# Review of Passive Flow Control Methods for Compressor Linear Cascades
## 2 Chronological Evolution of Linear Cascade  
Research on linear cascades in turbomachinery has evolved significantly over the decades, with foundational studies before 1970 laying the groundwork for understanding flow behaviours, loss mechanisms and the efficiency of cascade designs. Early investigations primarily focused on two-dimensional cascade flows, establishing fundamental principles that would guide subsequent advancements in compressor blade optimization. The principle of linear cascades can be considered to have emerged during World War II and developed afterward. Locating the exact primary publication can be challenging, with most experimental campaigns on linear cascades attributed to the National Advisory Committee for Aeronautics (NACA) [20] and disseminated in a series of publications called Wartime Reports [21]. One of these reports can be considered the first to describe experimental work on a linear cascade; titled \"Preliminary Experimental Investigation of Airfoils in Cascade\" [22], it focused on cascade arrangements of airfoils and examined aerodynamic performance factors like pressure distribution and airflow through the blades. This study became a critical early reference for cascade testing methods in compressors and turbines. It represented one of the first structured approaches to studying airfoil behaviour in cascades and provided data crucial to advancing blade designs in turbomachinery. The rudimentary experimental setup can be observed in Figure 1a. Subsequent technical reports on linear cascades followed. Another report from the same series, titled \"Systematic Two-Dimensional Cascade Tests of NACA-65 Series Compressor Blades at Low Speed\" [23], describes the 5-inch cascade installation at Langley, identifying it as a fully functioningsystem built in the 1940s and improved in the early 1950s. The Langley cascade is pictured in Figure 1b. By 1955, theoretical studies had identified three primary vorticity components in non-uniform fluid flow through turbine or compressor blade cascades: distributed secondary circulation due to flow curvature, trailing shed circulation resulting from spanwise variations along the blade, and trailing filament circulation caused by vortex stretching in blade wakes [25]. These principles applied to both cascades and isolated airfoil flows, providing a framework for subsequent research. That same year, [PERSON] [26] correlated experimental cascade data to explore variations in performance, proposing simplified rules for predicting losses and angles. However, the work also highlighted the need for further investigations into high Mach number effects and three-dimensional influences. Building on this foundation, [PERSON] and [PERSON] [23] developed theoretical loss relations based on wake characteristics, improving the prediction of loss coefficients and influencing blade design methods. In 1965, [PERSON] [27] explored the impact of boundary layer characteristics on cascade performance, highlighting differences between laminar and turbulent flows. The study revealed the role of clearance leakage and wall effects in creating complex three-dimensional flow behaviours and identified corner separation on the low-pressure surface of blades, worsened at high angles of attack due to adverse pressure gradients. During the same period, a study on stall propagation in circular cascades proposed a theoretical model to predict stall cell velocity and conditions for cell splitting [28]. In 1957, [PERSON] [29] analyzed compressible flows in high-speed cascade wind tunnels, examining the effects of Mach and Reynolds numbers. Concurrently, research on low-speed cascades established correlations between loss and velocity diffusion, showing that higher diffusion ratios increased stall risk by thickening wake momentum [30]. [PERSON] et al. [31] emphasized the role of dynamic loading parameters, such as blade camber and angle of attack, in optimizing compressor design.