Effect of annular seal on the lateral-axial bi-direction coupled dynamic characteristics of a multi-stage pump wet rotor

Because of the increasingly rigid and complex operating conditions for multi-stage pumps, the annular seal is playing an important role in determining the dynamic characteristics of a rotor system. The annular seal can prevent fluid leakage to ensure that the pump system can satisfy the design requirements, such as the head and efficiency. However, the fluid-induced force that is caused inside the annular seal by the pressure reduction and nonconcentric motion directly acted on the rotor system, which presents transient characteristics with a variation in the operating conditions. Based on the Euler angle transformation and the finite element method, the differential equations of motions for impeller and shaft were determined in this study, and the coupled effects, including the fluid-induced force of the annular seal and multiple axial forces, were considered. These equations of motions and coupled effects were conducted to investigate the effect of the annular seal on the lateral-axial bi-direction coupled vibration for a multi-stage pump rotor system. Finally, the lateral-axial bi-direction coupled vibration model for a multi-stage pump wet rotor was integrated with the matrix operation,and the corresponding coupled transient dynamics were solved using the Newmark method. The changing rules of the coupled vibration characteristics and fluid-induced force were mainly investigated for different sealing lengths, pressure drops, and clearances. The calculated results imply that the influence of the annular seal on the Lomakin effect for rotor lateral vibration becomes increasingly obvious with increasing length and pressure drop and with decreasing clearance. The convergence rate for the lateral vibration is observed to be faster than that for the axial vibration, and the vibration frequencies for the lateral-axial bi-direction presents different features. Furthermore, the fluid-induced force between the sealing lengths presents a nonlinear relation, whereas that between the pressure drop and clearance exhibits a linear relation.