# Review of Passive Flow Control Methods for Compressor Linear Cascades
## 2 Chronological Evolution of Linear Cascade
### Passive Control Methods
#### 2.1.2 Secondary Flow and Separation Control
These findings reaffirmed the effectiveness of non-axisymmetric shaping, though additional tests were neededto validate multi-row interactions and downstream effects [102]. In the same year, the optimization of end slots on NACA65 cascade blades using the NSGA2 algorithm resulted in a 10% reduction in total pressure loss at a 4\({}^{\circ}\) incidence angle, significantly enhancing cascade performance by reducing sensitivity to incidence variations [108]. [PERSON]'s [109] study on three-dimensional separation at the juncture of the endwall and blade corner region aimed to use prediction parameters to gain an early insight into the flow field behaviour within the cascade, prior to conducting experimental and numerical analyses. The equivalent diffusion factor \(DF_{eq}\) Equation (1) [33] is employed to predict separation at mid-span. The experimental \(DF_{eq}\) values are derived from the five-hole pressure probe measurements. It is observed that the flow at mid-span does not separate at \(i=4^{\circ}\) but does separate at \(i=6^{\circ}\), as shown in Figure 7, which presents both experimental and numerical results of the parameter. Another factor was earlier, proposed by [PERSON] [110], the diffusion parameter \(D\) Equation (2) [111] to predict the size and intensity of the corner stall. The size and strength of the corner stall increase with incidence. According to this prediction, large separation regions on both the suction side and the endwall occur when \(i>8.3^{\circ}\). \[DF_{eq} = \frac{\cos\beta_{2}}{cos\beta_{1}}\bigg{[}1.12+\alpha|i-i^{*}|^{1.43}+0.61\frac{cos^{2}\beta_{1}}{\sigma}|tan\beta_{2}-tan\beta_{1}|\bigg{]} \tag{1}\] \[D = \bigg{[}1-\bigg{(}\frac{cos(i+\gamma+\varphi/2)}{cos(\gamma- \varphi/2)}\bigg{)}^{2}\bigg{]}\frac{(i+\varphi-\Delta\eta)}{\sigma} \tag{2}\]  
where \(i\) is the incidence, \(i^{*}\) is the optimum incidence, \(\sigma\) is the solidity, \(\beta_{1}\) and \(\beta_{2}\) are upstream flow angle and downstream flow angle, \(\gamma\) stagger angle, \(\varphi\) blade camber angle, \(\Delta\eta\) additional turning angle due to skewed incoming endwall boundary layer. The limitation of \(DF_{eq}\) is that it is unreliable when \(i<i^{*}\). Further studies in 2017 investigated the use of end-wall vortex generators (VGs) for controlling secondary flows in high-turning compressor cascades. These VG systems resulted in notable improvements, such as a 21.5% reduction in secondary flow losses at a 60\({}^{\circ}\) camber angle, along with additional improvements at other incidence angles, including a 13.2% reduction at \(-5^{\circ}\) and 32.5% at \(+5^{\circ}\) incidence [112]. Another innovative approach involved a self-supplied jet separation control method, which introduced an arc slot connecting the pressure and suction sides to induce a jet flow that mitigated suction side separation. Experimental results showed a 21.9% decrease in total loss and an increase in the flow turning angle by 2.1\({}^{\circ}\), significantly enhancing the stability margin and improving the operating margin by at least 3\({}^{\circ}\) with respect to the incidence angle [113]. The use of  
Figure 6: Topology of corner separation [105]. vortex generator jets on endwalls also demonstrated improved aerodynamic performance in a high subsonic compressor cascade, with reductions in total pressure loss by up to 14.6% at optimal incidence angles [114]. In a combined flow control study, the integration of a blade slot and VG in a high-load compressor cascade resulted in a 30.9% reduction in total pressure loss, a 2\({}^{\circ}\) increase in flow turning, and a 69.9% enhancement in the pressure coefficient. The slot reattached suction side separations, while the VG suppressed passage vortex and corner separation, contributing to better flow structure and reduced sensitivity to incidence, thus improving overall cascade efficiency [115].