## 4 Results and Discussion
### Flow Control of Plasma Actuators in Flowing Air  
During the simulation, the building model has an unsteady wind load in the initial three seconds, and for comparison of the control effects of different plasma actuator arrangements, the stable stage (subsequent fifteen seconds) is used for analysis. The quantitative data of mean and fluctuating wind loads under all cases are given in Table 2 for comparative analysis. Compared with the no actuation situation, all cases have no effect on the mean drag coefficient, and case A has the smallest mean \(C_{l}\) value (an about 5% reduction). This indicates that the control effect is closely related to the configuration and position of the active plasma actuators. Since the actuators are only placed on the roof, they mainly affect the wind load on the roof (i.e., the \(z\)-direction wind load) and there is no change in the mean drag coefficient. For the vortex-induced vibration, the RMS value of the wind load (i.e., the fluctuating wind load) is much more concerning than the mean value due to the better reflection of the structural vibration characteristic. Among all cases, case A has the lowest fluctuating \(C_{d}\) (a 15.79% reduction) and the lowest fluctuating \(C_{l}\) (a 15.45% reduction). Such results mean that case A is the best configuration of multi-SDBD plasma actuators for reducing fluctuating wind load. Moreover, cases B and C also show good control of the fluctuating \(C_{d}\) and \(C_{l}\) with decrements of over 6.30%. This shows that the vibration amplitude of the roof along the \(x\)-direction and \(z\)-direction can be significantly reduced by all  
Figure 9: Pressure contours: (**a**) case A; (**b**) case B; (**c**) case C.  
cases. Compared with the no actuation situation, the Strouhal numbers of cases A and B are decreased, implying the delay of the vortex shedding period, and the Strouhal number is increased for case C. This indicates that the active actuators can affect the vortex shedding frequency. Figure 10 shows the time histories of the drag coefficients acting on the building model from the simulation results of different cases. It can be seen that the drag coefficient of the no actuation situation is highly unsteady, with its amplitude fluctuating randomly and significantly as a function of the time. The drag coefficient fluctuation amplitudes of all cases are obviously reduced in comparison to the no actuation situation. This indicates that the active actuators can reduce the instability of the drag coefficient. Figure 11 illustrates the power spectral density (PSD) of the fluctuating drag coefficient acting on the building model from the simulation results of different cases. In this figure, \(f\) is the frequency. For a blunt body, such as a low-rise building, the vortex shedding seems to be the primary source of the fluctuating pressure of the building surface [27]. Large-scale vortex shedding often means the strong fluctuating wind load. When the reduction frequency is around 0.196, the PSD peaks of all cases are much lower than the no actuation situation, suggesting a sharp weakening of the strength of the shedding vortex led by the flow separation. Besides, the PSD of all cases at the reduction frequencies of 0.32, 0.36, 0.41, and 0.46 is significantly increased in comparison to the no actuation situation, implying that the active actuators can induce the small-scale vortex with high frequency. \begin{table}
\begin{tabular}{c c c c c} \hline  & **No Actuation** & **Case A** & **Case B** & **Case C** \\ \hline Mean C\({}_{d}\) & \(-2.22\) & \(-2.21\) & \(-2.21\) & \(-2.23\) \\ Mean C\({}_{l}\) & 0.565 & 0.540 & 0.561 & 0.560 \\ RMS C\({}_{d}\) & 0.152 & 0.128 & 0.137 & 0.137 \\ RMS C\({}_{l}\) & 0.110 & 0.093 & 0.103 & 0.099 \\ \(S_{t}\) & 0.196 & 0.148 & 0.191 & 0.209 \\ \hline \end{tabular}
\end{table} 
Table 2: Mean and RMS values of drag and lift coefficients.