Oppp ptimal perturbations on flat plate Turbulent Boundary ... · Grégory Pujals – GdR Contrôle...

Optimal perturbations on flat plate p p pTurbulent Boundary Layer: E i l i i iExperimental investigation

Colloque GdR Contrôle des Décollements 25/11/2009

Gregory Pujals (LadHyX – PSA Peugeot Citroën)Carlo Cossu (LadHyX, CNRS Ecole Polytechnique)present adress: IMFT, Toulouse

GREGORY PUJALS – GdR Contrôle des Décollements – 25/11/2009

present adress: IMFT, ToulouseSébastien Depardon (PSA Peugeot Citroën)

Lift-up and streaks formationStreamwise vortices in a shear flow streamwise streaksTaylor 1939, Moffatt 1967,..., Landahl 1980, Ellingsen & Palm 1985...

high streamwise velocity

high low

tices

low streamwise velocity

speed

streak

speed

streak

mw

ise

vort

streamwise vorticeslow streamwise velocity

high speed streak

U(z)

stre

am

high speed streak

low speed streak

2Grégory Pujals – GdR Contrôle des Décollements – 25/11/2009

Strongly related to non normality of the linearised operatorreviews in Trefethen et al 1993, Schmid & Hennigson 2001

Optimal perturbations : optimizing the lift-up

Optimal transient growtht=tmax optimal streaks

p g


t=0 optimal vorticesSchmid & Henningson 2001

Using streaks to perform passive control of laminar flows

ith t kno streaks: turbulent flow

with streaks: laminar flow

F d t k d l t iti !!!

4Grégory Pujals – GdR Contrôle des Décollements – 25/11/2009Fransson et al. PoF, 2005; Fransson et al. PRL, 2006

Forced streaks delay transition !!!

Why using the lift-up to control a flow ?

Large energy amplification rate low energy actuators

Perturbations are amplified by the base flow

Actuators are located upstream

( d t th h l t l d d i )(and not on the whole contoled domain)

Transition delay is ok but not a big deal for cars…


Motivations : Car External Aerodynamics

Side edges : 5% Rear end : 30%

Wheels : 15%Side mirrors and other equipment: 7%

Front end : 3%

Cooling circuit : 8%Sides of the vehicle : 2%

i i i

Underbody : 30%

Skin-friction drag no more than 20% of the total drag

Pressure drag more than 80% of the total drag

Can we manipulate a TBL with streaks to d d ?


reduce pressure drag ?

Streaky structures in wall-bounded turbulent flows

y+=9.6

Kline et al. JFM, 1967 Hutchins & Marusic JFM, 2007

y 9.6

Large scale streaks in a turbulentboundary layer (experimental)

Near-wall streaks in a turbulent boundary layer (experimental) boundary layer (experimental)

mean streaks spacing λz+ = 100 streaks spacing at least 2δ

boundary layer (experimental)


Are those natural streaks the most amplified structures in wall-bounded turbulent flows?

Compute the optimal perturbations sustained by :

Zero-Pressure Gradient Turbulent Boundary Layer

Cossu, Pujals & Depardon JFM, 2009


Optimal perturbations in Turbulent Boundary Layer Op p y y

δ99 ~0.223Δ

Primary peak atλ = 7.6 δ99

Secondary peak λz 7.6 δ99at λ+ = 81.5

Structures withStructures withδ99 < λz < 30 δ99

strongly amplified

9Grégory Pujals – GdR Contrôle des Décollements – 25/11/2009Cossu, Pujals & Depardon JFM, 2009

Questions Q

No observation of such large-scale structures (unlike near-wall streaks):

Not selected for self-sustained process?

Need to be artificially forced to be detected?Need to be artificially forced to be detected?

Need for experimental validation !!


