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

Abstract

Abstract Though simple and fast, bulk-flow models (BFMs) for gas labyrinth seals (LSs) often predict the mass flow inaccurately. The BFM models 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 (Cr) and operating conditions on the prediction of LS mass flow, and then derives an updated kinetic energy carry-over coefficient (μ1i) to improve the accuracy of Neumann's leakage equation. μ1i 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 14-teeth on stator LS (length/diameter = L/D = 0.29) with clearance Cr = (1/733)D and operating at nominal supply (Pin) and discharge (Pout) 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 Cr, a gas supply pressure from 60 bar to 100 bar, and with various discharge pressures giving a pressure ratio (PR = Pout/Pin) 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 (μ1i) increases with respect to the seal radial clearance (Cr). μ1i shows a parabolic correlation with PR; at first, μ1i increases with a rise in PR from a low value; and then, a further increase in PR leads to a decrease in μ1i. The coefficient μ1i is only sensitive to the PR 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 μ1i, a function of the seal geometry and the PR condition. Integration of the new μ1i correlation into a BFM code improves its accuracy to predict LS mass flow rate, a 19% difference against test data reduces to within 6%. A TOS LS tested by Ertas et al. (2012, Rotordynamic Force Coefficients for Three Types of Annular Gas Seals With Inlet Preswirl and High Differential Pressure Ratio,” ASME J. Eng. Gas Turbine Power, 134(4), p. 4250301) serves to further validate the accuracy of the modified leakage model.