# Air Entrainment and Air Demand in the Spillway Tunnel at the Jinping-I Dam
## 1 Introduction  
High-velocity flow often occurs on spillways, particularly for high dams, which can cause severe cavitation damage to the hydraulic structures. Some measures, such as optimizing the structure body, smoothening the concrete surface, and applying anti-cavitation materials are commonly implemented to prevent the cavitation, but the potential damage cannot be completely eliminated. Engineering experiences show that artificial air entrainment is an economical and effective way to protect the concrete surface from cavitation damage by means of setting auxiliary devices on the bottom of spillways and sometimes on sidewalls [1; 2; 3; 4; 5]. Aeration devices have been widely used in many projects since the successful application of a groove in the Great Coulee Dam in 1960 [6], and significant damage reduction has been achieved. [PERSON] [7] proposed that when the air concentration in the flow layers close to the channel bottom reaches 5-8%, the concrete surface can be completely protected from cavitation damage. [PERSON] [8], who conducted a number of surface erosion experiments with a variety of measuring instruments, confirmed that 0.8-1.0% volume of small air bubbles in the water flow could also effectively play a protective role to the concrete surface. [PERSON] [9] suggested that the critical air concentration to avoid cavitation damage is 2.8%. Research on air entrainment is mainly conducted through theoretical analysis, laboratory experiments, and prototype observations. Theoretical analysis on the mechanism of air entrainment mainly focuses on the occurrence of cavitation, and processes of air in-flow and out-flow. Many researchers ([PERSON] [10], [PERSON] [11], [PERSON] [12], [PERSON] [13], [PERSON] [14]) investigated the relationship between the critical cavitation number with surface irregularity, turbulent boundary layer thickness and flow velocity. Jet aeration is mainly caused by the turbulent exchange of air-water interface. It is generally believed that when the flow velocity exceeds 5-7 m/s, the upper surface of the flow begins to be aerated. However, for the lower surface, there exist different opinions on critical aeration from different researchers, such as those of [PERSON] et al. [15], [PERSON] [5], [PERSON] and [PERSON] [16], [PERSON] and [PERSON] [2], [PERSON] et al. [17] and [PERSON] and [PERSON] [18]. In general, the law of single bubble motion in the water is the basis for understanding the aeration mechanism. [PERSON] and [PERSON] [19] conducted an earlier study on the theory of single bubble motion in still water. Following this study, [PERSON] [20] considered the effects of resistance, gravity and buoyancy on bubble motion. [PERSON] [21], who compared the movement of bubbles in moving and still waters, found that rising velocity of bubbles in moving water is only 1/10 of that in still water. Although considerable work has been done, due to the complexity of air entrainment phenomenon, particularly for the spillways constructed in a tunnel, an accurate theoretical model is yet to be established. In laboratory experiments, the air entrainment phenomenon is known to be difficult to accurately model because of the unknown scale effects [22]. Traditional hydraulic model tests, generally designed based on the gravity similarity, may exclude the effects of viscosity and surface tension, so the turbulence intensity cannot be properly represented, whilst the air entrainment phenomenon is strongly related to flow turbulence intensity. The model scale required to accurately represent the turbulence-induced air demand is yet to be quantified. Given the fact that mathematical models for air entrainment have not yet been well established and the traditional model tests are affected by the scale effect, prototype observations become important in the air entrainment research [23].