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 ASME Turbo Expo 2009: Power for Land, Sea, and Air Thermohydrodynamic Analysis of Bump Type Gas Foil Bearings: A Model Anchored to Test Data Texas A&M University Luis San Andrés Tae Ho Kim Mast-Childs Professor Research Associate ASME GT2009-59919 Accepted for J. Eng. Gas Turbines Power (In-Press)

2. Gas Foil Bearings – Bump type Series of corrugated foil structures (bumps) assembled within a bearing sleeve. Integrate a hydrodynamic gas film in series with one or more structural layers. PROVEN TECHNOLOGY!! Applications: Aircraft ACMs, micro gas turbines, turbo expanders, turbo compressors, Damping from dry-friction and operation with limit cycles Tolerant to misalignment and debris, also high temperature Need coatings to reduce friction at start-up & shutdown Often need cooling flow for thermal management of rotor-GFB system

3. Gas Foil Bearings (+/-) Increased reliability: large load capacity (< 100 psi) No lubricant supply system, i.e. reduce weight High & low temperature capability (up to 1,200º F) No scheduled maintenance with increased life Less load capacity than rolling or oil bearings Thermal management (cooling) issues Little test data for rotordynamic force coefficients Predictive models lack validation. Difficulties in accessing full test data – geometry and operating conditions

4. Overview – GFB computational models Salehi et al. (2001): Couette flow approximation to estimate bearing temperatures. Heshmat (1983), Carpino and Talmage (2003, 2006), Kim and San Andrés (2005, 2007), Lee, et al. (2006), Le Lez, et al. (2008): Predict static/dynamic performance of bump-type GFBs with isothermal flow model and simple to complex foil models Le Lez et al. (2007): Nonlinear elastic bump model. THD model predicts larger load capacity than isothermal flow model. Peng and Khonsari (2006): Thermal management of GFB from cooling gas stream underneath top foil. Feng and Kaneko (2008), San Andrés and Kim (2009): FE top foil & support structure model. Predicted bearing temperatures in agreement with test data (Radil and Zeszotek, 2006), obtained at room temperature (~21°C) without cooling flow. Thermohydrodynamic (THD) model predictions:

5. Overview – Rotordynamic measurements DellaCorte and Valco (2000): Review open literature and estate Rule of Thumb to estimate load capacity of GFBs. Salehi et al. (2001) : Measure temperatures in foil bearing operating with axial cooling stream flow. San Andrés et al. (2006, 2008): Large imbalances cause subsync. whirl motions due to FB structure hardening. Ruscitto et al (1978): Load capacity tests on simple GFB. Full test data & bearing geometry Heshmat (1994): Demonstrates maximum speed of 132 krpm, i.e. 4.61 ×10 6 DN. Ultimate specific load (~100 psig). Most designs operate at 10 psig or below. Radil and Zeszotek (2006): Measure temperatures in foil bearing operating with changes in load and rotor speed.

6. Foil Bearing Research at TAMU Test Gas Foil Bearing (Bump-Type) Generation II. Diameter: 38.1 mm 25 corrugated bumps (0.38 mm of height) Reference: DellaCorte (2000) Rule of Thumb 2003-2009: Funded by NSF, Capstone Turbines, NASA GRC, Turbomachinery Research Consortium

7. THD model GFB with cooling flows (inner and outer) Gas film Reynolds equation with inlet swirl effect 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∞

8. THD model governing equations Convection of heat by fluid flow + diffusion to bounding surfaces = compression work + dissipated energy Bulk-flow film temperature transport: - 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

9. Configuration of control volume for integration of flow equations (Ψ = P f or T f ) Subscripts E,W,N,S for east, west, north, and south nodes; and subscripts e,w,n,s for east, west, north, and south faces of control volume Numerical solution of Reynolds and thermal energy transport equations implement exact advection control volume model (Faria and San Andrés, 2000) Numerical solution procedure Bulk-flow equations of continuity, momentum and energy transport (n, s, e, w denote the north, south, east and west faces )

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 flux paths in rotor - GFB system Simple representation in terms of thermal resistances within a GFB supporting a hot hollow shaft Heat conducted into the bearing Cooling gas stream carries away heat Heat flow model

