Lock-in phenomenon of tip clearance flow and its influence on aerodynamic damping under specified vibration on an axial transonic compressor rotor

In this study, the lock-in phenomenon of Tip Clearance Flow(TCF) instabilities and their relationship to blade vibration are investigated numerically on an axial transonic rotor with a large tip clearance. The capabilities of simulating instability flow and lock-in phenomenon are verified on a transonic rotor and a NACA0012 airfoil by comparing with the test data, respectively.The lock-in phenomenon is first numerically confirmed that may occur to TCF instabilities when its frequency is close to the blade vibration frequency. The lock-in region becomes wider with the vibration amplitude increasing, and it is also affected by modal shapes. For the rotor at the simulation conditions in this study, the bending mode results in a wider lock-in region than the torsional mode. In the lock-in region, the phase difference between the Tip Clearance Vortex(TCV)and the blade vibration changes with the flow condition and the frequency ratio of the blade vibration and the TCV instabilities. The frequency of the TCV instabilities reduces with the mass flow decreasing. Therefore, reducing mass flow and increasing frequency ratio have similar effects on the TCV phase, which causes a significant variation on the unsteady pressure amplitude in the blade tip area. Thus, the aerodynamic damping changes significantly with the TCV phase. The aerodynamic damping displays a nonlinear relationship with the vibration amplitude, and it changes from negative to positive with the vibration amplitude increasing at the same frequency ratio. The negative damping is mainly provided by the tip area of the blade. For unlocked conditions, the period of the TCF instabilities fluctuates over time, and it cannot be directly separated by their frequency features. Inter Blade Phase Angle(IBPA) also has an important influence on the feature of the TCV instabilities. The occurrence of frequency lock-in also requires ‘‘appropriate” IBPA. For the examined working conditions, the frequency lock-in occurs under 0 ND(Nodal Diameter), but not under 8 ND. However, no matter 0 ND or 8 ND, the phase of TCV always locks onto the IBPA at the examined conditions.