1. This material is based upon work supported by NASA Research Announcement NNH06ZEA001N-SSRW2, Fundamental Aeronautics: Subsonic Rotary Wing Project 2 # 32525/39600/ME and the Turbomachinery Research Consortium Luis San Andrés Mast-Childs Professor Fellow ASME Texas A&M University Keun Ryu Research Assistant Texas A&M University Tae Ho Kim Senior Research Scientist Korea Institute of Science and Technology ASME TURBO EXPO 2010, Glasgow, Scotland, UK ASME paper GT2010-22983 Thermal Management and Rotordynamic Performance of a Hot Rotor-Gas Foil Bearings System Part 2: Predictions vs. Test Data J. Eng. Gas Turbines Power (In-Press)

2. Gas Foil Bearings Issues Endurance: performance at start up & shut down (lift off speed) Little test data for rotordynamic force coefficients & operation with limit cycles (sub harmonic motions) Thermal management for high temperature applications (gas turbines, turbochargers) Predictive models lack validation for GFB operation at HIGH TEMPERATURE

3. To develop a detailed, physics- based computational model of gas-lubricated foil journal bearings including thermal effects to predict bearing performance. The result of this work shall include a fully tested and experimentally verified design tool for predicting gas foil journal bearing torque, load, gas film thickness, pressure, flow field, temperature distribution, thermal deformation, foil deflections, stiffness, damping, and any other important parameters. Main Objective Agreement NASA NNH06ZEA001N-SSRW2

4. 4 Benchmark TEHD computational model for prediction of GFB performance at high temperatures and quantify effectiveness of thermal management Perform physical analysis, derive equations, implement numerical solution, and construct GUI for User ready use Compare GFB predictions to published test data (TAMU mainly) Objective & tasks ASME GT2010-22981 ASME GT2009-59919

5. Why thermal effects are important? isothermal flow models are adequate in most applications but those with hot rotors such as in turbochargers and gas turbines. Models couple the gas film pressure generation and thermal energy transport to the underspring (bumps) structure with thermal conduction and convection paths. Gas bearings (when airborne) are nearly friction free, hence the show small (drag) power loss and temperature raise. With hot rotors the “lubricant” in the bearings must also cool components. But gases have small thermal capacity and conductivity, and hence, get hot! Rises in temperature change material properties (solids and gas), and most importantly, change bearing clearances!

6. Overview – GFB TEHD models Le Lez et al. (2007): THD model predicts larger load capacity because of increase in gas viscosity but forgets thermo-mechanical deformations Peng and Khonsari (2006): Noted importance of side cooling flow with incorrect THD model Feng and Kaneko (2008), San Andrés and Kim (2009), Kim (2010): TEHD models predict temperatures agreeing with test data (Radil and Zeszotek, 2006) for room temperature & without cooling flow Few models incorporate thermo-mechanical deformations needed to ensure proper thermal management od the foil bearings But little is known from test bearings and operating conditions! Many assumptions to match test data. Need independent data base

7. Our GFB TEHD model ASME GT2009-59919 Gas film Reynolds eqn. for hydrodynamic pressure generation Energy transport eqn. for mean flow temperature Various surface heat convection models Mixing of temperature at leading edge of top foil Top foil & underspring Thermo-elastic deformation eqns. Finite Elements and discrete parameter for bump strips. Thermal energy conduction paths to side cooling flow and bearing housing. Bearing clearance Material properties (gas & foils) = f (Temperature) Shaft thermal and centrifugal growth Bearing thermal growth Excel GUI + executable licensed by TAMU

8. 8 Gas film pressure generation - Ideal gas with density, - Gas viscosity, - Gas Specific heat (c p ) and thermal conductivity (κ g ) at an effective temperature Bump strip layer Top foil Hollow shaft Bearing housing External fluid medium Inner flow stream Outer flow stream Thin film flow X Y X=RΘ Side view of GFB with hollow shaft Reynolds equation in thin film

