Perspective on Turbulence Modeling using Reynolds Stress Models : Modification for pressure gradients
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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 Folie 2 IMPULSE progress meetingslide 2 slide 2
![[28] Hoffenberg & Sullivan, 1998 Interaction of wake flow and boundary layer at APG Interaction of strake](/docs-images/74/70373540/images/3-7.jpg "vortex and boundary layer at APG Separation in the wing-body junction at APG Folie 3 IMPULSE progress")
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 [28] Hoffenberg & Sullivan, 1998 Interaction of wake flow and boundary layer at APG Interaction of strake vortex and boundary layer at APG Separation in the wing-body junction at APG Folie 3 IMPULSE progress meetingslide 3 slide 3
4 DLR strategy for RANS model improvement High-quality data base (exp., DNS/LES) Folie 4 IMPULSE progress meetingslide 4 slide 4
5 DLR strategy for RANS model improvement High-quality data base (exp., DNS/LES) (Empirical) laws of turbulence Folie 5 IMPULSE progress meetingslide 5 slide 5
6 DLR strategy for RANS model improvement High-quality data base (exp., DNS/LES) (Empirical) laws of turbulence Physics-based improvement of RANS Folie 6 IMPULSE progress meetingslide 6 slide 6
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 Folie 7 IMPULSE progress meetingslide 7 slide 7
8 DLR strategy for RANS model improvement High-quality data base (exp., DNS/LES) Surface roughness (Empirical) laws of turbulence Δu + =f(k r+ ) k r+ = k r u τ / ν Physics-based improvement of RANS Folie 8 IMPULSE progress meetingslide 8 slide 8
9 DLR strategy for RANS model improvement High-quality data base (exp., DNS/LES) Surface roughness (Empirical) laws of turbulence Physics-based improvement of RANS ν t = κu τ (y k r ) Folie 9 IMPULSE progress meetingslide 9 slide 9
10 DLR strategy for RANS model improvement High-quality data base (exp., DNS/LES) Surface roughness (Empirical) laws of turbulence Physics-based improvement of RANS Folie 10 IMPULSE progress meeting Slide 10 slide 10
11 DLR strategy for RANS model improvement High-quality data base (exp., DNS/LES) Turbulent boundary layer at APG (Empirical) laws of turbulence Physics-based improvement of RANS Folie 11 IMPULSE progress meeting Slide 11 slide 11
12 DLR strategy for RANS model improvement High-quality data base (exp., DNS/LES) Turbulent boundary layer at APG Relevant parameter space? (Empirical) laws of turbulence Physics-based improvement of RANS Folie 12 IMPULSE progress meeting Slide 12 slide 12
13 Data base set-up: The parameter space Pressure gradient parameter Reynolds number Folie 13 IMPULSE progress meeting Slide 13 slide 13
14 Data base set-up: The parameter space Pressure gradient parameter A320 flap Reynolds number Folie 14 IMPULSE progress meeting Slide 14 slide 14
15 Data base set-up: The parameter space A320 flap A380 flap Folie 15 IMPULSE progress meeting Slide 15 slide 15
16 Data base set-up: The parameter space A380 flap A350 wing A380 wing Folie 16 IMPULSE progress meeting Slide 16 slide 16
17 Data base set-up: The parameter space DLR institute AS decision 2009: New data needed! Only experiments can give large Re! Folie 17 IMPULSE progress meeting Slide 17 slide 17
18 Data base set-up: The parameter space Exp I. Assess PIV at moderate Re Folie 18 IMPULSE progress meeting Slide 18 slide 18
19 Experiment #1 (2011): RETTINA I exp. (DLR + UniBw Munich) Large scale overview 2D2C PIV 2D3C PIV LR μptv U = 6 12m/s Re θ up to and δ 99 =0.1m Thick boundary layers enable PIV Folie 19 IMPULSE progress meeting Slide 19 slide 19
