Fluid-structure interaction analysis of annular seals and rotor systems in multi-stage pumps

Annular seals play an important role in determining the vibrational behavior of rotors in multi-stage pumps. To determine the critical speeds and unbalanced responses of rotor systems which consider annular seals, a fluid-structure interaction (FSI) method was developed, and the numerical method was verified by experiments conducted on a model rotor. In a typical FSI process, rotor systems are modeled based on a node-element method, and the motion equations are expressed in a type of matrix. To consider the influence of annular seals, dynamic coefficients of annular seals were introduced into the motion equations through matrix transformation. The test results of the model rotor showed good agreement with the calculated results. Based on the FSI method proposed here, the governing equations of annular seals were solved in two different ways. The results showed that the Childs method is more accurate in predicting a rotor’s critical speed. The critical speeds of the model rotor were calculated at different clearance sizes and length/diameter ratios. Tilting coefficients of long seals were added to the dynamic coefficients to consider the influence of tilting. The critical speeds reached their maximum value when the L/D ratio was around 1.25, and tilting enhanced the rotor’s stability when long annular seals were located in either end of the shaft.