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
Numerical simulation based future aircraft design
Challenges
A/δ99 extremely large: large Re and large A
#simulations large for design and optimization
=> RANS, not LES
The flow over an aircraft wing is dominated by turbulent boundary layers.
At take-off and landing we have strong adverse pressure gradients

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

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

5. DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence

6. DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of RANS

7. DLR strategy for RANS model improvement
Surface roughness
High-quality data base (exp., DNS/LES)
Experiments by Nikuradze
(Empirical) laws of turbulence
Physics based improvement of RANS

8. DLR strategy for RANS model improvement
Surface roughness
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Figure by Aupoix
Δu+=f(kr+)
kr+ = kr uτ / ν
Physics-based improvement of RANS

9. DLR strategy for RANS model improvement
Surface roughness
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of RANS
νt = κuτ (y kr)

10. DLR strategy for RANS model improvement
Surface roughness
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of RANS

11. DLR strategy for RANS model improvement
Turbulent boundary layer at APG
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of RANS

12. DLR strategy for RANS model improvement
Turbulent boundary layer at APG
High-quality data base (exp., DNS/LES)
Relevant parameter space?
(Empirical) laws of turbulence
Physics-based improvement of RANS

13. Data base set-up: The parameter space
Pressure gradient
parameter
We characterize the parameter space by the pressure gradient parameter and the Reynolds number
We characterize the parameter space, we characterize the parameter space, we characterize the parameter space we characterize the parameter space
Reynolds number

14. Data base set-up: The parameter space
Pressure gradient
parameter
A320 flap
We characterize the parameter space by the pressure gradient parameter and the Reynolds number
We characterize the parameter space, we characterize the parameter space, we characterize the parameter space we characterize the parameter space
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 scale overview 2D2C PIV
2D3C PIV
LR μPTV
U∞= 6 … 12m/s
Reθ up to 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 (shake the box)

25. Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich)
Challenge: Large range of scale of turbulent boundary layer
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 range of scale of turbulent boundary layer
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 range of scale of turbulent boundary layer
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 range of scale of turbulent boundary layer
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
Clauser chart (y+-range depends on ZPG, FPG, APG)
μPTV: Viscous sublayer mean velocity
Oil film interferometry

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

31. DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of 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
Ξ-1 = y+

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
In a decelerating boundary layer the Karman constant is decreased
In an accelerating boundary layer the Karman constant is increased
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
In a decelerating boundary layer the Karman constant is decreased
In an accelerating boundary layer the Karman constant is increased
ZPG
APG

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
In a decelerating boundary layer the Karman constant is decreased
In an accelerating boundary layer the Karman constant is increased
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
In a decelerating boundary layer the Karman constant is decreased
In an accelerating boundary layer the Karman constant is increased
APG

50. DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of RANS

51. DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Assumptions:
Blended log-law + sqrt-law
linear shear stress
Physics-based improvement of RANS

52. DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Assumptions:
Blended log-law + sqrt-law
linear shear stress
Physics-based improvement of RANS
Blending for eddy visc. νt

53. Idea: A composite wall-law for the turbulent viscosity
log-law at APG
(Galbraith et al. 1977)
sqrt-law at APG
Δpx+ = 0.012
Exp. by Skare & Krogstad

54. RANS modification
HGR01 airfoil at Rec=25Mio, incidence angle α=10°

55. RANS modification
HGR01 airfoil at Rec=25Mio, incidence angle α=10°

56. Idea #1: New terms with Δpx+-dependent local blending
Pressure diffusion at APG (Rao & Hassan)
Modifications should be activated only in parts of the boundary layer
Blending for y<0.15δ99
Activate only in the sqrt-region

57. Idea #2: RANS model coefficients sensitized to pressure gradient Δpx+
Coefficient γ controls the slope of the log-law
Standard calibration is for ZPG
κ=0.41 = const
First step is to identify the coefficient which controls the slope of the log-law
The second step is to make this coefficient a function of the local flow

58. Idea #2: RANS model coefficients sensitized to pressure gradient Δpx+
The RANS model coefficient which controls the log-law slope (“Karman-constant”) becomes a function depending on local flow
First step is to identify the coefficient which controls the slope of the log-law
The second step is to make this coefficient a function of the local flow

59. Data structure of wall-normal lines for Δpx+
Extension of unstructured flow solver TAU
Wall-normal lines
Method to determine δ99, δ*, θ, H12
Coding efforts vs. Improvements in predictive accuracy
Field point
Surface point Δpx+ from dp/dx and uτ
δ99, δ*, θ, H12

60. RANS model sensitized to pressure gradient Δpx+
Field distribution of Δpx+
Map to corresponding field points
Surface quantities Δpx+ from dp/dx and uτ

61. RANS model sensitized to pressure gradient Δpx+
RANS model coefficient γ becomes a function of Δpx+

62. Validation of RANS models
U=36m/s

63. Questions to the audience

64. Turbulent Boundary Layer at ZPG

65. Turbulent Boundary Layer at ZPG
Δcf=5%!

66. Conclusions

67. Conclusions
DLR strategy: Physics based improvement of RANS using new laws of turbulence
First step: Wall law at APG
Composite wall law at APG (Brown & Joubert)
Small log-region around y+~100
Sqrt-law region above log-region
Machine learning for further tuning of first theoretical ideas
Optimism to improve RANS models for aerodynamic flows during next decades
Great potential for future research
DNS/LES at relevant Re possible
New smart DNS flows (e.g., work of Spalart & Coleman, Soria & Jimenez)
Large improvements in measurement techniques (e.g. advances in PIV/PTV)

68. End of the presentation
Experimental data shown in cooperation with
Daniel Schanz, Matteo Novara, Erich Schülein, Andreas Schröder DLR AS
Nico Reuther, Nicolas Buchmann, Rainer Hain, Christian Cierpka, Christian Kähler, UniBw München
Funding of measurement campaign by DFG within „Investigation of turbulent boundary layers with pressure gradient at high Reynolds numbers with high resolution multi-camera techniques“