Main Seminar Abu

8/3/2019 Main Seminar Abu

1/33

velocityprofile

FlowControlLab,KAISTAbuSeena

Phd Student


2/33

1 Lo lawvelocit rofilesinsmoothwallturbulent

channelflows.2) Laglawforturbulentflowsintransitionalroughpipe.

3) Reynoldsstressmodel(Sreenivasan 2005).


3/33

Introduction


4/33

u

uT 2

Tw


5/33

Osborne Reynolds : Turbulent Motion can

),,('),( += tyxuyxuU

random fluctuations (u) on mean flow (u).

),,('),(

),,('),(

),,('),(

+=

+=

+=

tyxpyxpP

tyxwyxwW

tyxvyxvV

'''''

ns,fluctuatioofmeanSuch that

),,('),(

=====

+= tyxTyxTTe

0''

but

vu


6/33

'''''

2

2

'

wuvuu

'''''

appears,resseseyno s2

Re

=

wwvwu

wvvvu

equationmomentumMean

:owc anneeve opeu y

Viscous Shear stress

:ConditionsBoundary

'' =

dx

vuyy

''

0'',0,0:Wall

==

====

u

vuvuy

(unknown)

,,y


7/33

era ure ev ew


8/33

"It became clear for me that it is unrealistic to hope for thecreation of a pure self-contained theory [of turbulent flows

...

we have to rely upon hypothesis obtained by processingexperimental data... I did not carry out experiment workm sel but i s ent a lot o ener on calculations andgraphical processing of data obtained by otherresearchers.

1) Boussinesq eddy viscosity model2) Prandtls mixing length model

- , .

Present Approach:Open or under-determined equations


9/33

InnerLa er WallLaw Prandtl 1925

ViscousSheardominates

OuterLayer DefectLaw (vonKarman,1930)

TurbulentSheardominates

OverlapRegion LogLaw (Izakson1937&Millikan1939)


10/33


11/33

elocity.friction vis/,DominatesShearViscous =

= u

y

uww

groupslessdimensionatindependen1

)dimensionstindependen3,parameters(4analysisldimensiona

,,,ParameterslDimensiona

yw

yuu ==u ++ ,

+++

= yuuLaw of the wall :


12/33

ParameterslDimensiona

''DominatesShearTurbulent =

uU

vuw

groupsessdimensionltindependen1

)dimensionstindependen3,parameters(4analysisldimensiona

c

channelofdepthsemi,and ==

Yy

u

uUc

yuUc ==

Velocity Defect Law :

u


13/33

OverlapRegion

Izakson(1937)&Millikan(1939)

YFuUuu =

numberReynoldslargelysufficientFor

DominatesShearTurbulentandViscousBoth

FYuy

c

== ++ 1

getweating,Differenti

Fu

or

y

+

11

Yyy=

=

++


14/33

Lo Law :

uU

kByku

uu

=+== ++

1

ConstantKarmanvonln1

Inner log law

uRDBRUc =++= ,ln

1

DY

ku

c += ln

Skin Friction Law :

ku

Uniformly valid solution :

===

+=+= ++

lawwake-wallComposite

1)1(,0)0((1956),ColesoffunctionwakeW(Y)

,ln)()(,ln)()(

WW

DYk

YFYWk

DYk

YFyuuu

+= ++

sublayerviscoustheAbove

)()( YWk

yuuu

++= + )(ln YW

kBy

kuu


15/33

Traditional Log Region in Overlap Domain

Innerloglaw

SemilogScale

Byk

yu += +++ ln1)(

DYk

YuU += ++ ln1

)(


16/33

Rou hness

Lettheroughnessheightbeh

h

Thenroughnessparameter

If Equivalent to smooth wall

Viscous sub layer destroyed

Transitionally Rough wall

Major impact of the wall roughness is to perturb wall layer. Which leads to increase in wall shear stress accompanied by wall heat

transfer and mass transfer.


17/33

LiteratureReview

Millikan(1938)proposedtwolayertheory(InnerandOuterlayer)fortransitional,fullysmoothandfullyroughpipestoobtainloglawsdependenton

k Karmanconstantandadditiveconstantdependingonroughness.

Clauser &Hama(1954) Introducetheroughnessfunction ,asan

additionaltermtosmoothwallloglaw,where

itisusefuldescriptorofsurfaceroughnesseffectonmeanvelocitypro e nt e nnerreg on

itphysicallyrepresentroughnessdominatedshiftinvelocityprofile

fromloglawofsmoothwall

t es t s ownwar ueto ncreaseo rag. theshiftisupwardduetoreductionofdrag.


18/33

LiteratureReview

BZku

uZu +== +++ ln

1)(

Fully Rough wall Log law

Bh

Z

ku

uZu +==+

+++ ln

1)(

Log law for transitionally rough wall

BUZku

u

Zu+==

++++ ln

1

)(

Present Approach

++ =+==Z

Bu

u ,ln1

)(

)(exp += Uk


19/33

AlternateScales

ew on mens ona roug nesssca e,

oug nesscoor natean oug nessve oc ty

Base ona ternateroug wa var a es,t e nnervar a esare e ne as

RoughnessFrictionReynoldsnoR

andRoughnessReynoldsnoRe

2

228

82

===

bbb

U

u

UU

d

dx

dp


20/33

Power law region in Overlap Domain

Velocityprofile Velocityprofile

Innerwallvariables OuterPowerLaw

Reynoldsshearstress Reynoldsshearstress

The inner la er e uation becomes The outer la er e uation becomes

Matching


21/33

Lo Law :Inner log law , k = vonkarman conatantB

ku

uu +==+

ln1

)(

Skin Friction Law :

Composite velocity profile solutions:

W(Y) = wake function of Coles(1956), with BC W(0)=0 and W(1) = 1and


22/33

Nikuradse Sand Grain Roughness data (inflectional roughness)


23/33

Shockling Superpipe data (with machine honed surface)


24/33

FrictionFactor:


25/33

CommercialandSandGrainRoughness

Colebrooks Equation(commercialroughness)

+=

f

D

f Re

51.2

7.3log2

1

++

===

+=

BBBBk

hkU

FF

5.8,5.5)],(exp[

)1ln(1

ForInflectionalroughness(Loselevich andPilipenko)

++= h 1

)25.2/(ln),(sin)ln5.8( 1 ++

+ =+= hqqhkBU .n

+=

jh ex1

j=0 forColebrooksmonotonicroughness

j=11forinflectionalroughness

+h


26/33

ConclusionA) Openequations Functionalapproach

1) The open momentum equation in fully developed turbulent channel flowconsists of two la ers, inner la er near the wall and outer la er awafrom the wall. The matching of the inner and outer layer in overlap

region gives velocity profiles in terms of log law.

=Zinnervariable, theroughnessfrictionReynoldsnumber

and theroughnessReynoldsnumber.

3 The velocit rofile in transitional wall rou hness inner variable

/RR =

Re/Re =

, isuniversalforalltypesofwallroughness,in

contrasttotraditionalwallvariableZ+orZ/h.

4 The friction factor vs rou hness Re nolds number Re is also

+=Z

universal,explicitlyindependentofwallroughness.


27/33

ClosureModel:

Lo arithmicEx ansionsforRe noldsStress


28/33

ClosureModel:ReynoldsShearStress

Sreenivasan,K.R.andBershadskii(2006,JFMVol554pp477498):

ProposedReynoldsShearStressModel

2=

( )2/1

87.1 Rym

m

=+

++

Re nolds momentum e uation in a channel

Maxima occurs at

+

+

+

+ =+ yRdy

du 11

1111 ,1)]/[ln()(where

)2()]2/()([const

kpkkpeyyppyg

Ryygyu

omo =+=+=

+=

+++

++++

o ut on or ve oc ty str ut on:

.Reas1andenough,highisitleast whenatnumber,

ReynoldsoftindependenbetoandConstants:Assumption 1

kk

.


29/33

PresentAnalysisonClosureModelforReynoldsShearStress

[ ]kRy

yyk

mm

m

==

+=

++

++

,

...........)]/[ln(1 21Reynolds Shear stress:

Maxima occurs at

givesat0 Ry == ++

221

1 )]/[ln()]/[ln()( RyR m == +

Boundary conditions (imposed):

,1)]/[ln()(where

)]2/()([const

kpkkpeyyppyg

Ryygyu

=+=+=

+= ++++

Solution for velocity distribution


30/33

Velocity Distribution


31/33

Conclusion

1. TheclosuremodelofReynoldsshearstressintermsoflogarithmsofnon

dimensionalverticalcoordinateappearstoworksroughlyfory+ >10.

. eve oc y ncoor na es u+ y+ +y+ , y+ area so ngoo agreemen

withthedataalmostallthewaytocenterline.3. But velocityprofile(u+,y+) showappreciabledepartureintheoverlapregion,

.


32/33

ThankYou


33/33

References

Afzal,N.andAbuSeena 2007,AlternateScalesforTurbulentFlowinTransitionalRoughPipes:UniversalLogLaws J.FluidEngg,Vol 129,pp8090.

Millikan,C.B.,1938,ACriticalDiscussionofTurbulentFlowinChannelsandCircularTubes,Proc.5thInt.

Cong.Appl.Mech.Cambridge,J.P.denHartog andH.Peters,eds.,Wiley/ChapmanandHall,NewYork

, . .

Clauser,F.H.,1954,TurbulentBoundaryLayersinAdversePressureGradients,J.Aeronaut.Sci.,21,pp.91

108.

Hama,F.R.,1954,BoundaryLayerCharacteristicsforRoughandSmoothSurfaces,TransSocietyofNaval

, , . .

Abe,K.,Matsumoto,A.,Munakata,H.,andTani,I.,1990,DragReductionbySangGrainRoughness,In

StructureofTurbulenceandDragReduction,A.Gyr,ed.,SpringerVerlag,Berlin,pp.341348.

Nikuradse,J.,1933,LawsofFlowinRoughPipe,VI,Forchungsheft N361,EnglishtranslationNACATM1292,

1950.

Shockling,M.A.,2005,TurbulentFlowinRoughPipe,MSEthesis,PrincetonUniversity.

Shockling,M.A.,Allen,J.J.,andSmits,A.J.,2006,RoughnessEffectsinTurbulentPipeFlow,J.FluidMech.,

564,pp.267285.

Colebrook,C.F.,1939,TurbulentFlowinPi esWithParticularReferencetotheTransitionRe ionBetweenthe

SmoothandRoughPipeLaws,J.Inst.

Civ.

Eng,11,pp.133156.

Allen,J.J.,Shockling,M.A.,andSmits,A.J.,2005,EvaluationofaUniversalTransitionalResistanceDiagram

forPipesWithHonedSurfaces,Phys.Fluids,17,pp.121702.

Abe,H.,Kawamura,H.,andMatsuo,Y.,2001,DirectNumericalSimulationofaFullyDevelopedTurbulent

ChannelFlowWithRespecttoReynolds Number,J.FluidsEng.,123,pp.382393.

Afzal,N.,1982,FullyDevelopedTurbulentFlowinaPipe:AnIntermediateLayer,Ing.Arch.,53,pp.355377.

Date post:	06-Apr-2018
Category:	Documents
Upload:	abeer-zahid
View:	220 times
Download:	0 times

Main Seminar Abu

Documents