Entrapped Air in Long Water Tunnels During Transition from a Pressurized to Free-Surface Flow Regime

Air-water two-phase flow usually occurs during a sudden rise in water level at a tunnel or during the falling of the water level at an upstream reservoir while entering the conduit. When this happens, different flow patterns are generated, due to the hydraulics of flow and fluid properties. An analytical/numerical model, based on the assumption of a rigid incompressible water column and a compressible air bubble, is derived, to simulate pressure fluctuation, void fraction, air/water flow rate and water velocity in a closed conduit, including water depth at the upper reservoir, due to air bubbles becoming trapped in the water, for the highest possible number of flow patterns. It is a comprehensive model, which can generate different hydraulic situations in closed conduits such as tunnels and culverts, based on a hydraulic approach. The boundary conditions are a system of algebraic or/and simple differential equations. The steady solution of the governing differential equations is, generally, performed as the initial data. The frequency of pressure fluctuation and air/water flow rate predicted by the model is in close agreement with the results of the experiments and the numerical model referred to in the literature. Hence, the present model, which is simply derived due to one-dimensional assumptions, shows itself to be a good tool for predicting the characteristics of a two-phase flow.