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Part II : High-Re pitching flow prediction around airfoils
GDR Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
S. Bourdet, M. Braza, Y. Hoarau, G. Martinat, R. El Akoury, P. Chassaing, G. Harran, A. Sevrain
z
2
GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
NACA0012 oscillating airfoil in pitch
Mc Alistair Test-case, Re=0.98 x 106, incidence 10°(+-)15°
reduced frequency 0.1 : DESIDER EU pgm test-case
Grid : 500 x 226
Turbulence Macrosimulation approach :
Organised Eddy Simulation
in comparison with URANS
Turbulence Models:
k--SST-URANS, K--OES, k--OES
Use of NSMB code where OES modelling is implemented in collaboration IMFT –CFS Enineering (J. Vos)
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Part II : High-Re pitching flow prediction around airfoils
GDR Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
S. Bourdet, M. Braza, Y. Hoarau, G. Martinat, R. El Akoury, P. Chassaing, G. Harran, A. Sevrain
z
Challenges in simulating dynamic stall phenomena
Image from UNSI Europeen Program (Vol. 85, Vieweg, 2000)
Forced unsteadiness
Separation
Irreversibility in hysteresis loops
Need of accurate prediction of unsteady drag and lift coefficients
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
1ère partie
Modélisation statistique avancée
Écoulements instationnaires avec structures cohérentes
Approche OES
Organised Eddy Simulation
Recent developments (2005-2006):
Anisotropic eddy-viscosity OES modelling
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
Coherent structures visualisation from: Brown & Roshko (1974, J. Fluid Mech. Vol. 64)
The OES macrosimulation approach
The turbulent motion in unsteady aerodynamics and especially in fluid-structure interaction involves organised modes (coherent motion) interacting non-linearly with the fine-scale (incoherent) turbulence. The frequencies (wavenumbers) of the two kinds of the motion (organised and chaotic) are distinctive, because the organised modes belong often to the low or moderate frequency range in the spectrum.
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
Distinction between the structures to be resolved and those to be modelled: based upon their organised or random character. Part (2) : modelled by reconsidered,.advanced statistical turbulence modelling, efficient in high-Re unsteady wall flows, (Dervieux, Braza, Dussauge, Notes on Num. Fluid Mech., 1998, Vol. 65), Vol. 81, Braza et al, Flomania book Vol. 94 in print (2006)).
OES: Schematic separation of coherent/random turbulence parts in the spectral domain
In the physical domain: ensemble average/phase average decomposition: U=<U>+u
The Organised Eddy Simulation approach, OES
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
Circular cylinder (IMFT) - Re=140000
- Blockage coefficient D/H= 20%- Aspect ratio L/D= 4.8
- Free stream turbulence intensity: u’/Uo=1.5%Previous work:
Measurements:- Wall pressure- PIV 2D-2C- Stereoscopic PIV- Time resolved PIV
Results:- drag coefficient : 65000< Re<190000- mean fields (velocity and stresses)- phase averaging of the 2C PIV fields (pilot signal : pressure at =70)
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uv
{
R. Perrin, E. Cid, S. Cazin, A. Sevrain
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
Temporal PIV
Streamlines Streaklines
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse high-resolved PIV (2D)
Streaklines (left); Iso-velocity phase-averaged field, time-resolved PIV (small plane) and phase-averaged PIV-2D (larger plane) . Very good agreement between the two approaches
Left: Time-dependent velocity signal (red), phase-averaging (blue), fluctuation (black). Time-resolved PIV signals.
Decomposition:
U=<U>coherent+uincoherent_fluctuation
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
Left: Comparison between LDV (Djeridi, Braza et al J. Flow Turb & Combust., 71) and PIV spectra (present study, PhD R. Perrin/IMFT, Exps in Fluids, 2006), x/D=1 y/D=0.375;
Right: PIV spectrum at x/D=1 y/D=0.5 : original signal (red), spectrum issued from the phase-averaged decomposition (blue), and fluctuation spectrum (green).
Vertical velocity spectra past the cylinder Re=140000
(n)(n-1)
(-p)=-1.33
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
Turbulence spectrum slope variation in the inertial range
Time-resolved PIV-2D
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
E((n))=( n)-(2/5).(5/3) [1-(n-1)/(n)]( -5/3)e(n) /[(n)-(n-1)] Equilibrium Turbulence -p=-
5/3=-1.66
E((n))=( n)-(2/5)p( [1-(n-1)/(n)]( -p)e(n) /[(n)-(n-1)] Non-equilibrium Turbulence -
p#-5/3
in the inertial range
E : spectral energy diminishes in the inertial region in comparison with équilibrium spectrum.
k0.5 : velocity scale diminishes in consequence comparing to the equilibrium turbulence
The turbulence length scale l diminishes comparing to equilibrium turbulence, l=k3/2/.
Therefore, the spectrum shape yields an equivalent reduction of the eddy-diffusion coefficient C, in the relation: t= C k0.5 l involved in statistical turbulence modelling.
