LEAKAGE AND DYNAMIC FORCE COEFFICIENTS FOR TWO LABYRINTH GAS SEALS:

Transcription

1 Proceedings of ASME Turbo Expo 2018: Turbine Technical Conference and Exposition, June 11-15, 2018, Oslo, Norway Paper GT LEAKAGE AND DYNAMIC FORCE COEFFICIENTS FOR TWO LABYRINTH GAS SEALS: Teeth-on-Stator and Interlocking Teeth Configurations. A CFD approach to their Performance Luis San Andrés Mast-Childs Chair Professor ASME Fellow Tingcheng Wu Graduate Research Assistant Texas A&M University Funded by Turbomachinery Research Consortium

2 Presentation Outline 1 Introduction to Labyrinth Seals CFD Method & Validation against Published Test Data CFD Model & Grid Independence Analysis CFD Predictions for Labyrinth Seals: Teeth on Stator vs. Interlocking 5 Conclusion 2

3 Introduction to labyrinth seals (TOS, TOR & ILS) TOS: Teeth on Stator TOR: Teeth on Rotor ILS: Interlocking Seal: TOR+TOS 3

4 Types of labyrinth seals (1) TOS: all teeth on stator (2) TOR: all teeth on rotor (3) ILS : teeth on both rotor and stator Restrict secondary flow; Affect rotor system dynamic stability. TOS TOR ILS To accurately predict LS leakage and rotordynamic force coefficients is a must for efficient and rotordynamic stable operation of turbomachinery. 2

5 Labyrinth seals: How do they work? Core Flow: jet flow along leakage path plays dominant role. Pressure drop across sharp teeth dissipates energy. Vortex Flow: Vortices (recirculation zones) in a cavity contribute to mechanical energy dissipation. 5

6 Background for current development Prior tests and field experience show an ILS leaks up to 30% less than either a TOR or a TOS LS does. Engineering needs High efficiency turbomachines demand of lesser secondary leakage ILS is a good choice to satisfy need. Field data for ILS rotordynamic characteristics are still vague and scarce Recent tests at TAMU prove difficulties and show little insight. Bulk-flow models (BFM) can not deliver accurate predictions must develop better models. Justification: accurate assessment of compressor & steam turbine efficiency and stability relies on 6 reliable seal performance predictions.

7 A short review of the literature Experimental Benckert and Wachter, measure stiffness of LSs and investigate the influence of rotor speed and inlet pre-swirl velocity on seal forces. Childs and Scharrer, report TOR & TOS LS force coefficients. First to show direct damping coefficients. Childs et al., report coefficients for ILS and TOS LS. ILS leaks +less (60%) than TOS LS. Ertas et al., 2012, & Vannini et al., report LSs showing frequency dependent rotordynamic force coefficients. Childs et al., report ILS force coefficients at low pressures: Unreliable. Physical Modeling Childs et al., One Control Volume (1-CV) Bulk-flow Model (BFM), widely in use to date. Moore, 2003, & Li et al., 2013 CFD analyses for LSs good correlation to 7 test data for both leakage and dynamic force coefficients.

8 Predictive tools: BFM vs. CFD Bulk-Flow Model (BFM) CFD Pros Quick Easy set up High fidelity No empirical coefficients required Cons Lacks accuracy Needs empirical coefficients Computationally expensive Requires knowledge on CFD (pre and post processing) Available computational capability and desire for extreme fidelity push CFD analyses into common engineering practice

9 What is this paper about? Recent experiments with an ILS proved too difficult and did not deliver reliable test results; hence, a CFD analysis for labyrinth seals is useful to benchmark an ILS vs. a TOS LS. This paper details the CFD numerical analysis process, produces leakage and force coefficients for published LSs as a validation, and reports leakage and force coefficients for the designed labyrinth seals. 9

10 CFD Method & Validation y Rotor speed Ω Whirl frequency ω f t Ω ω f r x Periodic force components along radial and tangential direction: f r, f t 10

11 Coordinate transformation Staubli and Bissig introduce a rotating coordinate frame to model a periodic (whirling) flow into a steady state flow. Y Rotor Speed + Ω X Rotor whirl speed ω Periodic flow state Steady flow state for observer in rotating frame Gas seals likely show frequency dependent force coefficients analysis requires of multiple flows at +/- whirl frequencies to extract seal force coefficients.

