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

Abstract

The BFM models rely on classical Neumann's equation model to characterize the flow through a labyrinth tooth. Presently, a 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. The analysis selects a 14 teeth on stator LS with clearance Cr=(1/733)D and operating at nominal supply pressure Pin=73 bar and discharge pressure Pout=51 bar, and at a rotor speed of 12 krpm. 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 the 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. µ1i increases with respect to the seal radial clearance (Cr). µ1i shows a parabolic correlation with PR. The coefficient µ1i 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 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%.

Nonuniform Clearance Effects on Pressure Distribution and Leakage Flow in the Straight-through Labyrinth Seals

“…The definition is shown in Total pressure drop is an important characterization of the labyrinth seal. For the whole labyrinth seal, the pressure load of labyrinth seal Δψ seal is defined as the pressure coefficient difference between the inlet and the outlet, as shown in Equation (6). For a single stage of the labyrinth tooth, the pressure load of labyrinth tooth Δψ i is defined as the pressure coefficient difference between the front and rear tooth cavity, regarded as the contribution to the total pressure drop, shown in Equation (7).…”

“…Hu et al [5] illustrated that flow resistant characteristics of straight-through labyrinths were related to the ratio of equivalent diameter (double sealing clearance) to seal length. Wu and Andrés [6] found cavity pressure reduced, but seal leakage rose with the increase of sealing clearance. Wu and Andrés [11] also investigated the effect of sealing clearance on wall friction factors, relating to sealing flow in labyrinth seals.…”

“…A large number of scholars have made detailed studies on the factors affecting the sealing flow of labyrinths, including rotational speed [2][3][4], Reynolds number [5], pressure ratio [6], and geometric parameters [5][6][7][8][9]. The structure of labyrinth is complex, and there are many geometric parameters that affect the sealing flow, such as radius, sealing clearance, tooth tip width, tooth height, tooth pitch, stage number, and inclination angle.…”

“…Zhao and Wang [10] carried out shape optimization of a straight labyrinth seal to reduce gas leakage and pointed out that the sealing clearance was one of the important optimized parameters. Other researches also revealed that the influence of labyrinth sealing clearance on sealing flow is particularly significant [3,5,6,[11][12][13][14]. Nayak [3] claimed that the effects of rotation on leakage characteristics of straight-through labyrinths were not exactly the same under different sealing clearance.…”

Tortuous flow path design for leakage reduction of labyrinth seal

“…Labyrinth seal is widely applied in various turbomachines to limit the leakage [1,2]. The leakage of the working fluid leads to the efficiency decrease [3].…”