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Research Papers: Gas Turbines: Structures and Dynamics

Leakage and Dynamic Force Coefficients for Two Labyrinth Gas Seals: Teeth-on-Stator and Interlocking Teeth Configurations. A Computational Fluid Dynamics Approach to Their Performance

[+] Author and Article Information
Tingcheng Wu

Turbomachinery Laboratory,
Texas A&M University,
College Station, TX 77843
e-mail: wutingcheng29@gmail.com

Luis San Andrés

Fellow ASME
Turbomachinery Laboratory,
Texas A&M University,
College Station, TX 77843
e-mail: lsanandres@tamu.edu

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 13, 2018; final manuscript received July 18, 2018; published online October 29, 2018. Editor: Jerzy T. Sawicki.

J. Eng. Gas Turbines Power 141(4), 042501 (Oct 29, 2018) (12 pages) Paper No: GTP-18-1491; doi: 10.1115/1.4041123 History: Received July 13, 2018; Revised July 18, 2018

Labyrinth gas seals (LSs) 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 are 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 Cr = 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 Pin = 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 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 the 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 1.5 Ω. An increase in exit/inlet pressure ratio decreases the direct damping for both seals. The effective damping coefficient, Ceff = (C-k/ω), whenever positive aids to damp vibrations, whereas Ceff < 0 is a potential source for an instability. For frequencies ω/Ω < 1.3, Ceff 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 demonstrates that 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, “Rotordynamic Force Coefficients for Three Types of Annular Gas Seals With Inlet Preswirl and High Differential Pressure Ratio,” ASME J. Eng. Gas Turbines Power, 134(4), pp. 04250301–04250312) and Vannini et al. (2014, “Labyrinth Seal and Pocket Damper Seal High Pressure Rotordynamic Test Data,” ASME J. Eng. Gas Turbines Power, 136(2), pp. 022501–022509.)

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References

Ek, M. , 1978, “ Solution of the Subsynchronous Whirl Problem in the High-Pressure Hydrogen Turbomachinery of the Space Shuttle Main Engine,” 14th Joint Propulsion Conference, Las Vegas, NV, July 25–27, pp. 100201–100226.
Childs, D. W. , 1993, “ Rotordynamic Models for Annular Gas Seals,” Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis, Wiley, New York, Chap. 5.
Gao, R. , and Kirk, G. , 2013, “ CFD Study on Stepped and Drum Balance Labyrinth Seal,” Tribol. Trans., 56(4), pp. 663–671. [CrossRef]
Kuwamura, Y. , Matsumoto, K. , Uehara, H. , Ooyama, H. , Tanaka, Y. , and Nishimoto, S. , 2013, “ Development of New High-Performance Labyrinth Seal Using Aerodynamic Approach,” ASME Paper No. GT2013-94106.
Benckert, H. , and Wachter, J. , 1978, “ Studies on Vibrations Stimulated by Lateral Forces in Sealing Gaps,” AGARD Seal Technology in Gas Turbine Engineering, UK.
Leong, Y. , and Brown, R. , 1984, “ Experimental Investigation of Lateral Forces Induced by Flow Through Model Labyrinth Glands,” Workshop on Rotordynamic Instability Problems in High-Performance Turbomachinery, Edinburgh, UK, pp. 187–210.
Childs, D. W. , and Scharrer, J. K. , 1986, “ Experimental Rotordynamic Coefficient Results for Teeth-on-Rotor and Teeth-on-Stator Labyrinth Gas Seals,” ASME J. Eng. Gas Turbines Power, 108(4), pp. 599–604.
Thieleke, G. , and Stetter, H. , 1990, “ Experimental Investigations of Exciting Forces Caused by Flow in Labyrinth Seals,” Workshop on Rotordynamic Instability Problems in High-Performance Turbomachinery, pp. 109–134.
Childs, D. W. , Elrod, D. A. , and Hale, K. , 1988, “ Rotordynamic Coefficient and Leakage Test Results for Interlock and Tooth-on-Stator Labyrinth Seals,” ASME Paper No. 88-GT-87.
Baumann, U. , 1999, “ Rotordynamic Stability Tests on High-Pressure Radial Compressors,” 28th Turbomachinery Symposium, pp. 12–15.
Picardo, A. , and Childs, D. W. , 2005, “ Rotordynamic Coefficients for a Tooth-on-Stator Labyrinth Seal at 70 Bar Supply Pressures: Measurements Versus Theory and Comparisons to a Hole-Pattern Stator Seal,” ASME J. Eng. Gas Turbines Power, 127(4), pp. 843–855. [CrossRef]
Wagner, N. G. , Steff, K. , Gausmann, R. , and Schmidt, M. , 2009, “ Investigations on the Dynamic Coefficients of Impeller Eye Labyrinth Seals,” 38th Turbomachinery Symposium, Houston, TX, Sept. 14–17, pp. 53–69.
Ertas, B. H. , Delgado, A. , and Vannini, G. , 2012, “ Rotordynamic Force Coefficients for Three Types of Annular Gas Seals With Inlet Preswirl and High Differential Pressure Ratio,” ASME J. Eng. Gas Turbines Power, 134(4), pp. 04250301–04250312. [CrossRef]
Vannini, G. , Cioncolini, S. , Del Vescovo, G. , and Rovini, M. , 2014, “ Labyrinth Seal and Pocket Damper Seal High Pressure Rotordynamic Test Data,” ASME J. Eng. Gas Turbines Power, 136(2), pp. 022501–022509. [CrossRef]
Moore, J. J. , 2003, “ Three-Dimensional CFD Rotordynamic Analysis of Gas Labyrinth Seals,” ASME J. Vib. Acoust., 125(4), pp. 427–433. [CrossRef]
Li, Z. , Li, J. , and Yan, X. , 2013, “ Multiple Frequencies Elliptical Whirling Orbit Model and Transient RANS Solution Approach to Rotordynamic Coefficients of Annual Gas Seals Prediction,” ASME J. Vib. Acoust., 135(3), pp. 031005–031014. [CrossRef]
San Andrés, L. , Wu, T. , Maeda, H. , and Ono, T. , 2018, “ A Computational Fluid Dynamics Modified Bulk-Flow Analysis for Circumferentially Shallow Grooved Liquid Seals,” ASME J. Eng. Gas Turbines Power, 140(1), pp. 0125041–0125049. [CrossRef]
Ramirez, M. A. , 2017, “ Development and Validation of Test Rig for Measurements of Leakage and Rotordynamic Performance of Interlocking Gas Labyrinth Seals,” M.S. thesis, Texas A&M University, College Station, TX.
ANSYS, 2013, “ Fluent Theory Guide 15.0,” ANSYS, Canonsburg, PA.
Thorat, M. R. , 2010, “ Impact of Rotor Surface Velocity, Leakage Models and Real Gas Properties on Rotordynamic Force Predictions of Gas Labyrinth Seals,” M.S. thesis, Texas A&M University, College Station, TX.
D'Souza, R. , and Childs, D. W. , 2002, “ A Comparison of Rotordynamic-Coefficient Predictions for Annular Honeycomb Gas Seals Using Three Different Friction-Factor Models,” ASME J. Tribol., 124(3), pp. 524–529. [CrossRef]

