## 1 Introduction  
Wind tunnel testing of linear cascades provides crucial experimental data to understand the aerodynamic behavior of compressor blades and to further enhance the overall performance of compressor systems. Moreover, linear cascade experimental campaign is relatively cheap compared to full-scale annular geometries as it allows rapid prototyping and uses cheaper, less complex manufacturing techniques. Nevertheless, it is necessary to obtain reliable results from experiments, meaning that the flow pattern in a linear cascade should correspond to the flow pattern inside a turbomachinery. Therefore, a Computational Fluid Dynamic (CFD) analysis of the test rig is required to establish a suitable configuration. Blade periodicity, which is a crucial factor for reproducing real turbomachinery fluid flow conditions, has been extensively studied in various sources. [PERSON] et al. [1] focused on the design of a linear cascade test rig for turbine components. Their research revealed that blade periodicity was obtained at first at two thirds of the axial chord length, while for full periodicity, further analysis that involved different angles of the tailboards was necessary. Another study by [PERSON] et al. [2] emphasized the sensitivity of tailboard angles as a significant factor influencing the periodicity of a cascade. Besides the tailboard angle, the outlet pressure also plays a crucial role in determining the position of shock waves. A comprehensive investigation of fluid flow periodicity under both steady-state and unsteady conditions was conducted by [PERSON] and [PERSON] [3]. Their investigation specifically focused on a transonic cascade and revealed that unsteady pressure reflections on the tailboards play a significant role and must be taken into account during wind tunnel testing. Furthermore, the bottom tailboard was found to cause more pronounced unsteady reflections compared to the upper tailboard [4]. This finding highlights the importance of considering the specific characteristics and effects of each tailboard to accurately analyze fluid flow periodicity in transonic/supersonic cascades [5; 6; 7; 8]. In [9], [PERSON] investigated the impact of side cascade walls on periodicity and developed a parametric model that encompassed the entire geometry, including the inlet/outlet side walls and blade row. The study findings indicated that the outlet wall angles exerted the most significant influence on the periodicity of the test rig. [PERSON]'s study [10] presents a series of numerical analysis using URANS (Unsteady Reynolds-Averaged Navier-Stokes) and LES (Large Eddy Simulation) models. The simulations were performed based on a linear compressor cascade and validated against the experimental results obtained by [PERSON] [11]. When comparing the two simulation approaches, it was found that the results obtained by LES were closer to the experimental data, while the RANS approach tended to overestimate the occurrence of corner separation. Despite this discrepancy, the RANS approach still holds value in the industrial sector, providing a reasonably accurate representation of the mean trend relationship with experimental data [12]. While RANS simulations may not attain the same level of precision as LES/DNS methods, they are standing as a practical and valuable tool for engineering applications. For this research purpose, RANS models offer valuable insights into the overall flow structure of linear cascades, yielding reliable predictions [13; 14]. Additionally, when coupled with essential components such as grid resolution, numerical schemes, and turbulence models, the accuracy of a model can be significantly enhanced. [PERSON]'s paper [11] explores the influence of incidence angles ranging from \(-2^{\circ}\) to \(6^{\circ}\) on pressure and losses. This study revealed that the maximum total pressure loss occurred at an incidence angle of \(4^{\circ}\), which resulted in a large separation bubble in the corner region.