1. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 1 Automatic Transition Prediction in Unsteady Airfoil Flows Using an Unstructured CFD Code Andreas Krumbein, Normann Krimmelbein, Cornelia Seyfert German Aerospace Center Institute of Aerodynamics and Flow Technology C²A²S²E Center for Computer Applications in AeroSpace Science and Engineering

2. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 2 Introduction Transition Prediction Coupling Structure Extension of the e N method for unsteady base flows Test Cases & Computational Results Conclusion & Outlook Overview

3. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 3 Introduction Transition Prediction in RANS-based CFD of External Flows Current status of transition prediction in RANS solvers RANS solvers have become a standard approach for the design and the aerodynamic analysis of aerodynamic configurations. Requirement from Aircraft Industry and Research for a long time: RANS solver with integrated general transition prediction functionality Automatic: no intervention of the user Autonomous: as little additional information as possible Major aims: Reduction of modeling based uncertainties Improvement of simulation accuracy Accuracy of results from fully turbulent computations or from computations with prescribed transition often not satisfactory Exploitation of the full potential of advanced turbulence models Most important, at present, improved simulation of the interaction between transition locations and separation, especially for high-lift configurations.

4. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 4 Introduction Transition Prediction in RANS-based CFD of External Flows Current status of transition prediction in RANS solvers Incorporated transition prediction has become a state-of-the-art technique for various RANS codes in the last years. Details of the concepts are different. They have in common that they are able to be applied to complex geometries: multi-element configurations, full aircraft, high-lift configurations, wind turbines, fuselages, etc. Much development and validation work has been carried out and, today, the approaches have gained a high level of confidence. Standard approaches of the transition prediction functionalities regularly used in aircraft industry. Currently, increasing use of advanced approaches at universities and research organizations. Growing computer capacities will allow for more complex geometries and more points. M = 0.2, Re = 2.3x10 6,  = -4.0°, i HTP = 4° inviscid stream lines transition lines line of laminar separation predicted transition lines Re = 3.5 x 10 6, Ma = 0.17

5. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 5 Introduction Transition Prediction in RANS-based CFD of External Flows Currently most commonly used approaches for 3D RANS simulations RANS solver + laminar BL code +e N database methods/empirical criteria RANS solver + laminar BL code +automated stability code + e N methods RANS solver ++e N database methods/empirical criteria RANS solver ++ automated stability code + e N methods RANS solver + + transition transport equation models

6. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 6 Introduction Transition Prediction in RANS-based CFD of External Flows Currently most commonly used approaches for 3D RANS simulations RANS solver + laminar BL code +e N database methods/empirical criteria RANS solver + laminar BL code +automated stability code + e N methods(1)  standard approach, industrial applications, standard grids can be used: only c p RANS solver ++e N database methods/empirical criteria RANS solver ++ automated stability code + e N methods(2)  advanced approach, accurate in regions where BL codes can not be applied RANS solver + + transition transport equation models (3)  still under test, works well and yields accurate results for streamwise transition

7. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 7 Introduction Transition Prediction in RANS-based CFD of External Flows Current application spectrum 2d airfoils, infinite swept + 3d wings, winglets, fuselages and nacelles single + multi-element configurations attached flow + flow with laminar separation fully validated: Tollmien-Schlichting, cross flow, separation induced transition validation started: attachment line transition, by-pass transition All for steady flow problems Objectives of the talk Can the existing transition prediction techniques be applied to unsteady flows and if yes, how? What are the differences in the results due to the different approaches? Can some kind of best practice be derived? Which is the most suitable approach for unsteady flows emphasizing dynamic stall test cases?

8. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 8 cycle = k cyc external BL approach internal BL approach Transition Prediction Coupling Structure Iteration of the Transition Points

9. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 9 Transition Prediction Coupling Structure Transition Prediction Module Treatment of separation induced transition external BL approach Yields very accurate laminar BL profiles using grids with standard resolution. BL code stops at the point of laminar separation. The laminar separation point approximates the transition point if transition is located downstream of the separation point. internal BL approach Needs very fine grid resolution in wall normal direction for sufficient accuracy of laminar BL profiles including the 1 st and 2 nd derivatives which are input for the stability code, ≈ 40 points in prismatic layer of a hybrid grid for streamwise instabilities. Stability analysis can be carried out inside the separation bubble. Sufficiently high resolution of the bubble must be ensured also in streamwise direction, factor 2 ÷ 2.5 compared to normal resolution (≈ 256 points airfoil contour).

10. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 10 Transition Prediction Coupling Structure Unstructured RANS Solver TAU 3D RANS, compressible, steady/unsteady Hybrid unstructured grids: hexahedra, tetrahedra, pyramids, prisms Finite volume formulation Vertex-centered spatial scheme (edge-based dual-cell approach) 2 nd order central scheme, scalar or matrix artificial dissipation Pseudo-time integration: explicit Runge-Kutta or implicit approximate factoriza- tion scheme (LU-SGS), multi-grid acceleration, local time stepping, explicit residual smoothing, low Mach number preconditioning Physical time integration: dual time stepping using pseudo-time integration for the inner iterations Turbulence models: 1- and 2-equation eddy viscosity models (SA type, k-  type) differential RSM DES

11. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 11 Steady case The n factor of a frequency f (circular frequency  r = 2  f ) describes the ratio of a disturbance‘s amplitude at position x and the position x 0 where the disturbance was first amplified by integrating its spatial amplification rate  i. From the set of n factor curves for all frequencies in a certain frequency band the maximum value at the position x, the maximum N factor N, is compared to the critical N factor N crit, which has to be determined experimentally. N crit x tr Extension of the e N method for Unsteady Base Flows

12. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 12 Unsteady case In a steady flow, one finds this situation of amplified disturbances at every moment when time passes. In an unsteady flow, this situation is only found at time t. At time t +  t, this situation is convected downstream due to the unsteadyness. The Gaster relation tranfers spatial into temporal theory expressing the spatial amplification rates through the temporal amplification rates  i. spatial theory temporal theory Extension of the e N method for Unsteady Base Flows

13. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 13 The idea of the convection of amplification rates in an unsteady base flow *,** n factor evolution between t and  t:  time integration scheme for the values of the n factor: n = n(t,  r ; x) * R. Radespiel, J. Windte, U. Scholz: „Numerical and Experimental Flow Analysis of Moving Airfoils with Laminar Separation Bubbles‘, AIAA Journal, Vol. 45, No. 6, June 2007, pp. 1346-1356, also: AIAA 2006-501 ** J. Windte, R. Radespiel: „Propulsive Efficiency of a Moving Airfoil at Transitional Low Reynolds Numbers“, AIAA Journal, Vol. 46, No. 9, Sep. 2008, pp. 2165-2177 Extension of the e N method for Unsteady Base Flows

14. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 14 Application modes of the e N method RANS + BL(BL code) + stability code + e N method RANS + BL(RANS code) + stability code + e N method RANS + BL(RANS code)+ stability code + unsteady e N method  -Re ,t transition transport model Transport equations for the intermittency value  and the momentum loss Reynolds number at transition onset Covers streamwise transition mechanisms due to instabilities and by-pass (criterion) and laminar separation (specific control of  production at separation) Unsteadyness is taken into account by the time derivatives of the two variables in the transport equations. Extension of the e N method for Unsteady Base Flows Different Approaches for Unsteady Base Flows laminar separation from BL code approximates transition in case of laminar separation bubble BL steady + transition steady transition location inside laminar separation bubble possible BL unsteady + transition steady transition location inside laminar separation bubble possible BL unsteady + transition unsteady

15. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 15 Test Cases & Computational Results Pitching Oscillations with Dynamic Stall NACA0012 hybrid grid with 79,000 points, 512 along contour, 128 in prismatic layer M  = 0.16, Re  = 1.8 mio.  (t) = 10.0° - 10.0° sin(  t), k =  f c/U  = 0.1 Tu ∞ = 0.083% → N crit = 8.59 Spalart-Allmaras (SA) turbulence model 3 periods with all e N approaches dual time stepping 600 physical time steps per period 300 inner pseudo-time iterations with LU-SGS with 4w multigrid cycle started at  min from well converged fully turbulent steady solution for  min transition prediction at the physical time steps initial phase with reasonably estimated fixed transition locations

16. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 16 Test Cases & Computational Results Pitching Oscillations with Dynamic Stall NACA0012 Temporal convergence lift moment ▪ FT, BL + steady: well converged ▪ RANS + steady: converged ▪ RANS + unsteady: not yet converged during downstroke between 13 deg and 0 deg

17. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 17 NACA0012 Differences in the results ▪ FT, BL + steady: very similar during upstroke ▪ RANS: formation of stall vortex at lower  ▪ transition: all similar during downstroke, amplitudes different between 13 deg and 0 deg Test Cases & Computational Results Pitching Oscillations with Dynamic Stall lift moment

18. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 18 NACA0012 Transition locations BL code separation Start of dynamic stall vortex found in experiment at  = 15 deg separations and oscillations differences due to method differences due to representation of BL Test Cases & Computational Results Pitching Oscillations with Dynamic Stall

19. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 19 OA209 – airfoil of a rotorblade section hybrid grid with 37,000 points, 940 along contour, 40 in prismatic layer DS1 (light stall): M  = 0.16, Re  = 1.8 mio.  (t) = 13.0° + 5° sin(  t), k =  f c/U  = 0.1 Tu ∞ = 0.057% → N crit = 9.5 DS2 (deep stall): M  = 0.31, Re  = 1.2 mio.  (t) = 13.0° + 7° sin(  t), k =  f c/U  = 0.05 Tu ∞ = 0.056% → N crit = 9.54 SA, Menter k-  SST, SSG/LRR-  settings as before all e N approaches some results with  -Re ,t model Test Cases & Computational Results Pitching Oscillations with Dynamic Stall

20. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 20 OA209 Test Cases & Computational Results Pitching Oscillations with Dynamic Stall Converged: DS1 with SA FT BL + steady RANS + steady RANS + unsteady ▪ FT, BL + steady e N : almost identical, transition locations are separation points ▪ RANS: some qualitative improvement (vortex, moment peak) ▪ RANS + unsteady e N : strong oscillations of upper transition point lift moment

21. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 21 OA209 Test Cases & Computational Results Pitching Oscillations with Dynamic Stall Converged: DS1 with SST FT BL + steady RANS + steady ▪ FT, BL + steady e N : almost identical, transition locations are separation points, lift qualitatively OK, moment not as good ▪ RANS + steady e N : strong oscillations of upper transition point, yields the existance of a moment peak ▪ RANS + unsteady e N : NOT converged, similar to RANS + steady e N lift moment

22. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 22 OA209 Test Cases & Computational Results Pitching Oscillations with Dynamic Stall Converged: DS1 with RSM FT BL + steady ▪ FT, BL + steady e N : almost identical, transition: separations ▪ RANS: NOT converged, strong oscillations of upper transition point, yield the existance of a moment peak ▪ RANS + unsteady e N : oscillations earlier and stronger than with steady e N, downstroke reattachment looks best, as with SA/SST lift moment

23. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 23 OA209 Test Cases & Computational Results Pitching Oscillations with Dynamic Stall Converged: DS2 with SA FT BL + steady RANS + steady RANS + unsteady, upstroke ▪ FT, BL + steady e N : very similar, lift and moment qualitatively OK, first peaks exist near to exp. data ▪ RANS: both approaches very similar, stall vortex too early, ▪ Second peaks do not exist. lift moment

24. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 24 OA209 Test Cases & Computational Results Pitching Oscillations with Dynamic Stall Converged: DS2 with SST FT BL + steady RANS + steady RANS + unsteady, upstroke ▪ FT, BL + steady e N : almost indentical, lift and moment qualitatively OK, both peaks exist near to exp. data ▪ RANS: both approaches very similar, stall vortex too early, both peaks exist lift moment

25. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 25 OA209 Test Cases & Computational Results Pitching Oscillations with Dynamic Stall Converged: DS2 with RSM FT BL + steady RANS + steady RANS + unsteady, upstroke until  = 18 deg ▪ FT, BL + steady e N : very similar, lift and moment qualitatively OK, first peaks exist near to exp. data, second peaks very much less pronounced ▪ RANS: both approaches very similar, stall vortex too early, existance of second unclear. lift moment

26. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 26 OA209 Test Cases & Computational Results Pitching Oscillations with Dynamic Stall ▪ Dependance on initial conditions? ▪ Different initializations: FT vs. free stream ▪ There are different temporally converged solutions. ▪ RANS: all not converged ▪ FT, BL + steady: some converged ▪ different:DS1 with SA – FT, BL + steady DS2 with SA – FT, BL + steady DS2 with SST – FT lift moment

27. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 27 OA209 Test Cases & Computational Results Pitching Oscillations with Dynamic Stall lift moment ▪ DS1 with RSM + free stream initialization + RANS + steady e N : not converged! ▪ Only here, the direction of the lift loop is represented as in the measurement. Why? ▪ Problem: New DS1 experiment carried out recently using a new model and new oscillation system both being stiffer  no lift loop anymore  another source of uncertainty

28. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 28 OA209  -Re ,t model Test Cases & Computational Results Pitching Oscillations with Dynamic Stall ▪ Also not converged in the third cycle. ▪ Very similar to the results from RANS + steady e N. ▪ Differences mainly during the downstroke, significantly essentially for DS1. ▪ The results show the high potential of this modeling approach. ▪ At present, the reduction of the computational effort is appealing.

29. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 29 All results are of preliminary character and will be re-computed in the nearest future. Transition can significantly improve the results of dynamic stall simulations. At present, it seems that light stall simulations – DS1 – are more sensitive to the effects of transition and improvements are more obvious. High sensitivity to temporal resolution when transition downstream if separation is taken into account. New computations with considerably higher temporal resolution of one oscillation period. At present, significant interaction between the transition points and the turbulence model found, which makes a clear assessment impossible. New computations will use a much finer grid. This seems to be necessary especially for the RSM. For DS2, the fully turbulent results seem to match the measured results best. This was unexpected. Was the flow in DS2 experiment fully turbulent? The new DS1 measurements will be taken into account for the assessment based on the new computations. Conclusion & Outlook

30. Andreas Krumbein > 28 June 2011 29th AIAA Applied Aerodynamics Conference, Honolulu, Hawaii, Slide 30 The approach BL(BL code) + steady e N is not suitable for dynamic stall simulations and will not be used anymore. Work program for the new computations: Fully turbulent, BL(RANS code) + steady e N, BL(RANS code) + unsteady e N,  -Re ,t (SST) Finer grid Increase of the number of periods n T in order to ensure temporal convergence Reduction of the physical time step  t per period in order to promote temporal convergence Reduction of the number of inner iterations n inner per physical time step in order to save computational time while keeping convergence within the inner iterations Reduction of the number of transition prediction steps  n tr from one prediction step at every physical time step,  n tr = 1, to  n tr ≈ 10÷20 in order to save computational time Initialization with free stream conditions, fully turbulent solution and solution with reasonably estimated or predicted, fixed transition locations. Derivation of a best practice combination of these parameters for a reliable, but fast simulation Conclusion & Outlook