20 Data base set-up: The parameter space Exp I. Assess PIV at moderate Re Folie 20 IMPULSE progress meeting Slide 20 slide 20
21 Data base set-up: The parameter space Exp II. Higher Re Folie 21 IMPULSE progress meeting Slide 21 slide 21
22 Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich) Funded by DLR institute AS and by DFG Defined inflow condition. Flow relaxation ZPG Log-law APG region Defined outflow condition U = 10m/s, 23m/s, 36m/s Slide 22 STELAR 2. Projekttreffen > DLR Göttingen >
23 Experiment #2 (2015): RETTINA II exp. (DLR + UniBw Munich) ZPG Log-law APG region U = 36m/s Re θ =41000 Slide 23 STELAR 2. Projekttreffen > DLR Göttingen >
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) Slide 24 STELAR 2. Projekttreffen > DLR Göttingen >
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 Re θ =41000 ν/u τ = 20μm δ 99 = 0.2m Slide 25 STELAR 2. Projekttreffen > DLR Göttingen >
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 Re θ =41000 ν/u τ = 20μm δ 99 = 0.2m Slide 26 STELAR 2. Projekttreffen > DLR Göttingen >
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 Re θ =41000 ν/u τ = 20μm δ 99 = 0.2m Slide 27 STELAR 2. Projekttreffen > DLR Göttingen >
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 Re θ =41000 ν/u τ = 20μm δ 99 = 0.2m STB= shake-the-box Particle-tracking-approach Schanz, Schröder, DLR-AS Slide 28 STELAR 2. Projekttreffen > DLR Göttingen >
29 Measurement technique. Skin friction Clauser chart (y+-range depends on ZPG, FPG, APG) μptv: Viscous sublayer mean velocity Oil film interferometry Slide 29 STELAR 2. Projekttreffen > DLR Göttingen >
30 Experiment #3 (August 2017) within DLR internal project Mild separation and reattachment Folie 30 IMPULSE progress meeting Slide 30 slide 30
31 DLR strategy for RANS model improvement High-quality data base (exp., DNS/LES) (Empirical) laws of turbulence Physics-based improvement of RANS Folie 31 IMPULSE progress meeting Slide 31 slide 31
32 Empirical wall law at APG Mean velocity profiles 2D2C Reynolds stresses Folie 32 IMPULSE progress meeting Slide 32 slide 32
33 Empirical wall law at APG Aim: Empirical wall-law at APG for y<0.1δ 99 U=36m/s Δp x+ =0.015 y<10%δ 99 Folie 33 IMPULSE progress meeting Slide 33 slide 33
34 Empirical wall law at APG Aim: Empirical wall-law at APG for y<0.1δ 99 U=36m/s Δp x+ =0.015 y<10%δ 99 Folie 34 IMPULSE progress meeting Slide 34 slide 34
35 Empirical wall law at APG Hypothesis #1: Resilience of a small log-region U=36m/s Δp x+ =0.015 y<0.1δ 99 Folie 35 IMPULSE progress meeting Slide 35 slide 35
36 Empirical wall law at APG Hypothesis #1: Resilience of a small log-region U=36m/s Δp x+ =0.015 Galbraith et al. (1977), Granville (1985), Bradshaw (1995), Perry & Schofield (1973), Durbin & Belcher (1992) Skare & Krogstad (1994) Spalart & Coleman y<0.1δ 99 Folie 36 IMPULSE progress meeting Slide 36 slide 36
37 Results and analysis Ξ -1 = y + Folie 37 IMPULSE progress meeting Slide 37 slide 37
38 Empirical wall law at APG U=36m/s Δp x+ =0.015 y<0.1δ 99 Folie 38 IMPULSE progress meeting Slide 38 slide 38
39 Empirical wall law at APG Hypothesis #2: square-root (sqrt)-law above the log-region U=36m/s Δp x+ =0.015 Szablewski (1954), Townsend (1961), McDonald (1969), Brown & Joubert y<0.1δ 99 Folie 39 IMPULSE progress meeting Slide 39 slide 39
40 Results and analysis Hypothesis #2: square-root (sqrt)-law above the log-region U=36m/s Re θ =41000 Δp x+ =0.015 y<0.1δ 99 Folie 40 IMPULSE progress meeting Slide 40 slide 40
41 Results and analysis Composite profile Brown & Joubert 1969 y + log,max Folie 41 IMPULSE progress meeting Slide 41 slide 41
42 Results and analysis Hypothesis #3: transition from log-law to sqrt-law depends on Δp x + (probably more complex ) Composite profile Brown & Joubert 1969 y + log,max Folie 42 IMPULSE progress meeting Slide 42 slide 42
