1. 1 ASME Turbo Expo 2011: Power for Land, Sea and Air June 6-10, 2011, Vancouver, BC Luis San Andres Mast-Childs Tribology Professor Turbomachinery Laboratory Texas A&M University ASME GT2011-45264 Rotordynamic Force Coefficients of Bubbly Mixture Annular Pressure Seals Accepted for publication J Eng. Gas Turb. Power Presentation available athttp://rotorlab.tamu.edu Supported by TAMU Turbomachinery Laboratory (Prof. D. Childs)

2. 2 Annular Pressure Seals Seals in a Multistage Centrifugal Pump or Compressor Radial seals (annular, labyrinth or honeycomb) separate regions of high pressure and low pressure and their principal function is to minimize the leakage (secondary flow); thus improving the overall efficiency of a rotating machine extracting or delivering power to a fluid. Impeller eye or neck ring seal Balance piston seal Inter-stage seal

3. 3 Annular Pressure Seals The dynamic force response of pressure seals has a primary influence on the stability response of high- performance turbomachinery. Annular seals, although geometrically similar to plain journal bearings, show a flow structure dominated by turbulence and fluid inertia effects. Operating characteristics unique to seals are the * large axial pressure gradients, * large clearance to radius ratio (R/c) < 500, while * the axial development of the circumferential velocity determines the magnitude of cross-coupled (hydrodynamic) forces. Childs, D., 1993, Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis, John Wiley & Sons, Inc., New York, New Yor, Chap. 4.

4. 4 Seals and rotordynamics Straight-Through and Back-to-back Compressors and 1st Mode Shapes Due to their relative position within a rotor- bearing system, seals modify the system dynamic behavior. Seals typically "see" large amplitude rotor motions. This is particularly important in back-to-back compressors and long- flexible multiple stage pumps Childs, D., 1993, Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis, John Wiley & Sons, Inc., New York, New Yor, Chap. 4.

5. 5 Force Coefficients in Annular Seals Seal reaction forces are functions of the fluid properties, flow regime, operating conditions and geometry. For small amplitudes of rotor lateral motion: forces are linearized with stiffness, damping and inertia force coefficients :

6. 6 Annular Pressure Seals Intentionally roughened stator surfaces (macro texturing) reduce the impact of undesirable cross- coupled dynamic forces and improve seal stability. Annular seals acting as Lomakin bearings have potential as support elements (damping bearings) in high speed compressors and pumps. Childs, D., and Vance, J., 1997, “Annular Gas Seals and Rotordynamics of Compressors and Turbines”, Proc. of the 26th Turbomachinery Symposium, Texas A&M University, Houston, TX, September, pp. 201-220

7. 7 Bubbly Mixture Annular Pressure Seals As oil fields deplete compressors work off-design with liquid in gas mixtures, mostly inhomogeneous. Similarly, oil compression station pumps operate with gas in liquid mixtures The flow condition affects compressor or pump overall efficiency and reliability. Little is known about seals operating under 2-phase conditions, except that the mixture affects seal leakage, power loss and rotordynamic force coefficients; perhaps even inducing random vibrations that are transmitted to the whole rotor-bearing system. Justification Seals operate with either liquids or gases, but not both……

8. 8 Background literature Experimental – Seals (two phase) Iwatsubo, T., and Nishino, T., 1993, “An Experimental Study on the Static and Dynamic Characteristics of Pump Annular Seals,“ 7th Workshop on Rotordynamic Instability Problems in High Performance Turbomachinery. Computational – Seals (two phase) Annular Seals Hendricks, R.C., 1987, "Straight Cylindrical Seals for High Performance Turbomachinery," NASA TP-1850 Arauz, G., and San Andrés, L., 1998, “Analysis of Two Phase Flow in Cryogenic Damper Seals, I: Theoretical Model, II: Model Validation and Predictions,” ASME J. Tribol., 120, pp. 221-227, 228- 233 Beatty, P.A., and Hughes, W.F., 1987, "Turbulent Two-Phase Flow in Annular Seals," ASLE Trans., 30, pp. 11-18. Arghir, M., Zerarka, M., Pineau, G., 2009 "Rotordynamic analysis of textured annular seals with mutiphase (bubbly) flow, “Workshop : “Dynamic Sealing Under Severe Working Conditions” EDF – LMS Futuroscope, October 5,

