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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,

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Présentation au sujet: "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,"— Transcription de la présentation:

1 Part II : High-Re pitching flow prediction around airfoils GDR Interaction Fluide-Structure, May 2006, IMFT, Toulouse S. Bourdet, M. Braza, Y. Hoarau, G. Martinat, R. El Akoury, P. Chassaing, G. Harran, A. Sevrain z 1

2 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 2 NACA0012 oscillating airfoil in pitch Mc Alistair Test-case, Re=0.98 x 10 6, 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)

3 Part II : High-Re pitching flow prediction around airfoils GDR Interaction Fluide-Structure, May 2006, IMFT, Toulouse S. Bourdet, M. Braza, Y. Hoarau, G. Martinat, R. El Akoury, P. Chassaing, G. Harran, A. Sevrain z 3 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

4 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 4 1ère partie Modélisation statistique avancée Écoulements instationnaires avec structures cohérentes Approche OES Organised Eddy Simulation Recent developments ( ): Anisotropic eddy-viscosity OES modelling

5 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 5 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.

6 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 6 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 The Organised Eddy Simulation approach, OES

7 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 7 Circular cylinder (IMFT) - Re= Blockage coefficient D/H= 20% - Aspect ratio L/D= 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< mean fields (velocity and stresses) - phase averaging of the 2C PIV fields (pilot signal : pressure at =70 ) { R. Perrin, E. Cid, S. Cazin, A. Sevrain

8 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 8 Temporal PIV Streamlines Streaklines

9 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 9 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= coherent +u incoherent _ fluctuation

10 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 10 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= (n) (n-1) (-p)=-1.33

11 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 11 Turbulence spectrum slope variation in the inertial range Time-resolved PIV-2D

12 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 12 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. k 0.5 : velocity scale diminishes in consequence comparing to the equilibrium turbulence The turbulence length scale l diminishes comparing to equilibrium turbulence, l=k 3/2 /. Therefore, the spectrum shape yields an equivalent reduction of the eddy-diffusion coefficient C, in the relation: t = C k 0.5 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

13 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 13 Equations de Navier-Stokes en moyenne de phase

14 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 14 The phase-averaged Navier-Stokes equations, after the decomposition: U i = + u i 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 considerations because of the modified energy spectrum shape / t + / x j + / x j Temporal non-linear convection new turbulent stresses =- /dx i + ² / x j ² pressureviscous diffusion All the success in unsteady turbulence modelling depends on the way of modelling of the time-dependent turbulence stresses, esp. near wall

15 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 15 The heading lines of modelling In first order modelling: A phenomenological relation is adopted: - = ( / x j + / x i )-2/3 ij + F 1 + F 2 + F( D ij ° ) Boussinesq linear law (Isotropisation of turbulence via a scalar concept) extended also in non-linear quadratic forms, F 1 ( / x j * / x i ) or higher-order (cubic) forms F 2 (S ij *W jk *S ki ), (Craft, Launder, Suga, 1996) or/and including time-dependent Oldroyd derivatives, (Speziale, 1987) D ij ° (memory effects)

16 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 16 The heading lines of modelling In second-order modelling: No phenomenological relation for but full differential transport No eddy-viscosity concept Transport Equations of motion for each component of : / t=…+F(u i u j u k ) where F(u i u j u k ) 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 done by means of the DRSM in OES

17 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 17 Modélisation au second ordre : Pas de relation phénoménologique pour Pas de concept de viscosité turbulente Résolution dune 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 Thèse Y. Hoarau

18 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 18 NSMB meeting, May 13-14, 2002 From Bradshaw (1973): BL without adverse pressure-gradient BL with adverse pressure-gradient: Decrease of -uv/k Production = Dissipation It can be proven: C =(-uv/k) 2 (0.30) On presence of organised separated coherent structures: Production < Dissipation C has to decrease The anisotropy tensor b 12 =(-uv/k) near the wall In two-eq. modelling: t =C k 2 / C eddy-diffusion coeff. depending on turbulence length and time scale

19 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 19 (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 = instead of the 0.09 value in equilibrium turbulence

20 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 20 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

21 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 21 OES - Modeles anisotropes a viscosité turbulente PhD R. Bourguet

22 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 22 Hypothèse de Boussinesq (1877) ij : tenseur danisotropie MODELE DE TURBULENCE ANISOTROPE AU PREMIER ORDRE Collinéarité des deux tenseurs et donc de leurs directions principales Turbulence isotrope Surproduction dénergie cinétique turbulente

23 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 23 Existence de désalignement entre le tenseur danisotropie 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 lIMFT

24 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 24 Termes croisés –tenseur danisotropie et du taux de déformation, de lénergie cinétique turbulente à langle 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 dun cylindre circulaire à Re= OES: MODELE DE TURBULENCE ANISOTROPE AU PREMIER ORDRE

25 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 25 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

26 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 26 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 diso-valeur Q=3. PhD R. Bourguet,

27 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 27 Vers un modèle de turbulence anisotrope au premier ordre Premiers vecteurs propres de –a et S ( =50°) superposés à la viscosité turbulente directionnelle et à la ligne diso-valeur Q=3. critère de désalignement critère de déséquilibre de la turbulence Viscosité de turbulence directionnelle Définition tensorielle Sommation pondérée des éléments spectraux de S

28 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 28 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 langle de phase =50°.

29 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 29 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

30 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 30 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

31 Part II : High-Re pitching flow prediction around airfoils GDR Interaction Fluide-Structure, May 2006, IMFT, Toulouse S. Bourdet, M. Braza, Y. Hoarau, G. Martinat, R. El Akoury, P. Chassaing, G. Harran, A. Sevrain z 31 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 cycles 2D approximation

32 Part II : High-Re pitching flow prediction around airfoils GDR Interaction Fluide-Structure, May 2006, IMFT, Toulouse S. Bourdet, M. Braza, Y. Hoarau, G. Martinat, R. El Akoury, P. Chassaing, G. Harran, A. Sevrain z 32 Comparison with Experimental data Experimental Result OES/K- ε model OES/K- ω model K- ω SST model Cx (min - max.) Cz (min - max.) – 1.96 Cm (min - max.) – – – 0.2

33 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 33 Global parameters – hysteresis loops Coeff de portance Coeff de trainée Coeff de moment

34 Part II : High-Re pitching flow prediction around airfoils GDR Interaction Fluide-Structure, May 2006, IMFT, Toulouse S. Bourdet, M. Braza, Y. Hoarau, G. Martinat, R. El Akoury, P. Chassaing, G. Harran, A. Sevrain z 34 K-ω with SST limiter α = 5.2°α = 11°α = 16.9° α = 22.3°α = 24.9°α = -24.8°

35 Part II : High-Re pitching flow prediction around airfoils GDR Interaction Fluide-Structure, May 2006, IMFT, Toulouse S. Bourdet, M. Braza, Y. Hoarau, G. Martinat, R. El Akoury, P. Chassaing, G. Harran, A. Sevrain z 35 k- ω/OES model α = -22.2°α = -19.4°α = -16.2° α = -12.8°α = -7.1°α = 5°

36 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 36 NACA0012 oscillating (Mc Alistair et al) k- /OES

37 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 37 NACA0012 oscillating k/eps_OES k/omega_OES

38 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 38 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

39 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 39 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

40 GDR – Interaction Fluide-Structure, May 2006, IMFT, Toulouse 40


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