11. Equivalent heat transfer coefficients : Heat transfer from film flow to outer bearing cartridge Without outer cooling flow stream : Heat transfer from film flow to inner cooling flow With inner cooling flow stream Gas film -> top foil -> bump strip layer -> bearing cartridge : Heat transfer from film flow to outer cooling flow With outer cooling flow stream (simplified model) Gas film -> top foil -> outer cooling flow Gas film -> hollow shaft -> inner cooling flow

12. Thermal energy mixing process At gap in between trailing and leading edge of top foil. mass conservation and energy balances at feed gap: λ : empirical thermal mixing coefficient enforced. Top foil detachment doest not allow for gas film pressure to fall below ambient pressure. No ingress of fresh gas

13. Width of arrow denotes intensity of energy transport Balance of thermal energy transport 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 % Example only

14. Top foil thickness,Bump foil thickness,Bump height,Gas Constant,Viscosity,1.73Conductivity,Density, Parameters Value / comment Bearing cartridge Bearing inner radius25 mmRef. [7] Bearing length41 mmRef. [7] Bearing cartridge thickness5 mmAssumed Nominal radial clearance20 μmAssumed Top foil and bump strip layer Top foil thickness127 μmRef. [21] Bump foil thickness127 μmRef. [21] Bump half length1.778 mmAssumed Bump pitch4.064 mmAssumed Bump height0.580 mmAssumed Number of bumps x strips39 x 1Assumed Bump foil Young’s modulus200 GPa Bump foil Poisson’s ratio0.31 Bump foil stiffness 10.4 GN/m 3 ParametersValue Gas properties at 21 °C Gas Constant287 J/(kg-°K) Viscosity10 -5 Pa-s Conductivity0.0257 W/m°K Density1.164 kg/m 3 Specific heat1,020 J/kg°K Ambient pressure1.014 x 10 5 Pa GFB model: Generation I GFB with single top foil and bump strip layer Model Validation: geometry & operating conditions Gas viscosity, density & conductivity, foil material props., and clearance change with temperature Ref. [7, 21]: Radil and Zeszotek, 2004 Dykas and Howard, 2004

15. Predicted peak film temperature Static load (vertical:180°) Comparison to test data (Radil and Zeszotek, 2004) Peak film temperature grows as static load increases and as rotor speed increases. Peak film temperatures higher than ambient temperature, even for small load of 9 N. T Supply =21 °C Test data (Mid-plane) Predictions (Mid-plane) 30,000 rpm 40,000 rpm 50,000 rpm 20,000 rpm W/LD= 16 psi= 1.1 bar T shaft =T bearing =T ambient = 21 °C

16. 40,000 rpm 20,000 rpm Predictions (Edge) Predictions (Mid-plane) Test data (Mid-plane) Test data (Edge) Mid-plane & edge film temperatures Difference in film temperatures at mid-plane and edge (axial thermal gradient) increases as rotor speed increases. Higher film temperatures at bearing mid-plane evidence absence of axial cooling flow path Static load (vertical:180°). Comparison to test data (Radil and Zeszotek, 2004) T Supply =21 °C T shaft =T bearing =T ambient = 21 °C

17. 20,000 rpm 30,000 rpm 40,000 rpm Test dataPredictions Film axial temperature Film temperature is maximum at bearing mid-plane, and drops slightly at side edges (circumferential angle ~190°). Predictions in good agreement with test values Static load 133 N (vertical: 180°) for rotor speeds: 20 - 40 krpm. Comparison to test data (Radil and Zeszotek, 2004) T Supply =21 °C W/LD= 9.5 psi= 0.64 bar T shaft =T bearing =T ambient = 21 °C

18. More predictions of GFB performance Gas film (a) pressure and (b) temperature fields Axial node number Dimensionless pressure, p/p a (a) Pressure Circumferential angle [deg] Axial node number Temperature [° C] Circumferential angle [deg] (b) Temperature 0 < θ < 200 °: Temperature rises due to shear induced mechanical energy θ > 200 °: Temperature drops due to gas expansion (cooling gas film) Static load: 89N 20 krpm W/LD= 6.32 psi= 0.43 bar T shaft =T bearing =T ambient = 21 °C

