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Application of a Hybrid Navier-Stokes Solver with Automatic Transition Prediction

This paper discusses the application of a hybrid Navier-Stokes solver with automatic transition prediction for improved simulation of flow separation and interaction with turbulence. Different prediction approaches and coupling methods are explored. The capabilities of the solver are demonstrated using various application modes. The paper serves as documentation for future production application in the industry.

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Application of a Hybrid Navier-Stokes Solver with Automatic Transition Prediction

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  1. Application of a Hybrid Navier-Stokes Solver with Automatic Transition Prediction Andreas KrumbeinGerman Aerospace Center, Institute of Aerodynamics and Flow Technology, Numerical MethodsNormann KrimmelbeinTechnical University of Braunschweig, Institute of Fluid Mechanics, Aerodynamics of AircraftGéza SchraufAirbus

  2. Outline Outline • Introduction • Transition Prescription • Transition Prediction Coupling Structure • Test Cases & Computational Results • 2D two-element configuration • 3D generic aircraft configuration • Conclusion & Outlook

  3. Introduction Introduction • Background of considering transition in RANS-based CFD tools • Better numerical simulation results • Capturing of physical phenomena, which were discounted otherwise • Quantitatively, sometimes even qualitatively the results can differ significantly w/o transition • Long term requirement from research organisations and industry • Transition prescription • Some kind of transitional flow modelling • Transition prediction • Automatically: no intervention by the code user • Autonomously: as little additional information as possible • Main objectives of thefunctionality • Improved simulation of interaction between transition and separation • Exploitation of the full potential of advanced turbulence models • Objectives of the paper • Demonstration of the capabilities using different application modes • Documentation for future production application in industry

  4. Introduction • Different prediction approaches: • Empirical/semi-empirical transition criteria for some mechanisms the only thing available, cheap, can be inaccurate • Local, linear stability theory + eN method state-of-the-art method in engineering, relatively cheap, relatively accurate • Parabolic stability equations (PSE) non-local, linear&non-linear, rather expensive, very accurate, initial conditions: ? • Large eddy simulation (LES) unsteady, can be very accurate, not yet mature, very expensive • Direct numerical simulation (DNS) of Navier-Stokes equations unsteady, high end approach, nothing is more accurate, unaffordable

  5. Introduction  2  1 • Different prediction approaches: • Empirical/semi-empirical transition criteriafor some mechanisms the only thing available, cheap, can be inaccurate • Local, linear stability theory + eN methodstate-of-the-art method in engineering, relatively cheap, relatively accurate • Parabolic stability equations (PSE) non-local, linear&non-linear, rather expensive, very accurate, initial conditions: ? • Large eddy simulation (LES) unsteady, can be very accurate, not yet mature, very expensive • Direct numerical simulation (DNS) of Navier-Stokes equations unsteady, high end approach, nothing is more accurate, unaffordable

  6. Introduction • Different coupling approaches: • RANS solver + stability code + eN method • RANS solver + boundary layer code + stability code + eN method • RANS solver + boundary layer code + eN database method(s) • RANS solver + transition closure model or transition/turbulence model

  7. Introduction • Different coupling approaches: • RANS solver + stability code + eN method • RANS solver + boundary layer code + stability code + eN method • RANS solver + boundary layer code + eN database method(s) • RANS solver + transition closure model or transition/turbulence model

  8. Introduction • Different coupling approaches: • RANS solver + stability code + eN method • RANS solver + boundary layer code + fully automated stability code + eN method • RANS solver + boundary layer code + eN database method(s) • RANS solver + transition closure model or transition/turbulence model

  9. Introduction • Different coupling approaches: • RANS solver + fully automated stability code + eN method • RANS solver + boundary layer code + fully automated stability code + eN method • RANS solver + boundary layer code + eN database method(s) • RANS solver + transition closure model or transition/turbulence model •  2 •  1 • 3 • future

  10. Introduction • Hybrid 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 artifical dissipation • Time integration: explicit Runge-Kutta with multi-grid acceleration or implicit approximate factorization scheme (LU-SGS) • Turbulence models and approaches: • Linear and non-linear 1- and 2-equation eddy viscosity models (SA type, k-w type) • RSM  RST, EARSMs (full & linearized) • DES

