A Numerical Investigation on High-Reynolds-Number Gravity Currents in Pressurized and Free-Surface Systems using Shallow Water Equation and Integral Model Approaches

Abstract

Multiphase flows in the form of gravity currents are prevalent in various natural systems, as well as in some open channels and closed conduits. Thus, accurate flow simulation and efficient modeling tools are important in such applications. Laboratory experiments and numerical models are utilized in this work to study different types of gravity currents focusing on the lock-exchange problem. Both Boussinesq and non-Boussinesq flows are analyzed in the context of high-Reynolds-number gravity currents. The numerical modeling efforts focus on solving the shallow water equations for Boussinesq gravity currents. In addition, an integral model is proposed for non-Boussinesq flows in closed conduits, and a Reynolds-averaged Navier-Stokes model was developed in OpenFOAM for selected flow cases to compare model accuracy and computational efficiency.

A two-layer shallow water equation model was developed for Boussinesq gravity currents using shock-capturing theory. The proposed model differs from existing shock-tracking models in that it uses shock-capturing theory in a finite volume framework to seamlessly predict shocks that develop in the lock-exchange problem. This feature allows for simpler numerical implementation particularly when the direction of these flow discontinuities is unknown apriori. A leading edge boundary condition was proposed for the two-layer model that can be implemented identically for one- and two-layer shallow water equation models. The new boundary condition was compared with two alternatives based on the method of characteristics in which results were a good compromise between computational efficiency and continuity errors. Experiments were conducted alongside numerical model simulations for numerical validation and to analyze internal velocities that were measured with MicroADV devices. Two MicroADV probes that measured velocities in both fluid layers are utilized in this work at three different depths. Depth-averaged velocity hydrographs were developed that compare well to shallow water equation model predictions.

Non-Boussinesq gravity currents are also investigated focusing on air-water interactions in closed conduits. When air becomes entrapped in storm sewers during intense rain events, pipelines may experience pressures much greater than driving pressure heads (Martin, 1976). These air pockets may propagate in the form of non-Boussinesq gravity currents and can lead to structural damage through urban geysering (Vasconcelos, 2005). Instead of resolving the free-surface interface, an integral model is proposed to simulate air pocket motion that assumes uniform air pocket depth. This new approach builds on the work of Benjamin (1968) and Wilkinson (1982) in which a known quantity of air is suddenly released in a closed conduit. The integral model was tested with a large range of air pocket volumes and background flow velocities in experiments conducted by Chosie (2013). Results indicate that air pocket velocities are predicted with an average error of 4% or less. An extension to favorable and adverse slopes is expected in future extensions of the proposed integral model.