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A Novel Bulk-Flow Model for Improved Predictions of Force Coefficients in Grooved Oil Seals Operating Eccentrically

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## A Novel Bulk-Flow Model for Improved Predictions of Force Coefficients in Grooved Oil Seals Operating Eccentrically

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**ASME Turbo Expo 2011Power for Land, Sea and Air June 6-10,**2011, Vancouver, BC A Novel Bulk-Flow Model for Improved Predictions of Force Coefficients in Grooved Oil Seals Operating Eccentrically Adolfo Delgado Mechanical Engineer GE Global Research Center Luis San Andrés Mast-Childs Professor Texas A&M University ASME GT2011-45274 accepted for journal publication Presentation available at http://rotorlab.tamu.edu Supported by TAMU Turbomachinery Research Consortium**Oil Seals**Oil seal in a compressor [1] commonly used to prevent leakage of process fluid in centrifugal compressors. - 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 Kirk, R., 1986, “Oil Seal Dynamic Considerations for Analysis of Centrifugal Compressors,” Proc. 15thTurbomachinery Symposium, Houston, TX, pp. 25-34.**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 Predictive Models Semanate and San Andrés, (1993) - Bulk flow equation model • KXY (1 land)= 4 KXY(2 lands) • CXX (1 land)= 4 CXX(2 lands) - Grooves should reduce force coefficients by a factor of four, i.e. -Fluid inertia effects not predicted (assumed negligible)**30c**L 5c Coeffs are ¼ of original seal c Damping, Cross-coupled Stiffness & Inertia 2L c Journal Constant pressure 2-land seal: (deep groove divides lands) Short length seal**Smooth& grooved oil seals: test results**17 mm 25 mm Oil supply Seal length 136c 76c c Journal Parallel oil seal configuration [1] Childs et al., (2006, 2007) Parallel seal configuration (balance thrust force due to pressure drop across the seals) Includes ‘deep’ inlet (central) groove to feed seals Parameter identification:FSEAL= 1/2 FTest conf. Predictions do not consider groove or fluid inertia effects (Zirkelback and San Andrés1996) 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) [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.**≠**Old Predictions Experiments Inlet (central) groove not considered (null dynamic pressure). Ignores fluid inertia Large added mass coefficients ≠ Inner land groove should reduce crossed-coupled stiffness and direct damping coefficients by a factor of four Groove does not effectively separate seal lands • At most: KXY (1 land)= 2 KXY(2 lands) CXX (1 land)= 2 CXX(2 lands) Kxy (1 land)= 4 Kxy(2 lands) Cxx (1 land)= 4 Cxx(2 lands) ≠ Large added mass coefficients, increasing with increasing groove depth Null (neglected) added mass coefficients Need for better predictive models**Fluid flow predictive model**• Bulk flow for incompressible liquid • Qualitative observations of laminar flow field • Boundary Conditions • Characteristic groove depth oil supply, Ps Streamlines in axially symmetric grooved annular cavity. feed plenum groove mid-land groove Ps- Pd >0 Pd :discharge pressure Pd Pd z y 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**Linear fluid inertia model**No fluid inertia advection Oil supply 4 3 n 1 2 N n+1 IV III II I zN zIV zII zIII zI In each flow region: Reynolds equation with temporal fluid inertia**Finite Element Solution**Off-centered operation x= qR h W w e R Y De Film thickness X**Boundary conditions**Oil supply 4 3 n 1 2 N n+1 IV III II I zN zIV zII zIII zI Laminar flow Ps= supply pressure Pa= ambient pressure Ps Pa Pa First-order pressures and axial flow rates must be equal Null axial flow rate (axial symmetry) No generation of dynamic pressure**Finite Element for solution of Reynolds Eqn.