A Study of Multi-Step Overfall Flows by Computational Fluid Dynamics

Abstract

This paper proposes the least-squares finite element method (LSFEM) for simulating the free surface flows in multi-step free overfalls. Motion of the free surface flows is represented with two-phased surface profiles by solving the Navier-Stokes equations. The fluid is considered to be incompressible and the dynamic and kinematic boundary conditions of free surface are described in an Eulerian coordinate system. In this simulation, the volume of fluid (VOF) method and continuous stress force (CSF) models in association of color function are incorporated for the determination of the interface between water and air. The simulation results from the LSFEM model are carefully verified for the unit-step free overfall case. The quantitative comparisons in terms of the parameters such as different inflow rates, reattached length, water height after the fall and critical depth with previous numerical results or experimental measurements are shown to be in good agreement. In order to understand more about the complicate free surface profile of a dual-step free overfall, the LSFEM model is simulated for different inflow rates. In comparison with the available experimental data, it is shown that the LSFEM can effectively simulate the multi-step free overfall flow phenomena. Our study presents some regression formula for the dual-step free overfall, it is hoped that these formula will be helpful for the engineering designs and applications.