THREE-DIMENSIONAL CIRCULATION IN STEADY AND UNSTEADY FREE SURFACE FLOWS

Abstract

Based on the three-dimensional Navier-Stokes equations, an efficient and simple multi-level hydrodynamic model is developed to simulate circulation in steady and unsteady free surface flows. In this model, the two-step Euler predictor-corrector algorithm is introduced to predict and correct the free surface water levels. The governing equations are discretized into finite difference forms with the central/upstream scheme in a non-uniform staggered grid system. To save computational time and improve the stability of the numerical method, the momentum equations in the horizontal directions are discretized in explicit scheme for the component velocities u and v, and the continuity equation is discretized in implicit scheme for the velocity w. The three-dimensional multi-level hydrodynamic model has been tested against analytical solutions for three standard cases of steady and unsteady free surface flows in a rectangular basin. Subsequently, the model is used to study the flow characteristics in a sudden contraction and expansion. A hydraulic experiment involving sudden contraction and expansion flow in an open channel is carried out to provide necessary data on flow characteristics for validating the numerical model. The results of the numerical simulation are compared with the experimental data. The numerical results for the surface elevations and velocity fields are in good agreement with analytical and experimental results in the above cases. The numerical flow patterns for the sudden contraction and expansion flow show that large-scale eddies occur downstream of the opening in the vertical and cross-sectional planes as well as in the horizontal plane.