Effect of Liquid Viscosity on Instability of High-spinning Partially-filled Shell Rotors

In this study, the instability of spinning cylindrical shells partially filled with viscous liquid is investigated. Based on the Navier–Stokes equations for the incompressible flow, a 2D model is developed for liquid motion at each section of the cylinder. The governing equations of the cylinder vibrations are obtained based on the first_order shear deformable shell theory. The nonpenetration and no-slip boundary conditions of the flow on the wetted surface of the cylinder relate the liquid motion to the shell vibrations. Also the liquid pressure exerted on the cylinder wall combines the vibrations of the rotary cylinder to the liquid motion. By using the obtained coupled liquid-structure model, the instability conditions of the system are determined. The governing parameters of the rotor vibrations are introduced and their influence on the stability boundaries of the rotor is studied.