1. 1212 19 September, 20061 Numerical simulation of particle-laden channel flow Hans Kuerten Department of Mechanical Engineering Technische Universiteit Eindhoven 1

2. 1212 19 September, 20062 Contents: 1.DNS of particle-laden flow 2.Large-eddy simulation (LES) 3.LES of particle-laden flow 4.Reynolds-averaged Navier-Stokes 5.Conclusions

3. 1212 19 September, 20063 1. DNS of particle-laden flow Turbulent channel flow Particles Only drag force: Elastic collisions with walls

4. 1212 19 September, 20064 x y z Spectral method: Fourier-Chebyshev 128 x 129 x 128 points Second-order accurate time integration Fourth-order interpolation for fluid velocity at particle position

5. 1212 19 September, 20065 Wall concentration: t + c wall

6. 1212 19 September, 20066 Explanation for turbophoresis: 01 0 0.2 0.4 0.6 y <u y 2 >

7. 1212 19 September, 20067 Comparison with expansion: y + <v y + -u y p+ > St=1

8. 1212 19 September, 20068 2. Large-eddy Simulation: Filter with typical size  Top-hat filter  x 

9. 1212 19 September, 20069 Effect on energy spectrum: 10 0 1 2 -10 10 -5 10 0 k z E resolved scales subgrid scales DNS filtered DNS

10. 1212 19 September, 200610 Effect on velocity fluctuations: DNS filtered DNS <u y 2 > y

11. 1212 19 September, 200611 A priori simulations: Filter fluid velocity as calculated in DNS with top-hat filter. Solve particle equation of motion with filtered fluid velocity:

12. 1212 19 September, 200612 10 1 2 3 4 5 15 20 St=1 St=5 St=25 Effect on turbophoresis: t + c wall A priori

13. 1212 19 September, 200613 3. Real LES of particle-laden flow: Subgrid model in Navier-Stokes –Smagorinsky eddy viscosity –Dynamic eddy viscosity –LES grid 32 x 33 x 64

14. 1212 19 September, 200614 Subgrid model in particle equation Retrieve unfiltered velocity from filtered Only possible for scales present in LES grid

15. 1212 19 September, 200615 LES velocity fluctuations: y <u y2 > -0.500.51 0 0.2 0.4 0.6 DNS filtered DNS dynamic Smagorinsky

16. 1212 19 September, 200616 Wall concentration: t + c wall St=5 10 2 3 4 0 2 4 6 8 DNS a priori dynamic dynamic inverse Smagorinsky Smag. inverse

17. 1212 19 September, 200617 10 0 0 20 40 60 80 y + c DNS dynamic dynamic inverse Smag. Smag. inverse Concentration in steady state (St=5):

18. 1212 19 September, 200618 Dispersion (St=25): 050100150 0 1 2 3 4 y + v x,rms DNS dynamic dynamic inverse Smag. Smag. inverse

19. 1212 19 September, 200619 Linear velocity interpolation: t + c wall St=5 10 2 3 4 0 2 4 6 8 DNS a priori 4th order 4th order inverse 2nd order 2nd order inverse

20. 1212 19 September, 200620 Linear velocity interpolation: 050100150 0 0.2 0.4 0.6 0.8 DNS fourth order fourth order inverse 2nd order 2nd order inverse y + v z,rms

21. 1212 19 September, 200621 First conclusions: Dynamic model performs better than Smagorinsky. Linear interpolation is inaccurate. Inverse filtering improves results of dynamic model. Still discrepancy with DNS results: –A priori results do not agree well with LES. –Inverse filter is arbitrary.

22. 1212 19 September, 200622 Approximate Deconvolution Model (Stolz et al., 2001): Approximate unfiltered velocity in LES: Add relaxation term for dissipation. Deconvolution also in particle equation.

23. 1212 19 September, 200623 Dispersion (St=25): y + v x,rms 050100150 0 1 2 3 4 DNS dynamic dynamic inverse ADM ADM inverse

24. 1212 19 September, 200624 Concentration (St=5): 10 0 0 20 40 60 80 y + c DNS dynamic dynamic inverse ADM ADM inverse

25. 1212 19 September, 200625 Drift velocity (St=1): 050100150 -20 -15 -10 -5 0 5 x 10 -3 y + <v y -u y p > DNS dynamic dynamic inverse ADM ADM inverse Smag. Smag. inverse

26. 1212 19 September, 200626 High Reynolds number simulations: No DNS of particle-laden flow. DNS data of channel flow is available (Moser, Kim & Mansour) at Re=590. Particle velocity rms should be close to fluid velocity rms at low Stokes number.

27. 1212 19 September, 200627 Dispersion (Re=590, St=1): y + v x,rms 0200400600 0 1 2 3 4 DNS (fluid) dynamic dynamic inverse ADM ADM inverse

28. 1212 19 September, 200628 y + v y,rms 0200400600 0 0.5 1 1.5 DNS (fluid) dynamic dynamic inverse ADM ADM inverse

29. 1212 19 September, 200629 y + v z,rms 0200400600 0 0.5 1 1.5 DNS (fluid) dynamic dynamic inverse ADM ADM inverse

30. 1212 19 September, 200630 4. Reynolds-averaged Navier-Stokes Often used in CFD packages Only mean velocity is known and some information about turbulence

31. 1212 19 September, 200631 k-ε model k and ε are known isotropic Reynolds-stress model all Reynolds stresses and ε are known anisotropic For both models: w is constant during time interval eddy-turnover time, t e =ck/ ε crossing trajectories, t c depends on τ p

32. 1212 19 September, 200632 Results: a priori: obtain RANS quantities from DNS a posteriori: real RANS simulations performed with fluent on fine grid same test case as in DNS and LES

33. 1212 19 September, 200633 Velocity fluctuations (St=1): 050100150 0 0.5 1 1.5 2 DNS real k-  real RSM a priori k-  a priori RSM y + v y,rms

34. 1212 19 September, 200634 Velocity fluctuations (St=1): y + v x,rms 050100150 0 1 2 3 DNS real k-  real RSM a priori k-  a priori RSM

35. 1212 19 September, 200635 Particle concentration (St=1): 00.511.52 x 10 4 0 5 10 15 DNS real k-  real RSM a priori k-  a priori RSM t + c wall

36. 1212 19 September, 200636 5. Conclusions (LES): A priori: turbophoresis is changed if eqs of motion are solved with. Real LES confirms this. Inverse filtering improves results. Similar results for particle dispersion. Inverse ADM gives best results for concentration and dispersion. Also applicable at higher Reynolds number.

37. 1212 19 September, 200637 Conclusions (cont.) Linear interpolation of fluid velocity is inaccurate. Smagorinsky model is inaccurate. Inverse filtering hardly improves Smagorinsky results.

38. 1212 19 September, 200638 Conclusions (RANS) Reynolds-stress model gives accurate results for particle dispersion if stress tensor is accurately predicted. k-ε model is not accurate because of isotropy of velocity fluctuations. Turbophoresis is not well predicted since preferential concentration cannot be taken into account.