12 Rotor Whirl Motions with Multi-Frequency Y X Method introduced by Li et al. a = 1.5 μm X max ~ 10%C r b = 1 μm Y max ~ 5%C r ω i = Hz (14 frequencies, 20 Hz apart) ω i /Ω = N X a cos( t) ; Y b sin( t) i i 1 i 1 N i Input: rotor displacements (X,Y) output: seal reaction force 12

13 Seal Force Components Periodic reaction force f x and f y with multifrequency ω i x : radial direction y : tangential direction One period of multiple frequency

14 Force Coefficients Identification Time Domain Fourier Series Frequency Domain At each frequency ( j ): K i C j j j fx K k X C c X f y k K Y c C Y FX j K j k j C j c j x j i j F k Y j K j c j C j y j j (K, k) and (C, c) : stiffness and damping force coefficients. F a if b Xj a b 2 2 i jt i jt xj X ; yj Y, j 1 N f F e f F e x j = a; y j = b Yj k i c j j j if b F a Xj a b 2 2 Yj 14

15 CFD Settings Gas Model: Ideal CFD Package: ANSYS Fluent hosted by TAMU High Performance Computing Center Turbulence flow Model: Standard k-ε C μ = 0.09, C 1ε = 1.44, C 2ε =1.92, σ k = 1.0, σ ε = 1.3 Wall Function: Scalable Wall Function Energy Equation: Fluent default with adiabatic walls 15

16 Mesh Deformation Method Rotor whirl Speed ω Y + X Rotor Speed Ω Rotor displaces with distinct specified X, Y One transient response over a full period (T) delivers seal forces, f r and f t, on rotor surface. 16

17 Validation 1 Vannini, G., et al., 2014, "Labyrinth Seal and Pocket Damper Seal High Pressure Rotordynamic Test Data," ASME J Eng Gas Turb Power, 136(2). 17

18 TOS Labyrinth Seal (1) Mesh ~8M nodes Node number Radial clearance 30 Tooth section 30 Cavity depth/length 30 Circumferential 180 (2 apart) Min. mesh orthogonal quality

19 TOS Labyrinth Seal (1) Operating Conditions Supply pressure, P in 72.8 bar Discharge pressure, P out 50.9 bar Inlet/exit pressure ratio 1.4 Inlet swirl velocity, U m/s Rotor Speed, Ω 12 krpm (200 Hz) ½ DΩ 138 m/s Boundary Conditions Pre-swirl: 100 m/s Inlet gas and walls (R&S) at room T= 25 C (298K) Stator(stationary wall) 72.8 bar 50.9 bar RotorΩ = 12 krpm 19

20 TOS LS(1): Stiffnesses vs. frequency K k CFD predicted direct and cross-coupled stiffness (K, k) agree well with test data. Compared to BFM, CFD does better; k in particular. 20

21 TOS LS (1): Direct damping vs. frequency C 1X CFD over-predicts damping (C) at low frequency (< 80 Hz). BFM does better. CFD and BFM agree with test data at high frequencies, W (200 Hz). 21

22 Validation 2 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 Turb Power, 134(4). 22

23 TOS Labyrinth Seal (2) Mesh ~8M nodes Node number Radial clearance 30 Tooth section 30 Cavity depth/length 30 Circumferential 180 (2 apart) Min. mesh orthogonal quality

24 TOS Labyrinth Seal (2) Operating Conditions Supply pressure, P in 6.9 bar Discharge pressure, P out 1 bar Inlet/exit pressure ratio 6.9 choked flow Inlet swirl velocity, U 0 7 m/s Rotor Speed, Ω 7 krpm (116 Hz) ½DΩ 63 m/s Boundary Conditions Pre-swirl: 7 m/s Inlet gas and walls (R&S) at room T= 25 C (298K) Stator(stationary wall) 6.9 bar 1 bar Rotor Ω = 7 krpm 24

25 TOS LS (2): Stiffnesses vs. frequency K k ω i /Ω ω i /Ω CFD predicts poorly K with hardening effect ( /W > 1). BFM agrees well with test data. For cross stiffness (k) CFD does better whereas BFM shows an opposite sign. Flow choking may be reason for difference. Note test data covers large frequencies ( /W > 1). 25

26 TOS LS (2): Direct damping vs. frequency C ω i /Ω Both CFD & BFM under-predict direct damping. Ratio test/cfd ~ 2, test/bfm~ 4. Take a pick for best! 26

27 Finally, after a long preparation (including satisfying reviewers) the business at hand is 27

28 Compare performance of ILS vs TOS-LS representative seals for compressors 28

29 CFD models for both seals Geometry Overall length, L 42 mm Tooth pitch, L i 3.8 mm Rotor diameter, D 150 mm Height, B 3.0 mm Radial clearance, C r 0.2 mm Width at tip, b t 0.3 mm Teeth number, NT 7 ILS TOS 29

