Grooved Oil Seals: Force Coefficients GT A Novel Bulk-Flow Model for Improved Predictions of Force Coefficients in Grooved Oil Seals Operating Eccentrically accepted for journal publication ASME GT Luis San Andrés Mast-Childs Professor Texas A&M University Adolfo Delgado Mechanical Engineer GE Global Research Center Supported by TAMU Turbomachinery Research Consortium Presentation available at ASME Turbo Expo 2011 Power for Land, Sea and Air June 6-10, 2011, Vancouver, BC

Grooved Oil Seals: Force Coefficients GT Oil Seals Oil seal in a compressor [1] - Locked oil seal rings can induce instability in compressors. - A common remedy: seals are grooved to reduce cross-coupled stiffness and lower lock-up forces commonly used to prevent leakage of process fluid in centrifugal compressors. Kirk, R., 1986, “Oil Seal Dynamic Considerations for Analysis of Centrifugal Compressors,” Proc. 15th Turbomachinery Symposium, Houston, TX, pp

Grooved Oil Seals: Force Coefficients GT 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 (assumed negligible) Predictive Models Baheti and Kirk, (1995) - Reynolds and energy equation (FEM) - Grooves should effectively isolate seal lands - Cross-coupled stiffness and damping coefficients are reduced by ~60 % for grooved configurations - Bulk flow equation model

Grooved Oil Seals: Force Coefficients GT L2L c Journal Constant pressure Short length seal Damping, Cross-coupled Stiffness & Inertia 2-land seal: (deep groove divides lands) L c 30c 5c5c Coeffs are ¼ of original seal

Grooved Oil Seals: Force Coefficients GT [1] Graviss, M., 2005, “The Influence of a Central Groove on Static and Dynamic Characteristics of an Annular Liquid Seal with Laminar Flow,” M.S. Thesis, Texas A&M Univ., College Station, TX. Parallel oil seal configuration [1] 17 mm 76c c 25 mm 136c Oil supply Seal length Journal Parallel seal configuration (balance thrust force due to pressure drop across the seals) Includes ‘deep’ inlet (central) groove to feed seals Parameter identification: F SEAL = 1/2 F Test conf. Predictions do not consider groove or fluid inertia effects ( Zirkelback and San Andrés 1996) Smooth& grooved oil seals: test results Childs et al., (2006, 2007) Results Force coefficients are well predicted (C,K) except added mass coefficients Large added mass coefficients (~15 kg) Added mass predictions using Classical model (Reinhardt & Lund – 1975) (single land- i.e. not including inlet groove) (2.84 kg)

Grooved Oil Seals: Force Coefficients GT Old Predictions Experiments ≠ Inner land groove should reduce crossed-coupled stiffness and direct 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 Need for better predictive models Inlet (central) groove not considered (null dynamic pressure). Ignores fluid inertia Large added mass coefficients ≠ At most: K XY (1 land)= 2 K XY (2 lands) C XX (1 land)= 2 C XX (2 lands)

Grooved Oil Seals: Force Coefficients GT 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 Fluid flow predictive model Bulk flow for incompressible liquid Qualitative observations of laminar flow field Boundary Conditions Characteristic groove depth Delgado, A., and San Andrés, L., 2010, “A Model for Improved Prediction of Force Coefficients in Grooved Squeeze Film Dampers and Oil Seal Rings,” ASME J. Tribol., 132

Grooved Oil Seals: Force Coefficients GT Linear fluid inertia model n+1 Oil supply zIzI z III z II z IV zNzN n IV N III II I No fluid inertia advection In each flow region: with temporal fluid inertiaReynolds equation

Grooved Oil Seals: Force Coefficients GT Finite Element Solution Off-centered operation x=  R Y X ee  h  R e Film thickness

Grooved Oil Seals: Force Coefficients GT Boundary conditions No generation of dynamic pressure First-order pressures and axial flow rates must be equal Null axial flow rate (axial symmetry) PaPa PaPa P s = supply pressure P a = ambient pressure Laminar flow PsPs

Grooved Oil Seals: Force Coefficients GT Assemble system of equations, impose boundary conditions and solve Finite Element for solution of Reynolds Eqn.