Experimental resultspTurbulent boundary layer : Ue=20m.s-1

x=110mm:δ0 ~ 5.4mm, Reδ∗ ∼ 1000

Roughness elements :height: k=4mm (~ 0.8 δ0)

diameter: d

spacing : λz/d=4 cf White POF, 2002


{ }12,10,7,6,5,3/ 0 ∈δλz

Forcing large-scale coherent turbulent streaksg gNear-wall PIV at Y=k/2, Perturbations with λz ~ 6δ0 Inst

U/Uetantaneoous field

High speed streak

Low speed streakp

U/U

Time AvU/Ue

Averaged


field

Evaluate the finite amplitude of the streaksp

Amplitude Âst

Analytical fit to a sine fucntion Hollands & Cossu CRAS, 2009

⎤⎡ ( )YxÂ


( ) ( ) ( ) ⎥⎦

⎤⎢⎣

⎡ −+=

z

zzYxAzYxuzYxuλ

π 02sin,ˆ,,,,ˆ ( ) ( )e

st UYxAYxA ,,ˆ =

Streamwise evolution of the amplitudeS p

Streaks can reach 13% Ue

λz ↑

Most amplified wavelength are in the same range


Similarity of turbulent coherent streaksS y

Maximum amplitude reached around x ~ 3.5-4.5λz


Can we use turbulent coherent streaks for control purpose ?


Using coherent streaks to prevent separation on a bluff bodyU g p p y

Ahmed body : generic car model Ahmed et al 1984Ahmed body : generic car model, Ahmed et al. 1984

adverse pressure gradient on the roof

separation on the slanted surface

streamwise vortices originating from side edges

17Grégory Pujals – GdR Contrôle des Décollements – 25/11/2009 Brunn et al. 2007

Forcing coherent streaks on the roofg

Roughness elements

Separation line x0

Near-wall PIV at Y=k/2, Perturbations with λz ~ δ0 , Time Averaged field

High speed /low speedstreaks observed


Influence on the separation and/or vorticesp /

Flow around rear end : PIV in the symetry plane

Separation


Separation delayed

ConclusionsC

Optimal perturbations in a flat plate turbulent boundary layer

• Structures with δ < λz < 30 δ strongly amplified

• Mismatch between λzopt and observations

Forcing streaks in a flat plate turbulent boundary layer

Mismatch between λzopt and observations

• First experimental evidence of transient growth of coherent k i b l fl

Forcing streaks in a flat plate turbulent boundary layer

streaks in turbulent flow

• Large-scale coherent turbulent streaks can be forced in TBL and are well defined and reproductible

• ‘Self-similarity’ of streaks


• Scale selection confirms theoretical previsions

Work in progressW p g

• Coherent streaks can develop in spite of APG/3D effects

• Turbulent separation is avoided with coherent turbulent streaks

• Related to the mean flow modification observed by Duriez etRelated to the mean flow modification observed by Duriez et al.(ASME, 2006) in the laminar case ?


Thank you for your attentionThank you for your attention.


Turbulent boundary layer baseflowy y


Evaluate the finite amplitude of the streaksp

Analytical fit to a sine fucntion Hollands & Cossu CRAS, 2009

⎤⎡ ( )ˆ( ) ( ) ( ) ⎥⎦

⎤⎢⎣

⎡ −+=

z

zzYxAzYxuzYxuλ

π 02sin,ˆ,,,,ˆ ( ) ( )e

st UYxAYxA ,

ˆ,ˆ =

⎦⎣

PIV

Best fit


Streaks finite amplitude for λz = 6 δ0 disturbancesS p z δ0

Streaks reach 13.5% free-stream velocity


Streamwise evolution of the amplitudeS p

λz ↑

Maximum amplitude depends on λz


Comparison with theoretical previsionsC p p

Most amplified wavelength are in the same range


Separation controlS p


Oppp ptimal perturbations on flat plate Turbulent Boundary ... · Grégory Pujals – GdR Contrôle...

Documents

Transcript of Oppp ptimal perturbations on flat plate Turbulent Boundary ... · Grégory Pujals – GdR Contrôle...