Automatic Transition Prediction in Unsteady Airfoil Flows Using an Unstructured CFD Code

1. Automatic Transition Prediction inUnsteady Airfoil Flows Using an Unstructured CFD Code Andreas Krumbein, Normann Krimmelbein, Cornelia Seyfert German Aerospace CenterInstitute of Aerodynamics and Flow TechnologyC²A²S²E Center for Computer Applications in AeroSpace Science and Engineering

2. Overview • Introduction • Transition Prediction Coupling Structure • Extension of the eN method for unsteady base flows • Test Cases & Computational Results • Conclusion & Outlook

3. IntroductionTransition 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. IntroductionTransition Prediction in RANS-based CFD of External Flows M = 0.2, Re = 2.3x106, a = -4.0°, iHTP = 4° 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. inviscid stream lines line of laminar separation transition lines predicted transition lines Re = 3.5 x 106, Ma = 0.17

5. IntroductionTransition Prediction in RANS-based CFD of External Flows Currently most commonly used approaches for 3D RANS simulations • RANS solver + laminar BL code + eN database methods/empirical criteria • RANS solver + laminar BL code + automated stability code + eN methods • RANS solver + + eN database methods/empirical criteria • RANS solver + + automated stability code + eN methods • RANS solver + + transition transport equation models

6. IntroductionTransition Prediction in RANS-based CFD of External Flows Currently most commonly used approaches for 3D RANS simulations • RANS solver + laminar BL code + eN database methods/empirical criteria • RANS solver + laminar BL code + automated stability code + eN methods (1) standard approach, industrial applications, standard grids can be used: only cp • RANS solver + + eN database methods/empirical criteria • RANS solver + + automated stability code + eN 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. IntroductionTransition 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. cycle = kcyc cycle = kcyc Transition Prediction Coupling Structure Iteration of the Transition Points external BL approach internal BL approach

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 1st and 2nd 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. 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) • 2nd 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-w type) • differential RSM • DES

11. Extension of the eN method for Unsteady Base Flows Steady case • The n factor of a frequency f (circular frequency wr = 2p f ) describes the ratio of a disturbance‘s amplitude at position x and the position x0 where the disturbance was first amplified by integrating its spatial amplification rate ai. • 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 Ncrit, which has to be determined experimentally. Ncrit xtr

12. Extension of the eN method for Unsteady Base Flows 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+Dt, 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 wi. spatial theory temporal theory

13. Extension of the eN method for Unsteady Base Flows The idea of the convection of amplification rates in an unsteady base flow *,** • n factor evolution between t and Dt:  time integration scheme for the values of the n factor: n=n(t,wr;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

14. Extension of the eN 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 Application modes of the eN method • RANS + BL(BL code) + stability code + eN method • RANS + BL(RANS code) + stability code + eN method • RANS + BL(RANS code) + stability code + unsteady eN method g-ReQ,t transition transport model • Transport equations for the intermittency value g 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 g production at separation) • Unsteadyness is taken into account by the time derivatives of the two variables in the transport equations. •transition location inside laminar separation bubble possible •BL unsteady + transition steady •transition location inside laminar separation bubble possible •BL unsteady + transition unsteady

15. Test Cases & Computational ResultsPitching 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.a(t) = 10.0° - 10.0° sin(wt), k = pf c/U= 0.1 Tu∞ = 0.083% → Ncrit = 8.59 • Spalart-Allmaras (SA) turbulence model • 3 periods with all eN approaches • dual time stepping • 600 physical time steps per period • 300 inner pseudo-time iterations with LU-SGS with 4w multigrid cycle • started at amin from well converged fully turbulent steady solution for amin • transition prediction at the physical time steps • initial phase with reasonably estimated fixed transition locations

16. Test Cases & Computational ResultsPitching Oscillations with Dynamic Stall ▪ FT, BL + steady: well converged ▪ RANS + steady: converged ▪ RANS + unsteady: not yet converged during downstroke between 13 deg and 0 deg NACA0012 • Temporal convergence lift moment

