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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 withDaniel Schanz, Matteo Novara, Erich Schülein, Andreas Schröder DLR AS
Nico Reuther, Nicolas Buchmann, Rainer Hain, Christian Cierpka, Christian KählerUniv Bundeswehr München, Institute for Fluid Mechanics and Aerodynamics
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IMPULSE progress meeting
Folie 2
slide 2Slide 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
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IMPULSE progress meeting
Folie 3
slide 3Slide 3
Optimism to describe “first order” steady state aerodynamic flow phenomena within the RANS concept
Separation in the wing-body junction at APG
Interaction of wake flow and boundary layer at APG
Interaction of strake vortex and boundary layer at APG
DLR strategy for RANS model improvement
Turbulent boundary layers at APG Separation and reattachment Wake flow at APG
[28] Hoffenberg & Sullivan, 1998
[21] Liu et al., 2002
[19] Roos, 1997
[22] Tummers et al., 2007
[20] Driver & Mateer, 2002
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IMPULSE progress meeting
Folie 4
slide 4Slide 4
DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
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IMPULSE progress meeting
Folie 5
slide 5Slide 5
DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
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IMPULSE progress meeting
Folie 6
slide 6Slide 6
DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of RANS
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IMPULSE progress meeting
Folie 7
slide 7Slide 7
DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics based improvement of RANS
Experiments by Nikuradze
Surface roughness
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IMPULSE progress meeting
Folie 8
slide 8Slide 8
DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of RANS
kr+ = kr uτ / νΔu+=f(kr
+)
Surface roughness
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IMPULSE progress meeting
Folie 9
slide 9Slide 9
DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of RANS νt = κuτ (y + 0.03kr)
Surface roughness
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IMPULSE progress meeting
Folie 10
slide 10Slide 10
DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of RANS
Surface roughness
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IMPULSE progress meeting
Folie 11
slide 11Slide 11
DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of RANS
Turbulent boundary layer at APG
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IMPULSE progress meeting
Folie 12
slide 12Slide 12
DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of RANS
Relevant parameter space?
Turbulent boundary layer at APG
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IMPULSE progress meeting
Folie 13
slide 13Slide 13
Reynolds number
Pressure gradientparameter
Data base set-up: The parameter space
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IMPULSE progress meeting
Folie 14
slide 14Slide 14
Reynolds number
Pressure gradientparameter
Data base set-up: The parameter space
A320 flap
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IMPULSE progress meeting
Folie 15
slide 15Slide 15
A380 flap
Data base set-up: The parameter space
A320 flap
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IMPULSE progress meeting
Folie 16
slide 16Slide 16
A380 flap A380 wingA350 wing
Data base set-up: The parameter space
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IMPULSE progress meeting
Folie 17
slide 17Slide 17
Data base set-up: The parameter space
DLR institute AS decision 2009:New data needed!Only experiments can give large Re!
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IMPULSE progress meeting
Folie 18
slide 18Slide 18
Exp I.Assess PIV at moderate Re
Data base set-up: The parameter space
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IMPULSE progress meeting
Folie 19
slide 19Slide 19
Experiment #1 (2011): RETTINA I exp. (DLR + UniBw Munich)
Large scale overview 2D2C PIV
LR μPTV
2D3C PIV
U∞= 6 … 12m/s Reθ up to 10000 and δ99 =0.1mThick boundary layers enable PIV
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IMPULSE progress meeting
Folie 20
slide 20Slide 20
Exp I.Assess PIVat moderate Re
Data base set-up: The parameter space
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IMPULSE progress meeting
Folie 21
slide 21Slide 21
Exp II.Higher Re
Data base set-up: The parameter space
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 22
Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich)
Flow relaxation
ZPGLog-law
APG region
Defined inflow condition. Defined
outflow condition
U∞=10m/s, 23m/s, 36m/s
Funded by DLR institute AS and by DFG
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 23
ZPGLog-law
APG region
U∞=36m/s
Reθ=41000
Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich)