Figures

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Fig. 1

Schematic views of flow passing through the clearance channel in a seal: (a) TOS LS, (b) TOR LS, (c) ILS, and (d) stepped LS

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Fig. 2

Schematic views of: (a) ILS and (b) TOS labyrinth seal

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Fig. 3

Seal geometry and mesh: (a) ILS and (b) TOS labyrinth seal

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Fig. 4

Mesh independence analysis results: mass flow rate and static force (fx, fy) components versus mesh density. TOS LS: Pin = 6.0 bar and PR = 0.8, 10 krpm (½DΩ = 79 m/s). Static eccentricity X = 0.1Cr.

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Fig. 5

Contours of gas axial velocity for an ILS and a TOS LS operating with Pin = 6.9 bar and pressure ratio PR = 0.8. Rotor spins at 10,000 rpm (½DΩ = 79 m/s).

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Fig. 6

Computational fluid dynamics predicted pressure ratio(P/Pin) versus axial location. ILS and TOS LS with supply pressure Pin = 6.9 bar and pressure ratio PR = 0.8, rotor speed = 10 krpm (½DΩ = 79 m/s).

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Fig. 7

Schematic view of typical rotor whirl motion, ωi = 20–280 Hz in steps of 20 Hz, maximum displacement ∼0.1 Cr, a = 1.5 μm and b = 1 μm

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Fig. 8

Applied multifrequency rotor motions (X, Y) versus time (t), for ILS and TOS LS

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Fig. 9

Seal reaction force components (fx, fy) versus time in one period (0.05 s). ILS and TOS LS operating with Pin = 6.9 bar, PR = 0.5, rotor speed 10,000 rpm (167 Hz). Note origin of time scale, t > 4T: (a) ILS and (b) TOS LS.

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Fig. 10

Real and imaginary components of seal reaction forcefx/a versus frequency. ILS and TOS LS operating with Pin = 6.9 bar, PR = 0.5, rotor speed 10,000 rpm (167 Hz).

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Fig. 11

Direct stiffness (K) versus frequency ratio (ω/Ω) for an ILS and a TOS LS operating at two supply pressures (Pin = 3.8, 6.9 bar) and pressure ratios (PR = 0.5, 0.8), and rotor speed 10,000 rpm

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Fig. 12

Cross coupled stiffness (k) versus frequency ratio (ω/Ω) for an ILS and a TOS LS operating at two supply pressures (Pin = 3.8, 6.9 bar) and pressure ratios (PR = 0.5, 0.8), and rotor speed 10,000 rpm: (a) ILS and (b) TOS ILS

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Fig. 13

Imaginary part of complex stiffness HIωC versus frequency. ILS and TOS LS operating at Pin = 6.9 bar, PR = 0.5, rotor speed 10,000 rpm (167 Hz).

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Fig. 14

Direct damping coefficient (C) versus frequency ratio (ω/Ω) for an ILS and a TOS LS operating at Pin = 3.8, 6.9 bar, pressure ratios PR = 0.5, 0.8, and rotor speed 10,000 rpm: (a) ILS and (b) TOS ILS

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Fig. 15

Cross coupled damping coefficient (c) versus frequency ratio (ω/Ω) for an ILS and a TOS LS operating at Pin = 6.9 bar and pressure ratio PR = 0.5, and rotor speed 10,000 rpm

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Fig. 16

Computational fluid dynamics predicted effective damping versus frequency ratio (ω/Ω) for an ILS and a TOS LS operating at two supply pressures (Pin = 3.8, 6.9 bar) and pressure ratios (PR = 0.5, 0.8), and rotor speed 10,000 rpm: (a) ILS and (b) TOS ILS

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Fig. 17

TOS LS: comparisons of CFD and BFM predicted rotordynamic force coefficients against test results in Ref. [13]: (a) direct stiffness (K), (b) cross coupled stiffness (k), (c) direct damping (C), and (d) effective damping (Ceff)

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Fig. 18

TOS LS: comparisons of CFD and BFM predicted rotordynamic force coefficients against test results in Ref. [14]: (a) direct stiffness (K), (b) cross coupled stiffness (k), (c) direct damping (C), and (d) effective damping (Ceff)

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