Numerical simulation of the flow in a conduit,in the presence of a confined air cushion

A rectangular conduit with a closed end has water flowing in/out at the other end. The water level at the open end has an imposed sinusoidal movement. When this level is higher than the ceiling of the conduit, a certain mass of air is trapped under the ceiling. In a previous article (T.D. Nguyen, La Houille Blanche, No. 2, 1990), it was supposed that this air is flowing out freely through the ceiling, so the relative pressure at the water surface is zero, and the water hammer at the dead end of the conduit was calculated when the conduit was thoroughly filled. In this article, it is supposed that the trapped air is compressed isothermally or adiabatically. The set of equations is resolved (water continuity and movement equations, air state equation) by supposing a regime of flow at each section (section submerged or not), a certain value for the air pressure and by using the sweep method to determine the water flow characteristics. The air volume calculated by iteration must converge, and the calculated regimes at each section (submerged or free) must agree with the supposed regimes. The simulation is performed first with a horizontal conduit then with an inclined conduit. As expected, adiabatic compression gives higher pressure than isothermal compression. The simulation shows also that when there is an air cushion, compared with the case when air is flowing out freely, the shock of the water hammer at the closed end of the conduit is significantly reduced. This method is aimed at calculating the flow with entrapped air in the inlet/outlet tunnel of a hydroelectric plant, or in sewer system pipe when a sudden discharge surge (due to turbin opening/closing or to urban storm) changes a previously free‐surface flow in a mostly full‐pipe flow, but with some air entrapped under the ceiling. Copyright © 1999 John Wiley & Sons, Ltd.