COMPUTATIONAL FLUID DYNAMICS MODIFIED BULK FLOW ANALYSIS FOR CIRCUMFERENTIALLY SHALLOW GROOVED LIQUID SEALS

Transcription

1 Proceedings of ASME Turbo Expo 2017: Turbine Technical Conference and Exposition, June 26-30, 2017, Charlotte, NC USA Paper GT COMPUTATIONAL FLUID DYNAMICS MODIFIED BULK FLOW ANALYSIS FOR CIRCUMFERENTIALLY SHALLOW GROOVED LIQUID SEALS Luis San Andrés Mast-Childs Chair Professor ASME Fellow Tingcheng Wu Research Assistant Hideaki Maeda Engineering General Manager Ono Tomoki Research Engineer Accepted for journal publication

2 Introduction In centrifugal pumps, annular seals reduce secondary leakage. Seals also have a significant impact on a pump rotordynamic performance. For small amplitude (e) rotor motions the seal reaction force (F X, F Y ) is modeled with constant force coefficients (K,C,M): F e F e X 2 K c M Y 2 k C m Multistage Barrel Process Pump ω Rotor whirl frequency. K, k Direct/cross-coupled stiffness. C, c Direct/cross-coupled damping. M, m Direct/cross-coupled added mass. Circumferentially Grooved Seal 2

3 Bulk flow model (BFM) for seal analysis Based on Hirs BFM, Marquette and Childs (1996) developed a 3 CV (control volume) BFM for a liquid grooved seal: Blasius friction factor: f nre m n and m are empirical coefficients. Penetration angle (α): In the groove section, the flow divides: (1) (CV II) through-flow (jet-like) (2) (CV III) deep cavity with recirculation zone. A stream line separates flows and a defines penetration angle to cavity wall. α C r Velocity Distribution in a grooved seal α 3

4 Background for current development Predicted BFN force coefficients for a shallow grooved seal (groove depth ~ C r, L/D>1) used to estimate dynamic performance of a commercial pump correlation with shop test results is poor. Reasons for discrepancy restrictive assumptions in three-cv BFM: wall shear stress, single vortex, etc. Friction factor derived from tests for short length (L/D) seals. Penetration angle (α) not readily known a flow condition. Justification: precise predictions for pump stability necessitate of a more accurate analysis tool. 4

5 CFD solution Solving Navier Stokes equations with an appropriate turbulence flow model could give accurate predictions of dynamic force coefficients (in lieu of test data). Using CFD to predict force coefficients of complex geometry seals is becoming common practice. CFD Predictions Avoid simplifying assumptions: (wall shear stress, single vortex, etc.) No empirical constants needed; Computationally intensive. Seal forces on whirling rotor 5

6 CFD solution a prior work Untaroiu et al. (2013) calculated CFD flows to predict the force coefficients of a shallow depth, arc grooved seal. Seal dimensions (mm) L D S ax c n L g L l d g Fluid-induced forces - Small amplitude perturbation approach - Pressure field from full 3D-CFD solution Rotordynamic force coefficients - Curve fitting of seal reaction forces F e F e X 2 K c M Y 2 k C m Untaroiu, A. et al., 2013, Numerical Modeling of Fluid-Induced Rotordynamic Forces in Seals with Large Aspect Ratios, J. Eng. Gas Turbines Power, 135(1). 6

7 Untaroiu et al. (2013) predictions Dynamic Coefficients From CFD and Bulk-Flow Code CFD BFM* K (MN/m) k C (kn s/m) c M (kg) m 1,436 - Used CFD derived force coefficients to estimate a pump s natural frequency and log dec. The RD estimations -when compared to OEM test data- show indirectly that the CFD-force coefficients are OK. ~13 hours/simulation NOT computationally efficient for routine engineering. * BFM based on SEALS program developed by Childs & Scharrer, Texas A&M University 7

8 BFM vs. CFD Pros Cons Bulk-Flow Model (BFM) CFD Quick Easy set up High fidelity No empirical coefficients required Lacks accuracy Needs empirical coefficients Computationally expensive Requires knowledge about CFD This work presents a CFD modified BFM to predict seal performance with improved accuracy and quick computation time. 8

9 What is this paper about? Original BFM of Marquette and Childs updated with CFD derived quantification of (a) penetration angle a f(operating conditions) (b) friction factor (n, m) coefficients 9

10 CFD modified BFM : The approach 3D CFD Analysis Modified BFM Obtain flow fields for a grooved seal - various operating conditions. Extract wall shear stresses and mean flow velocities to determine updated friction factors (f) at each operating condition. Extract penetration angle (α). Integrate friction factors (f) and penetration angle (α) into BFM predictive tool CFD modified BFM analysis shows improved accuracy with quick computation time. 10

