Analysis Method of Nonsynchronous Vibration and Influence of Tip Clearance Flow Instabilities on Nonsynchronous Vibration in an Axial Transonic Compressor Rotor

The relationship between the tip clearance flow (TCF) and the blade vibration in the lock-in region was numerically investigated on a transonic rotor. Both the bending (1B) and torsional (8th) modes were analyzed under 0 ND. The time marching method and a single-passage model were used, which were verified by citing and comparing with the results in references. The phase of the TCF (referring to the phase difference between the unsteady pressure caused by the TCF and the blade vibration) changed with the frequency ratio in the lock-in region. The strength of the TCF was influenced slightly by the blade vibration amplitude. A separation method of the unsteady pressure caused by the TCF and the blade vibration was developed and verified at different conditions. The unsteady pressure of nonsynchronous vibration (NSV) was separated into the components of the TCF and the blade vibration under the 1B and 8th modes. The unsteady pressure component of the TCF changed little with the vibration amplitude and mainly existed in the tip area. The unsteady pressure component of the blade vibration was larger at part spans and its distribution depended on the modal shape and the vibration amplitude. The unsteady pressure components of the TCF and the blade vibration determined the aerodynamic work/damping in the lock-in region. The aerodynamic work components of the TCF and the blade vibration increased linearly and at a rate of the square with the vibration amplitude, respectively. TCF was dominant in the initial stage of vibration. With the vibration amplitude increasing, the aerodynamic work done by the unsteady pressure component of the blade vibration gradually caught up. The aerodynamic damping of the TCF changed with the phase of the TCF. TCF provided positive damping at some phases and negative damping at other phases. In the initial stage of vibration, the system was stable at the phases TCF providing positive damping and unstable at the phases of negative damping. NSV occurred only when TCF provided negative damping and the unsteady pressure component of the blade vibration provided positive damping. If the aerodynamic damping of the blade vibration was negative, the vibration would be enlarged until failure. Regardless of other damping forms, the maximum amplitude of NSV can be obtained by calculating the balance of the aerodynamic work. For the 8th mode, the limit amplitude under 0 ND was 0.0926%C, which corresponded to vibration stress of about 60 MPa.