Part II : High-Re pitching flow prediction around airfoils GDR Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse S. Bourdet, M. Braza, Y. Hoarau,

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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

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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 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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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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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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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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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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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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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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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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Turbulence spectrum slope variation in the inertial range

Time-resolved PIV-2D

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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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Equations de Navier-Stokes en moyenne de phase

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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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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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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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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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(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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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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OES

- Modeles anisotropes a viscosité turbulente

PhD R. Bourguet

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• 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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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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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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• 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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• 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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• 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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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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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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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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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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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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Global parameters – hysteresis loops

Coeff de portance

Coeff de trainée

Coeff de moment

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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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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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NACA0012 oscillating (Mc Alistair et al)

k-/OES

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NACA0012 oscillating

k/eps_OES k/omega_OES

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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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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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Part II : High-Re pitching flow prediction around airfoils GDR Interaction Fluide-Structure, 18-19 May 2006, IMFT, Toulouse S. Bourdet, M. Braza, Y. Hoarau,

Documents

oes page

fluid structure interaction

oes macrosimulation

vos page

circular cylinder imft

lift coefficients page

urans turbulence models

oes use of nsmb code