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 24
Large-scale 2D2C-PIV 9 cams2D3C PIVmicro 2D2C PTV3D3C PTV STB (shake the box)
Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich)
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 25
Challenge: Large range of scale of turbulent boundary layer
Solution approach: Multi-resolution multi-camera PIV
Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich)
U=36m/sReθ=41000
ν/uτ = 20μmδ99 = 0.2m
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 26
Challenge: Large range of scale of turbulent boundary layer
Solution approach: Multi-resolution multi-camera PIV
Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich)
U=36m/sReθ=41000
ν/uτ = 20μmδ99 = 0.2m
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 27
Challenge: Large range of scale of turbulent boundary layer
Solution approach: Multi-resolution multi-camera PIV
Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich)
U=36m/sReθ=41000
ν/uτ = 20μmδ99 = 0.2m
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 28
Challenge: Large range of scale of turbulent boundary layer
Solution approach: Multi-resolution multi-camera PIV
Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich)
U=36m/sReθ=41000
ν/uτ = 20μmδ99 = 0.2m STB=„shake-the-box“
Particle-tracking-approachSchanz, Schröder, Novara@ DLR-AS
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 29
Measurement technique. Skin friction Clauser chart (y+-range depends on ZPG, FPG, APG)
μPTV: Viscous sublayer mean velocityOil film interferometry
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IMPULSE progress meeting
Folie 30
slide 30Slide 30
Mild separation and reattachment
Experiment #3 (August 2017) within DLR internal project
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IMPULSE progress meeting
Folie 31
slide 31Slide 31
DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of RANS
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IMPULSE progress meeting
Folie 32
slide 32Slide 32
Empirical wall law at APG
Mean velocity profiles2D2C Reynolds stresses
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IMPULSE progress meeting
Folie 33
slide 33Slide 33
U=36m/sΔpx
+=0.015
Aim: Empirical wall-law at APG for y<0.1δ99
y<10%δ99
Empirical wall law at APG
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IMPULSE progress meeting
Folie 34
slide 34Slide 34
U=36m/sΔpx
+=0.015
Aim: Empirical wall-law at APG for y<0.1δ99
y<10%δ99
Empirical wall law at APG
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IMPULSE progress meeting
Folie 35
slide 35Slide 35
U=36m/sΔpx
+=0.015
Hypothesis #1: Resilience of a small log-region
y<0.1δ99
Empirical wall law at APG
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IMPULSE progress meeting
Folie 36
slide 36Slide 36
U=36m/sΔpx
+=0.015
Hypothesis #1: Resilience of a small log-region
y<0.1δ99
Empirical wall law at APG
Galbraith et al. (1977),Granville (1985), Bradshaw (1995), Perry & Schofield (1973), Durbin & Belcher (1992)Skare & Krogstad (1994)Spalart & Coleman …
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IMPULSE progress meeting
Folie 37
slide 37Slide 37
Results and analysis
y+Ξ-1 =
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IMPULSE progress meeting
Folie 38
slide 38Slide 38
U=36m/sΔpx
+=0.015
y<0.1δ99
Empirical wall law at APG
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IMPULSE progress meeting
Folie 39
slide 39Slide 39
U=36m/sΔpx
+=0.015
Hypothesis #2: square-root (sqrt)-law above the log-region
y<0.1δ99
Empirical wall law at APG
Szablewski (1954), Townsend (1961), McDonald (1969),Brown & Joubert…
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IMPULSE progress meeting
Folie 40
slide 40Slide 40
Results and analysis
U=36m/sReθ=41000
Δpx+=0.015
Hypothesis #2: square-root (sqrt)-law above the log-region
y<0.1δ99
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IMPULSE progress meeting
Folie 41
slide 41Slide 41
Results and analysis
y+log,max
Composite profile Brown & Joubert 1969
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IMPULSE progress meeting
Folie 42
slide 42Slide 42
Results and analysis
Hypothesis #3: transition from log-law to sqrt-law depends on Δpx+
(probably more complex …)
y+log,max
Composite profile Brown & Joubert 1969
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IMPULSE progress meeting
Folie 43
slide 43Slide 43
Results and analysis
Hypothesis #3: transition from log-law to sqrt-law depends on Δpx+
(probably more complex …)
y+log,max
Composite profile Brown & Joubert 1969
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IMPULSE progress meeting
Folie 44
slide 44Slide 44
Results and analysis
Hypothesis #3: transition from log-law to sqrt-law depends on Δpx+
(probably more complex …)
y+log,max
Composite profile Brown & Joubert 1969
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IMPULSE progress meeting
Folie 45
