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Thermohydrodynamic Analysis of Bump Type Gas Foil Bearings: A Model Anchored to Test Data

This paper presents a thermohydrodynamic analysis of bump type gas foil bearings, integrating a hydrodynamic gas film in series with structural layers. The analysis is based on test data and computational models. The bearings offer increased reliability, high and low temperature capability, and reduced weight compared to other bearing types. However, they face challenges in accessing full test data and lack of validation for predictive models. The paper provides insights into these challenges and presents solutions.

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Thermohydrodynamic Analysis of Bump Type Gas Foil Bearings: A Model Anchored to Test Data

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  1. ASME Turbo Expo 2009: Power for Land, Sea, and Air Thermohydrodynamic Analysis of Bump Type Gas Foil Bearings: A Model Anchored to Test Data Luis San Andrés Tae Ho Kim Mast-Childs Professor Research Associate Texas A&M University ASME GT2009-59919 Accepted for J. Eng. Gas Turbines Power (In-Press) This material is based upon work supported by NASA Research Announcement NNH06ZEA001N-SSRW2, Fundamental Aeronautics: Subsonic Rotary Wing Project 2# 32525/39600/MEand the Turbomachinery Research Consortium

  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 • 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 Thermohydrodynamic (THD) model predictions: • Salehi et al. (2001):Couette flow approximation to estimate bearing temperatures. • Peng and Khonsari (2006):Thermal management of GFB from cooling gas stream underneath top foil. • Le Lez et al. (2007): Nonlinear elastic bump model. THD model predicts larger load capacity than isothermal flow model. • 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.

  5. Overview – Rotordynamic measurements • 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 ×106 DN. Ultimate specific load (~100 psig). Most designs operate at 10 psig or below. • DellaCorte and Valco (2000):Review open literature and estate Rule of Thumb to estimate load capacity of GFBs. • San Andrés et al. (2006, 2008):Large imbalances cause subsync. whirl motions due to FB structure hardening. • Radil and Zeszotek (2006):Measure temperatures in foil bearing operating with changes in load and rotor speed. • Salehi et al. (2001) : Measure temperatures in foil bearing operating with axial cooling stream flow.

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

  7. THD model Bearing housing “Bump” layer Top foil PCo,TCo Pa Thin film flow PCi, TCi Inner flow stream Gas film Reynolds equation with inlet swirl effect Hollow shaft Y Z X T∞ Bearing housing Outer flow stream z GFB with cooling flows (inner and outer) x ΩRSo z=0 z=L

  8. THD model governing equations Top foil Bump strip layer • Ideal gas with • density, Hollow shaft Inner flow stream Outer flow stream - Gas viscosity, Thin film flow - Gas Specific heat (cp) and thermal conductivity (κg) at an effective temperature Bearing housing External fluid medium Bulk-flow film temperature transport: Side view of GFB with hollow shaft X=RΘ Y X Convection of heat by fluid flow + diffusion to bounding surfaces = compression work + dissipated energy

  9. Numerical solution procedure Bulk-flow equations of continuity, momentum and energy transport (n, s, e, w denote the north, south, east and west faces ) Configuration of control volume for integration of flow equations (Ψ = Pf or Tf) Numerical solution of Reynolds and thermal energy transport equations implement exact advectioncontrol volume model (Faria and San Andrés, 2000) 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

  10. Heat flux paths in rotor - GFB system Heat conduction through shaft QCi TS Heat carried by inner flow stream QCo QB Drag dissipation power (gas film) Heat carried by thin film flow Heat carried by outer flow stream : Heat (-) : Heat (+) Heat flow model 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

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

  12. Thermal energy mixing process mass conservation and energy balances at feed gap: At gap in between trailing and leading edge of top foil. 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. Balance of thermal energy transport 11 % Advection of heat by gas film flow Conduction into bearing cartridge 2 % Dissipated energy + compression work Forced heat convection into outer cooling stream 100% Heat conduction into shaft 82 % 5 % Width of arrow denotes intensity of energy transport Example only

  14. Top foil thickness, Bump foil thickness, Bump height, Gas Constant, Viscosity, 1.73 Conductivity, Density, Model Validation:geometry & operating conditions GFB model: Generation I GFB with single top foil and bump strip layer Gas viscosity, density & conductivity, foil material props., and clearance change with temperature Ref. [7, 21]: Radiland Zeszotek, 2004 Dykas and Howard, 2004

  15. 50,000 rpm 40,000 rpm 30,000 rpm 20,000 rpm Test data (Mid-plane) Predictions (Mid-plane) Predicted peak film temperature Tshaft=Tbearing =Tambient = 21 °C Static load (vertical:180°) Comparison to test data (Radiland Zeszotek, 2004) TSupply=21 °C W/LD= 16 psi= 1.1 bar 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.