19. Film pressure and temperature at mid-plane Both peak pressure and temperature increase as static load increases. Note peak film temperature at trailing edge of top foil with smallest load of 9 N. At 20 krpm T shaft =T bearing =T ambient = 21 °C (a) Pressure Static load increases 9 N 44 N 89 N 133 N 178 N 222 N Static load increases 9 N 44 N 89 N 133 N 178 N 222 N (b) Temperature T Supply =21 °C

20. 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 70°C 68°C 67°C T Co Without forced cooling streams, GFB shows nearly uniform radial temperature distribution. Static load 89 N rotor speed= 20 krpm Radial peak temperature profile Natural convection on exposed surfaces of bearing OD and shaft ID T shaft =T bearing =T ambient = 21 °C

21. Predicted static load performance As static load increases, journal eccentricity increases and minimum film thickness decreases. Larger minimum film thickness (smaller journal eccentricity) for THD model. 40 krpm THD Isothermal THD Isothermal c' = 17 μm W/LD= 16 psi= 1.1 bar T shaft =T bearing =T ambient = 21 °C

22. Predicted static load performance As static load increases, journal attitude angle decreases and drag torque slightly increases. Larger drag torque and smaller journal attitude angle for THD model. 40 krpm W/LD= 16 psi= 1.1 bar T shaft =T bearing =T ambient = 21 °C

23.  Model predictions benchmarked against published test data !! Conclusions  THD model predicts smaller journal eccentricity (larger minimum film thickness) and larger drag torque than isothermal flow model  Predicted film peak temperature increases as static load increases and as rotor speed increases 09 AHS paper shows predictions with cooling flow and rotordynamic measurements in a HOT rotor-GFB test rig GFB model with thermal energy transport, axial cooling flow, and thermoelastic deformation of top foil and bump strip layers  Difference in predicted film temperatures at mid-plane and edge (axial thermal gradient) increases as rotor speed increases. ASME GT2009-59919

24. Acknowledgments  NASA GRC NASA Research Announcement NNH06ZEA001N-SSRW2, Fundamental Aeronautics: Subsonic Rotary Wing Project 2 # 32525/39600/ME Thanks to Dr. Samuel Howard for his interest and support  Turbomachinery Research Consortium Learn more: Visit http://phn.tamu.edu/TRIBGroup

25. More predictions

26. With forced cooling streams, inlet gas film temperature at ~ 0 deg (top foil leading edge) and peak film temperature at ~ 200 deg decrease significantly Forced cooling flows - F ilm temperature Temperature [°C] (a) Without cooling flow Axial node number Circumferential angle [deg] Outer cooling flow Hollow shaft Ω Bearing cartridge Axial node number Temperature [°C] (b) Outer cooling flow (350 lit/min) Circumferential angle [deg] Axial node number Temperature [°C] Circumferential angle [deg] (c) Inner (350 lit/min) and outer (350 lit/min) cooling flows Outer cooling flow Hollow shaft Ω Bearing cartridge Inner cooling flow Static load 89 N (vertical) rotor speed= 20 krpm. T shaft =T bearing =T ambient = 21 °C

27. 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 70°C 68°C 66°C T Co (a) Without cooling flow (b) Outer cooling flow (350 lit/min) (c) Inner (350 lit/min) and outer (350 lit/min) cooling flows With forced cooling streams, GFB operates 30 °C cooler. Outer cooling stream is most effective to take away heat from the back of the top Foil. Static load 89 N (vertical) rotor speed= 20 krpm Radial peak temperature profiles Natural convection on exposed surfaces of bearing OD and shaft ID 33°C 38°C 35°C 40°C 38°C 37°C T shaft =T bearing =T ambient = 21 °C

