A water hammer is an important natural phenomenon. The oscillatory injection of a column of water can be used to make a pipe water hammer. However, the optimal injection frequency to create a water hammer has not yet been found. In this study, we demonstrate for the first time that there can be significant supercharging phenomena in a water-filled pipe. We first find the optimal pulse frequency to reproduce the supercharging process. We also clarify the supercharging mechanism at an optimal frequency. First, the weakly compressible Navier-Stokes equations are developed to simulate the flow of water in a water-filled pipe. The computation code is developed using the MacCormack method, which is validated by experimental data. Then the pulse effects are studied, including the effects of pulse frequency, amplitude, pipe length, diameter, and wave speed. Finally, a new universal frequency model is built. The results show that there is a family of frequencies for which the fluid peak pressure can be significantly enhanced, and these frequencies include the optimal pulse frequency. The optimal frequency of a square pulse depends on the pipe length and wave speed. At the optimal pulse frequency, the maximum peak pressure of the fluid can be increased by 100% or more, and cavitation occurs. These new landmark findings are very valuable for understanding pulse supercharging in an internal water wave. In addition, a new universal frequency model is built to predict optimal pulse frequency. This study proposes a practical frequency-control model for the first time.

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Although two-phase flows containing gas and water have received extensive attention, the pulsating pressurization effect of a two-phase fluid in a pipe is unclear and the influence of the gas-phase content has not been revealed. This paper discusses the pulsating pressurization of such a two-phase fluid. First, the two-phase Navier–Stokes equations are derived and an algorithm is developed based on MacCormack's method. The reliability of the algorithm is examined and validated using Poiseuille's theory and existing experimental two-phase flow data. Finally, the influence of several key factors is discussed, including the gas-phase fraction and pipe slenderness. Our results show that a significant pulsating supercharging phenomenon occurs when the gas-phase fraction is less than 10−3. When the gas-phase fraction is greater than this critical value, the pulsating supercharging effect decreases significantly with the increasing gas-phase fraction. The equivalent elastic modulus of the two-phase fluid rapidly decreases as the gas-phase fraction increases, and the pressure disturbance is absorbed by the gas bubbles, causing an apparent weakening of the pulsating supercharging effect. Thus, decreasing the gas-phase content can enhance the pulsating supercharging effect. The pipe slenderness has a very limited influence on the pulsating pressurization process, and the maximum reduction is only 7.3% for slenderness ratios of up to 2000. Moreover, we derive and propose a new mathematical expression for the inlet boundary that is applicable to gas–liquid two-phase flows. To our knowledge, this paper extends the pulsating pressurization range from the single-phase to two-phase fluid for the first time and reports different physical phenomena and regularity. The present research clarifies the pulsating pressurization phenomenon in two-phase flows, providing a valuable reference for pulsating pressurization design.