this material is based upon work supported by nasa research announcement nnh06zea001n-ssrw2,...

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 Thermohydrodynamic Analysis of Bump Type Gas Foil Bearings: A Bump Type Gas Foil Bearings: A

Model Anchored to Test DataModel Anchored to Test Data

Texas A&M University

Luis San Andrés Tae Ho KimMast-Childs Professor Research Associate

ASME GT2009-59919Accepted for J. Eng. Gas Turbines Power (In-Press)

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

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

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:

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 ×106 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.

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

THD model

GFB with cooling flows (inner and outer)

Gas film Reynolds equation with inlet swirl effect3 3

( )12 12f f f f f f f f

m zf g f f g f g f

h P P h P P P hU

x T x z T z x T

Outer flow stream Top foil

Bearing housing “Bump” layer

zx

PCo, TCo

X

Y

Z

Bearing housing

PCi, TCi

Inner flow stream

ΩRSo

Hollow shaft

Pa

Thin film flow

z=0 z=L

T∞

THD model governing equations

Convection of heat by fluid flow + diffusion to bounding surfaces = compression work + dissipated energy

2212 1

3

f i o

f f f f f f f fp fF f F Sf S f

f f ff f f f f m f m

f

h U T h W Tc h T T h T T

x z

P PU h W h W U U U

x z h

Bulk-flow film temperature transport:

g

PT

v T

- Ideal gas with density,

- Gas viscosity,

- Gas Specific heat (cp)

and thermal conductivity (κg) at an effective

temperature

Ω

Bump strip layer

Top foil

Hollow shaft

Bearing housing

External fluid medium

Inner flow stream

Outer flow stream

Thin film flow

X

Y

X=RΘSide view of GFB with hollow shaft

ΨP ΨE Ψe ΨW Ψw

ΨN

Ψn

Ψs

x x

z

z eM

nM

sM

wM

ΨS

Circumferential direction

Axi

al d

irec

tio

n

Control volume

Configuration of control volume for integration of flow equations (Ψ = Pf or Tf)

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

e w n s

M M M M S

Bulk-flow equations of continuity, momentum and energy transport

(n, s, e, w denote the north, south, east and west faces )

1 Conservation of mass equation

Transport of circ. momentum velocity

Transport of axial momentum velocity

Transport of energy

: Source term

x

z

U

U

T

S

T∞

TBo

TBi

TFo

TSo

TSi

TFi

TCi

TO

Tf

S CQ

SoQ

BQ

BQ

F BiQ

f FQ

S fQ

FQ

F OQ

O BiQ

Top foil

Bump layer

Hollow shaft

Bearing housing

External fluid

Ω

dӨ

RSi RSo RFi RFo RBi RBo

SiQ

Q=Rq

QCi

Heat carried by thin film

flow

Heat carried by outer flow

stream: Heat

(-): Heat

(+)

QB

QCo

Drag dissipation power (gas

film)

Heat carried by inner flow

stream

Heat conduction through shaft

TS

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

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

1 1 1 1

1

ln

B i

Fi

i

i i

eq o

Feq fF BFo Bot

F BoF

B F FBi

F B B B B

h h Rh h

R RR

R RR

R h R

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)

1 1

iF

O o

Ft

Feq fF F FO

R

h h R hGas film -> top foil -> outer cooling flow

ln1 1

c

SiSo

So So

Seq Sf Sc Si

RR

R R

h h h RGas film -> hollow shaft -> inner cooling flow

Upstream end(trailing edge)

Downstream pad(leading edge)

R

mup

Tup

mInlet

TInlet

msupply

Tsupply

top foiltop foil

Upstream end(trailing edge)

Downstream pad(leading edge)

R

mup

Tup

mInlet

TInlet

msupply

Tsupply

top foiltop foil

Thermal energy mixing processAt gap in between trailing and leading edge of top foil.

Inlet up Supplym = m m Inlet Inlet up up Supply Supplym T = m T +m T

mass conservation and energy balances at feed gap:

λ : empirical thermal mixing coefficient

f aP P enforced. Top foil detachment doest not allow for gas film pressure to fall below ambient pressure. No ingress of fresh gas

Y

Housing

X

Journal

Ω

Structural bump

Thin foil

Recirculation air flow

Fresh air flow Inlet (mixing)

air flow

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

Parameters Value / comment

Bearing cartridge

Bearing inner radius 25 mm Ref. [7]

Bearing length 41 mm Ref. [7]

Bearing cartridge thickness 5 mm Assumed

Nominal radial clearance 20 μm Assumed

Top foil and bump strip layer

Top foil thickness 127 μm Ref. [21]

Bump foil thickness 127 μm Ref. [21]

Bump half length 1.778 mm Assumed

Bump pitch 4.064 mm Assumed

Bump height 0.580 mm Assumed

Number of bumps x strips 39 x 1 Assumed

Bump foil Young’s modulus 200 GPa

Bump foil Poisson’s ratio 0.31

Bump foil stiffness 10.4 GN/m3

Parameters Value

Gas properties at 21 °C

Gas Constant 287 J/(kg-°K)

Viscosity 10-5 Pa-s

Conductivity 0.0257 W/m°K

Density 1.164 kg/m3

Specific heat 1,020 J/kg°K

Ambient pressure 1.014 x 105 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, 2004Dykas and Howard, 2004

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.

TSupply=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

Ω

Load

Tshaft=Tbearing =Tambient = 21 °C

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°).


TSupply=21 °C

Ω

Load


20,000 rpm

30,000 rpm

40,000 rpm

Test data Predictions

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.


