## 4 Results and Discussion  
### Plasma Actuators in Quiescent Air  
To investigate the plasma influence in quiescent air, velocity magnitude and velocity component contours for all cases on the roof centerline are shown in Figures 7 and 8. In these figures and the subsequent similar figures, the upper and lower electrodes are illustrated by black rectangular regions, and the height of these regions is ten-times larger than the used electrode thickness to show the position of the actuators clearly. When the actuators are active, case A produces an induced near-wall jet with the direction from the trailing edge towards the leading edge, and the flow has a final velocity of approximately 2 m/s around the leading edge. An induced near-wall jet with the direction from the middle of the roof to leading and trailing edges is induced by case B, and the flow velocity reaches a maximum of around 1.8 m/s close to the leading and trailing edges. Moreover, case C generates an induced near-wall jet with the direction from leading and trailing edges to the middle of the roof, and the maximum velocity is about 1.8 m/s near the middle of the roof. Since the wall jet has opposite flow directions in the middle of the roof, a vertical synthetic jet appears above this region. The similar experimental result for the synthetic jet phenomenon was described by [PERSON] et al. (2015). The reason for increasing the jet velocity is that the flow moving along the induced wall-jet direction is accelerated every time it passes over the next actuator, and builds up to reach to the maximum velocity at the end of the jet.  
Figure 6: Mean pressure coefficient change rates along the roof centerline: (**a**) case A with the wall-jet direction from the trailing edge to the leading edge; (**b**) case B with the wall-jet direction from the middle of the roof to the leading and trailing edges; (**c**) case C with the wall-jet direction from the leading and trailing edges to the middle of the roof.  
Figure 8: Velocity component contours: (**a,b**) case A; (**c,d**) case B; (**e,f**) case C.  
Figure 7: Velocity magnitude contours: (**a**) case A; (**b**) case B; (**c**) case C.  
As can be seen from Figure 8a,c,e, the \(x\)-velocity of the induced jet for each case is larger than the \(z\)-velocity, indicating that the wall jet is dominated in the wall-parallel direction. This is consistent with a similar numerical study on the wind turbine blade by [PERSON] et al. [26]. According to Figure 8b,d,f, a negative \(z\)-velocity exists above every single-SDBD actuator, and a positive \(z\)-velocity appears downstream of the jet induced by each actuator. This shows that each plasma actuator exerts a suction force on the flow above itself and blows the flow downstream, thereby generating a pressure force on the downstream flow. The pressure contours of all cases shown in Figure 9 prove this. In this figure, the range and amplitude of negative pressure regions reduce continuously along the wall-jet direction, while the range and amplitude of positive pressure regions increase rapidly. This implies that in terms of the influence of the multi-SDBD plasma actuators, the suction effect quickly decreases along the induced jet direction, and at the same time the pressure effect increases dramatically.