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.
Highlights
As an undesired hydraulic phenomenon in pipe systems, water hammer is usually caused by a valve closing and opening, a pump shutting and starting, as well as misoperation in pipe systems [1,2].Various water hammer events commonly occur in water pipe systems, pump systems and hydro-power systems [3]
method of characteristic (MOC) canhammer give out reasonable maximum pressure, which is the key to water hammer prediction
Considering the restriction of the experimental scale of the pipe used in this research on the water hammer in gravitational pipe flow system with air entrainment, it may require a different friction coefficient in flow with air content after complete valve closing
Summary
As an undesired hydraulic phenomenon in pipe systems, water hammer is usually caused by a valve closing and opening, a pump shutting and starting, as well as misoperation in pipe systems [1,2]. Bergant et al [29,30] ascertained that water hammer attenuation may be significantly affected by unsteady friction, cavitation, and trapped air pockets In their researches, various cases with different conditions are studied and analyzed. Considering the real working conditions of water supply systems, it is more important to improve the accuracy of predictions on a water hammer in a pipeline with air content inside. Especially under low pressure conditions, different air content may occur in the pipelines. The proposed improved LWM model can well simulate the transient processes of pipe flow with continuous air entrainment. It is valuable in accurately predicting extreme pressure in water hammers with air entrainment, and is helpful in guiding suitable operations in water supply systems for extreme pressure control. Based on the equipped experimental platform, experiments in an inner visible pipeline will be conducted to trace the air entrainment, delivering, bubble forming and breaking processes by observing the actual inside transient process
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