# Influence of Active Flow Control of Synthetic Jet at
## 5 Influence and Analysis of Synthetic Jet on Compressor Performance  
### Effect of Synthetic Jet on Overall Performance of Compressor  
Define the flow stability margin improvement:  
\[\Delta{SM}=\left(\frac{m_{SW\cdot NS}}{m_{S\cdot NS}}-1\right)\times 100\% \tag{4}\]  
where \(m\) is the mass flow rate, the subscripts _SW_ and _SI_ represent the prototype and the compressor excited by the synthetic jet, respectively, and the subscript _NS_ represents the near-stall condition.  
Since the synthetic jet excitation has input energy to the compressor, the influence of this energy should be considered when calculating the efficiency of the compressor. The method proposed by [PERSON] is used to calculate the power required when the synthetic jet is injected into the compressor [19]:  
Figure 8: Schematic diagram of synthetic jet on the suction surface of subsonic axial compressor rotor.  
Figure 9: Synthetic jet velocity curves at different times.  
\[E=\frac{1}{2}\rho\cdot A\cdot(0.26v_{\max}^{3}) \tag{5}\]  
where \(E\) is the power, \(\rho\) is the density, and \(A\) is the inlet area of the synthetic jet. Therefore, the calculation formula of the compressor efficiency considering the energy input of the synthetic jet is as follows:  
\[\eta=\frac{(p_{b}^{*}/p_{a}^{*})^{(\kappa-1)/\kappa}-1}{T_{b}^{*}/T_{a}^{*}-1+E /m/(\kappa/(\kappa-1))/R/T_{a}^{*}} \tag{6}\]  
where \(p^{*}\) and \(T^{*}\) are the total pressure and total temperature, respectively, the subscripts \(a\) and \(b\) represent the compressor's inlet and outlet measurement sections, and \(\kappa\) is the adiabatic index.  
The amount of change in efficiency is defined as follows:  
\[\Delta\eta=\frac{\eta_{Sj}-\eta_{SW}}{\eta_{SW}}\times 100\% \tag{7}\]  
Figure 10 presents the effect of synthetic jet on the suction surface on the overall performance of the compressor rotor. It can be seen that the total performance of the compressor decreases slightly under high flow conditions, but the amplitude is very small. From before the maximum efficiency point, the total pressure ratio and efficiency of the compressor began to increase, and the total pressure ratio and efficiency at the peak efficiency point increased by 0.04% and 0.47%, respectively. It is worth noting that the near-stall flow of the compressor excited by the synthetic jet increased by 0.03755 kg/s, so the flow margin decreased by 1.3%. When studying the synthetic jet on the suction surface of the NASA Rotor37 blade, the literature [14; 15] only calculated the design point and the near-stall point and did not get the performance change of the compressor in the whole operating range after the synthetic jet on the suction surface was excited. Therefore, the change in the stability margin of the compressor was not obtained, and looking at the existing literature, this paper is the first to carry out this research. Since the flow rates of the two near-stall points are not significantly different, the flow rates of the two near-stall points are directly considered to be approximately equal in this paper. Compared with the prototype compressor, the total pressure ratio and efficiency of the compressor near-stall point increased by 0.08% and 0.79%, respectively.