28. Without cooling flow stream, ~ 58% of heat carried by gas film flow. ~12% convected naturally at back of top foil. ~ 31% conducted into bearing and shaft With outer cooling flow stream, ~ 11% of heat advected by the gas film. ~82% carried by outer cooling stream. ~ 7% conducted into bearing and shaft. Inner cooling flow stream aids to further cool gas film Thermal energy transport & balance (a) Without cooling flow Advection of heat by gas film flow - AXIAL (20.2 W) 57.5% Heat conduction into bearing cartridge (3.09 W) 8.8% Natural heat convection into outer gap (4.11 W) 11.7% Heat conduction into shaft (7.72 watt) 22.0% Mechanical dissipated energy (43.35 W) + compression work (-8.23 W) = 35.12 W 100% (b) Outer cooling flow (350 lit/min) Dissipated energy (36.31 W) + compression work (- 7.64 W) = 28.66 W 100% Advection of heat by gas film flow (3.21 W) 11.2% Forced heat convection into outer cooling stream (23.46 W) 81.9 % Conduction into bearing cartridge ( 0.43 W) 1.5% Heat conduction into shaft (1.57 W) 5.5 % (c) Inner (350 lit/min) and outer (350 lit/min) cooling flows Dissipated energy (36.06 W) + compression work (-7.60 W) = 28.46 W 100% Advection of heat by gas flow (3.39 W) 11.9% Conduction thru shaft and forced convection into inner cooling stream (5.55 W) 19.5% Forced convection to outer cooling stream (19.53 W) 67.4 % Conduction into bearing cartridge (0.35 W) 1.2% Static load 89 N (vertical) rotor speed= 20 krpm T shaft =T bearing =T ambient = 21 °C

29. 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 strength of cooling stream Peak film temperature decreases with strength of cooling stream. Sudden drop in temperature at ~ 200 lit/min (flow transitions from laminar to turbulent flow conditions) T Supply =21 °C Static load 89 N (vertica) rotor speed= 20 krpm T shaft =T bearing = T ambient = 21 °C

30. TAMU Hot GFB Rotordynamic Test Rig

31. Hot GFB rotordynamic test rig Drive motor (max. 65 krpm). Cartridge heater max. temperature: 360C Air flow meter (Max. 500 L/min), Test rig with a cartridge heater and instrumentation for operation at high temperature Insulated safety cover Infrared thermometer Flexible coupling Drive motor Cartridge heater Test GFBs Test hollow shaft (1.1 kg, 38.1mm OD, 210 mm length) Tachometer Eddy current sensors Hot heater inside rotor spinning 30 krpm

32. Schematic view of instrumentation 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 15 thermocouples : (4x2) GFB cartridges, (2) Bearing support housing surface, (3) Drive motor, (1) Test rig ambient and (1) Cartridge heater + Two noncontact infrared thermometers for rotor surface temperature

33. AIR SUPPLY Side feed gas pressurization (Max. 100 psi) Typically foil bearings DO not require pressurization. Cooling flow needed for thermal management to remove heat from drag or to reduce thermal gradients in hot/cold engine sections Cooling gas flow into GFBs

34. High temp. (heater up to 360C). Cooling flow up to 150 L/min Fixed rotor speed : 30 krpm Due to limited heater power Cooling rates > 100 LPM cool the heater! 21C100C200C 300C 360C No cooling& 50L/min 100L/min 150L/min Effect of cooling flow on heater temperature heater temperature

35. High temp. (heater up to 360C). Cooling flow up to 150 L/min Fixed rotor speed : 30 krpm Cooling method is effective for flows above 100 L/min and when heater at highest temperature T 1- T amb T 6- T amb 21C100C200C 300C 360C Cooling flow increases Effect of cooling flow on bearing temperatures Bearings temperature raises

36. Effect of cooling flow on bearing temperature Cooling flow increases T 1- T amb T 6- T amb Cartridge temperature (T hs ) increases 200C 100C No heating Rotor OD temperature decreases with cooling flow rate. Turbulent flow > 100 LPM High temp. (heater up to 360C). Cooling flow up to 150 L/min Bearing cartridge temperature Fixed rotor speed : 30 krpm

37. TAMU predictions vs test data Bearing & rotor cartridge temperatures Measurements at cartridge outboard #T6. TCo~21 °C. Static load ~ 6.5 N, 30 krpm

38. Code Executable & GUI : for licensing by TAMU

39. Graphical User Interface (GUI)

40. INPUT DATA

41. Graphical User Interface (GUI) OUTPUT DATA Peak temperature vs Load Radial temperature distribution