2024年3月14日发(作者：子车焱)

JournalofFluidsandStructures40(2013)42–51

ContentslistsavailableatSciVerseScienceDirect

JournalofFluidsandStructures

journalhomepage:/locate/jfs

Largeeddysimulationofvortexsheddingandpressure

fluctuationinaerostaticbearings

JinchengZhu

a

,HanChen

a,b

,XuedongChen

a,

n

StateKeyLaboratoryofDigitalManufacturingEquipmentandTechnology,HuazhongUniversityofScienceandTechnology,

Wuhan430074,China

b

DepartmentofMechanics,HuazhongUniversityofScienceandTechnology,Wuhan430074,China

a

articleinfo

Articlehistory:

Received21May2012

Accepted5March2013

Availableonline28April2013

Keywords:

Aerostaticbearing

Largeeddysimulation

Vortexshedding

Pressurefluctuation

Vibration

abstract

Inaerostaticbearings,highspeedairflowmayinducesmallvibration,whichhasbeen

harmfultotheimprovementofmovingandpositioningaccuracyofaerostatically

paper,thetransientflowfield

intheaerostaticbearingisnumericallyinvestigatedusingthelargeeddysimulation

entstructuresarestudiedandvortexsheddingphenomenonisdiscovered

putationalresultsdemonstratethatvortexsheddingcauses

onshipbetweenpressurefluctuation

andbearingvibrationisestablishedbasedonoursimulationresultsandexperimentally

measuredvibrationstrength.

&htsreserved.

uction

Aerostaticbearingshahemeritof

near-zerofrictionandlowheatgeneration,applicationsofaerostaticbearingsmakeitpossibleforsupporteddevicesto

r,withtheincreasingdemandofpositioningaccuracy,theinherentsmall

vibrationontheorderofnanometers(Kawaietal.,2005)severelydamagesstabilityandprecisionofthebearing,especially

rstandandeventuallysuppressthisharmfulvibration,traditionaldesign

andanalysismethodsformassflowrateandloadcarryingcapacitydonotsufficeanymore,andlotsofresearcheffortshave

beenmadeontheairflowfieldinaerostaticbearings.

Recently,therelationshipbetweenthehighspeedairflowandthesmallvibrationinaerostaticbearingshasbeen

tal.(2005)studiedthenano-vibrationinultra-precisionmachinetoolsandattributed

dHe(2006)foundvortexflowstructuresinthebearingrecess

bycomputationalfluiddynamics(CFD)simulationofthesteadyairflowfield,andsuggestedthattheseairvorticesare

etal.(2006)alsoobservedthisairvortexflowbyCFD

simulationandreachedasimilarconclusion,andaccordinglyproposedanewrestrictordesigntoweakenthevibration.

Zhangetal.(2007)analyzedthehighReynoldsnumber(Re)flowinthebearingclearance,andreducedthevibrationof

entwork,Yoshimuraetal.(2012)attributednano-vibrationofaerostatic

bearingswithsurfacerestrictiontoghthe

flow-inducednatureofbearingvibrationhasgenerallybeenrecognized,thepreviousworksonlyassumedasteadyflow

n

./fax:+862787557325.

E-mailaddress:chenxd@().

0889-9746/$-seefrontmatter&htsreserved.

/10.1016/structs.2013.03.012

l./JournalofFluidsandStructures40(2013)42–5143

Nomenclature

d

0

d

1

d

2

h

_

m

p

r

r

0

r

1

r

2

t

u

i

,u

j

,u

k

orificediameter

recessdiameter

bearingdiameter

airfilmthickness

massflowrate

pressure

radialdistance

orificeradius

recessradius

bearingradius

time

flowvelocitiesinvariousdirections

x

i

,x

j

,x

k

z

H

P

0

P

s

P

A

Re

T

Δt

δ

ij

μ

ρ

s

ij

τ

ij

coordinatesinvariousdirections

verticaldistance

recessdepth

atmospherepressure

airsupplypressure

area-weightedaveragedpressure

Reynoldsnumber

temperature

timestepsize

Kroneckerdeltafunction

airviscosity

airdensity

molecularviscositystresstensor

subgrid-scalestress

fieldoraveragedtheflowfieldinaReynoldsAveragedNavier–Stokes(RANS)hisflow-inducedvibrationis

apparentlyatimedependentprocess,timedependentisnecessarytoinvestigatethetransientairflowfieldinthebearing

clearanceinordertofurtherunderstandthisharmfulsmallvibration.

