# Air Entrainment and Air Demand in the Spillway Tunnel at the Jinping-I Dam
## 4 Discussion
### Model Scale Effect of Air Demand  
The physical model of the Jinping-I Dam spillway tunnel is designed according to gravity similarity, and the model scale is \(\mathrm{Lr}=1/30\). It is a complete model constructed of polymethyl methacrylate. Apparatuses and data acquisition systems employed in the model test are similar to the field measurement. The air demand measured in the model is converted to the prototype by Froude scaling, and the converted prototype air demand is defined as model air demand \(Q_{am}\) (the model air demand is equal to the air demand measured in the model multiplied by \(\left(1/\mathrm{L_{r}}\right)^{5/2}\)). Prototype and model results of air demand at flow rate of 3200 m\({}^{3}\)/s are shown in Figure 13a. Prototype values of the No. 2 aerator and No. 4 aerator are 3.39 and 2.29 times the model values, respectively. Air demand of the aerator in the prototype is considerably greater than that in the model, indicating that the model test designed according to gravity similarity does not obey similarity in air demand. A prototype and model comparison on air concentration is also made (as shown in Figure 13b). For a measurement point completely submerged in the water, owing to more air being entrained in the prototype, the prototype value is much greater than the model values near it, for example in measurement points C1 and C7. For the measurement point completely inside the cavity, since it is exposed to the air, the prototype and model results are similar, for example in measurement points C6 and C10. For the measurement point C11, which is located downstream of the No. 4 aerator, using an air content of 50% to 60% as the criterion for determining the air-water interface, it should be completely submerged in water in the prototype. However, according to the model result, it is inside the cavity. Cavity backwater is more likely to appear in chute with a small bottom slope, and there may be a small amount backwater inside the cavity downstream of the No. 4 aerator in the prototype. The range of the backwater covers C11, but it does not cover C10. The effect of flow aeration in the model test, by contrast, is not as strong as that in the prototype. Therefore, point C11 was inside the cavity in the model test. The significant difference in air concentration between prototype and model also indicates model scale effect exists in model test. Actually, as flow turbulence level is a key factor controlling the amount of air entrained by the flow, un-similarity in turbulence level in model test is mainly responsible for the un-similarity in aeration. If the model scale is greater, the difference in hydraulic parameters including turbulence level between model and prototype could become lesser. The model scale effect on similarity in aeration cannot be neglected. In reality, model scale effect on similarity in aeration could be quantified by air demand ratio between prototype and model air demand (\(n=Q_{ap}/Q_{am}\)). The closer to one air demand ratio, the less obvious the model scale effect is. Through gathering prototype and model air demand data of many  
Figure 13: Prototype-model comparison of air demand (**a**) and air concentration (**b**) at a flow rate of 3200 m\({}^{3}\)/s. The positions of model measurement points are listed as distances from their nearest filed measurement points, the negative value indicates the upstream, and the positive value indicates the downstream. The units are in m.  
projects, air demand ratios were calculated. These results, combined with the data of Jinping-I Dam spillway tunnel, are shown in Figure 14 (detailed parameters of aeration devices of these projects are illustrated in Table A2 in Appendix A). Model scales range from 1/70 to 1/10, and flow rates range from 8 to 250 m\({}^{3}\)/s. For most projects, only one model scale was used. Results of these projects show that the air demand ratio varies with flow rate at a particular model scale, and its sensitivity to flow rate varies from project to project.