## 4 Results and Discussion
### Flow Control of Plasma Actuators in Flowing Air
For example, the positive and maximal \(\eta_{p,mean}\) (approach to 1.5%) in Figure 11(e) is located near the middle of the roof, and the positive and bigger \(\eta_{p,mean}\) (about 5% and 0.3%, respectively) in Figure 11(g) is close to the leading edge and in the middle of the trailing edge. From further analyses, it is suggested that the roof region with the positive and maximal \(\eta_{p,mean}\) is placed at the beginning of the wall jet. The reason for this change is that the active actuators exert a suction force on the near-wall flow at the beginning of the induced jet. For the \(\eta_{p,mean}\), the absolute value of its minimum value is much bigger than that of its maximum value for each case, leading to the fact that the pressure effect of multi-SDBD actuators is much stronger than the suction effect. In summary, the wall jet slightly increases the mean wind load at the beginning of the jet and dramatically reduces this wind load at the end of the jet. The contours of the fluctuating pressure coefficient and its change rate on the whole roof from the simulation results are shown in Figure 13. When the actuators are inactive, the \(C_{p,rms}\) has an increasing trend along the flow direction, which is consistent with the experimental result of a similar cube observed by [PERSON] et al. [29] when approaching flow is uniform (\(Re\) is \(5\times 10^{4}\)). The reason for this trend is that the mean separated shear flow does not reattach to the roof. After the actuators are ignited, the \(C_{p,rms}\) distributions change significantly and the values of the \(\eta_{p,rms}\) on the whole roof are almost negative for all cases, indicating that the active actuators have an excellent control effect on the fluctuating pressure coefficient. It can be seen from Figure 12(c) that the minimum value of the \(\eta_{p,rms}\) (below \(-20\%\)) is near the middle of the roof. This may be owing to the fact that the counter-rotating vortex on the backward half of the roof is induced by the near-wall jet with the direction from the trailing edge to the leading edge [19]. Figure 12(g) shows that the minimal \(\eta_{p,rms}\) (less than \(-14\%\)) is close to the roof middle. This may be because after active actuators induce a directional near-wall jet, many counter-rotating vortices appear on the forward half of the roof and near the trailing edge [19]. These counter-rotating vortices succeed in suppressing the size of the shedding vortices, meaning that large-scale vortex shedding may become small-scale vortex shedding. This is why the wall jet reduces the fluctuating wind load on the roof. Figure 14 demonstrates the contours of the mean \(x\)-velocity component for all cases. With the discharge off, the near-wall flow velocity is between \(-1\) and \(1\) m/s. It is known that the flow on the front half of the roof surface moves toward the leading edge, while the flow on the rear half moves to the trailing edge. After the actuators are ignited, the near-wall flow direction for each case is changed to coincide with the velocity direction of the induced jet when there is no incoming flow. This indicates that the near-wall jet is successfully induced by each case with the incoming flow. Moreover, the flow velocity at the back of the near-wall jet is obviously increased by each case compared with the no actuation situation, showing that in the recirculation region the effect of the active actuators on the near-wall flow is stronger than that of the incoming flow. Such changes are due to the fact that the near-wall flow is subjected to a time-mean body force under the action of a high-frequency disturbance from the actuators. It can also be noted that in absence and presence of the plasma actuation the flow separation point is always located at the leading edge, there is no change in the position of the separation shear layer, and the shear layer never reattaches to the roof. This indicates that the active actuators have no effect on the flow separation point.