## 4 Discussion
### Flow Patterns  
The flow pattern of the ventilation system of a spillway tunnel is very complex. The analysis of the vector field of air velocity is helpful in clarifying the reason for air demand difference under different gate opening ratios. It is also helpful to understand the balances between air ducts and residual space in a tunnel.  
In the vector field of air velocity under the 100% gate opening ratio, it can be seen in Figure 13a that the flow pattern was relatively simple. The air flowing from air duct no. 1 generated several vortices in the gate chamber, and then flowed downstream to interconnect with the airflow flowing from air duct no. 2. Then, the confluence continued to flow downstream. Similarly, the airflow from the air duct no. 3 converged with the flow from upstream and flowed downstream until it is out of the tunnel. There was no obvious reverse flow in the residual space of the tunnel, and also no obvious airflow vortex.  
In the vector field of air velocity under the 25% gate opening ratio (seen in Figure 13b), the flow pattern became more complex. On the downstream side of the chamber, there was obvious reverse airflow, which means part of the air flow in the chamber came from the downstream. Near the air duct no. 2 in the tunnel, part of the airflow from upstream converged with the air from air duct no. 2 and flowed downstream, while the other part was hindered and turned around to form a countercurrent, flowing upstream along the roof of the spillway tunnel. The airflow characteristics near the air duct no. 3 were similar to the characteristics near the air duct no. 2. Between the air duct no. 2 and no. 3, the airflow flowing downstream met the reverse flow from downstream, forming a local vortex. At the outlet, while the airflow was dragged out by the water flow, a small amount of air flowed back along the top of the tunnel. This part of airflow will finally form a vortex when it meets the airflow from upstream. The different flow patterns can be summarized as follows:  
Pattern 1: as can be seen in Figure 14a, when the dragging capacity of water flow was sufficient, the air from the air duct was dragged downstream with the water flow, and  
Figure 12: The (**a**) average air velocity and (**b**) average air pressure over the cross-sections in the tunnel.  
there was little vortex in the residual space of the tunnel. In this case, the airflow field was simple, and the ventilation conditions were good.  
Pattern 2: as can be seen in Figure 14b, when the dragging capacity of water was insufficient relative to the residual space of the tunnel, only part of the airflow can finally get out of the tunnel, while the rest part was locked between air ducts and outlet. The locked air formed self-circulation (or vortex) and occupied the residual space in the tunnel, which inhibited the process of air supply from the air ducts to the tunnel and finally reduced  
Figure 14: Different flow patterns under different conditions: (**a**) pattern 1; (**b**) pattern 2.  
Figure 13: Vectors of air velocity in the free space above water in the tunnel. (**a**) 100% gate opening ratio, (**b**) 25% gate opening ratio.  
the air demand of the tunnel. The distribution area of the self-circulation was related to the equilibrium relationship between the dragging capacity of water flow and the size of residual space above water in a tunnel.