Grooved Oil Seals: Force Coefficients GT Consider small amplitude journal (rotor) motions about a static equilibrium position (SEP) Small amplitude journal motions about an equilibrium position An applied external static load ( W o ) determines the rotor equilibrium position ( e X, e Y ) o with steady pressure field P o and film thickness h o Let the journal whirl with frequency  and small amplitude motions (  e X,  e Y ) about the equilibrium position. Hence Perturbation analysis of flow equations

Grooved Oil Seals: Force Coefficients GT Seal dynamic reaction forces Stiffness coefficients Damping coefficients Force coefficients are independent of excitation frequency for incompressible fluid. Force coefficients depend on rotor speed & static load X Y Z Lateral displacements (X,Y) Inertia coefficients Measure of stability: Whirl frequency ratio WFR = K xy /(C xx 

Grooved Oil Seals: Force Coefficients GT Test Grooved Oil Seal & FE mesh Childs, D. W., Graviss, M., and Rodriguez, L. E., 2007, “The Influence of Groove Size on the Static & Rotordynamic Characteristics of Short, Laminar-Flow Annular Seals,” ASME J. Tribol, 129(2), 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 

Grooved Oil Seals: Force Coefficients GT 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 Zeroth and first order pressure and flow fields are periodic in circumferential direction Null dynamic pressure at exit plane Null axial flow rate (axial symmetry) If oil cavitation (P cav =0), the first order dynamic pressure field vanishes Flow continuity is automatically satisfied at boundaries Laminar flow

Grooved Oil Seals: Force Coefficients GT Groove effective 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 land groove close up (CFD -Pressure driven flow) Laminar flow P s = supply pressure P a = ambient pressure 10c 15c PaPa PsPs

Grooved Oil Seals: Force Coefficients GT Test Grooved Oil Seal Childs, D. W., Graviss, M., and Rodriguez, L. E., 2007, “The Influence of Groove Size on the Static & Rotordynamic Characteristics of Short, Laminar-Flow Annular Seals,” ASME J. Tribol, 129(2), x=R  Diameter117 mm Land length24.89 mm Radial land clearance, c85.9 mm Central groove length17 mm Central groove depth136c Inner land groove length2 mm Inner land groove depth0c and 15c Static journal eccentricity (e/c)0-0.7 Shaft speed4,000-10,000 rpm Supply pressure70 bar Oil density850 kg/m 3 Oil viscosity (smooth seal)0.016 Pa.s (54 0 C) Oil viscosity (grooved seal)0.019 Pa.s (49 0 C) Effective depths in model Central groove = 9c Inner land groove = 6c

Grooved Oil Seals: Force Coefficients GT Test oil seal operating conditions Load Journal center locus shows oil seal operates with oil cavitation at the largest test eccentricities (large static load) Journal locus Shaft speed: 10,000 rpm Static eccentricity ratio: 0, 0.3, 0.5, 0.7 Supply pressure: 70 bar Test data Childs, D. W., Graviss, M., and Rodriguez, L. E., 2007, “The Influence of Groove Size on the Static & Rotordynamic Characteristics of Short, Laminar-Flow Annular Seals,” ASME J. Tribol, 129(2),

Grooved Oil Seals: Force Coefficients GT Oil Seal Leakage Predicted leakage correlates very well with tests for both smooth land and grooved seal Smooth Seal Grooved Seal (c g = 15c) (c  = 7c) 10,000 rpm, 70 bar Figure 14

Grooved Oil Seals: Force Coefficients GT Oil Seal Forces At high eccentricity, test data shows larger seal reaction force for smooth & grooved seals Smooth Seal Grooved Seal K XX 10,000 rpm, 70 bar (c g = 15c) (c  = 7c) Figure 7

