Bruit de mélange des jets subsoniques initialement turbulents

Size: px

Start display at page:

Download "Bruit de mélange des jets subsoniques initialement turbulents"

Blaze Rodger Sharp
6 years ago
Views:

Turbulence and Aeroacoustics Research team of the Centre Acoustique École Centrale de Lyon & LMFA UMR CNRS 5509 GDR 2865 CNRS, Turbulence, Poitiers 15-17 octobre 2012 Bruit de mélange des jets

1 Turbulence and Aeroacoustics Research team of the Centre Acoustique École Centrale de Lyon & LMFA UMR CNRS 5509 GDR 2865 CNRS, Turbulence, Poitiers octobre 2012 Bruit de mélange des jets subsoniques initialement turbulents Christophe Bogey, Olivier Marsden & Christophe Bailly Université de Lyon Ecole Centrale de Lyon & LMFA - UMR CNRS 5509 & Institut Universitaire de France 1

2 Outline Bruit de mélange des jets subsoniques initialement turbulents Motivations Méthodologie pour la simulation des grandes échelles (LES-RF) Influence du taux de turbulence initial sur un jet à Reynolds Re D = 10 5 Quelques remarques sur les contraintes de maillage Jets trippés de Re D = à Bogey, Marsden & Bailly, 2012, J. Fluid Mech., , Phys. Fluids, 23, & 23, GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

Subsonic turbulent jets Initial conditions at the

André, ECL) Re D 3 10 7 Re D 3.3 10 4 Re D 1.

7 10 5 fully laminar u e/u j < 1% nominally laminar u

nominally turbulent u e/u j 10% Re D 3 10 5 fully

3 Subsonic turbulent jets Initial conditions at the nozzle exit (visualizations by T. Castelain & B. André, ECL) Re D Re D Re D Re D fully laminar u e/u j < 1% nominally laminar u e/u j 1% Re D 10 5 (Re δθ 300) transitional jets nominally turbulent u e/u j 10% Re D fully turbulent Re D Re D = u j D/ν Re δθ = u j δ θ /ν σ ue = u e/u j 3 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

Subsonic turbulent jets Free shear flows :

= u j D/ν Prasad & Sreenivasan (1989) Re D

(1983) Re D 10 4 Kurima, Kasagi & Hirata

Mollo-Christensen (1963) Re D 5.6 10 3 Re D 1.

4 Subsonic turbulent jets Free shear flows : subsonic turbulent jets Reynolds number Re D = u j D/ν Prasad & Sreenivasan (1989) Re D 4000 Dimotakis et al. (1983) Re D 10 4 Kurima, Kasagi & Hirata (1983) Ayrault, Balint & Schon (1981) Mollo-Christensen (1963) Re D Re D Re D = GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

5 Subsonic turbulent jets Disparity of scales Isothermal jet, λ a /δ θ Re D /(M a St) (Re D = 10 6, M a = 0.9, r/d 10) p 2 a θ=90 o M7.5 a u a/u 10 4 p a/p 10 3 u a p a λ a δ θ u j D u p x c λ a /δ θ 10 3 u /u j 0.16 Mollo-Christensen (1963), Re D = laminar potential core length x c 5 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

6 Large eddy simulation Closure : subgrid-scale model e.g. Sagaut (2006), Lesieur (2007) Projection modeling by a spacial convolution filtering ū = G u t ū + (ūū) + ( p/ρ) + ν 2 ū = σ sgs structural approach, find a model for the sgs stress tensor functional approach, surrogate the mean action turbulent kinetic energy balance is more important turbulent kinetic energy cascade is dominant dissipation Two main classes of methods in physical space turbulent eddy viscosity models hyperviscosity ( σ sgs ν h 2n ) or high-order explicit filtering Pruett et al. Domaradzki, Adams et al. Visbal, Gaitonde, Rizzetta ADM... LES - Relaxation filtering σ sgs = χg ũ Bogey & Bailly (2006), Berland et al., J. Comput. Phys. (2008) & JOT (2008) 6 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

7 Large eddy simulation Closure : LES based on relaxation filtering (LES-RF) Spectrum model E(k) = C K (εl) 2/3 (kl) 5/3 f L (kl)f η (kl η ) L L large-scale length scale, l η Kolmogorov length scale Governing equation, t ū + (ūū) + ( p/ρ) + ν 2 ū = χg ũ Ẽ(k) = Ĝ 2 (k)e(k), Lin s equation for Ẽ t Ẽ(k) = T (k) 2νk 2 Ẽ(k) 2χ [ 1 Ĝ(k) ] Ẽ(k) D ν (k) = 2νk 2 Ẽ(k) viscous dissipation D f (k) = 2χ [ 1 Ĝ(k) ] Ẽ(k) dissipation induced by the explicit filtering Reynolds effects. Given Mach number, u = cst and k t = cst Reynolds number Re L = u L/ν L, and space discretization L/ = cst = For a given wavenumber k α k η, D f (k α ) u 3 cst D ν (k α ) u 3 Re 1 L 7 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