11 Kinematics of rotor whirl motion Rotor whirl Speed ω Y + X Rotor Speed Ω Rotor spins (Ω) and whirls with frequency (ω) and small amplitude e = 0.05 C r 11

12 Seal reaction force & force coefficients Hydrodynamic pressure (P) on a rotor produces a fluid film reaction force with components (F X, F Y ). Rotordynamic force coefficients derived from curve fit model: 12

13 Coordinate transformation Staubli and Bissig introduce a rotating coordinate frameto model the unsteady (periodic) flow into a steady state flow. Y Rotor Speed Ω + Rotor whirl speed ω X Periodic flow state Steady flow state for observer in rotating frame Staubli, T., Bissig, M., 2001, Numerically Calculated Rotor Dynamic Coefficients of a Pump Rotor Side Space, Int. Symposium on Stability Control of Rotating Machinery (ISCORMA), California. 13

14 CFD model validation: smooth surface seal Seal dimensions [1] Rotor radius (R) mm Seal length (L) mm Radial clearance (C r ) mm Operating condition Pressure difference (P in -P out ) 68.9 bar Rotor speed (Ω) 10,200 [rpm] Inlet swirl ratio 0.0 Inlet loss coefficient (ξ) 0.1 Water viscosity (ν) [m 2 /s] 1 Ha, T,W, Choe, B.S., 2012, Numerical Simulation of Rotordynamic Coefficients for Eccentric Annular-Type-Plain-Pump Seal Using CFD Analysis, J. of Mechanical Science and Technology, 26. Test data used by Ha comes from Childs et al. (1997). 14

15 CFD model validation Smooth surface annular seal. Rotordynamic force coefficients (10% static eccentricity) Test (Childs et al.) BFM (Childs et al.) CFD (Ha et al.) CFD (current) Direct stiffness (K) [MN/m] Cross-coupled stiffness (k) [MN/m] Direct damping (C) [kns/m] CFD derived rotordynamic force coefficients agree well with test data 1. 1 Force coefficients in references are incomplete: cross-coupled damping c, direct and cross-coupled mass (M and m) coefficients missing. 15

16 A grooved seal for boiler feed pump Nominal operating condition 29.9 MPA 6,000 rpm 16

17 Dimensions of grooved seal & water properties Seal (L/D = 0.88) with 73 shallow grooves balance piston. Radial clearance (C r ) D Land length (L l ) 6.4 C r Groove length (L g ) 6.4 C r Groove depth (d g ) ~1 C r Water Density (ρ) at 166 C 902 kg/m 3 Dynamic viscosity (μ) cpoise Kinematic viscosity cst (ν=μ/ρ) Balance piston seal with inlet swirl brake. 17

18 CFD model L/D = 0.88 Shallow depth; Long seal; Large pressure drop. 18

19 CFD settings - Mesh Structured mesh Upstream zone: dense mesh to capture flow field rapid changes. Near walls: dense mesh. Node number/mesh size Groove depth direction (radial) 16 Circumferential 180 (2 degrees apart) Radial clearance 30 Axial length 0.1 mm/node Total mesh element number 15.9 Million Min. mesh orthogonal quality

20 Boundary conditions for grooved seal Nominal rotor speed ~6,000 rpm (Surface speed =78 m/s) Upstream Inlet pressure (P s ) 29.9 MPa Pre-swirl velocity 0 m/s Rotor wall angular velocity Ω-ω Stator wall angular velocity -ω Outlet pressure (Pa) at L 0 MPa 20

21 Rotordynamic force coefficients -F X /e -F Y /e Force coefficients from CFD results and (original) BFM K [MN/m] k [MN/m] C [MNs/m] c [MNs/m] M [kg] WFR =k/(ωc) CFD BFM BFM shows negative K and too low k 21

22 Improvements to BFM for grooved seal Three Control Volumes Bulk-flow flow velocities: Axial direction (W) W = U = 1 h 1 h R h R R h R wdr Circumferential direction (U) u dr 22

23 BFM governing equations Continuity Equation: H 1 ( HU) ( HW ) 0 t R Z Axial Momentum Equation: H P W U W W rz sz H W Z t R Z Wall shear stresses Circumferential Momentum Equation: H P U U U U r s H W R t R Z U and W are circumferential and axial velocities. 23