43 Results and analysis Hypothesis #3: transition from log-law to sqrt-law depends on Δp x + (probably more complex ) Composite profile Brown & Joubert 1969 y + log,max Folie 43 IMPULSE progress meeting Slide 43 slide 43
44 Results and analysis Hypothesis #3: transition from log-law to sqrt-law depends on Δp x + (probably more complex ) Composite profile Brown & Joubert 1969 y + log,max Folie 44 IMPULSE progress meeting Slide 44 slide 44
45 Results and analysis Hypothesis #3: transition from log-law to sqrt-law depends on Δp x + (probably more complex ) ZPG Δp x+ 0 Pure log-law Folie 45 IMPULSE progress meeting Slide 45 slide 45
46 Results and analysis Hypothesis #3: transition from log-law to sqrt-law depends on Δp x + (probably more complex ) Separation Δp x+ Pure sqrt-law (Stratford) Folie 46 IMPULSE progress meeting Slide 46 slide 46
47 Empirical wall law at APG Hypothesis #4: decrease of log-law slope parameter K i at APG Slope coefficient K von Karman constant κ=0.40+/-0.1 ZPG
48 Empirical wall law at APG Hypothesis #4: decrease of log-law slope parameter K i at APG Slope coefficient K von Karman constant κ=0.40+/-0.1 ZPG APG
49 Empirical wall law at APG Hypothesis #4: decrease of log-law slope parameter K i at APG Slope coefficient K von Karman constant κ=0.40+/-0.1 APG
50 Empirical wall law at APG Hypothesis #4: decrease of log-law slope parameter K i at APG Slope coefficient K von Karman constant κ=0.40+/-0.1 APG
51 Empirical wall law at APG Hypothesis #4: decrease of log-law slope parameter K i at APG Slope coefficient K ZPG
52 Empirical wall law at APG Hypothesis #4: decrease of log-law slope parameter K i at APG Slope coefficient K Increasing Δp x + APG ZPG
53 Empirical wall law at APG Hypothesis #4: decrease of log-law slope parameter K i at APG Slope coefficient K APG ZPG
54 Empirical wall law at APG Hypothesis #4: decrease of log-law slope parameter K i at APG Slope coefficient K APG ZPG
55 DLR strategy for RANS model improvement High-quality data base (exp., DNS/LES) (Empirical) laws of turbulence Physics-based improvement of RANS Slide 55 STELAR 2. Projekttreffen > DLR Göttingen >
56 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 Slide 56 STELAR 2. Projekttreffen > DLR Göttingen >
57 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. ν t Slide 57 STELAR 2. Projekttreffen > DLR Göttingen >
58 Idea: A composite wall-law for the turbulent viscosity log-law at APG (Galbraith et al. 1977) sqrt-law at APG Δp x + = Exp. by Skare & Krogstad Slide 58 STELAR 2. Projekttreffen > DLR Göttingen >
59 RANS modification HGR01 airfoil at Rec=25Mio, incidence angle α=10 Slide 59 STELAR 2. Projekttreffen > DLR Göttingen >
60 RANS modification HGR01 airfoil at Rec=25Mio, incidence angle α=10 Slide 60 STELAR 2. Projekttreffen > DLR Göttingen >
61 Idea #1: New terms with Δp x+ -dependent local blending Modifications should be activated only in parts of the boundary layer Pressure diffusion at APG (Rao & Hassan) Blending for y<0.15δ 99 Activate only in the sqrt-region Slide 61 STELAR 2. Projekttreffen > DLR Göttingen >
62 Idea #2: RANS model coefficients sensitized to pressure gradient Δp x + Coefficient γ controls the slope of the log-law Standard calibration is for ZPG κ=0.41 = const
63 Idea #2: RANS model coefficients sensitized to pressure gradient Δp x + The RANS model coefficient which controls the log-law slope ( Karman-constant ) becomes a function depending on local flow