Tonumericallyanalyzethedetailedflowcharacteristicsinaerostaticbearings,thefullNavier–Stokesequationsfor

hehighspeedairflowinthebearinggapneartheorificeoutletisturbulent,

RANSsimulationisusuallyemployed,andnumericalresultsdemonstrateadequateaccuracyinpredictingmeanflow

characteristics(ChenandHe,2006;LiandDing,2007).Pressuredepressions(Eleshaky,2009;Yoshimotoetal.,2007)and

vortexflowstructures(Chenetal.,2011)r,

RANSsimulationadoptsastatisticy,direct

numericalsimulation(DNS)canresolvethewholespectrumofturbulentscalesasnoturbulentmodelisassumed,butits

eeddysimulation(LES),largescaleturbulenteddiesaresolveddirectlyand

,coherentturbulentstructurescanbeobtainedwith

acceptablecomputationalcostinLES,whichhasbeenvalidatedinvariousapplications(Chengetal.,2012;Lametal.,2010;

Tucker,2011).

Inapreviousstudy(Chenetal.,2011),steadyRANSsimulationmethodwasusedtostudyairflowfieldsinvarious

aerostaticbearingswithdifferentparametersandrecessshapes,andtherelationshipbetweenvortexstrengthandvibration

r,notransientflowcharacteristicsintheaerostaticbearingcouldberesolved.

Inthispaper,theulationresultsreveal

ionofthebearingisalsomeasuredexperimentally,

anditisdemonstratedthatvibrationstrengthofthebearingincreaseswithincreasingpressurefluctuationinducedby

vortexsheddinginthebearingrecess.

calmodeling

InLES,largeeddiesofturbulencearedirectlyresolvedandeddieswithscalessmallerthangridspacingaremodeled.

ThegoverningequationsemployedinLESarethetime-dependentFavreFilteredNavier–Stokesequations,including

continuityandmomentumequations:

∂ρ∂

~

i

Þ¼0;

þ

ðρ

u

∂t∂x

i

~

ij

∂∂∂p

∂s

∂

~

i

Þþ

~

i

u

~

j

Þ¼−ðρ

u

ðρ

u

þ−ðτ~

ij

Þ;

∂t∂x

j

∂x

i

∂x

j

∂x

j

ð1Þ

ð2Þ

theFavrefilteristhedensity-weightedfilter,wheredensityandpressurearespatialfiltered(denotedby“

–

”)whilevelocity

isdensity-weighted(

e

üρÃ=ρ,

n

denotesageneralvariable).InEq.(2),s

ij

istheviscousstresstensorandτ

ij

isthesubgrid-

scale(SGS)stress,whicharedefinedas

2024年3月14日发(作者：子车焱)

JournalofFluidsandStructures40(2013)42–51

ContentslistsavailableatSciVerseScienceDirect

JournalofFluidsandStructures

journalhomepage:/locate/jfs

Largeeddysimulationofvortexsheddingandpressure

fluctuationinaerostaticbearings

JinchengZhu

a

,HanChen

a,b

,XuedongChen

a,

n

StateKeyLaboratoryofDigitalManufacturingEquipmentandTechnology,HuazhongUniversityofScienceandTechnology,

Wuhan430074,China

b

DepartmentofMechanics,HuazhongUniversityofScienceandTechnology,Wuhan430074,China

a

articleinfo

Articlehistory:

Received21May2012

Accepted5March2013

Availableonline28April2013

Keywords:

Aerostaticbearing

Largeeddysimulation

Vortexshedding

Pressurefluctuation

Vibration

abstract

Inaerostaticbearings,highspeedairflowmayinducesmallvibration,whichhasbeen

harmfultotheimprovementofmovingandpositioningaccuracyofaerostatically

paper,thetransientflowfield

intheaerostaticbearingisnumericallyinvestigatedusingthelargeeddysimulation

entstructuresarestudiedandvortexsheddingphenomenonisdiscovered

putationalresultsdemonstratethatvortexsheddingcauses

onshipbetweenpressurefluctuation

andbearingvibrationisestablishedbasedonoursimulationresultsandexperimentally

measuredvibrationstrength.

&htsreserved.

uction

Aerostaticbearingshahemeritof

near-zerofrictionandlowheatgeneration,applicationsofaerostaticbearingsmakeitpossibleforsupporteddevicesto

r,withtheincreasingdemandofpositioningaccuracy,theinherentsmall

vibrationontheorderofnanometers(Kawaietal.,2005)severelydamagesstabilityandprecisionofthebearing,especially

rstandandeventuallysuppressthisharmfulvibration,traditionaldesign

andanalysismethodsformassflowrateandloadcarryingcapacitydonotsufficeanymore,andlotsofresearcheffortshave

beenmadeontheairflowfieldinaerostaticbearings.