  11. Prescription Transition Prescription • automatic partitioning of flow field into laminar and turbulent regions • individual laminar zone for each element • different numerical treatment of laminar and turbulent grid points • in laminar regions: • control of TM’s source terms •  Sprod≤ 0 • Sprod: source of turbulence production equation PTupp(main) PTupp(flap) PTlow(flap) PTlow(main) - dlam, main = 20% chord length - dlam, flap = 1% chord length

  12. Prescription Transition Prescription • automatic partitioning of flow field into laminar and turbulent regions • individual laminar zone for each element • different numerical treatment of laminar and turbulent grid points • in laminar regions: • control of TM’s source terms •  Sprod≤ 0 • Sprod: source of turbulence production equation PTupp(main) PTupp(flap) PTlow(flap) PTlow(main) - dlam, main = 20% chord length - dlam, flap = 1% chord length

  13. Prescription Transition Prescription • automatic partitioning of flow field into laminar and turbulent regions • individual laminar zone for each element • different numerical treatment of laminar and turbulent grid points • in laminar regions: • control of TM’s source terms •  Sprod≤ 0 • Sprod: source of turbulence production equation PTupp(main) PTupp(flap) PTlow(flap) PTlow(main) - dlam, main = 20% chord length - dlam, flap = 1% chord length

  14. Prescription Transition Prescription • automatic partitioning of flow field into laminar and turbulent regions • individual laminar zone for each element • different numerical treatment of laminar and turbulent grid points • in laminar regions: • control of TM’s source terms •  Sprod≤ 0 • Sprod: source of turbulence production equation PTupp(main) PTupp(flap) PTlow(flap) PTlow(main) - dlam, main = 20% chord length - dlam, flap = 1% chord length

  15. Structure cycle = kcyc Transition Prediction Coupling Structure external BL approach

  16. Structure cycle = kcyc cycle = kcyc Transition Prediction Coupling Structure external BL approach internal BL approach

  17. Structure • Transition prediction module • transition module • line-in-flight cuts • or • inviscid stream lines • cp-extraction • or • lam. BL data from RANS grid • lam. BL code • swept, tapered  conical flow, 2.5d • streamline-oriented • external code • local lin. stability code • eN method for TS & CF • external code • or • eN database methods • one for TS & one for CF • external codes

  18. Structure • Transition prediction module • transition module • line-in-flight cuts • or • inviscid stream lines • cp-extraction • or • lam. BL data from RANS grid • lam. BL code • swept, tapered  conical flow, 2.5d • streamline-oriented • external code • local lin. stability code • eN method for TS & CF • external code • or • eN database methods • one for TS & one for CF • external codes RANS infrastructure

  19. Structure • Application areas • 2d airfoil configurations • 2.5d wing configurations: inf. swept • 3d wing configurations • 3d fuselages • 3d nacelles • Single-element configurations • Mulit-element configurations • Flow topologies • attached • with lam. separation: • - LS point as transition point • -bubble with criterion OR • real stability analysis with stability code inside bubble + many points in prismatic layer

  20. Structure • Application areas • 2d airfoil configurations • 2.5d wing configurations: inf. swept • 3d wing configurations • 3d fuselages • 3d nacelles • Single-element configurations • Mulit-element configurations • Flow topologies • attached • with lam. separation: • - LS point as transition point • -bubble with criterion OR • real stability analysis with stability code inside bubble + many points in prismatic layer streamlines necessary! lam. BL data from RANS grid needed! for 3d case: for CF  128 points in wall normal direction necessary!!!

