Theoretical Solutions for Dynamic Characteristics of Liquid Annular Seals with Herringbone Grooves on the Stator Based on Bulk-Flow Theory

Liquid annular seals are primarily used to control the leakage in high-speed turbomachinery, especially in nuclear and petrochemical pumps. In this paper, a theoretical analysis method for dynamic characteristics of liquid seals with herringbone grooves on the stator is proposed based on bulk-flow theory. Steady-state velocities and leakage rates within the upstream and downstream spiral parts and the middle plain part taking account of the pumping effects are figured out first with the inertia term of the fluid within the whole seal. Then, the dynamic characteristics of the whole seal are solved based on Childs’ finite-length solutions and verified by comparing with experimental hydraulic forces. Moreover, characteristic coefficients and instability parameters of the herringbone-grooved teeth-on-stator (TOS) seals and teeth-on-rotor (TOR) seals of the same size under different pressure differences are predicted and compared in detail. The influences of the lengths of constituent parts on the dynamic characteristics and instability parameters of the model seals are theoretically investigated. The results show that the stability of the TOS seal is much better than that of the TOR seal under most operating conditions. And the lengths of the middle plain part significantly affect the dynamic characteristics and the stability parameter