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.
Shaft vibration caused by rotor dynamic (RD) fluid force generated by the seal clearance flow has caused several problems. Because such vibration is a coupled phenomenon of clearance flow and shaft vibration, a coupling analysis is essential to solve these problems. In this study, a two-way coupling fluid–structure interaction (FSI) analysis of the seal clearance flow and shaft vibration of a rotor system was conducted and verified through experiments. The rotor system used was a vertical, flexible rotor system with a plain annular seal. In the numerical analysis of the seal clearance flow, the continuity equation and momentum equations, which were averaged across the film thickness, were numerically solved. To suppress the numerical instability, which is unique to the coupling analysis, and improve its numerical stability, a method of successively correcting pressure and shaft acceleration values was adopted so that the continuity equation and rotor equations of motion could be satisfied at every time step. By performing the coupling simulation, the frequency response characteristics of whirling amplitude and leakage flow were investigated. In regard to the stability of the system, the rotational speeds at which self-excited vibration occurs (onset speed of instability: OSI) in its increasing condition and ceases (onset speed of dropdown: OSD) in its decreasing condition were investigated. The coupling analysis results reasonably agree with the experimental results, which demonstrate the validity of the analysis method. In addition, the influence of static eccentricity and whirling amplitude on stability (OSI and OSD) was clarified, which are useful in the design stage of turbomachinery.
In recent years, along with demands for higher rotational speed and higher efficiency in the rotating machinery, shaft vibration has been a serious problem. One of the causes of this shaft vibration problem is the rotor-dynamic fluid force (RD fluid force) generated by working fluid at turbo machinery parts. It is important in the design stage of rotating machines to estimate the RD fluid force and predict the stability of the rotor system accurately. Therefore, many researches have been conducted to clarify the characteristics of RD fluid force. One of the traditional methods for analyzing the RD fluid force is the bulk flow theory. However, in conventional bulk flow analysis, it is assumed that the amplitude of the shaft displacement is sufficiently smaller than the clearance. Therefore, influence of nonlinearity in the large amplitude whirl may not be included in this analysis. Accordingly, this paper focuses on constructing a coupled analysis of the fluid force and the shaft vibration that describes each behavior of fluid and shaft at the same time. By using this coupled analysis, the interaction between fluid and shaft systems can be taken into consideration more accurately. Regarding the fluid region, finite difference method is used for bulk flow continuity and momentum transport equations. Incompressible fluid is assumed, and the pressure field is calculated by solving the Poisson equation of pressure. In solving the Poisson equation of pressure, a specific problem for this coupled analysis relating unknown shaft acceleration arises. In this paper, this problem is solved by obtaining the approximated acceleration based on Newmark-beta technique. This coupled analysis is conducted for a simple flexible rotor system with annular plain seal, and the frequency response is obtained. First, the case with isotropic support stiffness and with no gravitational force is considered. Then, the case with the constant load and the case with anisotropic support stiffness are analyzed. These analytical results show that both the constant load and structural anisotropy may affect the stability of the rotor system. As a result, the usefulness of the proposed coupled analysis procedure of the fluid force and the shaft vibration is validated.
In turbomachinery, the rotor dynamic (RD) fluid force generated in a fluid element is one of the causes of shaft vibration. RD fluid force is caused by the interaction between shaft vibration and fluid force, and its precise prediction for various rotor’s orbit is difficult. This study performs a two-way coupled analysis of the fluid flow in the annular plain seal and shaft vibration using the shooting method. The frequency response is obtained and compared with that obtained from a direct numerical simulation of the coupled system, and the validity of the analysis is confirmed. The onset speed of instability is effectively and accurately obtained using the two-way coupled analysis with the shooting method, and the effects of the parameters on it are investigated.
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