# Effect of Height and Geometry of Stepped Spillway on Inception Point Location
## 1 Introduction
[32] measured the air-water volume fraction of two-phase flow using k-\(\varepsilon\) models. [PERSON] and [PERSON] [33] used the VOF multiphase model to simulate the stepped spillway model with slope of 10\({}^{\circ}\) and to determine the characteristics of the skimming flow. Their results included velocity distribution, air concentration, and pressure distribution. It was concluded that the VOF model accurately simulates the flow pattern over a stepped spillway. [PERSON] et al. [34] used the VOF and renormalized group (RNG) turbulence model to simulate the stepped spillway with a slope of 53\({}^{\circ}\). They obtained the velocity distribution, and turbulent kinetic energy. [PERSON] et al. [35] numerically simulated the flow over a stepped spillway using different step configurations, using the ADINA software with the k-\(\varepsilon\) flow model. In the prediction of the water surface profile and energy dissipation values, the results showed good agreement between the numerical and experimental values. [PERSON] et al. [36] used ANSYS Fluent software to simulate the flow over a stepped spillway. A mixture flow model was used as the numerical model and the RNG k-\(\varepsilon\) model was used as the turbulence model. They studied the skimming flow region and determined the interaction between cavity recirculation and air bubbles present in the skimming flow zone. The velocity distribution on the steps was also determined in their investigation. [PERSON] et al. [37] used the VOF model and the turbulence models RNG and LES to simulate the interaction between air and water using stepped spillway models with a steep slope. [PERSON] and [PERSON] [38] simulated a different type of stepped spillway called the V-type stepped spillway. They analyzed the pressure distribution by five different turbulence models and compared it with the physical values. By comparing the values with the physical model, it was suggested that the realizable k-\(\varepsilon\) model gave better results for simulating the pressure distribution than the others turbulence models. [PERSON] and [PERSON] [39] simulated pooled stepped spillways with four types of pool wires (full pool, full pool and two-sided pool, full pool and central pool, two-sided and central pool) using the VOF and RNG turbulence models. It was suggested that the energy dissipation rate in the different types of pooled weirs followed the order, two-sided and central pool, full pool and central pool, full pool and two-sided pools, and full pool. [PERSON] et al. [40] measured the logarithmic velocity profile in a stepped spillway using numerical simulation and compared it with experiments. According to their researches, the air inception location over stepped spillways exits until the boundary layer thickness is between the range of 0.72 and 0.79. [PERSON] et al. [41] studied the adverse slope stilling basins with stepped chutes. They studied the momentum, the length of the hydraulic jump, and the energy dissipation by the numerical model, and then compared the results with the experimental data. [PERSON] et al. [42] predicted the cavitation damage in a high-speed smooth spillway using numerical simulation. VOF and the standard k-\(\epsilon\) turbulence model were used to simulate the high-speed flow and the potential cavitation region in the high-speed smooth spillway. The numerical results and the experimental measurement showed a good agreement. The main aim of this research was to study the effect of different parameters, i.e., the discharge, step height, and step geometry, on the inception point location by numerical simulations. Different numerical experiments were conducted on different step spillway models using multiphase VOF combined with the realizable k-\(\epsilon\) turbulence model. The different step spillway models differ in the various step heights and step geometry configurations, including flat, pooled and round. The data shows how the inception point location varies with the discharge, step height, and step geometry.