Experimental and Numerical Simulation of Water Hammer in Gravitational Pipe Flow with Continuous Air Entrainment

Abstract

Water hammer is an undesired hydraulic shock phenomenon in water supply pipe systems. It is very important to simulate water hammer for preventing the hazard of over pressure. In order to predict the transient pressure caused by a valve closing in a gravitational pipe with continuous air entrainment, a numerical model based on the Lax-Wendroff format is established, and the matched boundary model is provided. Compared with the traditional methods, this study provides another access by considering the influence of the pipe flow velocity on the wave propagation to simulate transient processes. A corresponding experiment is conducted to optimize the numerical model. Based on the experimental result, an additional friction function is proposed to evaluate the influence of the air content on the attenuation. The result shows that the energy dissipation of the shock waves may be underestimated in air-water mixture flow using the common steady friction. By introducing the additional friction function, the improved model can more accurately simulate the attenuation of the water hammer in the gravitational pipe with continuous air entrainment. As there are plenty of practical water supply systems running with air content, the improved Lax-Wendroff Method (LWM) is valued in accurately predicting water hammer processes especially in those conditions.

Investigation into Complex Boundary Solutions of Water Filling Process in Pipeline Systems

“…For a water supply pipeline system, where there is an upstream reservoir and the upstream gate remains at a stable open ratio, the upstream boundary condition is relatively simple. In this situation, the upstream hydraulic head is regarded as a constant, as the fluctuation of the water level in the reservoir can be ignored during a transient water hammer process [17,19]. However, in the case of an operation on the upstream gate, there may be changes in the discharge coefficient that depend on the upstream water level, the downstream water level, and the intensity of rainfall.…”

“…Among these, the most widely used nowadays is the method of characteristics (MOC) due to its high accuracy and convenience. Many researchers have investigated device controlling rules based on the MOC, including valve closing processes [10,[17][18][19][20] and pump failure [21].…”

Research on Hydraulic Characteristics in Diversion Pipelines under a Load Rejection Process of a PSH Station

“…The attenuation rate of the pressure wave measured by the 1D method is always slower than that of the experimental results, and a good agreement cannot be achieved. There are also some scholars who use some improved models to measure the pressure wave to explain the reason that the 1D calculation results do not agree with the experimental results [29]. Compared with the traditional methods, this study provides further access by considering the influence of the self-excited spiral flow on the pressure wave attenuation.…”

Development and Sensitivity Analysis of an Empirical Equation for Calculating the Amplitude of Pressure Head Loss of Oscillating Water Flow in Different Types of Pipe

“…This application differs from common transient flow, such as water hammers in water conservancy engineering structures (e.g., hydropower stations and pump stations), where instantaneous pressure head changes irregularly over time. The research on water hammers is relatively mature, and many methods, such as the method of characteristics, have been developed, which can calculate the instantaneous pressure head [27][28][29][30][31][32]. On the other hand, the instantaneous pressure head of oscillating water flow changes periodically over time, and both the maximum and minimum instantaneous pressure heads remain basically the same, as shown in Figure 1.…”