# Review of Passive Flow Control Methods for Compressor Linear Cascades
## 2 Chronological Evolution of Linear Cascade
### Passive Control Methods
#### 2.1.4 Boundary Layer Control  
Recent advancements in compressor cascade performance have been significantly driven by innovative flow control strategies, particularly bio-inspired designs and passive  
Figure 10: Illustration of a perforated airfoil designed for shock wave mitigation [139]. Figure 9: Geometry of shock control bump [137]. control methods, which aim to enhance aerodynamic efficiency. Among these advancements, slanting riblets, inspired by the microscopic patterns found on birds' secondary flight feathers, have shown great promise in reducing drag. [PERSON] et al. [144] demonstrated a 16.8% reduction in pressure loss when using slanting riblets in a linear cascade. Similarly, herringbone riblets have also been studied for their drag-reducing potential. These riblets improve flow turning angles and reduce pressure loss by up to 36.4% at low Reynolds numbers by suppressing flow separation and energizing the boundary layer [145]. In addition to riblet designs, bio-inspired structures, such as endwall bionic chambers modelled after dragonfly wings, have proven effective in reducing aerodynamic losses. These chambers optimize cascade incidence angles and enhance turbulent kinetic energy (TKE), leading to a 9.43% reduction in total pressure loss and an 8.35% increase in static pressure when placed between 25% and 50% of the chord length [146]. Sharkskin-inspired riblets, which align with the flow direction, have been shown to improve compressor blade performance by advancing boundary layer transition and reducing separation flow regions [147]. Furthermore, slotted wingtips, inspired by bald eagle flight dynamics, offer up to 80% greater lift compared to conventional designs. However, their effectiveness hinges on balancing flap frequency to avoid destabilizing the flow in practical turbomachinery applications [148]. Research on endwall effects, which significantly influence compressor blade performance, has led to improved blade designs. A promising combination of bowed blades and leading-edge stake blades (LESB) achieved substantial aerodynamic improvements, with the optimized bowed LESB cascade reducing total pressure loss by 59.7%, while maintaining static pressure rise and diffusion factor [149]. Overall, bio-inspired designs, particularly riblets, have proven highly effective in reducing drag and improving turbomachinery performance. Riblets, as a passive treatment, can reduce shear stress by up to 13.2%, enhancing flow mixing and suppressing near-wall turbulence, thus lowering drag [150]. In gas turbine compressors, riblets promote earlier transition to turbulent flow, reducing skin friction by up to 18%, even under variable conditions [151]. Additionally, bio-inspired leading edge designs help suppress separation bubbles and reduce aerodynamic losses, especially at low Reynolds numbers, improving efficiency in compressor blades [152]. Recent research has also highlighted the growing role of artificial intelligence (AI) in turbomachinery aerodynamics, particularly in optimizing design processes, validating turbulence models, and enabling predictive maintenance [153]. One key development has been the use of Physics-Informed Neural Networks (PINNs), which have proven especially useful in simulating compressor cascade flowfields. PINNs outperform traditional CFD methods, particularly in inverse problems where boundary conditions are often incomplete [154]. These networks provide a robust alternative for turbomachinery designers, significantly improving flow field predictions and the overall design process. Further advancements have been seen in bio-inspired herringbone grooves and fish-scale-inspired structures, which have demonstrated success in reducing flow separation and pressure losses while optimizing aerodynamic efficiency. For example, at lower Reynolds numbers (Re = 1.3 \(\times\) 10\({}^{5}\)), herringbone grooves generate secondary flows and micro-vortices, reducing profile loss by 8.33% and improving the static pressure ratio by 0.55%.