Grooved Oil Seals: Force Coefficients GT Oil Seal Direct Stiffness Model predicts well direct stiffness for smooth & grooved seals Smooth Seal Grooved Seal Smooth Seal Grooved Seal K YY K XX 10,000 rpm, 70 bar (c g = 15c) (c  = 7c) Figure 8

Grooved Oil Seals: Force Coefficients GT Oil Seal Cross Stiffness Model predicts well decrease in cross- stiffness when adding inner groove Smooth Seal Grooved Seal Smooth Seal Grooved Seal K YX K XY 10,000 rpm, 70 bar (c g = 15c) (c  = 7c) Figure 9

Grooved Oil Seals: Force Coefficients GT Model effectively predicts reduction in cross-coupled stiffness due to mid- land groove. Smooth Seal Grooved Seal K XY Eccentricity=0.3 Eccentricity=0  = 0.0, 0.3 Smooth Seal Grooved Seal (c g = 15c) (c  = 7c) Oil Seal Cross-Stiffnesses 70 bar Figure 10 rotor speed increases

Grooved Oil Seals: Force Coefficients GT Oil Seal Direct Damping Model predicts accurately reduction in direct damping due to inner land groove. Smooth Seal Grooved Seal Smooth Seal Grooved Seal C YY C XX 10,000 rpm, 70 bar (c g = 15c) (c  = 7c) Figure 11

Grooved Oil Seals: Force Coefficients GT Oil Seal Cross Damping Small cross-damping, test data shows larger magnitude than predictions Smooth Seal Grooved Seal Smooth Seal Grooved Seal C YX C XY 10,000 rpm, 70 bar (c g = 15c) (c  = 7c) Figure 12

Grooved Oil Seals: Force Coefficients GT Test data shows large added mass coefficients. Predictions correlate well with experimental results. Added mass coefficients are larger for grooved seal Classical theory (*) 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 M XX Smooth Seal Grooved Seal (c g = 15c) (c  = 7c) Oil Seal Added Mass 10,000 rpm, 70 bar Figure 13

Grooved Oil Seals: Force Coefficients GT Good correlation for direct force coefficients for the lower journal eccentricities (e/c=0,0.3) and moderate to good correlation for e/c=0.5. Cross-coupled stiffnesses also predicted accurately for the smaller eccentricities. FE model accurately predicts the reduction of the direct stiffness, direct damping, and cross-coupled stiffness coefficients when adding a circumferential groove to the seal land. Added mass coefficients for both seals (smooth and grooved) are also predicted accurately (within 20 %). Both analysis and test results show a grooved seal has larger direct added mass coefficient than a smooth seal. Conclusions:

Grooved Oil Seals: Force Coefficients GT Discrepancies between test results and predictions for large journal eccentricities (e/c)~0.70. Discrepancies due to (unknown) changes in seal clearance and oil viscosity induced by thermal effects. Current model is a significant improvement over prevailing predictive tools to analyze grooved oil seals. Deep grooves do not fully uncouple parallel film lands!! Model applied successfully to grooved SFDs (+ additional experimental verifications) Conclusions:

Grooved Oil Seals: Force Coefficients GT Thanks to TAMU Turbomachinery Research Consortium Acknowledgments Questions (?) Learn more at © 2011 Luis San Andres

Grooved Oil Seals: Force Coefficients GT Prediction: pressure fields for oil seal without inner groove Journal whirl motion with r=5  m,  =200 Hz) (b) Current – central groove interacts with film lands (a) Classical: central groove dyn. pressure = 0

Grooved Oil Seals: Force Coefficients GT Journal whirl motions with r=5  m,  =200 Hz) Prediction: pressure fields for oil seal with inner groove (a) Classical: central groove dyn. pressure = 0 inner land dyn. pressure = 0 (b) Current – central groove and inner groove interacts with film lands