24 Wall shear stresses Axial (τ sz, τ rz ) and circumferential (τ sθ, τ rθ ) on stator and rotor are: W U sz s, s s U s U s W U R rz r, r r U r U r U W U, U W ( U R ). s r Let f U 1 2 r, s r, s 2 r, s with f as a friction factor. 24

25 Friction factor on rotor & stator surfaces Rotor surface f r =n r Re r mr Re r = 2 (ρ/μ) C r U r Stator surface f s =n s Re ms s Re s = 2 (ρ/μ) C r U s Land section 25

26 Friction factor on groove wall CV III Stator Groove Section f n (Re h U ) Re m s g s s c III s c III s III III U W b U III III cc h z z 3 4 III( ) 1 tan( a) c1 Penetration Angle 2 d cw 0 Penetration angle α U siii = velocity in CV III, U III and W III are bulk-flow velocities in CV. W 0 =axial velocity, z=z/l g, b=rω/w 0, d g = groove depth, c 1 = C r /R, c 3 =C r /d g, c 4 = L g /R. 26

27 Friction factors on rotor surface f = n Re m Axial direction f rz Rotor n=0.071 m= zoom in Circ. direction f rθ zoom in 27

28 Friction factors on stator surface f = n Re m Axial direction f sz Stator n=0.067 m= zoom in L A N D GROOVE Circ. direction f sθ zoom in L A N D GROOVE 28

29 Friction factors on rotor & stator surfaces CFD Friction factors (f CFD ) Curve fitting f CFD New coefficients (n, m) f=n Re m n m Rotor Stator Smooth surface * 0.055~ * Hirs, G., 1973, "A Bulk-Flow Theory for Turbulence in Lubricant Films," ASME J. Tribol.,

30 Penetration angle (α) Flow Flow Recirculation Zone 30

31 3CV Bulk-flow Model Flow Recirculation Zone The penetration angle (α) from separation streamline affects the (groove wall) stator friction factor has a marked influence on seal direct stiffness (K). 31

32 Penetration angle of separation streamline (α) Flow field is fully developed from 50 th groove. Obtain a as an average from 50 th to 60 th grooves (z/l=0.7~0.8). 32

33 Penetration angle (α) Axial pressure drop P 1 2 ( R) 2 Dynamic pressure induced by fluid rotation Low pressure/ high speed β High pressure/ low speed α, a function of operating condition (β), decreases with a decrease in rotor speed or an increase in pressure drop. 33

34 Original BFM of Marquette and Childs updated with (a) penetration angle a f( ) (b) new friction factor (n,m) coefficients Improved BFM 34

35 Modified BFM vs. CFD predictions for flow rate (Q) Flow rate Case Q [L/s] ΔP=20 MPa, CFD Ω=4,570 rpm BFM 9.8 ΔP=22 MPa, CFD Ω=4,793 rpm BFM 10.2 ΔP=24 MPa, CFD Ω=5,006 rpm BFM 10.7 ΔP=28 MPa, CFD Ω=5,407 rpm BFM 11.6 ΔP=29.9 MPa, CFD Ω=5,588 rpm BFM 12.0 Max. difference 2% For nominal operating condition : measured leakage=12.6 L/s, ~5% difference with BFM prediction. 35

36 Modified BFM vs. CFD predictions for seal force -F X / e Radial direction: agrees with CFD prediction. Positive K -F Y / e Tangential direction: over-predicted but acceptable. k = k CFD : good improvement. 36

37 Modified BFM vs. CFD : force coefficients Stiffness Damping Case # Operating Conditions ΔP=20 MPa, Ω=4,570 rpm ΔP=22 MPa, Ω=4,793 rpm ΔP=24 MPa, Ω=5,006 rpm ΔP=28 MPa, Ω=5,407 rpm ΔP=29.9 MPa, Ω=5,588 rpm Modified BFM predictions: Agree well with CFD derived predictions; Maximum difference < 15%. 37

38 An example for further validation against test data R. Nordmann, et al., 1987, Rotordynamic Coefficients and Leakage Flow of Parallel Grooved Seals and Smooth Seals, NASA CP Report, N

39 Seal configuration and operating condition L/D = grooves Water (T=30 o C) Operating Condition Rotor radius(r) 23.5 mm Seal length (L) 23.5 mm Radial clearance (c) 0.2 mm Land length (L l ) 1.5 mm Groove length (L g ) 0.7 mm Groove depth (d g ) 0.5 mm Density (ρ) kg/m 3 Dynamic viscosity (μ) cpoise Inlet pressure (P s ) 7.3 bar Pre-swirl ratio 0.2 Rotor speed 2, 4, 6 krpm 39

