# 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
End-wall and corner separation control--shape modification to reduce losses at critical regions  
The optimization of endwall designs has become a crucial strategy for reducing secondary flows and losses in compressor cascades, thus enhancing overall compressor efficiency. Various design modifications have been explored to improve aerodynamic performance. A landmark study in 2004 on bulb-shaped endwalls demonstrated their ability to amplify horseshoe vortices, counteracting passage vortices and achieving a 28% reduction in secondary losses. Further investigations found that co-rotating vortices, generated by filled modifications, reduced losses, while blunt fillets exacerbated them, emphasizing the need for precise geometric optimization [97]. Non-axisymmetric endwall profiling (PEWs) has also been widely studied for axial compressors. Research from Cambridge University demonstrated that PEWs improved exit flow by reducing losses and under-turning in the secondary flow region, while also suppressing stator hub corner stall in a six-stage high-pressure compressor by redirecting the low-momentum core of the horseshoe vortex. Although PEWs showed limited benefits in modern compressors with advanced 3-D blades, it still offered promise when combined with 3-D blade shaping to increase aerodynamic loading and efficiency [98]. CFD simulations supported these findings, demonstrating enhanced cross-flow on the endwall that aids in secondary flow migration and corner stall control. Further studies on stator endwall profiling in transonic compressors revealed a 1.8% increase in efficiency, although reverse flow at the casing increased under off-design conditions, highlighting the need for further optimization [99]. In 2009, another numerical study confirmed that optimizing the stator hub endwall led to a 1.8% efficiency increase by reducing hub-corner stall. However, it also induced greater reverse flow at the casing, which became more pronounced at off-design conditions. Optimizing the shroud endwall improved off-design performance, yielding a 0.03% efficiency increase at the design point. These results demonstrated that endwall profiling, when applied alongside 3-D blading in high-loaded stator compressors, could effectively control separation and improve component characteristics [100]. Research in 2011 focused on combining non-axisymmetric profiled endwalls with boundary layer fences, which reduced cross-flow and delayed corner separation, resulting in an 8% reduction in cascade losses at the design point, as supported by high-fidelity RANS simulations [101]. Advancements in 2015 and 2016 highlighted the potential of non-axisymmetric endwall contouring to reduce secondary flow losses and mitigate corner stall. Optimized designs resulted in significant reductions in secondary flows, improving cascade efficiency and addressing challenges posed by three-dimensional flow interactions. Studies using Wall-Resolved Large Eddy Simulation (LES) provided detailed insights into corner separation phenomena in a linear compressor cascade. These simulations, validated against experimental data, accurately predicted static pressure coefficients, total pressure losses and velocity profiles. The results emphasized the role of turbulent structures, such as aperiodic vortex shedding, and turbulent anisotropy in affecting flow conditions at corner separation points. LES proved effective in capturing unsteady corner separation and guiding the development of separation control methods, providing more detailed results than RANS, which, while useful for parametric studies, tended to overestimate corner separation [102; 103; 104; 105]. Figure 6 presents a topology of corner separation near the trailing edge of a axial compressor blade. Optimization tools like DLR AutoOpti [106] and the TRACE RANS [107] solver in 2017 showed that non-axisymmetric endwall contours in highly loaded compressor cascades reduced total pressure losses and improved outflow homogeneity.