## 4 Case Study
### Analysis of Ventilation Local Resistance Characteristics  
In this section, a three-dimensional numerical simulation method is used to analyze the ventilation local resistance characteristics of the combined tee structure, and the RNG k-\(\varepsilon\) turbulence model is used to simulate the complex turbulent motion in the local region of the combined tee structure. The RNG k-\(\varepsilon\) turbulence model transport equation is based on the standard k-\(\varepsilon\) turbulence model with an added corresponding source term, which can accurately simulate the complex flow phenomena such as local vortex, jet collision, and high-speed strain flow [42]. In this paper, the outlet of the air duct is set as the velocity inlet boundary, and it is assumed that the airflow distribution of the outlet is uniform and the airflow direction is perpendicular to the section of the outlet. The left and right sides of the tunnel are set as the pressure outlet boundary, and the gauge pressure at the outlet is set to 0. The wall of the tunnel and the wall of the air duct are set as the solid wall boundary without slip [4]. In order to verify the reliability and accuracy of the numerical simulation results, the model experiment results of the local loss coefficient of the bifurcated tunnel under different bifurcation angles in the paper of [PERSON] et al. [43] are quoted in this paper for comparison and verification, and the local loss coefficient under different bifurcation angles and flow diversion ratios is simulated. The comparison between the numerical simulation and model experiment value is shown in Figure 7. As can be seen from Figure 7, when the bifurcation angle is 5\({}^{\circ}\), the error range of the local loss coefficient is 6.0-13.5% and the average error is 8.9%; when the bifurcation angle is 10\({}^{\circ}\), the error range of the local loss coefficient is 5.3-12.2% and the average error is 8.4%; and when the bifurcation angle is 15\({}^{\circ}\), the error range of the local loss coefficient is 4.2-12.9% and the average error is 7.8%. The error comparison results show that the numerical simulation results are in good agreement with the model test results in the reference [43]. Therefore, the three-dimensional numerical model of the ventilation local resistance of the combined tee structure of the water transmission tunnel can be used to solve the sample point calculation of the prediction model of the ventilation local resistance coefficient based on the IAJS-HKRVM. Figure 6: Diagram of engineering layout and maintenance ventilation ((**a**)—The project location diagram; (**b**)—The TBM tunnel layout diagram; (**c**)—Maintenance ventilation process diagram). In order to analyze the ventilation local resistance characteristics of the combined tee structure, the numerical simulation results with the parameters of an air pipe diameter of 1.2 m, number of air pipes of 4, a tunnel diameter of 8 m, and a wind speed of the outlet of 10 m/s are selected for analysis. Figure 8 shows the wind velocity distribution cloud map and vector map of the central longitudinal section of the combined tee structure under this working condition. After the high-speed airflow emitted from the top air duct outlet enters the tunnel, the flow direction changes sharply under the obstruction of the tunnel wall, and moves and diffuses to both ends, forming the wall-attached flow and collision wall-attached jet, as shown in Figure 8b 1 and 2. After the high-speed airflow emitted by the adjacent air pipe enters the tunnel, the overflow section suddenly expands, the turbulent edge develops and diffuses, the airflow reaching the bottom of the tunnel is diverted by the obstructing wall, and the adjacent jets collide with each other to form the local vortex region, as shown in Figure 8b 3. At the same time, after the airflow enters the tunnel, it diffuses to both ends of the tunnel, collides with the airflow in the upper space of the tunnel, and forms the vortex region, as shown in Figure 8b 4.