# Review of Passive Flow Control Methods for Compressor Linear Cascades
## 2 Chronological Evolution of Linear Cascade
### Passive Control Methods  
Since the 1970s, compressor airfoils for high Mach number applications have predominantly utilized circular arc design methodologies. These include Double Circular Arc (DCA) airfoils, which feature suction and pressure surfaces defined by two distinct radii, and Multiple Circular Arc (MCA) airfoils, which employ several arcs. The German Aerospace Center (DLR) has played a leading role in turbomachinery development since the 1970s, with a pivotal 1976 study examining transonic cascade performance influenced by the Axial Velocity Density Ratio. This research expanded to include L030 rotor investigations using DCA and MCA airfoils, with these early studies relying on empirical data and correlations to analyze transonic cascades [58; 59; 60; 61]. By the late 1980s, significant design advancements were made, including the introduction of viscous-inviscid interaction algorithms for manual cascade optimization and inverse design methodologies that achieved prescribed velocity distributions. These advancements facilitated the development of controlled diffusion airfoil designs, optimizing flow characteristics across the blade surfaces. In the realm of computational fluid dynamics (CFD), studies on axial flow compressor solidity demonstrated that decreasing solidity led to increased losses and reduced stall margins, with no identifiable minimum-loss condition. Comparing these results with [PERSON]'s correlations highlighted the impact of inlet Mach numbers and variations in pitch-to-chord ratios on losses [62]. While the Baldwin-Lomax model presented limitations, two-equation models proved to be more reliable, emphasizing the importance of experimental validation for optimizing compressor designs with respect to both efficiency and weight reduction. Optimization algorithms have revolutionized the design of blades, particularly under transonic conditions. A 2023 study focused on designing a compressor cascade for DLR's Transonic Cascade Wind Tunnel. By using optimization techniques with AutoOpti and TRACE solvers to improve efficiency across both the design and working ranges, the study achieved a remarkable 24% improvement in efficiency [63]. These findings provide valuable insights into blade optimization under complex transonic flows, marking a significant step forward in compressor design optimization. Research on boundary layer behaviour in single and tandem airfoils has also highlighted the significant effects of Reynolds numbers, turbulence intensities, and blade designs on performance. Tandem configurations, in particular, showed interdependent boundary layers, with thicker layers developing under higher turbulence conditions [64]. These results emphasize the importance of designing airfoils tailored to varying operating conditions, with particular attention to turbulence and flow behaviour. Furthermore, the passive control methods are categorized based on their primary mechanisms of action. is particularly noticeable from 70% of the blade span to the tip, with larger clearances worsening aerodynamic performance and reducing stall margin [65]. Further studies have investigated the impact of large tip clearances (up to 6% of the chord) on compressor performance, showing that losses stabilized beyond a 4% clearance, with blade loading increasing above 2%. This was attributed to the presence of a strong tip clearance vortex, which remained constrained, suggesting a delicate balance between optimizing performance and maintaining mechanical robustness [67]. A direct numerical simulation study highlighted the role of free-stream turbulence in the transition to turbulence and boundary layer attachment. Increased turbulence was shown to improve boundary layer attachment but delayed reattachment on the suction surface after separation, emphasizing the complex dynamics involved in managing boundary layers in compressor flows [68]. Studies using Doppler Global Velocimetry and hot-wire anemometry examined the dual role of tip clearance vortices in compressor cascades.