9. 9 THD model GFB with cooling flows (inner and/or outer) Outer flow stream Top foil Bearing housing “Bump” layer z x P Co, T Co X Y Z Bearing housing P Ci, T Ci Inner flow stream ΩR So Hollow shaft PaPa Thin film flow z=0z=L T∞T∞ Convection of heat by fluid flow + diffusion to bounding surfaces = compression work + dissipated energy Bulk-flow temperature transport equation

10. 10 Q Ci Heat carried by thin film flow Heat carried by outer flow stream : Heat (-) : Heat (+) QBQB Q Co Drag dissipation power (gas film) Heat carried by inner flow stream Heat conduction through shaft TSTS Heat flow paths in rotor - GFB system Heat flows & thermal resistances in a GFB & hollow shaft Heat conducted into bearing Cooling gas streams carry away heat

11. Top foil thickness,Bump foil thickness,Bump height,Gas Constant,Viscosity,1.73Conductivity,Density, Test Foil Bearings Parameter [mm] Bearing cartridge Outer diameter50.85 Inner diameter39.36 Top foil and bump strip layer Top foil axial length38.2 Top foil thickness0.100 Bump foil thickness0.100 Number of Bumps25 × 5 axial Bump pitch4.581 Bump length3.742 Bump height0.468 Bump arc radius5.581 Bump arc angle [deg]36.5 Elastic Modulus 214 GPa, Poisson ratio=0.29 (Gen II) Uncoated top foil Read ASME GT2010-22981 For test procedure and measurements. Complete bearing geometry and operating conditions DISCLOSED

12. 12 Typical predictions: P & T fields No cooling: Shaft temp. rise=79 °C with axial cooling at 150 L/min Shaft temp. rise=32 °C Reduction of ~ 50 °C!

13. 13 Top foil Bump layer Hollow shaft Bearing housing External fluid dӨ R Si R So R Fi R Fo R Bi R Bo T Ci T∞T∞ T Bo T Bi T Fo T So T Si T Fi TfTf Radial direction T Co With forced cooling, GFB will operate 50°C cooler. Outer cooling stream is most effective in removing heat Predictions radial temperature Natural convection on exposed surfaces of bearing OD and shaft ID Mean temperature No cooling Shaft temp. rise=79 °C 50 L/min Shaft temp. rise=67 °C 125 L/min Shaft temp. rise=39 °C 150 L/min Shaft temp. rise=32 °C Cooling stream increases DE FB Rotor speed : 30 krpm w/o & w cooling flow

14. 14 Width of arrow denotes intensity of energy transport Thermal energy transport and balance Dissipated energy + compression work 100% Advection of heat by gas film flow 11 % Forced heat convection into outer cooling stream 82 % Conduction into bearing cartridge 2 % Heat conduction into shaft 5 % Predictions: example

15. Temperatures in test rig Foil bearings Cartridge heater Heater stand T14 T10 T12 T13 Coupling cooling air Drive motor T15 T16 Th Hollow shaft T5 T11 Tamb T1 T4 T3 T2 45º Free end (FE) GFB g 45º T6 T7 T8 T9 Drive end (DE) GFB g Insulated safety cover Cooling air Thermocouples: 1 x heater, 2 x 4 FB outboard, 2 x Bearing housing outer surface, 1x Drive motor, 1 x ambient + infrared thermometers 2 x rotor, rotor surface temperature (Total = 17)

16. 16 Thermocouples in test foil bearing five (5) thermocouples placed within machined axial slots. at FB uncoated (Generation II)

17. 17 Recap: the test rotor and FB Outer flow stream Top foil Bearing housing “Bump” layer z x P Co, T Co Bearing housing PaPa Thin film flow z=0z=L T∞T∞   R So Heat source ThTh Cooling stream Hollow rotor Hot air (out) ambient Schematic view of rotor and heater cartridge + side cooling stream

18. No cooling 50 LPM Test data Predictions Error bar Max. Avg. Min. predictions & tests FB OD temperature rises with rotor speed and decreases with forced cooling stream ~ 50 LPM. Predictions agree with test data Room temperature 21 °C. static load ~ 6.5N Bearing outboard temperature Drive end FB Heater OFF Rotor speed : 30 krpm w/o and w low cooling rotor speed (krpm) Temperature rise (C)