9. 9 Background literature Experimental – Seals (two phase) Iwatsubo, T., and Nishino, T., 1993, “An Experimental Study on the Static and Dynamic Characteristics of Pump Annular Seals,“ 7th Workshop on Rotordynamic Instability Problems in High Performance Turbomachinery. Annular Seals NO description of water lubricated seal (L, D, c) or gas type….. Tests conducted at various speeds (1,500- 3,500 rpm) and supply pressures=1.2 - 4.7 bar. Air/liquid volume fraction  =0, 0.25, 0.45, 0.70 Mxx Cxx Kxx , gas volume fraction increases

10. 10 Background literature Experimental & Physical Modeling Tao, L., Diaz, S., San Andrés, L., and Rajagopal, K.R., 2000, "Analysis of Squeeze Film Dampers Operating with Bubbly Lubricants" ASME J. Tribol., 122, pp. 205-210 Squeeze film dampers Diaz, S., and San Andrés, L., 2002, “Pressure Measurements and Flow Visualization in a Squeeze Film Damper Operating with a Bubbly Mixture,” ASME J. Tribol., 124, pp. 346-350. Diaz, S., and San Andrés, L., 2001, “A Model for Squeeze Film Dampers Operating with Air Entrainment and Validation with Experiments,” ASME J. Tribol., 123, pp. 125-133. Diaz, S., and San Andrés, L., 2001, "Air Entrainment versus Lubricant Vaporization in Squeeze Film Dampers: An Experimental Assessment of their Fundamental Differences,” ASME J. Eng. Gas Turbines Power, 123, pp. 871-877 Sponsored by National Science Foundation and TAMU Turbomachinery Research Consortium, June 1998- May 2002

11. 11 Background literature Squeeze film dampers Sponsored by National Science Foundation and TAMU Turbomachinery Research Consortium, June 1998- May 2002 Effect of bubbly mixtures and air ingestion on SFD forced performance CCO L=31.1 mm D=129 mm c=0.254 mm

12. 12 Background literature Bubbly SFD Diaz, S., Beets, T., and San Andrés, L., 2000, “Pressure Measurements and Flow Visualization in a Squeeze Film Damper Operating With a Bubbly Mixture” 30 o Uniform Pressure Zone: Maximum Film Thickness Onset of Positive Squeeze Maximum Gas Volume Fraction Non-Uniform Streaks (fingering) Minimum Pressure Zone: Film Thickness Increasing Onset of Air Ingestion Incoming gas from Discharge Maximum Pressure Zone: Film Thickness Decreasing Minimum Gas Volume Fraction Uniform Mixture  =0.540 SFD (CCO): c=0.254 mm, e=0.180 mm, 500 rpm, ISO VG 68 See digital videos at http://rotorlab.tamu.edu

13. 13 A simple model for bubbly mixtures Mixture density Quasi-static model – ignores bubble dynamics - Homogenous mixture of 2-components; isothermal & static equilibrium - Both components move with same speed & occupy same volume Ideal gas Gas volume fraction (known at inlet) For oil, P V ~0.010 bar and S=0.035 N/m, and with c=0.152 mm, P V +2S/c=0.0146 bar Diaz, S., and San Andrés, L., 2001, “A Model for Squeeze Film Dampers Operating with Air Entrainment and Validation with Experiments,” ASME J. Tribol., 123, pp. 125-133

14. 14 A simple model for bubbly mixtures Mixture viscosity McAdams model McAdams, W.H., Woods, W.K., and Heroman, L.C., Jr., 1942, “Vaporization inside Horizontal Tubes- II -Benzene-Oil Mixtures,” ASME Trans., 64, p.193  Realistic model, not depending on mass fraction All liquid All gas

15. 15 Bulk-flow Analysis of Annular Seals Flow Continuity Circumferential Momentum transport Axial momentum transport - Turbulent flow with fluid inertia effects - Mean flow velocities – average across film (h) - No accounting for strong recirculation zones - Includes round-hole and honeycomb pattern (textured surface seal) z W  PsPs U San Andrés, L., and Soulas, T., 2007, “A Bulk Flow Model for Off-Centered Honeycomb Gas Seals,” ASME J. Eng. Gas Turbines Power, 129, pp. 185-194 PaPa

