Water hammer caused by air release in the operation of pipeline filling

In this paper, results of a numerical investigation performed over a large range of possible values of hydraulic and geometrical parameters are reported with the aim of providing a design criteria for the air release valve and for the optimization of pipeline filling time within the constraints imposed by the upsurge containment. By means of a mathematical model, accounting for the elasticity of the water column, we analyzed the water hammer phenomenon due to the flow stoppage which occurs when the liquid column strikes the plate of an automatic air vent device, after complete exhaustion of the air pocket. Results of the numerical experiments highlight different interesting features of the phenomenon. In particular we found that a smaller orifice allows to reduce the upsurge pressures which, on the other hand, result to increase with the filling rate. The initial volume of the air pocket, which in the considered scheme is determined by the pipeline diameter is practically not influent on the upsurge pressures for values of filling rates less than 0.6 times the maximum filling rate. Above such threshold the upsurge pressures increase with the initial air volume. By the light of the presented results we propose a design chart that allows to chose the optimal filling rate, as a function of the hydraulic and geometrical characteristic of the pipeline and of the maximum allowed overpressures.