8 Large eddy simulation Closure : LES based on relaxation filtering (LES-RF) k s c k g c = π/ Re L = 10 3 Re L = 10 5 E(k )/(u 2 L) E(k) energy spectrum k g c = π/ k s c = 2π/(5 ) k L/ = O(10) von Kármán (1948) - Pao (1965) E(k) = C K ε 2/3 k 5/3 f L (kl)f η (kl η ) 8 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

9 Large eddy simulation Closure : LES based on relaxation filtering (LES-RF) E(k )/(u 2 L) D(k )/u ks c Re L ր k g c = π/ k Re L = 10 3 Re L = 10 5 E(k) energy spectrum D ν (k) viscous dissipation k g c = π/ k s c = 2π/(5 ) S(k) = k 0 (Bailly & Comte-Bellot, 2003) T (k )dk 0 for kλ g 1 = ks cλ g 1 for a well-resolved LES 9 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

10 Large eddy simulation Closure : LES based on relaxation filtering (LES-RF) 10 0 E(k )/(u 2 L) D(k )/u Re L ր k s c Re L = 10 3 Re L = 10 5 Ẽ(k) energy spectrum D ν (k) viscous dissipation D f (k) explicit filtering π/1024 π/128 π/16 π/4 π k In the well-resolved wavenumber range, we must have D f (k) < D ν (k) constraint on the mesh size Regularization term corresponding to the net drain associated with the turbulent kinetic energy cascade, larger scales mostly unaffected 10 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

11 Large eddy simulation Closure : LES based on eddy viscosity concept 10 0 E(k )/(u 2 L) D(k )/u k s c Re L ց as ν t ր Re L = 10 3 Re L = 10 5 E(k) energy spectrum D ν (k) viscous dissipation D ν+νt (k) eddy-viscosity (with ν t /ν = 5) π/1024 π/128 π/16 π/4 π k In the well-resolved wavenumber range, D ν (k) is replaced by D ν+νt (k), same functional form, overestimation of the dissipation for resolved scales However user-friendly for unstructured grids 11 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

12 Large eddy simulation Status of large eddy simulation full-scale for laboratory jets (typically D = 2 cm, M = 0.9, Re D = ) and nearly mature numerical tool (basic statistics, turbulent kinetic energy budget, two-point space-time correlations, Reynolds effects) advances in «alternative subgrid-scale models» e.g. removing energy at the smallest resolved scale by explicit filtering with N 10 8 points, DNS at Re D 10 4 and LES at Re D 10 5, St GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

13 Tripped subsonic round jets Influence of initial turbulence level M = 0.9, Re D = 10 5, δ θ /r 0 = 1.8%, Re δθ = 900 σ ue = 0% σ ue = 3% σ ue = 6% n r n θ = n z = = 252 million pts as the exit turbulence level increases, coherent structures (and consequently vortex rolling-ups and pairings) gradually disappear σ ue = 9% higher initial turbulence levels lead to longer potential cores σ ue = 12% 13 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

14 Tripped subsonic round jets Influence of initial turbulence level M = 0.9, Re D = 10 5, δ θ /r 0 = 1.8%, Re δθ = 900 <u z u z > 1/2 /u j z/r 0 u z/u j along r = r 0 σ ue = 0% σ ue = 3% σ ue = 6% σ ue = 9% σ ue = 12% M = 0.9 & Re D = Fleury et al., AIAA Journal (2008) As the initial turbulence level increases, the shear layers develop more slowly with lower rms velocity peaks (overshoot around the pairing position for u e/u j 6%, but nearly monotonical growth for u e/u j 9%) 14 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

15 Tripped subsonic round jets Influence of initial turbulence level M = 0.9, Re D = 10 5, δ θ /r 0 = 1.8%, Re δθ = u c /u j z/r 0 Centerline mean axial velocity u c /u j σ ue = 0% σ ue = 3% σ ue = 6% σ ue = 9% σ ue = 12% Experiments at Mach 0.9 jets at Re D Lau et al. (1979), Arakeri et al. (2003), Fleury et al. (2008) 15 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

16 Tripped subsonic round jets Influence of initial turbulence level M = 0.9, Re D = 10 5, δ θ /r 0 = 1.8%, Re δθ = 900 peak rms velocity [u z] rms /u j centerline mean velocity u c /u j <u z u z > 1/2 /u j u c /u j z/r 0 z/r 0 σ e < 1% σ e = 1% σ e = 9% 16 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