40 Modified BFM predictions vs. test data Force Coefficients Flow Rate (C L ) ΔP=7.3 bar, Ω=2,000 rpm ΔP=7.3 bar, Ω=4,000 rpm ΔP= 7.3 bar, Ω= 6,000 rpm K k C c kn/m kn/m kns/m Ns/m Exp BFM Difference -3% 4% -1% 67% Exp BFM difference -6% 2% -2% 67% Exp BFM difference -13% 12% -5% 56% ΔP [bar] Mass Flow Rate ( 10-3 ) Exp. BFM Diff %.. ~ -4% % Modified BFM predictions agree best with test data validate model. * Q CL 2 R, Q is flow rate and C L is a seal flow coefficient. 2 2 P 40

41 Conclusion CFD MODIFIED BULK FLOW ANALYSIS FOR CIRCUMFERENTIALLY SHALLOW GROOVED LIQUID SEALS 41

42 Conclusion A BFM modified with CFD derived friction factors (f) and penetration angle (α) offers an improvement in predicted rotor dynamic force coefficients over those of an original BFM. Friction factors on land and groove sections are different, f Land 3 f Groove ; Penetration angle (α) is a function of the seal operating conditions β = ΔP/[½ ( R) 2 ]. Paper GT α has upper and lower bounds. Increasing the rotor speed or reducing the pressure drop raises α. The modified BFM program shows an accuracy comparable to the CFD method and is much quicker in delivering seal leakage and force coefficients. 42

43 Acknowledgements Thanks to Torishima Pump MFG. Co. LTD TAMU High Performance Computing Center Questions (?) Learn more at

44 Appendix-II Rotordynamic Force Coefficients Modified Bulk Flow Program vs. derived from CFD results Case K k C c M ΔP=20 MPa, Ω=4,570 rpm ΔP=22 MPa, Ω=4,793 rpm ΔP=24 MPa, Ω=5,006 rpm ΔP=28 MPa, Ω=5,407 rpm 5 ΔP=29.9MPa, Ω=5,588 rpm Flow rate Q WFR [MN/m] [MN/m] [MNs/m] [MNs/m] [kg] [L/s] ( k/ωc) CFD , BF , difference 0% 8% 0% 13% 3% 2% 8% CFD , BF , difference 1.4% 6% -2% 2% -1% 2% 9% CFD , BF , difference 0.8% 3% -5% 6% -0.5% 2% 9% CFD , BF , difference -5.7% 4.6% -3% -5% -6% 2% 8% CFD , BF , difference -0.8% 0.2% -9% -89% -10% 2% 10% 44

45 References [1] TAMU Turbomachinery Laboratory, XLCGrv Program (Version 2.0). Licensed software XLTRC2. [2] Rao, J. S., Saravanokumar, M., 2006, Numerical Simulation of Seal Flow and Determination of Stiffness and Damping Coefficient, 7th IFToMM-Conference on Rotor Dynamics, Vienna, Austria, pp [3] Staubli, T., Bissig, M., 2001, Numerically Calculated Rotor Dynamic Coefficients of a Pump Rotor Side Space, International Symposium on Stability Control of Rotating Machinery (ISCORMA), South Lake Tahoe, California, August 20-24, pp.20. [4] San Andrés, L., Wu, T., 2015, CFD Predictions of Turbulent Flow in a Grooved Annular Seal, Quarter I Research Progress Report to Torishima Pumps, December 3rd, Texas A&M University. [5] San Andrés, L., Wu, T., 2016, CFD Predictions of Turbulent Flow in a Grooved Annular Seal, Quarter II Research Progress Report to Torishima Pumps, March 24th, Texas A&M University. [6] Untaroiu, A., Untaroiu, C. D., Wood, H. G., Allaire, P. E., 2013, Numerical Modeling of Fluid-Induced Rotordynamic Forces in Seals with Large Aspect Ratios, Journal of Engineering for Gas Turbines and Power, 135(1), pp [7] Florjancic, S., 1990, Annular Seals of High Energy Centrifugal Pumps, Doctoral dissertation, Swiss Federal Institute of Technology, Zurich. [8] Scharrer, J., 1987, A Comparison of Experimental and Theoretical Results for Labyrinth Gas Seals, Ph.D. Dissertation, Texas A&M University, College Station. [9] Marquette, O. R., 1994, A New Three-Control-Volume Theory for Circumferentially- Grooved Liquid Seals, Master thesis, Texas A&M University, College Station. [10] Childs, D. W., 1993, Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis, John Wiley & Sons, Chap. 4.