Numerical analysis of subcritical open channel flow by the penalty function finite element method

Many free surface flow problems encountered in hydraulic engineering can be accurately analyzed by utilizing the depth-averaged equations of motion. A consequence of adopting this depth-averaged modeling approach is that closure approximations must be implemented to represent the so-called effective stresses. These effective stresses consist of the depth-averaged viscous stresses, which are usually small and therefore neglected, the depth-averaged turbulent Reynold's stresses, and additional stresses resulting from depth-averaging of the nonlinear 'convective acceleration terms (often called momentum dispersion terms). Attention is focused on examining closure for both the depth-averaged Reynold's stresses and the momentum dispersion terms. In the present study, the penalty function finite element technique is utilized to solve the governing hydrodynamic and turbulence model equations for a variety of flow domains. Alternative momentum dispersion and turbulence closure models are proposed and evaluated by comparing model predictions with experimental data for strongly curved open channel flow. The results of these simulations indicate that the depth-averaged (k-ε) turbulence model yields excellent agreement with experimental observations. In addition, it appears that neither the streamline curvature modification of the depth-averaged (k-ε) model, nor the momentum dispersion models based on the assumption of helicoidal flow in a curved channel, yield significant improvement in model predictions. Overall model predictions are found to be as good as those of a more complex and restricted three dimensional model. Ph. D.