slide 45Slide 45
Results and analysis
Hypothesis #3: transition from log-law to sqrt-law depends on Δpx+
(probably more complex …)
ZPG Δpx
+→0
Pure log-law
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IMPULSE progress meeting
Folie 46
slide 46Slide 46
Results and analysis
Hypothesis #3: transition from log-law to sqrt-law depends on Δpx+
(probably more complex …)
Separation Δpx
+→ ∞
Pure sqrt-law(Stratford)
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• SlopecoefficientK
ZPG
„vonKarmanconstant“κ=0.40+/-0.1
Hypothesis #4: decrease of log-law slope parameter Ki at APG
Empirical wall law at APG
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• SlopecoefficientK
ZPG
„vonKarmanconstant“κ=0.40+/-0.1
Hypothesis #4: decrease of log-law slope parameter Ki at APG
Empirical wall law at APG
APG
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• SlopecoefficientK
„vonKarmanconstant“κ=0.40+/-0.1
Hypothesis #4: decrease of log-law slope parameter Ki at APG
Empirical wall law at APG
APG
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• SlopecoefficientK
„vonKarmanconstant“κ=0.40+/-0.1
Hypothesis #4: decrease of log-law slope parameter Ki at APG
Empirical wall law at APG
APG
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• SlopecoefficientK
ZPG
Hypothesis #4: decrease of log-law slope parameter Ki at APG
Empirical wall law at APG
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• SlopecoefficientK
ZPG
Hypothesis #4: decrease of log-law slope parameter Ki at APG
Empirical wall law at APG
Increasing Δpx+
APG
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• SlopecoefficientK
ZPG
Hypothesis #4: decrease of log-law slope parameter Ki at APG
Empirical wall law at APG
APG
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• SlopecoefficientK
ZPG
Hypothesis #4: decrease of log-law slope parameter Ki at APG
Empirical wall law at APG
APG
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 55
DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of RANS
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 56
DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of RANS
Assumptions:§ Blended log-law + sqrt-law§ linear shear stress
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 57
DLR strategy for RANS model improvement
High-quality data base (exp., DNS/LES)
(Empirical) laws of turbulence
Physics-based improvement of RANS
Assumptions:§ Blended log-law + sqrt-law§ linear shear stress
Blending for eddy visc. νt
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 58
Idea: A composite wall-law for the turbulent viscosity
log-law at APG
sqrt-law at APG
(Galbraith et al. 1977)
Δpx+ = 0.012
Exp. by Skare & Krogstad
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 59
RANS modification
HGR01 airfoil at Rec=25Mio, incidence angle α=10°
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 60
RANS modification
HGR01 airfoil at Rec=25Mio, incidence angle α=10°
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 61
Idea #1: New terms with Δpx+-dependent local blending
Modifications should be activated only in parts of the boundary layer
Blending for y<0.15δ99 Activate only in the sqrt-region
Pressure diffusion at APG (Rao & Hassan)
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Idea#2:RANSmodelcoefficientssensitizedtopressuregradientΔpx+
Standard calibration is for ZPG κ=0.41 = const
Coefficient γ controls the slope of the log-law
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Idea#2:RANSmodelcoefficientssensitizedtopressuregradientΔpx+
• TheRANSmodelcoefficientwhichcontrolsthelog-lawslope(“Karman-constant”)becomesafunctiondependingonlocalflow
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 64
Data structure of wall-normal lines for Δpx+
Surface pointΔpx
+ from dp/dx and uτ
δ99, δ*, θ, H12
Field point
Extension of unstructured flow solver TAUWall-normal linesMethod to determine δ99, δ*, θ, H12
Coding efforts vs. Improvements in predictive accuracy
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RANSmodelsensitizedtopressuregradientΔpx+
Surfacequantities Δpx+fromdp/dxanduτ
Maptocorrespondingfieldpoints
FielddistributionofΔpx+
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RANSmodelsensitizedtopressuregradientΔpx+
RANSmodelcoefficientγ becomesafunctionofΔpx+
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 67
Validation of modified RANS
U=36m/s
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 68
Validation of modified RANS
U=36m/s
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 69
Validation of RANS
U=36m/s
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 70
Questions to the audience
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 71
Turbulent Boundary Layer at ZPG
-www.DLR.de • Folie 71
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STELAR 2. Projekttreffen > DLR Göttingen > 23.04.2012
Slide 72
Turbulent Boundary Layer at ZPG
-www.DLR.de • Folie 72
Δcf=5%!