16. 16 Wall shear stress differences Shear stresses Friction factors Other PaPa - Moody’s friction factor - Not affected by flow condition (single or two component) - Actual to be determined z W  PsPs U Salhi, A., Rey, C., and Rosant, J.M., 1992, “Pressure Drop in Single-Phase and Two-Phase Couette-Poiseuille Flow,” ASME J. Fluids Eng., 114, pp.80-84

17. 17 Bulk-flow Analysis of Annular Seals Boundary Conditions Numerical Solution Numerical solution for realistic geometries use CFD technique (staggered grids, upwinding, etc) and predict (4) K,C,M force coefficients. -Inlet pressure loss due to fluid inertia (Lomakin effect) - Inlet swirl determined by upstream condition (swirl-brake) -Exit pressure without recovery loss, typically. z VzVz  PsPs VxVx Anti swirl brake at inlet or pressure seal

18. 18 Model validation Air in Oil Mixture SFD SFD (CCO): c=0.254 mm, e=0.120 mm, 1000 rpm, ISO VG 68 Lines: predictions, Symbols: experiments , mixture volume fraction Tangential force Radial force Circular Centered orbit Diaz, S., and San Andrés, L., 2001, “A Model for Squeeze Film Dampers Operating with Air Entrainment and Validation with Experiments,” ASME J. Tribol., 123, pp. 125-133. Quasi-static bubbly flow model adequate for whole range of gas volume fractions (  =0.0-1.0)

19. 19 Example of analysis Geometry and operating conditions of seal with mixture Predict seal performance Mixture volume fraction  varies (0.0-1.0) Based on available test rig MIX OIL with N2 Table 1 Centered seal (e=0): No static load ~ smooth surfaces; L/D=0.75, c/R=0.002 Rotor speed,  1,047 rad/s (10 krpm) Diameter, D116.8 mmSupply Temperature, T S 298.3 K (25 C) Length, L87.6 mmSupply pressure, P S 71 bar Clearance, c126.7 mmExit pressure, P a 1 bar Smooth sealr r =0.0005r s =0.001 Entrance pressure loss,  0.25Inlet pre-swirl ratio, a0.50 Physical properties mixtureat P S, T S ISO VG 2Nitrogen (N 2 ) Viscosity,  2.14 c-Poise Viscosity,  0.0182 c-Poise Density,  784 kg/m 3 Density,  80.2 kg/m 3 Bulk-modulus,  20,682 barMolecular weight28 Surface tension, S0.035 N/mCompressibility, Z1.001 Vapor pressure0.010 bar  C P /C V 1.48 Sound speed, v s 1,624 m/sSound speed, v s 361 m/s Density at P a,  a 1.1 kg/m 3 Based on a proposed test rig

20. 20 Seal Flow rate vs. inlet gas volume fraction Figure 2 Mixture N 2 in ISO VG 2 oil (  P=71 bar, 10 krpm) All liquidAll gas Leakage decreases continuou sly as gas content increases

21. 21 Gas Mass fraction vs. inlet gas volume fraction Figure 3b Mixture N 2 in ISO VG 2 oil (  P=71 bar, 10 krpm) All liquidAll gas Gas/liquid mass content increases exponenti ally with gas volume content

22. 22 Exit gas volume fraction vs. inlet volume fraction Figure 3b Mixture N 2 in ISO VG 2 oil (  P=71 bar, 10 krpm) All liquidAll gas Gas volume fraction at exit plane increases quickly because of large pressure drop

23. 23 Axial pressure drop as gas fraction increases Figure 4 Mixture N 2 in ISO VG 2 oil (  P=71 bar, 10 krpm) inletExit All liquid: linear pressure drop. All gas: nonlinear with rapid changes near exit plane

24. 24 Drag power loss vs. inlet volume fraction Figure 5 Mixture N 2 in ISO VG 2 oil (  P=71 bar, 10 krpm) All liquidAll gas Steady decrease in power; but in region of flow transition

25. 25 Max. Reynolds # vs. inlet volume fraction Figure 6 Mixture N 2 in ISO VG 2 oil (  P=71 bar, 10 krpm) All liquidAll gas Axial flow dominates at high volume fractions. Circumf. flow Re# decreases.

