The flow phenomenon of rotating instability (RI) and its induced non-synchronous vibrations (NSV) in the last stage have gradually become a security problem that restricts the long-term flexible operations of modern large-scaled low-pressure steam turbines. Especially, if one structural mode of the last stage moving blade (LSMB) is excited, significant blade vibrations may potentially lead to high-cycle fatigue failure. A loosely coupled computational fluid dynamics reduced model with prescribed blade vibrations has been established to investigate NSV of the LSMB and the potential lock-in phenomenon under low-load conditions. Firstly, calculations with reduced multi-passage domain have been verified by comparing with the results of the full-annulus one, and an appropriate reduced domain is determined. Secondly, a set of calculations by controlling blade vibration parameters indicate that lock-in phenomenon between RI frequency and blade vibration frequency may occur when nodal diameters of cascade vibrations is coincident with the wave number of RI. Furthermore, dynamic modal decomposition technology has been employed to identify the unsteady pressure field around the blade surface and to reveal the interaction relationship between the flow modes of RI and vibration-induced pressure disturbance. Finally, the blade response evaluation based on harmonic analysis shows that in NSV, the global maximum dynamic response level of locked-in case is nearly 20 times than that of unlocked one.
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