Stability analysis of a flexible rotor partially filled with two liquid phases

This paper deals with the dynamic stability of a flexible rotor partially filled with two liquid phases. On the basis of the Navier-Stokes equations for the incompressible flow, a two-dimensional analytical model is developed for fluid motion. The perturbation method is employed to obtain the linearized Navier-Stokes and continuity equations. According to the boundary conditions of fluid motion, the fluid force exerted on the rotor is calculated. Then, combining the structural static equilibrium equation with the equations describing the fluid forces, the whirling frequency equation of the system, which is used to predict the system stability, is obtained. The stability and critical spinning speed of the coupled fluid-structure system are analyzed. To demonstrate the validity of the developed model, the analysis results are compared with the results reported in the previous study. The two analysis results are in good agreement. Finally, the effects of some main parameters on system stability are discussed.