By optimizing the sizing of air vessels, not only is the damage from water hammer prevented, but also the cost of water hammer protection systems is minimized. This paper presents a numerical simulation of an air vessel in a long-distance transfer main system against water hammer resulting from sudden pump stoppage. An optimal design of air vessel parameters is obtained using sequential quadratic programming (SQP) in this case. Three types of connection configuration (between the air vessel and the main pipeline) are tested in the case study, including a vertical cylindrical vessel with a bypass line (configuration 1), a vertical cylindrical vessel with a bypass line equipped with a throttle valve (configuration 2), and a horizontal cylindrical vessel with separated inflow and outflow lines (configuration 3). The variations of optimal volume of the air vessel, VT, are plotted as a function of the allowable maximum pressure head, Hmax*, with the diameter of the bypass line, db, or the throttle valv...

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.

Numerous studies on the pressure fluctuations and cavity volume variations of a transient cavitation flow in viscoelastic pipes are available in the literature. However, the effect of water temperature on the cavity volume and energy conversion has been studied less often. This paper employs the discrete vapor cavity model using quasi-steady friction and quasi-two-dimensional friction models to calculate the cavity volume for different water temperatures and investigates the effects of water temperature on the appearance of the first cavitation at the downstream valve, and on the pressure damping in a tank-piping-valve system using an integrated energy analysis approach. The results show that the differences between the pressure and energy variations of the transient cavitation flow simulated using different models were minimal under different water temperature conditions. Moreover, as the water temperature increased, the appearance time of the cavity is postponed, and the volume of the cavity decreases. The energy dissipation increases continuously with an increase in the volume of the cavitation and water temperature in viscoelastic pipes. This study provides valuable insights into the variation pattern of the cavity and the effect of vapor cavities on the rise and decay of the pipeline pressure in different situations.

Hydraulic analysis of a new water supply pipeline in Heilongjiang Province of China has been performed. The study consists of an appraisal of the hydraulic behavior under the steady state hydraulic analysis during the system operation and evaluation of transient conditions during the operation stoppage. Firstly, the steady state analysis is carried out. And then, the transient analysis is implemented by using the Method of Characteristics (MOC). Moreover, the Lattice Boltzmann Method (LBM) is presented as an alternative approach to modeling water hammer. The steady state analysis provides the basic framework for understanding the normal operational behavior of the pipeline. The results demonstrate the reasonable control of some valves will improve the resistance distribution along the pipeline. However, results of transient analysis are significant for individuals involved in making operational decisions of the pipeline to enhance their understanding of the behavior of the system during transient conditions. Furthermore, the accuracy and efficiency of the LBM is numerically investigated. The results indicate that the LBM is more efficient than the MOC.

Hydraulic analysis of steady state conditions is typically used in the design and operation of gas networks. However, operational gas network systems are never in the steady state as demands and pressures vary with time. By comparison, transient analysis is more valuable and helpful for engineering design and operational management. The method of characteristics (MOC) is often used to analyze the transient flow of gas networks because it has clear physical concepts and employs rigorous mathematical analysis and precision in calculation. However, with MOC a small time step has to be included for an accurate result, which costs a lot of computing time. In this paper, it is shown that the method of characteristics with an inertial multiplier is capable of providing a numerical simulation of the transient flow in gas networks. After the inertial multiplier is established, then the transient flow for a gas network system is numerically simulated. Two simulation outcomes are compared, one using the method of characteristics and another the method of characteristics with an inertial multiplier. Results show that the time step can be selected flexibly and the computational speed can be reduced by means of the method of characteristics with an inertial multiplier. The method of characteristics with an inertial multiplier is more efficient for transient analysis of gas networks than the method of characteristics alone.