17. Test Cases & Computational ResultsPitching Oscillations with Dynamic Stall ▪ FT, BL + steady: very similar during upstroke ▪ RANS: formation of stall vortex at lower a ▪ transition: all similar during downstroke, amplitudes different between 13 deg and 0 deg NACA0012 • Differences in the results lift moment

18. Test Cases & Computational ResultsPitching Oscillations with Dynamic Stall NACA0012 • Transition locations Start of dynamic stall vortex found in experiment at a = 15 deg separations and oscillations differences due to method differences due to representation of BL BL code separation

19. Test Cases & Computational ResultsPitching Oscillations with Dynamic Stall 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. a(t) = 13.0° + 5° sin(wt), k = pf c/U= 0.1 Tu∞ = 0.057% → Ncrit = 9.5 • DS2 (deep stall): M = 0.31, Re = 1.2 mio. a(t) = 13.0° + 7° sin(wt), k = pf c/U= 0.05Tu∞ = 0.056% → Ncrit = 9.54 • SA, Menter k-w SST, SSG/LRR-w • settings as before • all eN approaches • some results with g-ReQ,t model

20. Test Cases & Computational ResultsPitching Oscillations with Dynamic Stall ▪ FT, BL + steady eN: almost identical, transition locations are separation points ▪ RANS: some qualitative improvement (vortex, moment peak) ▪ RANS + unsteady eN: strong oscillations of upper transition point OA209 Converged: DS1 with SAFTBL + steadyRANS + steadyRANS + unsteady lift moment

21. Test Cases & Computational ResultsPitching Oscillations with Dynamic Stall ▪ FT, BL + steady eN: almost identical, transition locations are separation points, lift qualitatively OK, moment not as good ▪ RANS + steady eN: strong oscillations of upper transition point, yields the existance of a moment peak ▪ RANS + unsteady eN: NOT converged, similar to RANS + steady eN OA209 Converged: DS1 with SSTFTBL + steadyRANS + steady lift moment

22. Test Cases & Computational ResultsPitching Oscillations with Dynamic Stall ▪ FT, BL + steady eN: almost identical, transition: separations ▪ RANS: NOT converged, strong oscillations of upper transition point, yield the existance of a moment peak ▪ RANS + unsteady eN: oscillations earlier and stronger than with steady eN, downstroke reattachment looks best, as with SA/SST OA209 Converged: DS1 with RSMFTBL + steady lift moment

23. Test Cases & Computational ResultsPitching Oscillations with Dynamic Stall ▪ FT, BL + steady eN: 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. OA209 Converged: DS2 with SAFTBL + steadyRANS + steadyRANS + unsteady, upstroke lift moment

24. Test Cases & Computational ResultsPitching Oscillations with Dynamic Stall ▪ FT, BL + steady eN: 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 OA209 Converged: DS2 with SSTFTBL + steadyRANS + steadyRANS + unsteady, upstroke lift moment

25. Test Cases & Computational ResultsPitching Oscillations with Dynamic Stall ▪ FT, BL + steady eN: 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. OA209 Converged: DS2 with RSMFTBL + steadyRANS + steadyRANS + unsteady, upstroke until  = 18 deg lift moment

26. Test Cases & Computational ResultsPitching Oscillations with Dynamic Stall ▪ Dependance on initial conditions? ▪ Different initializations: FT vs. free stream ▪ There are different temporally converged solutions. OA209 ▪ 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. Test Cases & Computational ResultsPitching Oscillations with Dynamic Stall ▪ DS1 with RSM + free stream initialization + RANS + steady eN: 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 OA209 lift moment

28. Test Cases & Computational ResultsPitching Oscillations with Dynamic Stall OA209 • g-ReQ,t model ▪ Also not converged in the third cycle. ▪ Very similar to the results from RANS + steady eN. ▪ 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. Conclusion & Outlook • 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.

30. Conclusion & Outlook • The approach BL(BL code) + steady eN 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 eN, BL(RANS code) + unsteady eN,g-ReQ,t(SST) • Finer grid • Increase of the number of periods nT in order to ensure temporal convergence • Reduction of the physical time step Dt per period in order to promote temporal convergence • Reduction of the number of inner iterations ninner 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 Dntr from one prediction step at every physical time step, Dntr = 1, to Dntr ≈ 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