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
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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
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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…
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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 ?
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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)
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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
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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 !!
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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
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{ }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
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field
Evaluate the finite amplitude of the streaksp
Amplitude Âst
Analytical fit to a sine fucntion Hollands & Cossu CRAS, 2009
⎤⎡ ( )YxÂ
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( ) ( ) ( ) ⎥⎦
⎤⎢⎣
⎡ −+=
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
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Similarity of turbulent coherent streaksS y
Maximum amplitude reached around x ~ 3.5-4.5λz
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Can we use turbulent coherent streaks for control purpose ?
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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
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Influence on the separation and/or vorticesp /
Flow around rear end : PIV in the symetry plane
Separation
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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
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• 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 ?
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Thank you for your attentionThank you for your attention.
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Turbulent boundary layer baseflowy y
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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
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Streaks finite amplitude for λz = 6 δ0 disturbancesS p z δ0
Streaks reach 13.5% free-stream velocity
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Streamwise evolution of the amplitudeS p
λz ↑
Maximum amplitude depends on λz
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Comparison with theoretical previsionsC p p
Most amplified wavelength are in the same range
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Separation controlS p
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