17 Tripped subsonic round jets Influence of initial turbulence level M = 0.9, Re D = 10 5, δ θ /r 0 = 1.8%, Re δθ = GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

18 Tripped subsonic round jets Influence of initial turbulence level M = 0.9, Re D = 10 5, δ θ /r 0 = 1.8%, Re δθ = 900 σ e = 0% σ e = 3% σ e = 6% σ e = 9% σ e = 12% z = r 0 snapshots of vorticity ω z (r, θ) z = 2r 0 z = 4r 0 18 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

19 Tripped subsonic round jets Dissipation functions versus normalized wave number k Jetring1024drdz, /r 0 = 0.36% ( r at r = r 0 ) π/32 π/16 π/8 π/4 π/2 π k molecular viscosity relaxation filtering time integration negligible contribution of time integration damping from viscosity higher than that from the relaxation filtering for about k < π/3 = λ > 6 well discretized, i.e. numerical accuracy mainly affected by the molecular viscosity 19 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

20 Tripped subsonic round jets Discretization quality M = 0.9, Re D = 10 5, δ θ /r 0 = 1.8%, Re δθ = 900, σ ue = 9% (snapshot of ω at x = r 0 ) θ R (θ) 11 (θ) = u z(r, θ 0, z)u z(r, θ 0 + θ, z) u 2 z (r, θ 0, z) 1/2 u 2 z (r, θ 0 + θ, z) 1/2 = n=0 a (θ) n cos(nθ) k θ n/r 0 Large scales, i.e. integral length scales L (θ) ii, must be well discretized e.g. L (θ) 11 = 1 r 0 π 0 R (θ) 11 d(r 0θ) mesh grid should be nearly isotropic near the nozzle exit With r < δ θ /4, r 0 θ and z < δ θ /2, practically grid-converged results 20 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

21 Tripped subsonic round jets Discretization quality M = 0.9, Re D = 10 5, δ θ /r 0 = 1.8%, Re δθ = 900, σ ue = 9% Axial scales L (z) 11 /r 0 Azimuthal scales L (θ) 11 /r (z) L /r0 uu (θ) L /r0 uu z/r 0 z/r 0 n θ = 256 (Jetring256) n θ = 1024 (Jetring1024dz) n θ = 512 (Jetring512) n θ = 1024 (Jetring1024drdz) 21 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

22 Tripped subsonic round jets Azimuthal spectra of u z M = 0.9, Re D = 10 5, δ θ /r 0 = 1.8%, Re δθ = 900, σ ue = 9% PSD(u z ) k θ? n θ = 256 (Jetring256) n θ = 512 (Jetring512) n θ = 1024 (Jetring1024dz) n θ = 1024 (Jetring1024drdz) (at r = r 0 and z = 0.4r 0 ) 22 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

23 Tripped subsonic round jets Spectra of velocity u z M = 0.9, Re D = 10 5, δ θ /r 0 = 1.8%, Re δθ = 900, σ ue = 9% vs k z δ (using Taylor hyp.) vs k θ δ/r PSD(u z ) PSD(u z ) k z δ k θ δ/r 0 n θ = 1024, δ θ at r = r 0 and z = 0.4r 0 (Jetring1024drdz) n θ = 1024, 2δ θ at r = r 0 and z = 0.8r 0 (Jetring1024drdz2δ θ ) DNS turb. pipe flow, Eggels et al. (1994) (Re δθ = 236, x + 2 = 30 or x 2/δ 0.17) 23 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

24 Tripped subsonic round jets Concluding remarks Spectra (vs axial and azimuthal wavenumbers) near the nozzle exit similarity with boundary layer spectra (0 k z δ, k θ δ/r 0 16), peak at k θ δ/r Spalart (1988), Kim et al. (1987), Eggels et al. (1994), Tomkins & Adrian (2003) Tripped jets to deal with higher Reynolds number jets (many other things already discussed, Re D at a given Re δθ, Re δθ at a given Re D,...) LES is not a black box, and different configurations need to be clearly understood if the aim of numerics is to confidently extrapolate turbulence results at high Reynolds number. 24 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

Emmert, Vincent Fleury, Damien Desvignes, Nicolas de Cacqueray

25 Acknowledgments «CAA team» Christophe Bogey & Olivier Marsden with the contributions of Xavier Gloerfelt, Sébastien Barré, Julien Berland, Thomas Emmert, Vincent Fleury, Damien Desvignes, Nicolas de Cacqueray 25 GDR 2865 CNRS, Turbulence, Poitiers octobre cb1

Large-eddy simulations of round jets : effects of initial conditions on self-similarity region

19 ème Congrès Français de Mécanique Marseille, - août 9 Large-eddy simulations of round jets : effects of initial conditions on self-similarity region C. BOGEY a, C. BAILLY a,b a. Laboratoire de Mécanique