Two-Way Coupled Shooting Analysis of Fluid Force in the Annular Plain Seal and Vibration of the Rotor System

In turbomachinery, the rotor dynamic (RD) fluid force generated in a fluid element, by the interaction between the shaft behavior and the fluid flow, is one of the causes of the shaft behavior and has a great influence on the stability of the turbomachinery. In order to improve the reliability of turbomachinery, it is important to analyze the dynamical behavior considering the mutual influence of the RD fluid force and shaft motion. In this paper, the two-way coupled analysis between the fluid force in the annular plain seal and the vibration of the rotor system was expanded by introducing the shooting method in it. The frequency response was obtained, and the onset speed of instability (OSI) was predicted effectively. The influence of parameters on the OSI was investigated and discussed. Then, the numerical results obtained by this two-way coupled shooting analysis was compared with the experimental results and the validity of the analysis was confirmed. The influence of disturbance on the error of predicted OSI was also discussed. The transition region to instability was introduced for the predicted OSI using the spectral radius, and the error between the numerical and experimental results of the OSI was explained. As a result, the two-way coupled shooting analysis can predict the OSI values in various situations of two-way coupled system more effectively than the direct numerical simulation. Also, the robustness of stability for the predicted OSI can be evaluated simultaneously by investigating the spectral radius and defining the transition region to instability appropriately.