# Review of Passive Flow Control Methods for Compressor Linear Cascades
## 2 Chronological Evolution of Linear Cascade
### Simulation Techniques
DDES provides more accurate predictions of corner separation compared to RANS models,offering deeper insights into vortex structures and turbulence characteristics, which have significant implications for compressor design improvements [168]. Modifications to the Shear Stress Transport (SST) turbulence model, commonly used for corner separation predictions, have improved its accuracy. Adjustments for streamline curvature, Menter's production limiter, and the Kato-Launder production term were tested, revealing that while the original SST model was effective at low incidence angles, modifications--such as introducing helicity to account for energy backscatter--improved predictions at larger corner separations. These modifications enhanced accuracy, rivalling the Reynolds Stress model while offering better computational efficiency and robustness [169]. Research on separated flow over compressor blades has shown that higher Reynolds numbers promote laminar separation bubble (LSB) formation, which leads to turbulent eddies and transition. For example, the V103-F front-loaded blade demonstrated a 32.3% reduction in profile loss due to superior momentum exchange and the suppression of LSB formation [170]. Additionally, DDES has been used to study corner separation in low-speed axial compressor stators, revealing the critical impact of high turbulence and anisotropy in the corner region, which is essential for informing design improvements to mitigate separation issues [171]. Optimization of transonic cascades has seen significant progress through multi-objective optimization techniques such as the Non-Dominated Sorting Genetic Algorithm (NSGA II). This approach achieved performance improvements by optimizing camber line and thickness distribution, resulting in a 22% reduction in the total pressure loss coefficient and broadening the operational range of the cascade [172]. Further optimization Via Pareto front techniques revealed that low-loss profiles feature flatter camberlines, while high-pressure profiles are more cambered. This approach led to efficiency gains of up to 29% and a pressure ratio increase of 5.9%. At Mach numbers 1.45 and 1.58, loss reductions of 26.4% and 25.5% were achieved, surpassing results from previous studies [173]. In 2024, high-fidelity simulations of shock-boundary layer interactions in transonic cascades provided valuable insights into the complex dynamics of shock oscillations and their impact on cascade performance. These simulations, offering a level of accuracy far beyond lower-fidelity models, enable better predictions of performance and stability in high-pressure environments. Large Eddy Simulations further enhanced the understanding of shock wave/boundary layer interactions (SBLI), revealing the formation of large-scale vortex structures during boundary layer separation and shedding light on the transition mechanisms that dominate these interactions. Additionally, the introduction of the Partial Average Fluctuation Velocity (PAFV) model for analyzing SBLI in cascade and transonic compressor flows demonstrated superior accuracy compared to traditional models like k-\(\omega\), SST, and SA-neg. The PAFV model effectively controls turbulence viscosity near shock waves, making it a promising candidate for transonic compressor flow analysis [174; 175; 176].