64 Data structure of wall-normal lines for Δp x + Extension of unstructured flow solver TAU Wall-normal lines Method to determine δ 99, δ*, θ, H 12 Coding efforts vs. Improvements in predictive accuracy Field point Surface point Δp x+ from dp/dx and u τ δ 99, δ*, θ, H 12 Slide 64 STELAR 2. Projekttreffen > DLR Göttingen >
65 RANS model sensitized to pressure gradient Δp x + Field distribution of Δp x + Map to corresponding field points Surface quantities Δp x + from dp/dx and u τ
66 RANS model sensitized to pressure gradient Δp x + RANS model coefficient γ becomes a function of Δp x +
67 Validation of modified RANS U=36m/s Slide 67 STELAR 2. Projekttreffen > DLR Göttingen >
68 Validation of modified RANS U=36m/s Slide 68 STELAR 2. Projekttreffen > DLR Göttingen >
69 Validation of RANS U=36m/s Slide 69 STELAR 2. Projekttreffen > DLR Göttingen >
70 Questions to the audience Slide 70 STELAR 2. Projekttreffen > DLR Göttingen >
71 Turbulent Boundary Layer at ZPG - Folie 71 Slide 71 STELAR 2. Projekttreffen > DLR Göttingen >
72 Turbulent Boundary Layer at ZPG Δcf=5%! - Folie 72 Slide 72 STELAR 2. Projekttreffen > DLR Göttingen >
73 Conclusions
74 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)
75 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
76 Validation RETTINA II U=36m/s
77 Validation RETTINA II U=36m/s
78 Validation RETTINA II U=23m/s
79 Measuring technique Folie 79 IMPULSE progress meeting Slide 79 slide 79
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 Folie 80 IMPULSE progress meeting Slide 80 slide 80
81 Consistency with wall-law Summary of boundary layer analysis Consistency with log-law at APG Consistency with sqrtlaw at APG k-equation No No ω-equation Yes No Folie 81 IMPULSE progress meeting Slide 81 slide 81
82 Consistency with wall-law Summary of boundary layer analysis Consistency with log-law at APG Consistency with sqrtlaw at APG Modified k-equation Yes Yes Modified ω-equation Yes Yes Folie 82 IMPULSE progress meeting Slide 82 slide 82
83 Consistency with wall-law Summary of boundary layer analysis Blending active in loglaw region at APG Blending active in sqrtlaw region at APG Modified k-equation Yes Yes Modified ω-equation No Yes Folie 83 IMPULSE progress meeting Slide 83 slide 83
84 The ω-equation in the sqrt-law region Following ideas by Rao & Hassan, Catris & Aupoix Folie 84 IMPULSE progress meeting Slide 84 slide 84
85 The ω-equation in the sqrt-law region Following ideas by Rao & Hassan, Catris & Aupoix Folie 85 IMPULSE progress meeting Slide 85 slide 85
86 The ω-equation in the sqrt-law region Folie 86 IMPULSE progress meeting Slide 86 slide 86
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 Folie 87 IMPULSE progress meeting Slide 87 slide 87
88 Measurement technique combining different PIV systems 2D2C-PIV Large scale PIV 8 PCO 4000 cams side-by-side 2D3C stereo PIV overview 2D3C stereo PIV detail 6.38m 1.5m 0.78m 1.5m 1.5m x [m] Folie 88 IMPULSE progress meeting Slide 88 slide 88
89 Requirements/Design criteria on a new flow experiment 1. Large Re θ for sufficiently thick overlap region 2. Log-law established before entering the APG-section 3. Thick BL at low flow velocity so that PIV in viscous sublayer possible 4. Obtain large values for Δp x+, i.e. Δp x+ >0.06 U = 9m/s and U = 12m/s At x=6m Re θ up to 8000 and δ 99 =0.1m 6.38m Design of the test case using RANS-CFD with the DLR TAU code by DLR Folie 89 IMPULSE progress meeting Slide 89 slide 89
90 Data for mean velocity down to y + =1 using LR-PIV with PTV 2D2C PIV Long-range microscopic PIV with PTV 6.38m 0.78m 1.5m 1.5m x [m] Particle-tracking velocimetry algorithm (PTV) applied to the LR-PIV data see also Kähler et al., Exp. Fluids (2012) Folie 90 IMPULSE progress meeting Slide 90 slide 90
