1. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 1 e N Transition Prediction for 3D Wing Configurations using Database Methods and a local, linear Stability Code Andreas Krumbein German Aerospace Center Institute of Aerodynamics and Flow Technology, Numerical Methods

2. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 2 Outline Introduction Transition Prediction Coupling Structure Test Case: ONERA M6 wing Computational Results Conclusion Outlook

3. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 3 Introduction Aircraft industry requirements: RANS based CFD tool with transition prediction Automatic, no intervention of the user Reduction of modeling based uncertainties Accuracy of results from fully turbulent flow or flow with prescribed transition often not satisfactory Improved simulation of the interaction between transition locations and separation

4. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 4 Introduction Different approaches: RANS solver+ stability code + e N method RANS solver+ boundary layer code + stability code + e N method RANS solver+ boundary layer code + e N database method(s) RANS solver+ transition closure model or transition/turbulence model

5. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 5 Introduction Different approaches: RANS solver+ stability code + e N method RANS solver+ boundary layer code + stability code + e N method RANS solver+ boundary layer code + e N database method(s) RANS solver+ transition closure model or transition/turbulence model

6. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 6 Introduction Different approaches: RANS solver+ stability code + e N method RANS solver+ boundary layer code + stability code + e N method RANS solver+ boundary layer code + fully automated stability code + e N method RANS solver+ boundary layer code + e N database method(s) RANS solver+ transition closure model or transition/turbulence model

7. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 7 Transition Prediction Coupling Structure Coupling Structure cycle = k cyc

8. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 8 Coupling Structure Transition Prediction Module: Laminar boundary-layer method for swept, tapered wings (conical flow) 1.) e N database-methods for TS (Stock) and CF (Casalis/Arnal) instabilities 2.) local, linear stability code LILO (Schrauf) Laminar separation approximates transition if transition downstream of laminar separation point 2d, 2.5d (infinite swept) + 3d wings Single + multi-element configurations N factor integration along chordwise gridlines Attachment line transition, by-pass transition & transition inside laminar separation bubbles not yet covered

9. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 9 Coupling Structure Structured RANS solver FLOWer: 3D RANS, compressible, steady/unsteady Structured body-fitted multi-block meshes Finite volume formulation Cell-vertex and cell-centered spatial discretizations schemes Central differencing, 2 nd & 4 th order artificial dissipation scaled by largest eigenvalue Explicit Runge-Kutta time integration Steady: local time stepping & implicit residual smoothing, embedded in a multi-grid algorithm eddy viscosity TMs (Boussinesq) & alg./diff. RSMs

10. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 10 P T upp (sec = 1) P T upp (sec = 2) P T upp (sec = 3) Coupling Structure Transition Prescription: Automatic partitioning into laminar and turbulent zones individually for each element Laminar points: S t,p  0 or  e = 0 Independent of topology P T upp (sec = 4)

11. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 11 set s tr u and s tr l far downstream compute flowfield check for RANS laminar separation  set separation points as new s tr u,l c l  const. in cycles  call transition module  use outcome of e N -databases/LILO or BL laminar separation point as new transition point set new s tr u,l underrelaxed  s tr u,l = s tr u,l , 1.0 <  < 1.5 convergence check   s tr u,l <  noyes STOP Coupling Structure Algorithm:

12. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 12 Test Case M6 wing:single-element semi-span:A = 3.8 swept:  LE = 30°,  TE = 15.8° tapered: = 0.562 Grid: 384,000 points (176 in section, 32 spanwise ) M  = 0.262, Re  = 3.5  10 6,  = 0°, 5°, 10°, 15° Tu  = 0.2% ( WT: S2Ch, Chalais-Meudon) → N = 6.485 using Mack’s relationship transition detection in experiment: sublimation of naphtalene turbulence model: Baldwin-Lomax critical N-factors:N TS cr = N CF cr = 6.485 transition prediction in 3 wing sections near  = 0.22, 0.42, 0.86

13. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 13 Results Transition locations at  = 0.45 and maximum N factor curves for TS and CF waves at  = 0.45 and  = 5.0°  = 0.45 ls CF  =  5.0°

14. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 14 Results Stability boundary calibration of critical CF N factor for lower side and  = 5.0° at  = 0.42 → N CF cr = 5.157 Very probably the naphtalene has accelerated transition!

15. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 15 Results N TS (x sec ) = N CF (x sec ) = TS in database and LILO CF in database: travelling CF in LILO: stationary

16. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 16 Results upper side lower side upper side lower side  = 0°  = 5°  = 15°  = 0°  = 5°  = 15° taken from * ) * ) Schmitt, V., Cousteix, J., “Étude de la couche limite tridimensionelle sur une aile en flèche,” ONERA Rapport Technique N° 14/1713 AN, Châtillon, France, July 1975 all ls all CF ls TS ls TS CF TS Transition lines for 11 wing sections  =0.000, 0.110, 0.220, 0.325, 0.420, 0.800, 0.860, 0.900, 0.930, 0.960, 0.975 Calibration of both critical N factors for lower side and  = 5°: N CF cr = 5.157 →  = 0.42 N TS cr = 4.75 →  = 0.96

17. Andreas Krumbein > 6 October 2006 7 th ONERA-DLR Aerospace Symposium - ODAS 2006, ONERA, Centre de Toulouse, Folie 17 Conclusion/Outlook Transition information from experiments is often very limited so that problems can arise when validation work is done Usually no information in terms of the N factors is given; often Mack‘s relationship is not sufficient; in the worst case the CF factor must be guessed In cases with enough experimental transition points the critical N factors can/must be calibrated Stability boundary must be known based on sufficient experimental data at least 4 points in N cr CF -N cr TS –plane for different integration strategies (advantageous) transition points and c p in 7-8 sections over half-span on upper and lower side criterion for transition downstream of laminar separation necessary more validation cases, e.g. DLR F5 wing → transonic test case 3D high-lift multi-element configuration (European project EUROLIFT II) using LILO + criteria for - transition in laminar separation bubbles - bypass transition - attachment line transition