**Assemble system of equations, impose boundary conditions and solve**Perturbation analysis of flow equations**Consider small amplitude journal (rotor) motions about a static equilibrium position (SEP) An applied external static load (Wo) determines the rotor equilibrium position (eX, eY)owith steady pressure fieldPoand film thicknessho Let the journal whirl with frequencyand small amplitude motions(eX, eY)about the equilibrium position. Hence Small amplitude journal motions about an equilibrium position**Seal dynamic reaction forces**• Lateral displacements (X,Y) Y X Z Stiffness coefficients Damping coefficients Inertia coefficients Force coefficients are independent of excitation frequency for incompressible fluid. Force coefficients depend on rotor speed & static load Measure of stability: Whirl frequency ratio WFR = Kxy/(CxxW)**Test Grooved Oil Seal & FE mesh**Outlet plane Grooves z q 2p 0 Inlet plane 17 mm 25 mm Oil supply Seal length Discharge plenum 2 mm 136c 76c c Buffer seal Journal (0-15) c Parallel oil seals Configuration [Childs et al] 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), 398-406. x=Rq Clearance = 86 mm Journal diameter: 117 mm**Boundary conditions**Outlet plane Groove Groove z P=Psupply Inlet plane x P(q,z)=P(q+2p,z) Laminar flow Constantstatic pressure at exit plane P=Pexit Flow continuity is automatically satisfied at boundaries Null dynamic pressure at exit plane If oil cavitation (Pcav=0), the first order dynamic pressure field vanishes • Zeroth Order Pressure Field • First Order Pressure Field Constant static pressure at inlet plane Null axial flow rate (axial symmetry) Zeroth and first order pressure and flow fields are periodic in circumferential direction**Groove effective depth**CFD simulations show streamline separating flow regions IS aphysical boundarydelimiting the domain for squeeze film flow due to journal radial motions. Ps= supply pressure Pa= ambient pressure Ps Pa Test seal 10c Laminar flow 15c Inner land groove close up (CFD -Pressure driven flow)**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), 398-406. x=Rq Effective depths in model Central groove = 9c Inner land groove = 6c**Test oil seal operating conditions**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), 398-406. Shaft speed:10,000 rpm Test data Static eccentricity ratio:0, 0.3, 0.5, 0.7 Load Supply pressure:70 bar Journal center locus shows oil seal operates with oil cavitation at the largest test eccentricities (large static load) Journal locus**Oil Seal Leakage**10,000 rpm, 70 bar Predicted leakage correlates very well with tests for both smooth land and grooved seal Smooth Seal Grooved Seal (ch = 7c) (cg= 15c) Figure 14**Oil Seal Forces**10,000 rpm, 70 bar Smooth Seal KXX Grooved Seal (ch = 7c) (cg= 15c) At high eccentricity, test data shows larger seal reaction force for smooth & grooved seals Figure 7**Oil Seal Direct Stiffness**10,000 rpm, 70 bar Model predicts well direct stiffness for smooth & grooved seals Smooth Seal KXX Grooved Seal (ch = 7c) (cg= 15c) Smooth Seal KYY Grooved Seal Figure 8**Oil Seal Cross Stiffness**10,000 rpm, 70 bar KXY Model predicts well decrease in cross-stiffness when adding inner groove Smooth Seal Grooved Seal KYX (ch = 7c) Grooved Seal (cg= 15c) Smooth Seal Figure 9**Oil Seal Cross-Stiffnesses**70 bar e = 0.0, 0.3 Eccentricity=0 rotor speed increases Smooth Seal Grooved Seal Model effectively predicts reduction in cross-coupled stiffness due to mid-land groove. KXY Eccentricity=0.3 Smooth Seal Grooved Seal (ch = 7c) (cg= 15c) KXY Figure 10**Oil Seal Direct Damping**10,000 rpm, 70 bar Model predicts accurately reduction in direct damping due to inner land groove. CXX Smooth Seal Grooved Seal (ch = 7c) CYY (cg= 15c) Smooth Seal Grooved Seal Figure 11**Oil Seal Cross Damping**10,000 rpm, 70 bar Small cross-damping, test data shows larger magnitude than predictions Smooth Seal CXY Grooved Seal Smooth Seal (ch = 7c) CYX Grooved Seal (cg= 15c) Figure 12**Oil Seal Added Mass**10,000 rpm, 70 bar Figure 13 Test data shows large added mass coefficients. Predictions correlate well with experimental results. MXX Grooved Seal Added mass coefficients are larger for grooved seal Smooth Seal Classical theory (*) predicts ~ 1/10 of test value (ch = 7c) (cg= 15c) [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.**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:**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:**http://rotorlab.tamu.edu**Learn more at Acknowledgments Thanks to TAMU Turbomachinery Research Consortium Questions (?) © 2011 Luis San Andres**Prediction: pressure fields for oil seal without inner**groove Journal whirl motion with r=5 mm, w=200 Hz) • Classical:central groove dyn. pressure = 0 (b) Current – central groove interacts with film lands**Prediction: pressure fields for oil seal with inner groove**Journal whirl motions with r=5 mm, w=200 Hz) • Classical:central groove dyn. pressure = 0inner land dyn. pressure = 0 (b) Current – central groove and inner groove interacts with film lands