Quasi-Steady Solution of Rotor-Dynamic Forces Generated by Discharge-to-Suction Leakage Flows in Centrifugal Pumps

In order to investigate the flow-induced vibration in the impeller clearance of centrifugal pump, and make the dynamic prediction of centrifugal pump rotor system, the flow dynamic model is put forward in the present study based on the flow characteristics in the impeller clearance. The impeller clearance rotor-dynamic force model is established based on Muszynska model and gap annular flow dynamic model. And the coefficient in this model is confirmed by quasi-steady solution of the impeller clearance flow. After the confirmation of the rotor-dynamic force model, the non-linear stability and bifurcation of the Jeffcott rotor system under the rigid support is analyzed under condition of the rotor-dynamic force. The impact of the unbalance quantity to the impeller-rotor system is discussed. The research shows that complicated alternation by turns of Hopf bifurcation and period doubling bifurcation appears on the process of spin speed rising. As the fluid pressure and rotor flexibility increasing, the fluid-induced vibration in the clearance of centrifugal pump impeller becomes a very important factor to the instability of centrifugal pump rotor system. The clearance structure and the flow feature lead to complexity of the equations of fluid dynamics (J. J. Moore, et al, 2001). And it is difficult to describe the rotor-dynamic force by analytical expression, resulting in great difficulty for the dynamics analysis. The impeller clearance can be divided into shroud passage and wearing seal based on the structure and flow feature (C. E. Brennen, et al, 2006). The bulk flow model is mainly used for the wearing seal, which is based on film assumption (D. W. Childs, 1991). The Black-Childs model (H. F. Black, 1969; D. W. Childs, et al, 1985) and Muszynska model (D. E. Bently, et al, 1988) both are given on this, and were generally applied to the dynamic analysis of rotor-seal system. But for the shroud passage, its physical dimension of channel section is not constant; and the velocity magnitude and direction between the sections are also different. So the unit radius and axial velocity cannot be used to describe the flow in it, and the existing rotor-dynamic force model of the channel fluid is limited to the shroud passage flow. Some scholars combined CFD method and hydrodynamic lubrication theory to solve the time-averaged Navier-Stokes equations of the clearance flow (R. Barrio, et al, 2008, J. Gonzalez, et al, 2006, J. Gonzalez, et al, 2006), and to get the fluid-induced vibration characteristics of the impeller clearance flow. In this paper, a rotor-dynamic force model of the impeller clearance is given based on the clearance flow feature. A quasi-steady solution is given to determine the dynamic force coefficient. Apply this method to the flow field in different whirl ratio and rotor speed, to get the dynamic coefficient with least square method. Under the rotor-dynamic force, the nonlinear stability and bifurcation problems of the Jeffcott rotor system with rigid support are also studied.