The present analysis based on this physical experiment confirms our previous studies results issued from two different and complementary approches : the second-ordre moment modeling in phase-averaging and the DNS.
k
E(k)
(n-1) n
(-p)
(-5/3)
Part to be modeled
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
Equations de Navier-Stokes en moyenne de phase
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
The phase-averaged Navier-Stokes equations, after the decomposition: Ui = <Ui> + ui
yield the same form as the ‘Reynolds averaged Navier-Stokes equations’ plus the temporal term.
However, the new turbulent stresses have to be modeled by modified statistical turbulence modelling considerationsbecause of the modified energy spectrum shape
<Ui>/ t + <Uj> <Ui>/ xj+ <uiuj>/ xj
Temporal non-linear convection new turbulent stresses
= - <P>/dxi+ ²<Ui>/ xj² pressure viscous diffusion
All the success in unsteady turbulence modelling depends on the way of modelling of the time-dependent turbulence stresses, <uiuj> esp. near wall
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
The heading lines of modelling <uiuj>
In first order modelling: A phenomenological relation is adopted:
-<uiuj> = < t> ( <Ui>/ xj + <Uj>/ xi)-2/3 <k> ij + F1 + F2 + F( Dij° )
Boussinesq linear law
(“Isotropisation” of turbulence via a scalar concept)
extended also in non-linear quadratic forms, F1 ( <Ui>/ xj * <Uj>/ xi)
or higher-order (cubic) forms F2 (Sij*Wjk*Ski), (Craft, Launder, Suga, 1996)
or/and including time-dependent Oldroyd derivatives, (Speziale, 1987)
Dij°(memory effects)
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
The heading lines of modelling <uiuj>
In second-order modelling:
No phenomenological relation for <uiuj> but full differential transport
No eddy-viscosity concept
Transport Equations of motion for each component of <uiuj> :
<uiuj> / t=…+F(uiujuk)
where F(uiujuk) is modelled by phenomenological laws.Achievement: Universality and improved flow physics modelling
especially in respect to normal stresses anisotropy
Adaptation of the two-equation modelling has been doneby means of the DRSM in OES
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
Modélisation au second ordre : Pas de relation phénoménologique pour <uiuj> Pas de concept de viscosité turbulente Résolution d’une équation de transport différentielle pour
chaque composante du tenseur :
Modélisation des corrélations triples et de la corrélation gradient de pression - déformation Universalité et amélioration de la physique des écoulements
MAIS: Instabilité numérique par rapport aux modèles du 1er ordre
k
j
k
i
k
ji
kk
kji
ijk
i
k
jji
x
u
xu
x
uu
xx
uuu
xp
jxp
ixU
kjx
U
kit
uuuuuuuu
2)(
][][
Thèse Y. Hoarau
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse NSMB meeting, May 13-14, 2002
From Bradshaw (1973):
BL without adverse pressure-gradient
BL with adverse pressure-gradient:Decrease of -uv/k
Production = DissipationIt can be proven:C=(-uv/k)2 (0.30)2 0.09
On presence of organised separated coherent structures:Production < DissipationC has to decrease
The anisotropy tensor b12=(-uv/k) near the wall
In two-eq. modelling:t=Ck2/Ceddy-diffusion coeff. depending on turbulence length and time scale
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
(Order of magnitude in accordance with the spectral modification of the length scale and withi a considerable number of detached flow simulations in DESIDER EU program.
From DRSM in OES( phase-averaged N-S):Adaptation of the eddy-diffusion coefficient for two-equation
modelling; C=0.015-0.025 instead of the 0.09 value in equilibrium turbulence
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
OES approach and two-equation modelling(isotropic version)
*Use of the modified damping function(Jin & Braza, AIAA J. 1994) derived from DNS
*use of the eddy-diffusion coefficient adapted by OES/DRSM C=0.02
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
OES
- Modeles anisotropes a viscosité turbulente
PhD R. Bourguet
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
• Hypothèse de Boussinesq (1877)
ij: tenseur
d’anisotropie
MODELE DE TURBULENCE ANISOTROPE AU PREMIER ORDRE
Collinéarité des deux tenseurs et donc de leurs directions
principales
Turbulence isotrope
Surproduction d’énergie cinétique
turbulente
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
Existence de désalignement entre le tenseur d’anisotropie et les vitesses de déformation en turbulence instationnaire avec structures
cohérentes?
Effet du non-équilibre sur le plan physique
Etude par le moyen de la base de données expérimentale de l’IMFT
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
Termes croisés –tenseur d’anisotropie et du taux de déformation, de l’énergie cinétique turbulente à l’angle de phase =50°, et superposition des lignes de courants.
Les grandeurs physiques représentées sont des moyennes de phase issues du traitement des données PIV.
