Leakage and Dynamic Force Coefficients for Two Labyrinth Gas Seals: Teeth-on-Stator and Interlocking Teeth Configurations — A CFD Approach to Their Performance

Labyrinth gas seals (LS) commonly used in turbomachines reduce secondary flow leakage. Conventional see-through labyrinth seal designs include either all Teeth-On-Stator (TOS) or all Teeth-On-Rotor (TOR). Experience shows that an interlocking labyrinth seal (ILS), with teeth on both stator and rotor, reduces gas leakage by up to 30% compared to the conventional see-through designs. However, field data for ILS rotordynamic characteristics is still vague and scarce in the literature. This work presents flow predictions for an ILS and a TOS LS, both seals share identical design features, namely radial clearance C_r = 0.2 mm, rotor diameter D = 150 mm, tooth pitch Li = 3.75 mm, and tooth height B = 3 mm. Air enters the seal at supply pressure P_in = 3.8, 6.9 bar (absolute) and temperature of 25 °C. The ratio of gas exit pressure to supply pressure ranges from 0.5 to 0.8, and the rotor speed is fixed at 10 krpm (surface speed of 79 m/s). The analysis implements a computational fluid dynamics (CFD) method with a multi-frequency-orbit rotor whirl model. The CFD predicted mass flow rate for the ILS is ∼21% lower than that of the TOS LS, thus making the ILS a more efficient choice. Integration of the dynamic pressure fields in the seal cavities, obtained for excitation frequency (ω) ranging from 12% to 168% of rotor speed (sub and super synchronous whirl), allows an accurate estimation of the seal dynamic force coefficients. For all the considered operating conditions, at low frequency range the TOS LS shows a negative direct stiffness (K < 0), frequency independent; whereas the ILS has K > 0 that increases with both frequency and supply pressure. For both seals, the magnitude of K decreases when the exit pressure/inlet pressure ratio increases. On the other hand, the cross-coupled stiffness (k) from both seals is frequency dependent, its magnitude increases with gas supply pressure, and the k for the ILS is more sensitive to a change in the exit/inlet pressure ratio. Notably, k turns negative for subsynchronous frequencies below rotor speed (Ω) for both the TOS LS and ILS. The direct damping (C) for the TOS LS remains constant for ω > ½ Ω and has a larger magnitude than the damping for the ILS over the frequency range up to 1.5Ω. An increase in exit/inlet pressure ratio decreases the direct damping for both seals. The effective damping coefficient, C_eff = (C-k/ω) whenever positive aids to damp vibrations, whereas C_eff < 0 is a potential source for an instability. For frequencies ω /Ω < 1.3, C_eff for the TOS LS is higher in magnitude than that for the ILS. From a rotordynamics point of view, the ILS is not a sound selection albeit it reduces leakage. Comparison of the CFD predicted force coefficients against those from a bulk flow model demonstrate the later simple model delivers poor results, often contradictory and largely indifferent to the type of seal, ILS or TOS LS. In addition, CFD model predictions are benchmarked against experimental dynamic force coefficients for two TOS LSs published by Ertas et al. (2012) and Vannini et al. (2014).