A Computational Fluid Dynamics Modified Friction Factor and Leakage Model for an Improved Bulk-Flow Analysis of Labyrinth Gas Seals

Abstract

Bulk-flow predictive models (BFM), though simple and fast, often fail to accurately predict the performance of gas labyrinth seals (LSs). In this work, a Computational Fluid Dynamics (CFD) analysis quantifies the effects of LS tip clearance (Cvr) and operating conditions on the circumferential direction friction factors (fvr, fvs) at the rotor and stator surfaces, as well as on the kinetic energy carry-over coefficient (µv1i) for mass flow prediction. A fourteen teeth on stator LS seal (L/D=0.29) with clearance Cvr=1/733 D is selected for analysis. The analysis models the seal with a fine mesh of a few million nodes and a commercial CFD code calculates the flow field for the nominal operating conditions, includes wide changes in clearance, 80% to 200% of the nominal Cvr, shaft speed from 5 krpm to 15 krpm (58 m/s ~173 m/s), inlet pre-swirl velocity varying from 0% to 72% of rotor surface speed, a gas supply pressure ranging from 60 bar to 100 bar, and along with various discharge pressures producing a pressure ratio (PR = Pvout/Pvin) ranging from 0.40 to 0.85. The rotor surface friction factor fvrθ is independent of the changes in clearance (Cvr) or the inlet circumferential velocity pre-swirl ratio; whereas an increase in rotor speed or in pressure ratio (PR) decreases frθ. On the other hand, an increase in rotor speed, pressure ratio and inlet preswirl ratio decreases fsθ, the stator friction factor. Besides, fvsθ increases with an increase in radial clearance. Further, fvrθ and fvsθ are only sensitive to the pressure ratio, but not to the magnitude of either the supply pressure or discharge pressure. The kinetic energy carry-over coefficient (µv1i) increases with respect to the seal radial clearance (Cvr); whereas µv^1i shows a parabolic correlation with the pressure ratio PR. µv1i is only sensitive to PR, and not to the magnitude of either the supply pressure or the discharge pressure. Furthermore, based on the CFD derived results, this work presents a modified friction factor model, Rem f n = (where Re is the flow Reynolds number)^1 , as well as a modified kinetic energy carry-over coefficient model, both quantifying the effect of seal geometry and operating conditions. An independent case analysis serves to validate the model; and the modified BFM does improve the prediction of the direct stiffness (maximum discrepancy decreases from 320% to 70%), direct damping (discrepancy decreases from 90% to 50%), and mass flow rate (discrepancy decreases from 14% to 2%).The above coefficients and flow agree well with both CFD and experimental results. (Note: this dissertation is organized based on the author’s previous publications and reports during his PhD study; and the format follows American Society of Mechanical Engineers (ASME) journal publications format). 1 n = 0.079, m = -0.25 for the classical Blasius friction factor model, strictly valid for smooth surface pipelines