Recently,therelationshipbetweenthehighspeedairflowandthesmallvibrationinaerostaticbearingshasbeen

tal.(2005)studiedthenano-vibrationinultra-precisionmachinetoolsandattributed

dHe(2006)foundvortexflowstructuresinthebearingrecess

bycomputationalfluiddynamics(CFD)simulationofthesteadyairflowfield,andsuggestedthattheseairvorticesare

etal.(2006)alsoobservedthisairvortexflowbyCFD

simulationandreachedasimilarconclusion,andaccordinglyproposedanewrestrictordesigntoweakenthevibration.

Zhangetal.(2007)analyzedthehighReynoldsnumber(Re)flowinthebearingclearance,andreducedthevibrationof

entwork,Yoshimuraetal.(2012)attributednano-vibrationofaerostatic

bearingswithsurfacerestrictiontoghthe

flow-inducednatureofbearingvibrationhasgenerallybeenrecognized,thepreviousworksonlyassumedasteadyflow

n

./fax:+862787557325.

E-mailaddress:chenxd@().

0889-9746/$-seefrontmatter&htsreserved.

/10.1016/structs.2013.03.012

l./JournalofFluidsandStructures40(2013)42–5143

Nomenclature

d

0

d

1

d

2

h

_

m

p

r

r

0

r

1

r

2

t

u

i

,u

j

,u

k

orificediameter

recessdiameter

bearingdiameter

airfilmthickness

massflowrate

pressure

radialdistance

orificeradius

recessradius

bearingradius

time

flowvelocitiesinvariousdirections

x

i

,x

j

,x

k

z

H

P

0

P

s

P

A

Re

T

Δt

δ

ij

μ

ρ

s

ij

τ

ij

coordinatesinvariousdirections

verticaldistance

recessdepth

atmospherepressure

airsupplypressure

area-weightedaveragedpressure

Reynoldsnumber

temperature

timestepsize

Kroneckerdeltafunction

airviscosity

airdensity

molecularviscositystresstensor

subgrid-scalestress

fieldoraveragedtheflowfieldinaReynoldsAveragedNavier–Stokes(RANS)hisflow-inducedvibrationis

apparentlyatimedependentprocess,timedependentisnecessarytoinvestigatethetransientairflowfieldinthebearing

clearanceinordertofurtherunderstandthisharmfulsmallvibration.

Tonumericallyanalyzethedetailedflowcharacteristicsinaerostaticbearings,thefullNavier–Stokesequationsfor

hehighspeedairflowinthebearinggapneartheorificeoutletisturbulent,

RANSsimulationisusuallyemployed,andnumericalresultsdemonstrateadequateaccuracyinpredictingmeanflow

characteristics(ChenandHe,2006;LiandDing,2007).Pressuredepressions(Eleshaky,2009;Yoshimotoetal.,2007)and

vortexflowstructures(Chenetal.,2011)r,

RANSsimulationadoptsastatisticy,direct

numericalsimulation(DNS)canresolvethewholespectrumofturbulentscalesasnoturbulentmodelisassumed,butits

eeddysimulation(LES),largescaleturbulenteddiesaresolveddirectlyand

,coherentturbulentstructurescanbeobtainedwith

acceptablecomputationalcostinLES,whichhasbeenvalidatedinvariousapplications(Chengetal.,2012;Lametal.,2010;

Tucker,2011).

Inapreviousstudy(Chenetal.,2011),steadyRANSsimulationmethodwasusedtostudyairflowfieldsinvarious

aerostaticbearingswithdifferentparametersandrecessshapes,andtherelationshipbetweenvortexstrengthandvibration

r,notransientflowcharacteristicsintheaerostaticbearingcouldberesolved.

Inthispaper,theulationresultsreveal

ionofthebearingisalsomeasuredexperimentally,

anditisdemonstratedthatvibrationstrengthofthebearingincreaseswithincreasingpressurefluctuationinducedby

vortexsheddinginthebearingrecess.

calmodeling

InLES,largeeddiesofturbulencearedirectlyresolvedandeddieswithscalessmallerthangridspacingaremodeled.

ThegoverningequationsemployedinLESarethetime-dependentFavreFilteredNavier–Stokesequations,including

continuityandmomentumequations:

∂ρ∂

~

i

Þ¼0;

þ

ðρ

u

∂t∂x

i

~

ij

∂∂∂p

∂s

∂

~

i

Þþ

~

i

u

~

j

Þ¼−ðρ

u

ðρ

u

þ−ðτ~

ij

Þ;

∂t∂x

j

∂x

i

∂x

j

∂x

j

ð1Þ

ð2Þ

theFavrefilteristhedensity-weightedfilter,wheredensityandpressurearespatialfiltered(denotedby“

–

”)whilevelocity

isdensity-weighted(

e

üρÃ=ρ,

n

denotesageneralvariable).InEq.(2),s

ij

istheviscousstresstensorandτ

ij

isthesubgrid-

scale(SGS)stress,whicharedefinedas