Numerical modelling of the passage from free surface to pressurized flow in a closed pipe

W. Mokrane, A. Kettab


Abstract: Urban hydraulic pipelines may be subject to considerable damages while a sudden flow event occurs. However, a transition between free surface and pressurized flow arises; both overpressures and depressions will appear.  Controlling this phenomenon becomes a necessity and must be integrated in pipe dimensioning. Most of earlier works were focused on the fictitious piezometric slot. In this work, we aimed to simulate this flow passage as a shock wave and using the Saint Venant mathematical model. Although, in order to take into account the pressurized state; we modified the pressure term.  The transition from a type of flow to the other is composed of two discontinues states. Therefore, we solve it as a Riemann problem. To arrive to the most appropriate numerical scheme for the solution, we compare between the results of the Lax Fridricks, lax Wendroff and Godunov schemes. We do this considering the process time, the standard deviation and the Courant Friediricks Levy stability condition. On another hand, we carried out experimental tests, on a transparent and closed circular pipe, to measure pressure change with the flow rate. Hence, we give the physical stationary solution. Finally, we compare numerical results to experimental ones and deduce that the Godunov scheme is the most recommended tool to simulate the flow discontinuity between free surface and pressurized flow

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