## 4 Results and Discussion
### Flow Control of Plasma Actuators in Flowing Air
Figure 10: Time histories of drag coefficients: (**a**) no actuation and case A; (**b**) no actuation and case B; (**c**) no actuation and case C.  
The contours of the mean pressure coefficient and its change rate on the whole roof from the simulation results are shown in Figure 12. When the actuators are inactive, \(C_{p,mean}\) on the entire roof is a negative value and the absolute value increases along the flow direction. This is because the incoming flow separates from the building model at the blunt leading edge and a large recirculation region is formed on the roof, while the incoming flow stays attached to the windward surface of the building model. Then, the shear layer entrains the air flow of the recirculation zone to move downstream while the pressure-driven backflow must balance the air mass loss produced by the shear layer entrainment. The process leads to a strong negative pressure gradient on the roof. In addition, according to the experimental research [28], the approaching flow of the present research can be approximated as a uniform flow. After the actuators are ignited, the negative \(C_{p,mean}\) still appears on the whole roof surface and it is observed that the distribution of \(C_{p,mean}\) changes significantly for all cases, indicating that the negative pressure gradient effect caused by the flow separation still dominates and the wall jet has a significant impact on this negative pressure gradient. It can be seen from Figure 12c that the \(\eta_{p,mean}\) of the whole roof is negative and it is the smallest (about \(-20\%\)) in the vicinity of the entire leading edge, suggesting that case A with actuation sharply reduces the \(|C_{p,mean}|\) near the entire leading edge. Figure 12e shows that the \(\eta_{p,mean}\) has the lowest value (about \(-5\%\)) around leading edges and in the middle of the trailing edge, implying that case B in presence of actuation obviously reduces the \(|C_{p,mean}|\) around entire leading edges and in the middle of the trailing edge. According to Figure 12g, the \(\eta_{p,mean}\) has the smallest value (approach to \(-7\%\)) in the middle of the roof, showing that case C with excitation significantly reduces the \(|C_{p,mean}|\) in the entire middle part of the roof. By checking the changes described above, it is found that local roof regions with the negative and minimal \(\eta_{p,mean}\) are precisely placed at the end of the wall jet for each case. Similar to the effects of an active single-SDBD plasma actuator in the quiescent air, the actuator with the incoming flow still absorbs the near-wall flow upstream of the induced jet and blows the flow downstream, leading to a pressure force being applied on the downstream flow. In other words, the wall jet exerts a pressure on the downstream near-wall flow. Furthermore, this pressure is directly related to the speed of the wall jet. As the wall jet is continuously accelerated by each single-SDBD actuator, the wall jet has the greatest momentum at the end. At the same time, the maximum pressure is transmitted from the wall jet to the body surface during the interaction of the wall jet with the body surface, resulting in the negative and minimal \(\eta_{p,mean}\). This is why the absolute value of the mean wind pressure coefficient is reduced dramatically at the end of the wall jet. It is also seen from these analyses that multi-SDBD plasma actuators are selective for the position of roof areas with a significant reduction of mean wind load, and this roof area is limited. Figure 11: Power spectral density of RMS drag coefficient. Figure 12: Contours of the mean pressure coefficient and its change rate on the whole roof: (**a**) no actuation; (**b**,**c**) case A; (**d**,**e**) case B; (**f**,**g**) case C.  
Cases B and C have the ability to increase the absolute value of the \(C_{p,mean}\) on another partial area of the roof.