# Effect of Height and Geometry of Stepped Spillway on Inception Point Location
## 1 Introduction  
A stepped spillway is an important hydraulic structure widely used in hydraulic projects owing to its high energy dissipation function. Due to the increase of the energy dissipation rate, the stilling basin at the toe of the dam requires less size than that of a smooth spillway [1, 2]. Aeration is a process in which air enters the surface of a spillway. Without aeration, the spillway may be subjected to cavitation damage. Thus, aeration is necessary to prevent cavitation damage in stepped spillways. Air entrainment starts when the turbulent boundary layer coincides with the water depth. The point at which air entrainment starts is called the inception point, i.e., the location where a non-aerated flow zone is converted into an aerated flow zone [3, 4]. The performance of a stepped spillway depends on the air entrainment. Since cavitation often occurs in the non-aerated flow zone, measurement of the exact location of air entrainment is necessary to determine the area affected by cavitation. The inception point location indicates the length of the non-aerated flow zone. Thus, by measuring the exact location of the inception point, the aerated and non-aerated flow zones can be predicted [5, 6, 7]. The location of the inception point is also very important for measuring the length of the stilling basin, because energy dissipation in a stepped spillway depends on the location of the inception point. The energy dissipation downstream of the inception point is much larger than that upstream. In a smooth spillway, the location of the inception point is further downstream than in a stepped spillway. The location of the inception point in a stepped spillway depends on the discharge, the step height and step geometry [8, 9]. In a stepped spillway, three kinds of flows occur: nappe flow regime, transition flow regime, and skimming flow regime. The nappe flow regime occurs at very low discharge, where free fallingjets fall in the form of nappes from one step to another. Skimming flow occurs at high discharge. In the skimming flow regime, the water moves above the pseudo-bottom as a coherent stream, where the pseudo-bottom is formed by connecting the edges of the steps. Beneath the pseudo-bottom, recirculating vortices are formed causing energy dissipation in the stepped spillway [10; 11]. Skimming flow in a stepped spillway consists of two regions: non-aerated flow zone and aerated flow zone. The line connected to the edges of the step is called the pseudo-bottom. Beneath the pseudo-bottom, recirculating vortices are formed [12; 13]. In Figure 1, \(Li\) is the distance from the spillway crest to the inception point. The less \(Li\) is, the greater is the amount of air that enters the water and vice versa. At the inception point, the pseudo-bottom air concentration is 0.01 [14] and the air phase suddenly changes from entrapped to entrained. Entrained air is transported within the flow, while entrapped air is transported above the water surface and between the crest. The sum of the entrained and entrapped air in a stepped spillway is called the total air concentration. A 5-8% pseudo-bottom air concentration is required to prevent cavitation damage [15]. The point at which the pseudo-bottom air concentration reaches 5-8% is called the critical point [16]. Beyond the inception point, the air concentration increases rapidly at the pseudo-bottom and quickly reaches the critical point, and then increases to the maximum value. Air entrainment can prevent cavitation damage caused by the occurrence of low pressure [17]. On increasing the discharge, the length of the non-aerated flow zone and the risk of cavitation both increase. The zone near the inception point is closely related to cavitation damage. The inception point in a stepped spillway is observed when the boundary layer thickness reaches 80% of the flow depth. The flow upstream of the inception point is smooth, while it is very turbulent downstream [18; 19].