# Review of Passive Flow Control Methods for Compressor Linear Cascades
## 2 Chronological Evolution of Linear Cascade
### Simulation Techniques  
Computational simulations play a crucial role in analyzing and optimizing passive control methods in compressors. Various numerical techniques are employed to evaluate their effects on flow behaviour, pressure losses, and efficiency improvements. In this context, understanding boundary layer transition and turbulence modelling in compressor cascades is essential. [PERSON] et al. [162] research focuses on the impact of Reynolds number and free-stream turbulence on the transition location of the suction surface in controlled diffusion airfoils. Through experiments conducted in a high-fidelity cascade facility, Reynolds numbers ranging from 0.7 to a specified value and turbulence intensities from 0.7% to 4% were examined. The findings revealed that at low turbulence levels, transition occurs within a laminar separation bubble around 35-40% of the chord. However, as turbulence increases (Tu > 3%), transition shifts upstream, with bypass transition occurring as early as 7-10% of the chord at Tu = 4%. These results highlight the significant influence of early bypass transition induced by turbulence on velocity distributions in compressor blades designed for high Reynolds numbers. To ensure accuracy, the experimental results were validated against theoretical predictions using the MISES code. In the realm of computational fluid dynamics, LES has emerged as a powerful tool for predicting turbulent flows in axial compressors. Comparative studies have shown that LES captures unsteady flow characteristics near the casing with greater accuracy than traditional Unsteady Reynolds-Averaged Navier-Stokes (URANS) models. Despite its high computational cost, LES is considered a key tool for advancing turbomachinery simulations, particularly in predicting unsteady flow phenomena critical for optimizing compressor performance and design [163]. Turbulence modelling has continued to evolve, as evidenced by a 2016 evaluation of seven turbulence models for their ability to predict corner separation in compressor cascades. The Reynolds Stress model and V2-f turbulence model were found to be the most accurate in capturing the complex behaviour of corner separation. This research highlights the increasing anisotropy of turbulence, particularly in corner separation regions, and underscores the need for advanced turbulence models to accurately simulate these complex flow phenomena, which are crucial for optimizing compressor design [164]. Further advancements in supersonic compressor cascade optimization were demonstrated, where airfoil reshaping resulted in a 25% reduction in loss coefficient and a 6.5% improvement in static pressure ratio. However, the research also highlighted the challenge of managing shock wave losses, emphasizing the need to balance compression efficiency with shock management. Optimization of the forepart geometry played a pivotal role in performance improvement, contributing 95% of the overall enhancement, showcasing its critical role in compressor performance within practical design constraints [165]. Additionally, high-fidelity simulations such as wall-resolved LES are gaining traction for predicting laminar separation and airfoil losses in compressor cascades. Revisiting the 1950s NACA low-speed cascade experiments using modern LES techniques enabled detailed predictions of transition Via laminar separation, offering a powerful tool for compressor airfoil design and optimization [166]. The study of corner separation has progressed with comparative analyses of LES and RANS methods. While LES proved more accurate, RANS models remain a computationally efficient alternative for industrial applications. The research emphasized the critical role of incidence angle and boundary layer thickness in corner separation, highlighting the importance of accurate turbulence modelling to capture these complex flow behaviours in compressors [167]. Advanced simulation techniques, such as Delayed Detached Eddy Simulation (DDES), have also been applied to study corner separation in PVD cascades.