• 3C-PIV en aval d’un cylindre circulaire à Re=140 000
OES: MODELE DE TURBULENCE ANISOTROPE AU PREMIER ORDRE
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
• Etude de la collinéarité des directions principales des deux tenseurs
Premiers vecteurs propres de –a et S représentés à deux angles de phases (=50° et =222°) superposés au critère Q (à gauche) et angles observés entre les deux vecteurs (ci-dessus).
Désalignement significatif au sein des structures cohérentes et dans les régions cisaillées
MODELE DE TURBULENCE ANISOTROPE AU PREMIER ORDRE
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
• Critère de prédiction du désalignement selon chaque direction principale
• Transport du critère 3D de désalignement : équations de transport issues du DRSM version SSG (Speziale, Sarkar, Gatski, JFM 227, ’91)
Premiers vecteurs propres de –a et S (=50°) superposés au critère de désalignement et à la ligne d’iso-valeur Q=3.
PhD R. Bourguet,
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
• Vers un modèle de turbulence anisotrope au premier ordrePremiers vecteurs propres de –a et S (=50°) superposés à la viscosité turbulente directionnelle et à la ligne d’iso-valeur Q=3.
critère de désalignement
critère de déséquilibre de la turbulence
Viscosité de turbulence directionnelle
Définition tensorielleSommation pondérée des éléments spectraux de S
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
Loi constitutive des tensions de Reynolds
• Vers un modèle de turbulence anisotrope au premier
ordre : validation dans le cas expérimental
Comparaison entre les tensions de Reynolds en moyenne de phase observées directement sur la PIV ((a) et (c)) et celles obtenues grâce à la nouvelle loi constitutive ((b) et (d)) à l’angle de phase =50°.
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
Results for the pitching flow at Re=0.98 x 106, incidence 10°(+-)15°
Isotropic OES modeling as a first step
DESIDER Eu program test-case
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
OES approach and two-equation modelling(version based on Boussinesq law)
*Use of the modified damping function(Jin & Braza, AIAA J. 1994) derived from DNS
*use of the eddy-diffusion coefficient adapted by OES/DRSM C=0.02
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Part II : High-Re pitching flow prediction around airfoils
GDR Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
S. Bourdet, M. Braza, Y. Hoarau, G. Martinat, R. El Akoury, P. Chassaing, G. Harran, A. Sevrain
z
k-ε/OESk-ω/OESK-ω with SST limiter
Experimental Data from McCroskey et al.,1976 AIAA
Comparison with Experimental data
Time evolution of Lift Coefficient
IMFT computations : only 3 main periods at this stage. Need to provide over 15-20 cycles
2D approximation
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Part II : High-Re pitching flow prediction around airfoils
GDR Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
S. Bourdet, M. Braza, Y. Hoarau, G. Martinat, R. El Akoury, P. Chassaing, G. Harran, A. Sevrain
z
Comparison with Experimental data
Experimental Result
OES/K-ε model
OES/K-ω model
K-ω SST model
Cx (min - max.) 0 - 0.92 0 - 0.90 0 - 0.91 0 - 0.90
Cz (min - max.) 0 - 2.2 0.4 - 1.99 0.4 - 1.78 0.2 – 1.96
Cm (min - max.) 0.02 - 0.4 0.02 – 0.17 0.02 – 0.18 0.0 – 0.2
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
Global parameters – hysteresis loops
Coeff de portance
Coeff de trainée
Coeff de moment
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Part II : High-Re pitching flow prediction around airfoils
GDR Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
S. Bourdet, M. Braza, Y. Hoarau, G. Martinat, R. El Akoury, P. Chassaing, G. Harran, A. Sevrain
z
K-ω with SST limiter
α = 5.2° α = 11° α = 16.9°
α = 22.3° α = 24.9° α = -24.8°
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Part II : High-Re pitching flow prediction around airfoils
GDR Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
S. Bourdet, M. Braza, Y. Hoarau, G. Martinat, R. El Akoury, P. Chassaing, G. Harran, A. Sevrain
z
k- ω/OES model
α = -22.2° α = -19.4° α = -16.2°
α = -12.8° α = -7.1° α = 5°
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
NACA0012 oscillating (Mc Alistair et al)
k-/OES
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
NACA0012 oscillating
k/eps_OES k/omega_OES
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
Conclusions
•A first step of fluid-structure interaction analysis for moving bodies – rigid wall-
ICARE/IMFT code – compressible flows version
•Dynamic mesh adaptation approach developed in IMFT
•Promising approach by URANS/OES turbulence modelling
for high-Reynolds number applications in aerodynamics
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse
Outlook
•Study of flows in a range of circular cylinders – collaboration with EDF –
•in progress
•Implementation of the OES/anisotropic modelling in NSMB code – collaboration
•with CFS/EPFL – in progress
•Two-degrees of freedom aerofoil motion : pitching/plunging – DESIDER test-case
•Project of respiratory airways in Biomechanics – EU Collaboration and with GEMP/IMFT
•Future coupling with structural mechanics code
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GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse GDR – Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse