wallturb workshop lille april 21-23 2009 vortical ... 4/s4... · wallturb workshop lille april...

Wallturb Workshop Lille April 21-23 2009

M. Stanislas, L. Perret*, J.M. Foucaut, Ecole Centrale de Lille

Laboratoire de Mécanique de Lille* Ecole Centrale de Nantes

Vortical structures in the turbulentboundary layer: a possible route to a

universal representation


Vortices

Model Model ofof Adrian et Adrian et alal


• Shape and size of vortices?

• Role of vortices?

• Relations and interactions with other structures?

• Contribution to turbulence production and

dissipation near the wall?

…

QuestionsQuestions


• Use SPIV to detect, identify et quantify vortices

• Look at their scaling

• Look at their links with BL characteritics

ObjectivesObjectives


Model Model ofof Adrian et Adrian et alal

Legs


SPIV SPIV setset--upup


ToolsTools

Signed swirling strength

Velocity gradient tensor :

with img. part of complex Eig. Val.

Least square fit of

Oseen vortex model :

gives : ooo ru ,,Γ

ji xu ∂∂ /'

11/. ωωλλ cis = ciλ⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

− crci

cicrr

λλλλ

λ


LitteratureLitterature

Tanahashi et al (2004) Reτ = 800


tU λλ .=

Kolmogorov Kolmogorov scalesscales

4/13 )/( ενη = 2/1)/( εντ = 4/1)(νευ = 1=ν

ηυ

2

22

1

1 '.30'

30λ

ννε uxu

≅⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

∂

∂=

η+

y+


Vortex extractionVortex extraction

PDF of vortex radius, Reθ = 7 800, Reθ = 15 000, --- DNS Reτ = 1270Kang et al 2005



PDF of vortex intensity, Reθ = 7 800, Reθ = 15 000,



PDF of tang. Velocity, Reθ = 7 800, Reθ = 15 000, --- DNS Reτ = 1270Kang et al 2005

υ


VorticesVortices characteriticscharacteritics

η.60 ≅r τω 6.10 ≅

Vortices scale on Kolmogorov scales

--- Req = 7 800, - - - Req = 15 000


MeanMean square square vorticityvorticity equationequation

[1] convection [2] turb. diff. [3] production [4] stretching

[5] stretching [6] production [7] viscous diff. [8] dissipation

Tennekes & Lumley 1972 :« high Re, 2D mean flow »

η


VorticityVorticity equationequation revisitedrevisited

Buffer & log layers

1.' −≅ τω ai η.2 0 brl ≅= 1==ba


VorticityVorticity equationequation

Kolmogorov : a = b = 1 a2b2 = 1 τ ~ 100 μs

Coherent vortices : a = 1.6, b ~6 a2b2 ~ 100


WallWall frictionfriction

2

η+

y+

η+ =

ην

τ.2=u

30

4/1).( ++ = yκη


Turbulent Turbulent boundaryboundary layerlayer

Visc. Buffer Log Wake

y ~ η y ~ 10ηy ~ 100η y ~ 1000η


A new A new scalingscaling??

Laminar BL Turbulent BL

Ue Ue

ν η

Previous : external (Ue, uτ, δ)internal (uτ, ν)


0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1 10 100 1000

U/Ue

y/η

U/Ue

y/η



Previous : external (Ue, uτ, δ)internal (uτ, ν)


Laminar BL Turbulent BL

Ue Ue

ν η ⎟⎟⎠

⎞⎜⎜⎝

⎛=1000

,min* δηη


U/Ue

y/η* y/η*

UedydU *η

Mean velocity



y/η*

y/η*

u’i/Ue

u’1u’2/Ue2

Turbulence



y*/δ

? above Reθ ~ 35 000, (Ue,η)?



ConclusionsConclusions• Vortices scale on Kolmogorov scales

• Stretching by the mean velocity gradient is significant

• A new scaling of BL can be introduced (Ue, η*) (Ue, η)

• Wall friction scales with Kolmogorov :

1=ν

ηυ+ =

?

Application?


0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

1

1 10 100 1000

y/eta*

U/U

e

192.0ln11.0 +=ηy

UeU 60010 ≤≤

ηy

MeanMean velocityvelocity


eta+

1

10

100

1 10 100 1000 10000

y+

eta+

48.025.0

. ++=+ ⎟⎠⎞

⎜⎝⎛ yκη 200050 ≤+≤ y

Kolmogorov Kolmogorov lengthlength scalescale


0,001

0,010

0,100

1,000

1,00E-03 1,00E-02 1,00E-01 1,00E+00

3 m/s5 m/s7 m/s10 m/smod 3 m/smod 5 m/smod 7 m/smod 10m/s

6.08.06.1

−−= ⎟

⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

νδ

δη Ueyy

8.001.0 ≤≤ δy

Kolmogorov Kolmogorov lengthlength scalescale


192.0ln11.0 +=ηy

UeU

48.025.0

++=+ ⎟⎠⎞

⎜⎝⎛ yκη

6.08.06.1

−−= ⎟

⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

νδ

δη Ueyy η (and ε)

uτ

U

A new A new wallwall functionfunction

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛=

ηyF

Uek


Plane Plane channelchannel flowflow

4106.0

2106.012.0 ⎟⎟

⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛ −−−−=Hy

Hy

Hol

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛−=Ay

olml exp1

τ

νu

A .26=

Mixing length model

High Reynolds number


Plane Plane channelchannel flowflow

0

0,05

0,1

0,15

0,2

0,0 10,0 20,0 30,0 40,0 50,0

CB 514CB266CB126

Data ofG. Comte Bellot1965


0

0,05

0,1

0,15

0,2

0,0 10,0 20,0 30,0 40,0 50,0

CB 514

CB266

CB126

ml 514

ml 266

ml 126

0

0,05

0,1

0,15

0,2

0,0 10,0 20,0 30,0 40,0 50,0

CB 514CB266CB126wf 100+wf 100+wf 100+

ComparisonComparison

η wf at 100+

Standard ml (0.14)


0

0,05

0,1

0,15

0,2

0,0 10,0 20,0 30,0 40,0 50,0

CB 514

CB266

CB126

ml 514

ml 266

ml 126

0

0,05

0,1

0,15

0,2

0,0 10,0 20,0 30,0 40,0 50,0

CB 514

CB266

CB126

ml 514

ml 266

ml 126

ml 0.12

ml 0.14

EffectEffect ofof ml ml modelmodel


0

0,02

0,040,06

0,08

0,1

0,12

0,140,16

0,18

0,2

0,0 10,0 20,0 30,0 40,0 50,0

CB 514wf 100+wf 200+wf 300+

EffectEffect ofof ηη wfwf range range


Conclusion Conclusion

• a new wall function system can be designed

• good preliminary agreement with channel flow

• has to be checked on BL

• can be adapted to k-ε

wallturb workshop lille april 21-23 2009 vortical ... 4/s4... · wallturb workshop lille april...

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