Gas Labyrinth Seals: Improved Prediction of Leakage in Gas Labyrinth Seals Using an Updated Kinetic Energy Carry-Over Coefficient

Though simple and fast, bulk-flow models (BFMs) for gas labyrinth seals (LSs) often predict an inaccurate mass flow as they rely on classical Neumann’s equation model to characterize the flow through a labyrinth tooth. Presently, a Computational Fluid Dynamics (CFD) analysis quantifies the effects of tip clearance (C_r) and operating conditions on the prediction of labyrinth seal mass flow, and then derives an updated kinetic energy carry-over coefficient (µ_1i) to improve the accuracy of Neumman’s leakage equation. µ_1i is a function of the seal tip clearance (Cr), the tooth pitch, and the total teeth number; but it does not depend on the seal supply or discharge pressures. The analysis selects a fourteen teeth on stator labyrinth seals (Length/Diameter=L/D=0.29) with clearance C_r=1/(733 D) and operating at nominal  supply (P_in) and discharge  (P_out) pressures equal to 73 bar and 51 bar, respectively, and at a rotor speed of 12 krpm (surface speed=138 m/s.). The CFD produces flow fields for LSs with a clearance varying from 80% to 200% of the nominal C_r, a gas supply pressure from 60 bar to 100 bar, and with various discharge pressures giving a pressure ratio (PR=P_out /P_in) ranging from 0.40 to 0.85. The numerous predictions deliver the mass flow as well as the bulk-flow velocities and cavity pressures within the seals. The kinetic energy carry-over coefficient (µ_1i) increases with respect to the seal radial clearance (C_r). µ_1i shows a parabolic correlation with PR; at first µ_1i increases with a rise in PR from a low value; and then a further increase in PR leads to a decrease in µ_1i. The coefficient µ_1i is only sensitive to the pressure ratio and not to the magnitude of either the supply or discharge pressures. Lastly, for use with Neumann’s leakage model, the CFD predictions produce an updated µ_1i, a function of the seal geometry and the PR condition. Integration of the new µ_1i correlation into a BFM code improves its accuracy to predict LS mass flow rate, a 19% diference against test data reduces to just 1%. A TOS LS tested by Ertas et al. (2012) serves to further validate the accuracy of the modified leakage model.