## 1 Introduction  
Corner separations always occur at the corner between the suction surface and the endwall, and are inherent flow features in compressors [1]. With the increased compressor loading or incidence angle, this 3D separation phenomenon can lead to the corner stall, thus contributing greatly to blockage and passage losses; therefore, it is considered as one of the most important factors limiting the loading capacity of a compressor. In the past few decades, many researchers have focused on understanding the mechanism of corner separation by experiment [2,3] or advanced numerical simulation methods (Delayed detached-eddy simulation (DDES) [4], hybrid LES/RANS [5], and Large eddy simulation (LES) [6]). The onset of corner separations can be influenced by many parameters, such as compressor loading, inflow boundary layers, and real blade geometrical parameters including pitch-chord ratio, aspect ratio, and blade fillet. Many studies have been done to investigate the relationship between these parameters and the corner separation. The pitch-chord ratio is the inverse of the solidity, which is an important parameter for the loading assessment. In the mid-20 th century, [PERSON] et al. [7] and [PERSON] et al. [8] identified that the pitch-chord ratio (also solidity) is an important feature in compressor design. It strongly affects the flow turning angle, blade loading, and also the available range of incidence angles. In the past decades,lower pitch-chord ratio in compressors has become a routine design, as described by [PERSON] et al. [9]. Keeping the chord length constant, a lower pitch-chord ratio means an increased number of blades, which leads to the increased compressor weight, higher fuel consumption, and more NOx emissions. The advanced aero engines now demand a higher pitch-chord ratio in the compressor in order to reduce the number of blades. A higher pitch-chord ratio creates larger separation zones, including corner separation in blade passages, which leads to more serious consequences, such as increased passage blockage, considerably higher pressure loss, and reduced compressor efficiency. [PERSON] et al. [10] conducted a numerical study for the pitch-chord ratio effect on high Mach number flow regimes, which is more typical for modern compressors. This study concludes that at high positive incidence, the higher pitch-chord ratio cascade experiences more losses as compared to the lower pitch-chord ratio cascade. This can be explained by the higher loading endured for the higher pitch-chord ratio profile which also decreases the stability range of the cascade. In the earlier axial compressor design, high aspect ratios were characterized to make the flow within the blade-row to be two-dimensional. The current trend towards the designing of low aspect-ratio airfoils in pursuit of higher stage loading can increase the three dimensionality of the flow within the entire blade-row. By lowering the aspect ratio an increase in stall pressure limit, operating range, and peak efficiency has been observed by [PERSON] et al [11]. Some research has also been done to investigate the effects of blade fillet on three-dimensional separations. [PERSON] et al. [12] have considered the effects of blade fillet geometry on the three-dimensional separation in compressor blade rows. The effects of the fillet radius were found to be of secondary importance. The effect of removing fillets was found to be detrimental by increasing the hub losses by 18%. Increasing the fillet radius to 10% of the chord was found to cause a small decrease in hub losses. The geometry of the leading edge fillet was found to have no effect on losses, even when it was extended out of the hub boundary layer. [PERSON] [13] has reported that by varying the fillet radius, the separation size, as well as the blade losses, were both influenced. Furthermore, the lowest losses have occurred with no fillet, while the highest losses have occurred with the largest fillet tested (\(r_{\text{fillet}}/c=15\%\)). [PERSON] et al.