River bends are one of the common elements in most natural rivers, and secondary flow is one of the most important flow features in the bends. The secondary flow is perpendicular to the main flow and has a helical path moving towards the outer bank at the upper part of the river cross-section, and towards the inner bank at the lower part of the river cross-section. The secondary flow causes a redistribution in the main flow. Accordingly, this redistribution and sediment transport by the secondary flow may lead to the formation of a typical pattern of river bend profile. It is important to study and understand the flow pattern in order to predict the profile and the position of the bend in the river. However, there are a lack of comprehensive reviews on the advances in numerical modeling of bend secondary flow in the literature. Therefore, this study comprehensively reviews the fundamentals of secondary flow, the governing equations and boundary conditions for numerical simulations, and previous numerical studies on river bend flows. Most importantly, it reviews various numerical simulation strategies and performance of various turbulence models in simulating the flow in river bends and concludes that the main problem is finding the appropriate model for each case of turbulent flow. The present review summarizes the recent advances in numerical modeling of secondary flow and points out the key challenges, which can provide useful information for future studies.
River confluences are a common feature in natural water resources. The flow characteristics in confluences are complicated, especially at junction areas between tributaries and the main river. One of the typical characteristics of confluences is secondary flow, which plays an important role in mixing, velocity, sediment transport, and pollutant dispersion. In addition to the experimental and field studies that have been conducted in this area, the development of computational fluid dynamics has allowed researchers in this field to use different numerical models to simulate turbulence properties in rivers, especially secondary flows. Nowadays, the hydrodynamics of flows in confluences are widely simulated by using three-dimensional models in order to fully capture the flow structures, as the flow characteristics are considered to be turbulent and three-dimensional at river junctions. Several numerical models have been recommended for this purpose, and various turbulence models have been used to simulate the flows at confluences. To assess the accuracy of turbulence models, flows have been predicted by applying different turbulence models in the numerical model and the results have been compared with other data, such as field, laboratory, and experimental data. The purpose behind these investigations was to find the suitable model for each case of turbulent flow and for different types of confluences. In this study, the performances of turbulence models for confluences are reviewed for different numerical simulation strategies.
The impact of secondary flows on the flow velocity in open channel bends and confluences was simulated using three-dimensional (3D) numerical models. The Reynolds-averaged Navier–Stokes equation system was utilized as the governing equations and two different turbulence models were employed in this study: the standard k-ε model and the realizable k–ε model. In a recent study by the authors, the rigid lid approach was used, which does not allow for vertical displacement of the water surface. In this study, the simulation of free surface displacements was simulated using the volume of fluid free-surface tracking method. The numerical models were evaluated and validated by using the experimental data of a sharply curved channel and a confluent channel. The accuracies of the two turbulence models were evaluated and discussed. This study found that both models can satisfactorily reproduce the experimental data. However, the standard k–ε model performed better for the curved channel case while the Realizable k–ε model performed better for the confluent channel case.
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