19. predictions & tests FB cartridge temperature increases linearly with rotor temperature. Predictions follow test data: good at DEB (colder) Supply air (T Supply ) ~ 21 °C. Test data Predictions DE Bearing Temp Test data Predictions FE Bearing Temp static load ~ 6.5N static load ~ 3.5N Shaft temperature rise (C) Heater up to 360C. Rotor speed : 30 krpm No cooling flow Bearing outboard temperature Temperature rise (C)

20. As cooling flow rate increases, FB cartridge temperature decreases. Predictions agree with test data. Test dataPredictions No cooling 50LPM 150 LPM 125LPM 100LPM static load ~ 6.5N Supply air (T Supply ) ~ 21 °C. Heater up to 360C Rotor speed : 30 krpm w/o & w cooling flow DE Bearing temperature rise predictions & tests Bearing cartridge temperature Shaft temperature rise (C) Temperature rise (C)

21. 21 Cartridge heater temperature increases No heating T hs =360ºC T hs =200ºC Cartridge heater temperature increases No heating T hs =200ºC T hs =360ºC Static load parameters static load ~ 6.5 N No cooling flow As temperature increases, journal attitude angle and drag torque increase but journal eccentricity and minimum film thickness decrease due to reduction in operating clearance Drive End FB predictions Rotor speed (krpm)

22. 22 No heating K XY K YX Cartridge heater temperature increases T hs =200ºC T hs =360ºC No heating K XX K YY Cartridge heater temperature increases T hs =200ºC T hs =360ºC As temperature increases, stiffnesses (K XX, K YY ) increase significantly, while difference (K XY -K YX ) increases slightly at low rotor speeds and decreases at high rotor speeds static load ~ 6.5 N No cooling flow Drive End FB Bearing stiffnesses predictions Rotor speed (krpm)

23. 23 As temperature increases, damping (C XX, C YY ) increase. Cross damping (C XY,C YX ) change little above 30 krpm. C YX C XY No heating T hs =200ºC T hs =360ºC No heating C YY C XX Cartridge heater temperature increases T hs =200ºC T hs =360ºC Cartridge heater temperature increases static load ~ 6.5 N No cooling flow Drive End FB Bearing damping predictions Rotor speed (krpm)

24. 24 40,000 rpm 20,000 rpm Outer cooling flow Inner and outer cooling flows Laminar flow Turbulent flow Re D = 2300 Cooling flow rate increases No cooling flow Effect of cooling flow Peak temperature drops with strength of cooling stream. Sudden drop at ~ 200 LPM from transition of laminar to turbulent flow Supply air (T Supply ), shaft (T S ), and bearing OD (T B ) temperatures at 21 °C. Static load =89 N (180°). T Supply =21°C Rotor speed : 20 & 40 krpm predictions

25. 25 predictions & tests As heater temperature rises, rotor amplitude decreases for speed < 15 krpm & the critical speed increases from 14 krpm to 17 krpm Cartridge heater temperature increases T hs =360ºC T hs =200ºC No heating Predictions Test data Heater to 360C. No forced cooling Drive End (H) Rotor speed (krpm) 1X rotor response

26. 26 - A physics-based computational THD model predicts accurately measured FB OD temperatures for increasing shaft temperatures w/ and w/o cooling flow - THD Model prediction delivers static load parameters and dynamic force coefficients versus rotor speed for shaft increasing temperatures - Rotordynamic analysis integrating predicted FB force coefficients reproduces reduction in rotor peak amplitude and increase in system rigid-mode critical speed with increasing shaft temperature Predictive tool validated & benchmarked to reliable test data base !!! Conclusions

27. Acknowledgments Thanks support of NASA GRC (2007-09) & Dr. Samuel Howard NSF (2003-06), TRC (2004-08) Mechanical Solutions, Inc. [Foster-Miller] KIST (Korea Institute of Science & Technology) Learn more http://rotorlab.tamu.edu Questions ?