Theoretical Solutions for Dynamic Characteristics of Spiral-Grooved Liquid Seals

Abstract

ABSTRACTAnnular seals represent one of the solutions for controlling leakage in high-speed turbomachinery, especially in multistage centrifugal pumps. In this article, a theoretical analysis method for leakage rate and dynamic characteristics of spiral-grooved liquid seals based on the theory of Iwatsubo and Childs is proposed. Steady-state velocities and leakage rate are figured out first with the inertia term of the fluid within the seals. Subsequently, governing equations for the land part and the groove part including the axial momentum equation, circumferential momentum equation, and continuity equation are respectively built. A solution method for calculating the rotordynamic characteristics that has taken account of the circumferential velocity perturbation change with the axial location is developed by solving the first-order governing equations. Detailed comparisons between the experimental leakage rates and theoretical predictions show good agreement. Moreover, dynamic coefficients predicted by the proposed method are compared with the theoretical and experimental results of Iwatsubo. The results show that the predicted stiffness of the present solution method correlates well with the experimental evidence with an error of less than 35% in the given examples, which validates the analysis method developed in this article. The predicted accuracy of stiffness and damping coefficients has improved substantially compared to the accuracy of the solution method proposed by Iwatsubo.