A one-dimensional numerical model for predicting pressure and velocity oscillations of a compressed air-pocket in a vertical shaft

Abstract:

The presence of pressurized air pockets in combined sewer systems is argued to produce geyser flows, which is an oscillating jetting of a mixture of gas-liquid flows through vertical shafts. A 1D numerical model is developed for predicting pressure and velocity oscillations of a compressed air-pocket in a vertical shaft which in turn attempts to simulate geyser like flows. The vertical shaft is closed at the bottom and open to ambient pressure at the top. Initially, the lower section of the vertical shaft is filled with compressed air and the upper section with water. The interaction between the pressurized air pocket and the water column in the vertical shaft exhibits an oscillatory motion of the water column that decays over time. The model accounts for steady and unsteady friction to estimate the energy dissipation. The model also includes the falling flow of water around the external perimeter of the pressurized air pocket by assuming that any expansion in the pressurized air pocket would result in the falling volume of water. The acceleration of air-water interface is predicted through a force balance between the pressurized air pocket and the water column combined with the Method of Characteristics that resolves pressure and velocity within the water column. The expansion and compression of the pressurized air pocket is assumed to follow either isothermal process or adiabatic process. Results for both assumptions; isothermal and adiabatic processes, are presented. The performance of the developed 1D numerical model is compared with that of a commercial 3D CFD model. Overall, a good agreement between both models is obtained for pressure and velocity oscillations. The paper will also present a sensitivity analysis of the 3D CFD model.