Luis San Andrés Mast-Childs Professor Fellow ASME Texas A&M University

1. ASME TURBO EXPO 2010, Glasgow, Scotland, UK Thermal Management and Rotordynamic Performance of a Hot Rotor-Gas Foil Bearings SystemPart 2: Predictions vs. Test Data Tae Ho Kim Senior Research Scientist Korea Institute of Science and Technology Luis San Andrés Mast-Childs Professor Fellow ASME Texas A&M University Keun Ryu Research Assistant Texas A&M University ASME paper GT2010-22983 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 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. Main Objective 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. Agreement NASA NNH06ZEA001N-SSRW2

4. Objective & tasks • 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) ASME GT2009-59919 ASME GT2010-22981

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

7. ASME GT2009-59919 Our GFB TEHD model Excel GUI + executable licensed by TAMU

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

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

10. Heat flow 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 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, Conductivity, Density, 1.73 Test Foil Bearings (Gen II) Uncoated top foil Read ASME GT2010-22981 For test procedure and measurements. Complete bearing geometry and operating conditions DISCLOSED Elastic Modulus 214 GPa, Poisson ratio=0.29

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

13. Predictions radial temperature Cooling stream increases 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 Tf DE FB Natural convection on exposed surfaces of bearing OD and shaft ID TFo TBi TSi TFi TSo TBo Mean temperature w/o & w cooling flow T∞ TCi TCo Rotor speed : 30 krpm RSi RSo RFi RFo RBi RBo Radial direction Hollow shaft Top foil Bump layer Bearing housing External fluid dӨ With forced cooling, GFB will operate 50°C cooler. Outer cooling stream is most effective in removing heat

14. Thermal energy transport and balance 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 Predictions: example

15. Temperatures in test rig 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 Thermocouples: 1 x heater, 2 x 4 FB outboard, 2 x Bearing housing outer surface, 1x Drive motor, 1 x ambient + infrared thermometers2 x rotor, rotor surface temperature (Total = 17)

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

17. Recap: the test rotor and FB Bearing housing “Bump” layer Top foil Bearing housing Outer flow stream z x PCo ,TCo Pa Cooling stream Thin film flow WRSo Hot air (out) Heat source Th z=0 z=L ambient Hollow rotor T∞ Schematic view of rotor and heater cartridge + side cooling stream 17

18. Error bar Max. No cooling Avg. Test data Min. Predictions 50 LPM predictions & tests Bearing outboard temperature Drive end FB Temperature rise (C) Room temperature21 °C. Heater OFF static load ~ 6.5N w/o and w low cooling Rotor speed : 30 krpm rotor speed (krpm) FB OD temperature rises with rotor speed and decreases with forced cooling stream ~ 50 LPM. Predictions agree with test data

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

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

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

22. predictions Cartridge heater temperature increases Cartridge heater temperature increases Ths=360ºC KXY KXX Ths=200ºC No heating No heating Ths=200ºC KYX Ths=360ºC KYY Bearing stiffnesses static load ~ 6.5 N No cooling flow Drive End FB Rotor speed (krpm) Rotor speed (krpm) As temperature increases, stiffnesses (KXX, KYY) increase significantly, while difference (KXY-KYX) increases slightly at low rotor speeds and decreases at high rotor speeds

23. Cartridge heater temperature increases No heating CYX Ths=200ºC CYY Ths=360ºC Ths=200ºC Ths=360ºC CXX No heating CXY Bearing damping predictions static load ~ 6.5 N No cooling flow Drive End FB Cartridge heater temperature increases Rotor speed (krpm) Rotor speed (krpm) As temperature increases, damping (CXX, CYY) increase. Cross damping (CXY,CYX) change little above 30 krpm.

24. Effect of cooling flow predictions 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 Supply air (TSupply),shaft (TS), and bearing OD(TB) temperatures at 21 °C. Static load =89 N (180°). Rotor speed : 20 & 40 krpm TSupply=21°C Peak temperature drops with strength of cooling stream. Sudden drop at ~ 200 LPM from transition of laminar to turbulent flow

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

26. Conclusions • 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 !!!

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 ?