## 3 Results and Discussion
### The Influence of Extra Resistance  
It is observed that the total extra resistance, including the wire resistance and the equivalent serial resistance of the discharge capacitor, affects the performance of the PSJA array greatly. In this part, these factors are studied. The extra resistance is set as 0.1 \(\Omega\) and 10 \(\Omega\) in case 1 and case 2 respectively.  
The total discharge energy and discharge efficiency versus actuator number with different extra resistance are shown in Figure 19. In case 1, the extra resistance is only 0.1 \(\Omega\), and the discharge efficiency of one actuator is 72%. In contrast, the discharge efficiency of one actuator in case 2 (larger extra resistance) is as low as 5%. With the increase in the actuator number, the discharge efficiency in the two cases increases. However, the increased levels are different. When the actuator number increases to 20, the discharge efficiency in case 1 increases to 94%, which is 30% larger than the initial discharge efficiency (72%). But in case 2, the discharge efficiency increases to 38%, which is almost six times larger than the initial discharge efficiency (5%).  
The variation of total gas kinetic energy with actuator number under different extra resistance is shown in Figure 20. The revealed trends are completely different when different extra resistance is used. In case 1, the total gas kinetic energy decreases with the increase in the actuator number. However, in case 2, the opposite trend happens. Instead of decreasing, the total kinetic energy increases  
Figure 19: The total discharge energy and efficiency versus actuator number with different extra resistance.  
Figure 17: The total gas kinetic energy versus actuator number.  
Figure 18: The thermodynamic efficiency versus actuator number.  
when more actuators are used. In case 2, the total gas kinetic energy with 20 actuators is nearly four times of that with one actuator.  
The reason for the distinctive variations revealed in Figure 20 is given as follows. The discharge efficiency increases with actuator number, but the thermodynamic efficiency decreases, while the variation speed is different. The discharge efficiency and thermodynamics efficiency with different actuator numbers are normalized by that with only one actuator, as shown in Figure 21. The larger the extra resistance is, the larger the increase in the discharge efficiency is, and the smaller the decrease in the thermodynamic efficiency is. As a result, with a large extra resistance, the total efficiency grows with the increase in the actuator number. However, with a small extra resistance, the total efficiency decreases with the increase in the actuator number.  
In conclusion, when the extra resistance is large, the energy efficiency of the PSJA array is higher than that of conventional PSJA. Actually, in the practical application, the extra resistance is relatively large. In the experiment on control of the shock boundary layer interaction using PSJA by [PERSON] et al. [PERSON] et al. (2017), a resistance (max 1.5 k\(\Omega\)) is adopted in the discharge circuit. In the experiment of [PERSON] et al. (2016; [PERSON] et al., 2016; [PERSON] et al., 2016), a ballast resistance is also adopted in the discharge circuit. In the experiment of [PERSON] (2013; [PERSON] et al., 2014), a ballast resistance (max several kilo Ohm) is adopted in the discharge circuit as well. Therefore, there is reason to believe the PSJA array driven by the multichannel discharge technology can play an important role in the practical flow control application.  
Figure 21: The normalized discharge efficiency and normalized thermodynamic efficiency versus actuator number with different extra resistance.  
Figure 20: The total gas kinetic energy versus actuator number with different extra resistance.