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Conclusions
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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)- Improved measurement techniques (e.g. advances in PIV/PTV)
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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 ofturbulent boundary layers with pressure gradient at high Reynolds numbers with high resolution multi-camera techniques“
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Validation RETTINA II
U=36m/s
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Validation RETTINA II
U=36m/s
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Validation RETTINA II
U=23m/s
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IMPULSE progress meeting
Folie 79
slide 79Slide 79
Measuring technique
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IMPULSE progress meeting
Folie 80
slide 80Slide 80
Modification of the k-omega model
Modified consistent model
Modification of the k-equation:Pressure diffusion term (Rao & Hassan)
Modification of the ω-equation:Pressure diffusion term
Negative cross-diffusion term
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IMPULSE progress meeting
Folie 81
slide 81Slide 81
Consistency with wall-law
Summary of boundary layer analysis
Consistency with log-law at APG
Consistency with sqrt-law at APG
k-equation No No
ω-equation Yes No
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IMPULSE progress meeting
Folie 82
slide 82Slide 82
Consistency with wall-law
Summary of boundary layer analysis
Consistency with log-law at APG
Consistency with sqrt-law at APG
Modified k-equation Yes Yes
Modified ω-equation Yes Yes
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IMPULSE progress meeting
Folie 83
slide 83Slide 83
Consistency with wall-law
Summary of boundary layer analysis
Blending active in log-law region at APG
Blending active in sqrt-law region at APG
Modified k-equation Yes Yes
Modified ω-equation No Yes
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IMPULSE progress meeting
Folie 84
slide 84Slide 84
The ω-equation in the sqrt-law region
≠
Following ideas by Rao & Hassan, Catris & Aupoix
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IMPULSE progress meeting
Folie 85
slide 85Slide 85
The ω-equation in the sqrt-law region
≠
Following ideas by Rao & Hassan, Catris & Aupoix
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IMPULSE progress meeting
Folie 86
slide 86Slide 86
The ω-equation in the sqrt-law region
≠
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IMPULSE progress meeting
Folie 87
slide 87Slide 87
The ω-equation in the sqrt-law region
Conclusion: The ω-equation is not consistent with the assumed solution in the sqrt-law region at APG
≠
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IMPULSE progress meeting
Folie 88
slide 88Slide 88
Measurement technique combining different PIV systems
1.5m
6.38m
1.5m0.78m
0 x [m]7.88 8.66 10.166.38 11.66
2D2C-PIV§ Large scale PIV§ 8 PCO 4000 cams side-by-side 2D3C stereo PIV overview
2D3C stereo PIV detail
1.5m
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IMPULSE progress meeting
Folie 89
slide 89Slide 89
Requirements/Design criteria on a new flow experiment
1. Large Reθ for sufficiently thick overlap region2. Log-law established before entering the APG-section3. Thick BL at low flow velocity so that PIV in viscous sublayer possible4. Obtain large values for Δpx
+ , i.e. Δpx+>0.06
6.38m
U∞= 9m/s and U∞= 12m/s
At x=6mReθ up to 8000 and δ99 =0.1m
Design of the test case using RANS-CFD with the DLR TAU code by DLR
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IMPULSE progress meeting
Folie 90
slide 90Slide 90
Data for mean velocity down to y+=1 using LR-PIV with PTV
1.5m6.38m
1.5m0.78m
x [m]7.88 8.66 10.166.38 11.66
2D2C PIV Long-range microscopic PIV with PTV
Particle-tracking velocimetry algorithm (PTV) applied to the LR-PIV data see also Kähler et al., Exp. Fluids (2012)
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IMPULSE progress meeting
Folie 91
slide 91Slide 91
Boundary layer theory.An approximative model for the
shear stress
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IMPULSE progress meeting
Folie 92
slide 92Slide 92
Turbulent boundary layer equation
Consider the equation for wall-parallel mean velocity component U
Integration in wall-normal direction from y‘=0 to wall-distance y
Or in viscous inner units
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IMPULSE progress meeting
Folie 93
slide 93Slide 93
Review: Modeling the total shear stress (van den Berg 1973)
Aim: Relate the total shear stress and the mean velocity profile for U
by approximating the integrated convective (or: mean inertial) terms
Van den Berg makes the modeling assumption that
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IMPULSE progress meeting
Folie 94
slide 94Slide 94
Review: Modeling the total shear stress (van den Berg 1973)
Modeling assumption
Then
For the V-velocity and using the continuity equation
This gives for the mean inertial term
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IMPULSE progress meeting
Folie 95
slide 95Slide 95
Review: Modeling the total shear stress (van den Berg 1973)
This gives the model by van den Berg (1973)
Short notation:
With
Pressure gradient parameter
Wall shear-stress gradient parameter
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IMPULSE progress meeting
Folie 96
slide 96Slide 96
Extended modeling for the total shear stress
Modeling assumption
For the chain rule of differentiation we need
Then we obtain, e.g.
