A theoretical model for nonlinear orbital motions of rotors under fluid confinement

摘要

In previous papers Antunes and co-workers developed a the-oretical model for nonlinear planar motions of rotors under fluid confinement using simplified flow equations on the gap-averaged fluctuating quantities. The nonlinear solution obtained was compatible with linearised solutions for the same problem and showed an encouraging qualitative agreement between the non-linear theory and preliminary experimental results. following a similar aproach, the nonlinear theoretical model was extended to cope with orbital rotor motions and develop an exact formulation for the dynamic flow forces. Numerical simulations of the nonlinear rotor-flow coupled system are presented and compared with the linearised model. These yield similar results when the eccentrictiy and the spinning velocity are low. However, if such conditions are not met, the qualitative dynamics stemming from the linearised and nonlinear models are quite distinct. Preliminary experimetnal results also indicate that the nonlinear flow model leads to better predictions of the rotor dynamics when the eccentricity is significant, when approaching instability and for linearly unstable regimes.