## 3 Results
### Flow Discharge on Vehicle with Spoiler  
To investigate the physics underlying the reduction in the drag and downforce via flow discharging in a vehicle with a rear spoiler, a two-dimensional simplified vehicle model was analyzed. Figure 12 shows the two-dimensional simplified vehicle and spoiler configuration and a partial view of the computational mesh used for analysis. In the isolated spoiler, the flow discharge at 0.25C and 0.75C exhibited a pressure distribution similar to that in the case with no discharge; however, the discharge at 0.50C exhibited a large pressure difference due to the flow separation. Thus, for the configuration of a vehicle with a spoiler, numerical tests were conducted for flow discharge at 0.50C and 0.75C. Figure 11: Comparison of flow patterns for different discharge velocities when the discharge position is 0.75C and the discharge is tangential to the vehicle driving direction; (**a**) Surface pressure distribution; (**b**) Zoomed view of surface pressure distribution around the trailing edge; (**c**) Velocity magnitude scale from 0 m/s to 120 m/s. Figure 12: Geometry and computational mesh of the model of a vehicle with a spoiler. Figure 13 shows the aerodynamic coefficients for different vehicle driving speeds when the flow is discharged at 0.50C with Vb/U = 0.4. In the isolated spoiler, the drag tended to increase rapidly when the flow was injected at 0.5C; however, in case of the vehicle with a spoiler, the drag and downforce decreased by 2.1% and 15% on average, respectively, for the velocity range of 100-300 km/h. Figure 14 shows the aerodynamic coefficients for various discharge speeds at the vehicle driving speed of 300 km/h. The aerodynamic drag and downforce were reduced for most discharge flow velocities. For discharge speeds of 30-40% the driving speed, the drag and downforce decreased by 3.4% and 19.3%, respectively. Similar to in the case of the isolated spoiler, the drag of the spoiler itself increased; however, the drag of the vehicle decreased, resulting in the reduction of the drag of the entire system. This phenomenon indicates that the flow separation from the spoiler leads to a change in the wake of the vehicle. To verify this aspect, the velocity distributions before and after flow discharging were compared, as shown in Figure 15. Without flow discharge, separation occurred at approximately 75% chord of the spoiler, and the separation area was relatively narrow. In the case of the vehicle, the trunk lid kick-up design weakened the downwash flow, and lifted the wake of the vehicle upwards. In contrast, the flow discharge at 0.50C led to flow separation and increased the separation area of the spoiler. It is apparent that the increased separation area of the spoiler moved the vehicle wake toward the ground and reduced the wake area of the vehicle, thereby reducing the aerodynamic drag of the entire system. Figure 14: Comparison of aerodynamic coefficients flow when is discharged at 0.50C at a vehicle driving speed of 300 km/h. Figure 13: Comparison of aerodynamic coefficients when flow is discharged at 0.50C; (**a**) Aerodynamic drag; (**b**) Downforce coefficient. Figure 16 shows the aerodynamic performance pertaining to different vehicle driving speeds when flow discharging occurs at 0.75C. The aerodynamic drag and downforce were reduced by an average of 2.1% and 6.4%, respectively, for the entire range (100-300 km/h) of the vehicle speed. To investigate the effect of the discharge velocity, numerical tests were conducted considered the vehicle speed of 300 km/h. Figure 17 shows the change in the aerodynamic coefficients. The aerodynamic drag and downforce of the spoiler and vehicle tended to decrease; however, the reduction in the downforce was not significant compared to that when discharging occurs at 0.50C. The maximum reduction was observed at Yb/U = 0.4, during which the drag and downforce decreased by 3.1% and 7.8%, respectively.