With an additional parameter taking into account d²P/dx²
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IMPULSE progress meeting
Folie 97
slide 97Slide 97
Extended modeling for the total shear stress
This gives the extended model
With integrals
and with parameters
Pressure gradient parameter
Wall shear-stress gradient parameter
Cross parameter
d²P/dx² -parameter
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IMPULSE progress meeting
Folie 98
slide 98Slide 98
Characteristic non-dimensional parametersComparison of the characteristic non-dimensional parameters
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IMPULSE progress meeting
Folie 99
slide 99Slide 99
Turbulent shear stress in non-equilibrium flow
Mean inertial terms cause a significant reduction of the turbulent shear stress τ+=1+Δpx+y+
λ
Present exp.at x=8.18mΔpx+=0.0473
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IMPULSE progress meeting
Folie 100
slide 100Slide 100
Systematic trend/quantitative formula for variation of Ko
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IMPULSE progress meeting
Folie 101
slide 101Slide 101
Conclusion
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IMPULSE progress meeting
Folie 102
slide 102Slide 102
Conclusion.
Design of a flow experiment suitable to study the law-of-the-wall for flows at a substantial adverse pressure gradient
Sufficiently large overlap-layer due to large Reθ
Significant adverse pressure gradient Δpx+ up to Δpx
+ =0.065
Combination of different PIV techniques gives high-quality data setLarge number of velocity profilesHigh quality gradients and slope diagnostic functionsComparison of direct and indirect method for uτ locally
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IMPULSE progress meeting
Folie 103
slide 103Slide 103
Conclusion.
The log-law does no longer describe the overlap layer 300 < y+ < 0.2 δ99+
A generalized half-power law (or modified log-law) gives a good description
Idea of a composite wall-law by Brown & Joubert (1969) is supportedLog-law-fit region is thin 60 < y+ < 130
1/slope Ki decreasing with increasing Δpx+ as devised by Nickels (2004)
Modified log-law region for 300-400 < y+ < 0.2 -0.4 δ99+
1/slope Ko decreasing with increasing Δpx+
But mean inertial terms need to be accounted for Ko
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IMPULSE progress meeting
Folie 104
slide 104Slide 104
Characterization of the flow
ZPGlog-law
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IMPULSE progress meeting
Folie 105
slide 105Slide 105
Characterization of the flow
Favourable dp/dsLFPG ~ 5 δref
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IMPULSE progress meeting
Folie 106
slide 106Slide 106
Characterization of the flow
Focus region:
Adverse dp/dsLAPG ~ 5 δref
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IMPULSE progress meeting
Folie 107
slide 107Slide 107
Universal log-law in zero-pressure gradient region
Universal log-law at the inlet of the adverse pressure gradient section
6.38m
At x=6mReθ=8000
U∞=12m/s
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IMPULSE progress meeting
Folie 108
slide 108Slide 108
Systematic trend/quantitative formula for variation of Bi
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IMPULSE progress meeting
Folie 109
slide 109Slide 109
Systematic trend/quantitative formula for variation of Bi
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IMPULSE progress meeting
Folie 110
slide 110Slide 110
Measurement technique using PIV
Quanta Ray 400
Innolas Spitlight 1000
8 PCO 4000
Superelliptical nose
Flat plate of length 6.38m
Flap
APG region
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IMPULSE progress meeting
Folie 111
slide 111Slide 111
Large-scale 2D2C PIV. Instantaneous flow field
Cam 5Cam 6
Cam 7Cam 8
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IMPULSE progress meeting
Folie 112
slide 112Slide 112
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
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IMPULSE progress meeting
Folie 113
slide 113Slide 113
Motivation: Turbulent boundary layers at adverse pressure gradient
During take-off and landingSignificant adverse pressure gradient (APG)
Goals:Þ Wall-laws at APGÞ Improvement RANS models