91 Boundary layer theory. An approximative model for the shear stress Folie 91 IMPULSE progress meeting Slide 91 slide 91
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 Folie 92 IMPULSE progress meeting Slide 92 slide 92
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 Folie 93 IMPULSE progress meeting Slide 93 slide 93
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 Folie 94 IMPULSE progress meeting Slide 94 slide 94
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 Folie 95 IMPULSE progress meeting Slide 95 slide 95
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 Folie 96 IMPULSE progress meeting Slide 96 slide 96
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 Folie 97 IMPULSE progress meeting Slide 97 slide 97
98 Characteristic non-dimensional parameters Comparison of the characteristic non-dimensional parameters Folie 98 IMPULSE progress meeting Slide 98 slide 98
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=8.18m Δpx + = Folie 99 IMPULSE progress meeting Slide 99 slide 99
100 Systematic trend/quantitative formula for variation of K o Folie 100 IMPULSE progress meeting Slide 100 slide 100
101 Conclusion Folie 101 IMPULSE progress meeting Slide 101 slide 101
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 Re θ Significant adverse pressure gradient Δp x+ up to Δp x+ =0.065 Combination of different PIV techniques gives high-quality data set Large number of velocity profiles High quality gradients and slope diagnostic functions Comparison of direct and indirect method for u τ locally Folie 102 IMPULSE progress meeting Slide 102 slide 102
103 Conclusion. The log-law does no longer describe the overlap layer 300 < y + < 0.2 δ 99 + A generalized half-power law (or modified log-law) gives a good description Idea of a composite wall-law by Brown & Joubert (1969) is supported Log-law-fit region is thin 60 < y + < 130 1/slope K i decreasing with increasing Δp x+ as devised by Nickels (2004) Modified log-law region for < y + < δ /slope K o decreasing with increasing Δp + x But mean inertial terms need to be accounted for K o Folie 103 IMPULSE progress meeting Slide 103 slide 103
104 Characterization of the flow ZPG log-law Folie 104 IMPULSE progress meeting Slide 104 slide 104
105 Characterization of the flow Favourable dp/ds L FPG ~ 5 δ ref Folie 105 IMPULSE progress meeting Slide 105 slide 105
106 Characterization of the flow Focus region: Adverse dp/ds L APG ~ 5 δ ref Folie 106 IMPULSE progress meeting Slide 106 slide 106
107 Universal log-law in zero-pressure gradient region Universal log-law at the inlet of the adverse pressure gradient section U =12m/s At x=6m Re θ = m Folie 107 IMPULSE progress meeting Slide 107 slide 107
108 Systematic trend/quantitative formula for variation of B i Folie 108 IMPULSE progress meeting Slide 108 slide 108
109 Systematic trend/quantitative formula for variation of B i Folie 109 IMPULSE progress meeting Slide 109 slide 109
110 Measurement technique using PIV Superelliptical nose Flat plate of length 6.38m 8 PCO 4000 Flap Quanta Ray 400 Innolas Spitlight 1000 APG region Folie 110 IMPULSE progress meeting Slide 110 slide 110
111 Large-scale 2D2C PIV. Instantaneous flow field Cam 5 Cam 6 Cam 7 Cam 8 Folie 111 IMPULSE progress meeting Slide 111 slide 111
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 Folie 112 IMPULSE progress meeting Slide 112 slide 112
113 Motivation: Turbulent boundary layers at adverse pressure gradient During take-off and landing Significant adverse pressure gradient (APG) Goals: Þ Wall-laws at APG Þ Improvement RANS models Folie 113 IMPULSE progress meeting Slide 113 slide 113
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