26. 26 Rotordynamic coefficients – lateral motions Seal reaction forces: - Model for centered operation K XX = K YY, K XY = -K YX C XX = C YY, C XY = -C YX M XX = M YY, M XY = -M YX Whirl frequency ratio WFR ~ K XY C XX  : measure of rotordynamic stability Assumes: No static load X Y Force coefficients are functions of frequency  for gases, and also for a two-component (gas/liquid) mixture.

27. 27 Seal stiffnesses vs. inlet volume fraction Figure 7a Mixture N 2 in ISO VG 2 oil (  P=71 bar, 10 krpm) SYNCHRONOUS SPEED All liquidAll gas Liquid seal (oil) has large cross- coupled stiffness. Gas seal shows strong direct stiffness KXY=-KYX K XX =K YY K XY =-K YX Synchronous speed force coefficient  Mixture viscosity decreases

28. 28 Seal damping vs. inlet volume fraction Figure 7b Mixture N 2 in ISO VG 2 oil (  P=71 bar, 10 krpm) SYNC SPEED All liquidAll gas Direct damping decrease s as gas content increases, but in flow transition zone Cross- damping small. C XX =C YY C XY =-C YX N-s/m Mixture viscosity decreases

29. 29 Whirl frequency ratio – Stability indicator - WFR always 0.50 for inlet swirl = 0.50 – Stable operation up to 2 x critical speed Mixture N 2 in ISO VG 2 oil (  P=71 bar, 10 krpm) SYNC SPEED

30. 30 force coefficients – frequency dependency Seal reaction forces (centered seal): X Y Force coefficients are functions of frequency  for gases, and also for a two-component (gas/liquid) mixture.

31. 31 Seal direct stiffnesses vs. whirl frequency Figure 8a Mixture N 2 in ISO VG 2 oil (  P=71 bar, 10 krpm) All liquid shows added mass effect (K-  2 M). All gas (  =1) has large K XX. Note increase (*) in K XX for small  =0.1 K XX =K YY  K (*)  =0.1: Stiffness hardening is typical in textured gas damper seals (= negative added mass)

32. 32 Seal cross-stiffnesses vs. whirl frequency Figure 8b Mixture N 2 in ISO VG 2 oil (  P=71 bar, 10 krpm) K XY =-K YX  All liquid shows largest k. Cross- stiffness decreases with gas content. Small effect of frequency k

33. 33 Seal direct damping vs. whirl frequency Figure 9a Mixture N 2 in ISO VG 2 oil (  P=71 bar, 10 krpm) C XX =C YY Cross damping coefficients are one order of magnitude lower  C All liquid shows largest C. Same as cross-K. Small effect of frequency

34. 34 Equivalent force coefficients (K e,C e ) Seal reaction forces (circular orbits): X Y Radial and tangential components of force e tt FrFr FtFt

35. 35 Seal equivalent stiffness vs. whirl frequency Figure 10a Mixture N 2 in ISO VG 2 oil (  P=71 bar, 10 krpm) Cross damping small. All liquid shows added mass effect. All gas (  =1) has large K e. Note increase (*) in K e for small  =0.1 

36. 36 Seal equivalent damping vs. whirl frequency Figure 10a Mixture N 2 in ISO VG 2 oil (  P=71 bar, 10 krpm)  All liquid shows largest C e. Steady decrease of C e with gas content. Note C e =0 at  =0.5

37. 37 Conclusions Rotordynamic force coefficients of bubbly mixture annular pressure seals 1.Leakage and power loss decrease with the gas in liquid volume content – except in transition region from laminar to turbulent flow 2.Seal force coefficients show strong dependency on whirl frequency. Cross-coupled stiffnesses and direct damping coefficients decrease steadily as gas volume fraction raises. 3.Direct stiffness coefficients show atypical behavior, in particular a mixture of gas volume fraction  S=0.1 produces stiffness hardening as the excitation frequency increases. 4.Predictions justify an experimental program to quantify the static and dynamic forced performance of annular seals operating with (bubbly) mixtures GT2011-45264 Advanced (simple) computational physics bulk-flow model for prediction of seal performance static and dynamic. Assumed homogenous mixture of two components (liquid and gas). Mixture N 2 in ISO VG 2 oil (  P=71 bar, 10 krpm)

38. 38 Rotordynamic force coefficients of bubbly mixture annular pressure seals GT2011-45264 Questions (?) Learn more at http://rotorlab.tamu.edu © 2011 Luis San Andres