Tobias Knopp, Bernhard Eisfeld DLR Institute of Aerodynamics and Flow Technology

1. Perspective on Turbulence Modeling using Reynolds Stress Models : Modification for pressure gradients Tobias Knopp, Bernhard Eisfeld DLR Institute of Aerodynamics and Flow Technology Experimental data shown were obtained in cooperation with Daniel Schanz, Matteo Novara, Erich Schülein, Andreas Schröder DLR AS Nico Reuther, Nicolas Buchmann, Rainer Hain, Christian Cierpka, Christian Kähler Univ Bundeswehr München, Institute for Fluid Mechanics and Aerodynamics

2. Motivation: Digital aerospace products Numericalsimulationbasedfutureaircraft design Challenges • A/δ99extremely large: large Re and large A • #simulations large for design andoptimization => RANS, not LES

3. Optimism to describe “first order” steady state aerodynamic flow phenomena within the RANS concept DLR strategy for RANS model improvement Turbulent boundary layers at APG Separation and reattachment Wake flow at APG Interaction of strake vortex and boundary layer at APG Separation in the wing-body junction at APG Interaction of wake flow and boundary layer at APG

4. DLR strategy for RANS model improvement High-quality database (exp., DNS/LES)

5. DLR strategy for RANS model improvement High-quality database (exp., DNS/LES) (Empirical) lawsofturbulence

6. DLR strategy for RANS model improvement High-quality database (exp., DNS/LES) (Empirical) lawsofturbulence Physics-basedimprovementof RANS

7. DLR strategy for RANS model improvement Surface roughness High-quality database (exp., DNS/LES) Experiments by Nikuradze (Empirical) lawsofturbulence Physicsbasedimprovementof RANS

8. DLR strategy for RANS model improvement Surface roughness High-quality database (exp., DNS/LES) (Empirical) lawsofturbulence Figure by Aupoix Δu+=f(kr+) kr+ = kruτ / ν Physics-basedimprovementof RANS

9. DLR strategy for RANS model improvement Surface roughness High-quality database (exp., DNS/LES) (Empirical) lawsofturbulence Physics-basedimprovementof RANS νt = κuτ (y + 0.03kr)

10. DLR strategy for RANS model improvement Surface roughness High-quality database (exp., DNS/LES) (Empirical) lawsofturbulence Physics-basedimprovementof RANS

11. DLR strategy for RANS model improvement Turbulent boundary layer at APG High-quality database (exp., DNS/LES) (Empirical) lawsofturbulence Physics-basedimprovementof RANS

12. DLR strategy for RANS model improvement Turbulent boundary layer at APG High-quality database (exp., DNS/LES) Relevant parameter space? (Empirical) lawsofturbulence Physics-basedimprovementof RANS

13. Data base set-up: The parameter space Pressure gradient parameter Reynolds number

14. Data base set-up: The parameter space Pressure gradient parameter A320 flap Reynolds number

15. Data base set-up: The parameter space A320 flap A380 flap

16. Data base set-up: The parameter space A380 flap A350 wing A380 wing

17. Data base set-up: The parameter space DLR institute AS decision 2009: New data needed! Only experiments can give large Re!

18. Data base set-up: The parameter space Exp I. Assess PIV at moderate Re

19. Experiment #1 (2011): RETTINA I exp. (DLR + UniBw Munich) Large scaleoverview 2D2C PIV 2D3C PIV LR μPTV U∞= 6 … 12m/s Reθ up to 10000 and δ99 =0.1m Thick boundary layers enable PIV

20. Data base set-up: The parameter space Exp I. Assess PIV at moderate Re

21. Data base set-up: The parameter space Exp II. Higher Re

22. Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich) Funded by DLR institute AS and by DFG Defined inflow condition. Defined outflow condition APG region Flow relaxation ZPG Log-law U∞= 10m/s, 23m/s, 36m/s

23. Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich) APG region ZPG Log-law U∞= 36m/s Reθ=41000

24. Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich) Large-scale 2D2C-PIV 9 cams 2D3C PIV micro 2D2C PTV 3D3C PTV STB (shakethe box)

25. Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich) Challenge: Large rangeofscaleof turbulent boundarylayer Solution approach: Multi-resolution multi-camera PIV U=36m/s Reθ=41000 ν/uτ = 20μm δ99 = 0.2m

26. Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich) Challenge: Large rangeofscaleof turbulent boundarylayer Solution approach: Multi-resolution multi-camera PIV U=36m/s Reθ=41000 ν/uτ = 20μm δ99 = 0.2m

27. Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich) Challenge: Large rangeofscaleof turbulent boundarylayer Solution approach: Multi-resolution multi-camera PIV U=36m/s Reθ=41000 ν/uτ = 20μm δ99 = 0.2m

28. Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich) Challenge: Large rangeofscaleof turbulent boundarylayer Solution approach: Multi-resolution multi-camera PIV U=36m/s Reθ=41000 ν/uτ = 20μm δ99 = 0.2m STB=„shake-the-box“ Particle-tracking-approach Schanz, Schröder, Novara @ DLR-AS

29. Measurement technique. Skin friction

30. Mild separation and reattachment Experiment #3 (August 2017) within DLR internal project

31. DLR strategy for RANS model improvement High-quality database (exp., DNS/LES) (Empirical) lawsofturbulence Physics-basedimprovementof RANS

32. Empirical wall law at APG • Mean velocity profiles • 2D2C Reynolds stresses

33. Empirical wall law at APG Aim: Empirical wall-law at APG for y<0.1δ99 U=36m/s Δpx+=0.015 y<10%δ99

34. Empirical wall law at APG Aim: Empirical wall-law at APG for y<0.1δ99 U=36m/s Δpx+=0.015 y<10%δ99

35. Empirical wall law at APG Hypothesis #1: Resilience of a small log-region U=36m/s Δpx+=0.015 y<0.1δ99

36. Empirical wall law at APG Hypothesis #1: Resilience of a small log-region U=36m/s Δpx+=0.015 Galbraith et al. (1977), Granville (1985), Bradshaw (1995), Perry & Schofield (1973), Durbin & Belcher (1992) Skare & Krogstad (1994) Spalart & Coleman … y<0.1δ99

37. Results and analysis y+ Ξ-1 =

38. Empirical wall law at APG U=36m/s Δpx+=0.015 y<0.1δ99

39. Empirical wall law at APG Hypothesis #2: square-root (sqrt)-law above the log-region Szablewski (1954), Townsend (1961), McDonald (1969), Brown & Joubert … U=36m/s Δpx+=0.015 y<0.1δ99

40. Results and analysis Hypothesis #2: square-root (sqrt)-law above the log-region U=36m/s Reθ=41000 Δpx+=0.015 y<0.1δ99

41. Results and analysis Composite profile Brown & Joubert 1969 y+log,max

42. Results and analysis Hypothesis #3: transition from log-law to sqrt-law depends on Δpx+ (probably more complex …) Composite profile Brown & Joubert 1969 y+log,max

43. Results and analysis Hypothesis #3: transition from log-law to sqrt-law depends on Δpx+ (probably more complex …) Composite profile Brown & Joubert 1969 y+log,max

44. Results and analysis Hypothesis #3: transition from log-law to sqrt-law depends on Δpx+ (probably more complex …) ZPG Δpx+→0 Pure log-law

45. Results and analysis Hypothesis #3: transition from log-law to sqrt-law depends on Δpx+ (probably more complex …) Separation Δpx+→ ∞ Pure sqrt-law (Stratford)

46. Empirical wall law at APG Hypothesis #4: decrease of log-law slope parameter Ki at APG • Slope coefficient K „von Karman constant“ κ=0.40+/-0.1 ZPG

47. Empirical wall law at APG Hypothesis #4: decrease of log-law slope parameter Ki at APG • Slope coefficient K „von Karman constant“ κ=0.40+/-0.1 APG ZPG

48. Empirical wall law at APG Hypothesis #4: decrease of log-law slope parameter Ki at APG • Slope coefficient K „von Karman constant“ κ=0.40+/-0.1 APG

49. Empirical wall law at APG Hypothesis #4: decrease of log-law slope parameter Ki at APG • Slope coefficient K „von Karman constant“ κ=0.40+/-0.1 APG

50. DLR strategy for RANS model improvement High-quality database (exp., DNS/LES) (Empirical) lawsofturbulence Physics-basedimprovementof RANS