1. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals A novel FE Bulk-Flow Model for Improved Predictions of Force Coefficients in Off- Centered Grooved Oil Seals 28th TRC Annual Meeting 2008 TRC Project: 32513/1519 T7 TRC-SEAL-1-08 Luis San Andrés Mast-Childs Professor Adolfo Delgado Research Assistant

2. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Oil Seals Oil seal in a compressors[1] - Locked oil seal rings can induce instability in compressors. - Seals are grooved to reduce cross-coupled stiffness and lower lock-up forces Oil seals are commonly used to prevent leakage of process fluid in centrifugal compressors.

3. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals 2L c Journal Constant pressure Short length seal Damping, Cross-coupled Stiffness & Inertia 2-land seal: (deep groove divides lands) L c 30c 5c Coeffs are ¼ of original seal

4. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Childs et al., (2006) Single groove and multiple groove oil seal (single clearance) Large added mass coefficients (~30 kg) Childs et al., (2007) Test Grooved Oil Seals Experimental Results One groove with groove depths (5c,10c,15c) Groove does not effectively separate seal lands Results Force coefficients are underpredicted (grooved seal) Added mass versus eccentricity ratios [Childs et. al]

5. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Grooved Oil Seal: Predictions Experiments ≠ Groove should reduce crossed- coupled stiffness and damping coefficients by a factor of four Groove does not effectively separate seal lands K xy (1 land)= 4 K xy (2 lands) C xx (1 land)= 4 C xx (2 lands) ≠ Null (neglected) added mass coefficients Large added mass coefficients, increasing with increasing groove depth ≠ At most K xy (1 land) ~2 K xy (2 lands) C xx (1 land) ~2 C xx (2 lands) Need for better predictive models

6. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals P s - P d >0 P d :discharge pressure y z feed plenum groove mid-land groove oil supply, P s Streamlines in axially symmetric grooved annular cavity. PdPd PdPd Improved predictive model Bulk flow, centered operation, incompressible fluid Qualitative observations of laminar flow field Boundary Conditions Characteristic groove depth TRC-SFD-2-07

7. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Bulk flow model n+1 Oil supply zIzI z III z II z IV 1 2 3 4 zNzN n IV N III II I No fluid advection Separate flow regions Reynolds eqn with temporal fluid inertia Centered operation

8. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Finite Element Solution Off-centered operation x=  R Y X ee  h  R e Reynolds eqn. with temporal fluid inertia Film thickness

9. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals FEM for solution of Pressure field Assemble system of equations, impose boundary conditions and solve

10. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Excel® GUI: XFEGLOSeal User inputs: -Fluid properties: Density and viscosity -Operating conditions: Inlet and outlet pressures, static journal eccentricity. -Geometry: Rotor diameter, clearance, groove depth, number of grooves, inlet and outlet land length, inter-groove length, groove length. ( XF inite E lement G rooved L aminar O il S EAL )

11. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Test Grooved Oil Seal & FE mesh Childs, D. W., Graviss, M., and Rodriguez, L. E., 2007, “The Influence of Groove Size on the Static and Rotordynamic Characteristics of Short, Laminar-Flow Annular Seals,” ASME J. Tribol, 129(2), 398-406. Clearance= 86  m Journal diameter: 117 mm Parallel oil seals Configuration [Childs et al] 17 mm 76c c (0-15) c 25 mm 136c Oil supply Seal length Discharge plenum Buffer seal Journal 2 mm Outlet plane  z Inlet plane 0 22 Grooves x=R 

12. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Effective groove depth Test seal CFD simulations show: streamline separating flow regions IS a physical boundary delimiting the domain for squeeze film flow due to journal radial motions. Inner groove close up (CFD -Pressure driven flow) Laminar flow PsPs PaPa P s = supply pressure P a = ambient pressure 10c 15c

13. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Seal operating conditions Load Journal center locus indicates seal operates with oil cavitation at the largest test eccentricities Journal locus Shaft speed: 10,000 rpm Static eccentricity ratio: 0, 0.3, 0.5, 0.7 Supply pressure: 70 bar Test data

14. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Leakage Predicted leakage correlates well with experiments for both smooth land and grooved seal Smooth Seal Grooved Seal (c g = 15c) (c  = 7c) 10,000 rpm, 70 bar

15. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Direct Damping Model predicts accurately reduction in direct damping due to inner land groove. Smooth Seal Grooved Seal Smooth Seal Grooved Seal CyyCyy CxxCxx 10,000 rpm, 70 bar (c g = 15c) (c  = 7c)

16. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Cross-coupled Stiffness Model effectively predicts reduction in cross-coupled stiffness due to mid-land groove. Smooth Seal Grooved Seal K xy Eccentricity ratio=0.3 Eccentricity ratio=0  = 0, 0.3 Smooth Seal Grooved Seal 70 bar (c g = 15c) (c  = 7c)

17. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Added Mass Experimental data shows relatively large added mass coefficients. Predictions correlate well with experimental results. Added mass coefficients are larger for grooved seal Classical theory [1] predicts ~ 1/10 of test value [1] Reinhardt, F., and Lund, J. W., 1975, “The Influence of Fluid Inertia on the Dynamic Properties of Journal Bearings,” ASME J. Lubr. Technol., 97(1), pp. 154-167. M xx 10,000 rpm, 70 bar Smooth Seal Grooved Seal (c g = 15c) (c  = 7c)

18. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Predictions accurately capture the reduction of force coefficients on oil seals due to the addition of circumferential grooves. Predicted force coefficients (K,C,M) correlate well with experimental data. Boundary conditions reproduce well physical system. A groove does not fully uncouple adjacent film lands!! Conclusions:

19. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Boundary Conditions P=P exit Zeroth Order Pressure Field Constant static pressure at inlet plane Constant static pressure at exit plane First Order Pressure Field For both the zeroth and first order fields the pressure field be periodic in the circumferential direction Null dynamic pressure at exit plane Null axial flow rate (geometrical symmetry) In the occurrence of oil cavitation (P cav =0), the first order dynamic pressure field vanishes Flow continuity is automatically satisfied at boundaries Laminar flow

20. TRC Project: Predictions of Force Coefficients in Off-Centered Grooved Oil Seals Grooved Oil Seals - Grooves should reduce force coefficients by a factor of four, i.e. Semanate and San Andrés, (1993) K xy (1 land)= 4 K xy (2 lands) C xx (1 land)= 4 C xx (2 lands) -Fluid inertia effects not predicted (considered negligible) Baheti and Kirk, (1995) Predictive Models - Reynolds and energy equation (Finite element solution) - Grooves should effectively isolate seal lands - Cross-coupled stiffness and damping coefficients are reduced by ~60 % for grooved configurations - Bulk flow equation model