A review of numerical simulations on stepped spillways using the k-ε turbulence model

For centuries, stepped spillways and cascades have been employed to effectively dissipate the kinetic energy of flowing water and promote aeration. The origins of stepped chute construction can be traced back to ancient Greece and Crete. In antiquity, this design served three main purposes: as stepped spillways, for stormwater and irrigation channels, and in municipal water supply systems. Initially crafted from cut-stone masonry or timber, the 19th century witnessed the introduction of various construction materials, such as composite materials and non-reinforced concrete. Over the last forty years, renewed interest in the staircase chute design has emerged, thanks to advancements in construction materials and techniques. The stepped invert in these designs significantly enhances energy dissipation above the steep chute, reducing the need for large downstream stilling structures. Stepped chutes are now applied not only in traditional uses but also in in-stream re-aeration and water treatment plant cascades, improving the transfer of atmospheric gases and volatile organic components between air and water. However, the engineering of stepped spillways is complex due to hydrodynamic challenges, involving different flow regimes, intricate two-phase air-water fluid dynamics, and a substantial rate of energy dissipation above the stepped chute. This study aims to compile recent research on stepped spillways, employing numerical approaches to address these engineering challenges. FLUENT and Flow-3D have been the most useful software in simulating stepped spillways among the researchers and compared with the experimental results they have proved to be quite beneficial.  Here we provide a review of numerical simulations on stepped spillways using FLUENT and k-ε turbulence model, the most utilized methods in this software. The study illustrates that the RNG k-ε turbulence model has been the most popular model among researchers to simulate the flow over stepped spillways and is suggested as one of the models that shows a great correlation with the experimental results