TSupply=21 °C

W/LD= 9.5 psi= 0.64 bar

Ω

Load


More predictions of GFB performanceGas film (a) pressure and (b) temperature fields

Axial node number

P

Dim

ensi

onle

ss

pres

sure

, p/

pa (a) Pressure

Ω

Load

Circumferential angle [deg]

T

Axial node number

Tem

pera

ture

[°

C]


(b) Temperature

(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


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 krpmTshaft=Tbearing =Tambient = 21 °C

(a) Pressure Static load increases

9 N44 N89 N

133 N178 N

222 N

Static load increases

9 N44 N89 N

133 N178 N

222 N(b) Temperature

TSupply=21 °C

Ω

Load

Top foil

Bump layer

Hollow shaft

Bearing housing

External fluid dӨ


TCi T∞

TBoTBiTFoTSoTSi TFi

Tf

Radial direction

70°C

68°C67°C

TCo

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

Ω

Load


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 krpmTHD

Isothermal

THD

Isothermal

c' = 17 μm

Ω

Load



0

10

20

30

40

50

60

70

80

90

0 50 100 150 200 250 300

Static load [N]

Jou

rnal

att

itu

de

ang

le [

deg

]

0.00

0.01

0.02

0.03

Dra

g t

orq

ue

[N-m

]THD

Isothermal

THD

Isothermal

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

Ω

Load



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

Acknowledgments

NASA GRCNASA 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

More predictions

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 - Film temperatureTemperature field

T

Tem

pera

ture

[°C

]

(a) Without cooling flow

Axial node number


Ω

Load

Outer cooling flow Hollow shaft Ω

Bearing cartridge

Temperature field

T

Axial node number

Tem

pera

ture

[°C

] (b) Outer cooling flow (350 lit/min)


Temperature field

T

Axial node number

Tem

pera

ture

[°C

]


(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.


Top foil

Bump layer

Hollow shaft

Bearing housing

External fluid dӨ


TCi T∞

TBoTBiTFoTSoTSi TFi

Tf

Radial direction

70°C

68°C66°C

TCo

(a) Without cooling flow

(b) Outer cooling flow (350 lit/min)


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°C38°C 35°C

40°C38°C37°C

Ω

Load


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 W100%

(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 %


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

Ω

Load


40,000 rpm

20,000 rpm

Outer cooling flow

Inner and outer cooling flows

Laminar flow Turbulent flow

Re

D = 2

300

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)

TSupply=21 °C

Static load 89 N (vertica) rotor speed= 20 krpm


TAMU Hot GFBRotordynamic Test Rig

Hot GFB rotordynamic test rig

Drive motor (max. 65 krpm). Cartridge heater max. temperature: 360CAir 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

Schematic view of instrumentation

Foil bearings

Cartridge heaterHeater stand

T14

T10

T12

T13

Coupling cooling air

Drive motor

T15

T16Th

Hollow shaftT5

T11

TambΩ

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

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

Free End Drive End

T11 T12

T1 T6Th

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!

21C 100C 200C 300C 360C

No cooling& 50L/min

100L/min

150L/min

Effect of cooling flow on heater temperature

heater temperature

Free End Drive End

T11 T12

T1 T6Th



Cooling method is effective for flows above 100 L/min and when heater at highest temperature

T1-Tamb

T1-Tamb

T1-Tamb

T6-Tamb

T6-Tamb

T6-Tamb

21C 100C 200C 300C 360C

Cooling flow increases

Effect of cooling flow on bearing temperatures

Bearings temperature raises

Free End Drive End

T11 T12

T1 T6Th

Effect of cooling flow on bearing temperature

Cooling flow increases

T1-Tamb

T6-Tamb

Cartridge temperature (Ths) increases

200C

100C

No heating

Rotor OD temperature decreases with cooling flow rate.

Turbulent flow > 100 LPM


Bearing cartridge temperature


TAMU predictions vs test data

Bearing & rotor cartridge temperatures

45 °

Bearing cartridge

Top foil

Bump strip layer

Spot weld

X

Y

g

Θ

Ω

Outer cooling stream

Heat flux (Shaft → bearing,

Shaft → outer stream)

Hot shaft (Isothermal)

0

10

20

30

40

50

60

0 20 40 60 80 100

Shaft temperature rise [ºC]

Bea

rin

g t

em

pe

ratu

re r

ise

[ºC

]

Test data

Predictions

DE Shaft and GFB

No cooling

50L/min

100L/min

150L/min

125L/min

Measurements at cartridge

outboard #T6. TCo~21 °C.

Static load ~ 6.5 N, 30 krpm

Code Executable & GUI : for licensing by TAMU

Graphical User Interface (GUI)


INPUT DATA


OUTPUT DATA

Peak Temperature

0.0

40.0

80.0

120.0

160.0

200.0

240.0

0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00

Load-X [N]

Foster-Miller Tech 2nd GEN GAS FOIL BEARING

[deg

C]

Pea

k te

mp

era

ture

Peak temperature vs Load

0.0

20.0

40.0

60.0

80.0

100.0

120.0

140.0

160.0

180.0

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0

Radial location

Peak Temp

Mean Temp

Top foil

Bump layer

Hollow shaft

Bearing housing

External fluid dӨ

Radial direction

Foster-Miller Tech 2nd GEN GAS FOIL BEARING

[de

gC

]T

em

pe

ratu

re

Radial temperature distribution

this material is based upon work supported by nasa research announcement nnh06zea001n-ssrw2,...

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