Bi-global stability analysis on flow separation of two-dimensional compressor cascade

Abstract

Bi-Global stability analysis (BGSA) is employed to assess the flow separation (FS) in two-dimensional compressor cascades, aiming to investigate the unstable phenomena and underlying mechanisms. The prediction results are correlated with the separation bubble (SPB) on suction surface (SS) or the trailing edge vortex (TEV) and exhibit good agreement with the unsteady numerical simulation (UNS), thereby confirming the instability of these two flow structures. Meanwhile, the prediction results can also partially reflect the initiation of unsteady blade loading. The perturbation distributions obtained from the eigenvectors corresponding to the physically meaningful eigenvalue, reveal two primary unstable regions: one located in the wake region and another coinciding with the SPB. With the increase of incidence angle (IA), the growth rate (GR) of small perturbations transitions from negative to positive, corresponding to the flow state shifting from stable to unstable. Additionally, the inception position of eigenmodes on SS moves upstream until it reaches the leading edge (LE) of the blade. The velocity magnitude distributions in the circumferential direction were further analyzed, demonstrating good agreement with predicted perturbation distributions, and suggesting that the K-H instability mechanism contributes to unstable phenomena. In the analysis of a two-passage flow domain, it is further observed that there exists a time delay in the vortex shedding within the wake, which is not evident at the single-passage condition.