, 31, and 38.5 °C. Higher temperatures result in a delay in the rate of work and a decrease in the frequency of work performed by viscoelastic pipes. Viscoelastic properties play a more important role than frictional ones in calculating peak pressure damping as the water temperature increases. In addition, the one-dimensional quasi-steady friction model can accurately simulate peak pressure damping within a specified water temperature range.

The flow characteristics of raw sewage directly affect the technical and economic performance of sewage-source heat pump systems. The purpose of this research is to characterize the flow characteristics of sewage by experimental means. A sophisticated and flexible experimental apparatus was designed and constructed. Then the flow characteristics of the raw sewage were studied through laboratorial testing and theoretical analyses. Results indicated that raw sewage could be characterized as a power-law fluid with the rheological exponentnbeing 0.891 and the rheological coefficientkbeing 0.00175. In addition, the frictional loss factor formula in laminar flow for raw sewage was deduced by theoretical analysis of the power-law fluid. Furthermore, an explicit empirical formula for the frictional loss factor in turbulent flow was obtained through curve fitting of the experimental data. Finally, the equivalent viscosity of the raw sewage is defined in order to calculate the Reynolds number in turbulent flow regions; it was found that sewage had two to three times the viscosity of water at the same temperature. These results contributed to appropriate parameters of fluid properties when designing and operating sewage-source heat pump systems.

The term “viscoelastic pipe” refers to high polymer pipes that exhibit both elastic and viscoelastic properties. Owing to their widespread use in water transport systems, it is important to understand the transient flow characteristics of these materials for pipeline safety. Despite extensive research, these characteristics have not been sufficiently explored. This study evaluates the impact of friction models on the transient flow of viscoelastic pipes across various Reynolds numbers by employing an energy analysis approach. Given the complexity and computational demands of two-dimensional models, this paper compares the accuracy of one-dimensional and quasi-two-dimensional models. Notably, the superiority of the quasi-two-dimensional model in simulating viscoelastic pipelines is demonstrated. Owing to the interaction between pressure waves and fluid within viscoelastic pipes, fluid–structure coupling significantly attenuates pressure waves during transmission. These findings shed light on the constitutive properties of viscoelastic pipes and the influence of pipe wall friction models on transient hydraulic characteristics, building upon prior studies focused on elastic pipes. Nevertheless, numerous factors affecting transient flow in viscoelastic pipes remain unexplored. This paper suggests further analysis of strain effects, starting with temperature and pipe dynamics, to enhance the understanding of the coupling laws and flow mechanisms in viscoelastic pipelines.

Quasi-two-dimensional (quasi-2D) friction models have been widely investigated in transient pipe flows. In the case of viscoelastic pipes, however, the effect of different values of the Reynolds number (Re) on pressure fluctuations (which can lead to water hammer) have not been considered in detail. This study establishes a quasi-2D friction model employing an integral total energy method and investigates the work due to frictional and viscoelastic terms at different Re values. The results show that viscoelastic work (W_P) and frictional work (D_f) increase with an increase in Re. However, when the initial Re values are high, the D_f values are much larger than the W_P values. In addition, for Re < 3 × 10⁵, the 1D model underestimated the viscoelastic terms. There was no significant difference between the two models for Re > 3 × 10⁵. In the case of different initial Re values, the two models produced almost the same values for W_P. This study provides a theoretical basis for investigating transient flow from the perspective of energy analysis.

To address the problem of pipeline blockage detection, a mathematical model of pipeline blockage detection is established based on fluid oscillation theory. This paper proposes a governing equation of the water hammer of fluid motion in a pipeline with a blockage point, and The Dirac function is introduced for dimensionlessness and linearization. The amplitude of the harmonic of each component in different periods is expressed by a Fourier series. The blocking position can be determined by the ratio of the two-component harmonics, and the blocking magnitude can be determined by the blocking attenuation parameters of each component’s harmonics. The numerical simulation and experimental results show that the application of fluid oscillation theory to detect the location and magnitude of pipeline blockages is effective, and the accuracy of the detection method is verified, which lays a theoretical foundation for the application of the proposed method in engineering practice.