30 ILS & TOS Labyrinth Seal Operating Conditions Supply Pressure P in = 3.8, 6.9 bar Pressure Ratio P out /P in = 0.5, 0.8 Rotor Speed Ω = 10 krpm (167 Hz) (½DΩ = 79 m/s) Inlet pre-swirl ratio α = 0 Boundary Conditions Pre-swirl: 0 m/s Inlet gas and walls (R&S) at room T= 25 C (298K) Stator (stationary wall) P in P out Rotor Ω = 10 krpm 30

31 Grid Independence Study for TOS LS & ILS Node number Radial clearance 30 Tooth section 30 Cavity depth/length 30 Circumferential 180 (2 apart) Mesh: 4 to 8 million nodes Min. mesh orthogonal quality

32 Mesh Convergence of flow and forces node # Mesh with 4M nodes is accurate enough. 32

33 CFD Predictions TOS LS vs. ILS + BFM results TOS ILS 33

34 Pressure Field P/P in P in = 6.9 bar, PR =0.8. ILS shows lesser pressure drop at inlet than TOS LS Mass flow rate [g/s] P in [bar] PR ILS TOS Diff. 3.8 bar % % 6.9 bar % % Leakage ILS<TOS 34

35 Direct Stiffness (K) P in = 3.8, 6.9 bar, PR = 0.5, 0.8 [kn/m] K: ILS > TOS positive K P in K PR K ω i /Ω K <0 K is small compared to the structural stiffness of a rotor-bearing system. 35

36 Cross-coupled stiffness (k) P in = 3.8, 6.9 bar, PR = 0.5, 0.8 [kn/m] ILS TOS LS ω i /Ω ω i /Ω ω k. BFM k < 0, opposite to CFD. ω/ω < 0.7, ILS and TOS LS show same (small) k P in k PR k k < 0 will add to effective damping! 36

37 Direct Damping (C) P in = 3.8, 6.9 bar, PR = 0.5, 0.8 ω/ω < 0.5 ω/ω > 0.5 ω C ILS: ω C ILS [Ns/m] TOS: ω C ~ constant. P in C PR C For ω/ω < 1.5 TOS LS has more damping whereas for ω/ω > 1.5 ILS shows more damping BFM predicts same C for both seals and is just a fraction of CFD result! TOS LS ω i /Ω ω i /Ω 37

38 Cross-coupled Damping (c) P in = 3.8, 6.9 bar, PR = 0.5, 0.8. [Ns/m] CFD predicted c ~ C c> 0 rises dynamic stiffness (K+ ωc) > 0 BFM underpredicts c for both seals. 38

39 Effective Damping (C eff = (C k/ω)) P in = 3.8, 6.9 bar, PR = 0.5, 0.8 P in C eff PR C eff ω/ω = C eff TOS LS > ILS ω/ω > 1.3 C eff : TOS LS < ILS For ω/ω = TOS LS delivers more eff. damping a better rotordynamic choice. ILS ωi /Ω TOS LS ω i /Ω 39

40 Conclusion Paper GT

41 ILS vs TOS LS CFD analysis for an interlocking (ILS) and a tooth-on-stator (TOS) labyrinth seal delivers flow rate and the rotordynamic force coefficients: ILS leaks up to 30% less than TOS LS. For ω/ω = TOS LS provides more effective damping than ILS. BFM predictions quite different from CFD model results. Caution needed when using a simple BFM tool! Currently, an interlocking labyrinth seal (ILS) is under testing at TAMU Turbomachinery Laboratory. Later, the test data will reveal more useful information. 41

42 Acknowledgments Paper GT Turbomachinery Research Consortium (TRC) TAMU High Performance Research Computing (TAMU HPRC) Questions (?) Learn more at 42 Scan me to visit our site

43 New (2018) Seals and Housing Redesign 1. Inlet air 2. ADM Integral swirl vane and swirl-brakes 3. TOS Laby seal, drive end 4. TOS Laby seal, non-drive end 5. TOR Laby seal 6. Rotor 7. Exit air (end caps) 8. Exit labyrinth seal 9. Axial alignment bolts Split casing hosting stator for seal Pressurized air in Pressurized air in Cap for end seal and exit reservoir End seal 43

44 Axial Velocity Field P in = 6.9 bar, PR =0.8. ILS exit speed < TOS LS exit speed 44