  16. Mid-plane & edge film temperatures Predictions (Mid-plane) Predictions (Edge) 40,000 rpm 20,000 rpm Test data (Mid-plane) Test data (Edge) Tshaft=Tbearing =Tambient = 21 °C Static load (vertical:180°) . Comparison to test data (Radiland Zeszotek, 2004) TSupply=21 °C 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

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

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

  19. Film pressure and temperature at mid-plane Static load increases Static load increases 222 N 222 N 178 N 178 N 133 N 133 N 89 N 89 N 44 N 44 N 9 N 9 N (a) Pressure At 20 krpm Tshaft=Tbearing =Tambient = 21 °C (b) Temperature 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. TSupply=21 °C

  20. Radial peak temperature profile 70°C 67°C 68°C Tf TFo TBi TSi TFi TSo TBo Tshaft=Tbearing =Tambient = 21 °C Static load 89 N rotorspeed= 20 krpm T∞ TCi TCo Radial direction RSi RSo RFi RFo RBi RBo Natural convection on exposed surfaces of bearing OD and shaft ID Hollow shaft Top foil Bump layer Bearing housing External fluid dӨ Without forced cooling streams, GFB shows nearly uniform radial temperature distribution.

  21. Predicted static load performance Isothermal THD THD Isothermal 40 krpm c' = 17 μm Tshaft=Tbearing =Tambient = 21 °C W/LD= 16 psi= 1.1 bar As static load increases, journal eccentricity increases and minimum film thickness decreases. Larger minimum film thickness (smaller journal eccentricity) for THD model.

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

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

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

  27. Radial peak temperature profiles 70°C 66°C 68°C (a) Without cooling flow (b) Outer cooling flow (350 lit/min) 40°C 38°C 37°C 35°C 38°C 33°C (c) Inner (350 lit/min) and outer (350 lit/min) cooling flows Tf TFo TBi TSi TFi TSo TBo Tshaft=Tbearing =Tambient = 21 °C Static load 89 N (vertical) rotor speed= 20 krpm T∞ TCi TCo Radial direction Natural convection on exposed surfaces of bearing OD and shaft ID RSi RSo RFi RFo RBi RBo Hollow shaft Top foil Bump layer Bearing housing External fluid dӨ 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.

  28. Thermal energy transport & balance Advection of heat by gas film flow - AXIAL (20.2 W) 57.5% Heat conduction into bearing cartridge (3.09 W) Mechanical dissipated energy (43.35 W) + compression work (-8.23 W) = 35.12 W 8.8% Natural heat convection intoouter gap (4.11 W) 11.7% 100% Heat conduction into shaft (7.72 watt) 22.0% Advection of heat by gas film flow (3.21 W) 11.2% Conduction into bearing cartridge ( 0.43 W) 1.5% Dissipated energy (36.31 W) + compression work (- 7.64 W) = 28.66 W 81.9 % Forced heat convection into outer cooling stream (23.46 W) 100% Heat conduction into shaft (1.57 W) 5.5 % 11.9% Advection of heat by gas flow (3.39 W) Conduction into bearing cartridge (0.35 W) 1.2% Dissipated energy (36.06 W) + compression work (-7.60 W) = 28.46 W 67.4 % Forced convection to outer cooling stream (19.53 W) 100% Conduction thru shaft and forced convection into inner cooling stream (5.55 W) 19.5% (a) Without cooling flow Static load 89 N (vertical) rotor speed= 20 krpm Tshaft=Tbearing =Tambient = 21 °C (b) Outer cooling flow (350 lit/min) 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 (c) Inner (350 lit/min) and outer (350 lit/min) cooling flows

  29. Effect of strength of cooling stream No cooling flow Cooling flow rate increases Laminar flow Turbulent flow ReD = 2300 Outer cooling flow 40,000 rpm Inner and outer cooling flows 20,000 rpm Static load 89 N (vertica) rotor speed= 20 krpm Tshaft=Tbearing = Tambient = 21 °C TSupply=21 °C 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)

  30. TAMU Hot GFB Rotordynamic Test Rig

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

  32. Schematic view of instrumentation Free end (FE) GFB Drive end (DE) GFB 45º g g T12 T13 T10 Tamb Th T11 Cooling air T9 T5 T4 T8 T3 T2 T6 T7 T14 T16 T15 T1 Insulated safety cover 45º Hollow shaft Coupling cooling air Drive motor Cartridge heater Heater stand Foil bearings 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. Cooling gas flow into GFBs 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 AIR SUPPLY

  34. Effect of cooling flow on heater temperature High temp. (heater up to 360C).Cooling flow up to 150 L/min Fixed rotor speed : 30 krpm heater temperature 360C 300C 21C 100C 200C No cooling& 50L/min 100L/min Due to limited heater power 150L/min Cooling rates > 100 LPM cool the heater!

  35. Effect of cooling flow on bearing temperatures High temp. (heater up to 360C).Cooling flow up to 150 L/min Bearings temperature raises Fixed rotor speed : 30 krpm 360C Cooling method is effective for flows above 100 L/min and when heater at highest temperature 300C 21C 100C 200C T1-Tamb T6-Tamb T1-Tamb Cooling flow increases T6-Tamb T1-Tamb T6-Tamb

  36. Effect of cooling flow on bearing temperature High temp. (heater up to 360C).Cooling flow up to 150 L/min Fixed rotor speed : 30 krpm Cooling flow increases Turbulent flow >100 LPM 200C T6-Tamb T1-Tamb 100C No heating Cartridge temperature (Ths) increases Bearing cartridgetemperature Rotor OD temperature decreases with cooling flow rate.

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

  38. Code Executable & GUI : for licensing by TAMU

  39. Graphical User Interface (GUI)

  40. Graphical User Interface (GUI) INPUT DATA

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

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