A numerical analysis of free-surface flow in curved open channel with velocity–pressure-free-surface correction

Abstract

This paper presents a numerical study onfree-surface flow in curved open channel. An improved SIMPLEC algorithm with velocity-pressure-free-surface coupled correction is developed and validated. Such algorithm differs from the traditional SIMPLEC algorithm and includes three correction equations which are named as the velocity correction equation, the free-surface correction equation derived from the continuity equation with the kinematic boundary conditions on the free-surface and the bottom bed, and the pressure correction equation taking the same formulation as the traditional SIMPLEC algorithm does. In this study, the improved method is used to solve the incompressible, three-dimensional, Reynolds-averaged Navier–Stokes equation set combined with the standard k–ℇ model and/or the low Reynolds number k–ℇ model for free-surface viscous flow in curved open channels. The power law scheme (POW) is used to discretize the convection terms in these equations with a finite-volume method. The practical cases studied are free-surface flow through the 180° curved open channel with different hydraulic discharge rates. The comparisons between computations and experiments reveal that the model is capable of predicting the detailed velocity field, including changes in secondary motion, the distribution of bed shear, and the variations of flow depth in both the transverse and the longitudinal directions. In summary, the improved SIMPLEC algorithm is feasible and effective for numerical study of free-surface viscous flows in curved open channels.