  21. Structure • Algorithm • set stru and strl far downstream (  start mit quasi fully-laminar conditions) • compute flow field • check for lam. separation in RANS grid  set laminar separation points as new stru,l  stabilization of the computation in the transient phase • clconst. in cycles call transition module •  use a.) new transition point directly or • b.) lam. separation point of BL code as approximation • see new stru,l underrelaxed  stru,l = stru,ld, 1.0 < d < 1.5  damping of oscillations in transition point iteration

  22. Structure no yes STOP • Algorithm • set stru and strl far downstream (  start mit quasi fully-laminar conditions) • compute flow field • check for lam. separation in RANS grid  set laminar separation points as new stru,l  stabilization of the computation in the transient phase • clconst. in cycles call transition module •  use a.) new transition point directly or • b.) lam. separation point of BL code as approximation • see new stru,l underrelaxed  stru,l = stru,ld, 1.0 < d < 1.5  damping of oscillations in transition point iteration • check convergence Dstru,l < e

  23. Results Test Cases & Computational Results • 2d two-element configuration: • NLR 7301 with flap • gap: 2.6% cmain, cflap/cmain = 0.34 • M = 0.185, Re = 1.35 x 106, a = 6.0° • grid: 23,000 triangles + 15,000 quadriliterals on contour: main  250, flap  180, 36 in both prismatic layers • SAE • NTS= 9.0 (arbitrary setting) • exp. transition locations: upper  main: 3.5% & flap: 66.5% lower  main: 62.5% & flap: fully laminar • different mode combinations: a) laminar BL code & stability code  BL mode 1 b) laminar BL inside RANS & stability code  BL mode 2 grid: Airbus

  24. Results Transition iteration convergence history: BL mode 1 • pre-prediction phase  1,000 cycles • every 20 cycles • prediction phase starts at cycle = 1,000 every 500 cycles • fast convergence

  25. Results cp-field and transition points: BL mode 1 • all transition points up-stream of experimental values • no separation in final RANS solution • good approxi-mation of the measured transition points • further im-provement possible using crite-rion for tran-sition in lami-nar separa-tion bubbles

  26. Results Transition iteration convergence history: BL mode 2, run a • no convergence • 1st numerical instability on flap  induced by transition iteration • 2ndnumerical instability on main induced by RANS procedure • pre-prediction phase  1,000 cycles • every 20 cycles • prediction phase starts at cycle = 1,000 every 1,000 cycles stops at cycle = 10,000

  27. Results Transition iteration convergence history: BL mode 2, run b • limited convergence • 1st numerical instability on flap  remains • 2ndnumerical instability on main damped by the procedure • pre-prediction phase  1,000 cycles • every 20 cycles • prediction phase starts at cycle = 1,000 every 500 cycles

  28. Results cp-field and transition points: BL mode 2 • all transition points down-stream of experimental values • two separa-tions in final RANS solu-tion • flap separa-tion oscilla-tion remains • improved transition lo-cations using calibrated N factor • individual, au-tomatic shut-down of tran-sition module necessary

  29. Results • 3D generic aircraft configuration: • M = 0.2, Re = 2.3x106, a = – 4°, iHTP = 4° • grid: • 12 mio. points • 32 cells in prismatic layers • at HTP: 48 cells in prismatic layers • SAE • NTS= NCF= 7.0 (arbitrary setting) • transition prediction on HTP only, upper and lower sides • different mode combinations: a) laminar BL code & stability code & line-in flight cuts BL mode 1 b) laminar BL inside RANS & stability code & inviscid streamlines BL mode 2 • parallel computation: either 32, 48, or 64 processes • 2.2 GHz Opteron Linux cluster with 328 CPUs geometry: Airbus, grid: TU Braunschweig

  30. Results BL mode 2 •cf-distribution•wing sections( (thick white)•skin friction lines(thin black) BL mode 1

  31. Results BL mode 2 BL mode 1 •cp-distribution•transition lines( (thick red with symbols)•skin friction lines(thin black)

  32. Results •pre-pre-diction un- til cycle: 500every 20 cycles •convergence of transition lines calls at cycles:500, 1000, 1500, 2000 out of 2500

  33. Results •convergence history of the coupled RANS computations:

  34. Conclusion Conclusion and Outlook • RANS computations with integrated transition prediction were carried out without intervention of the user. • The transition tools work fast and reliable. • Complex cases (e.g. transport aircraft) can be handled; experience up to now limited to one component of the aircraft. • Use of lam. BL code leads to fast convergence of the transition prediction iteration; not always applicable, because transition may be located significantly downstream of lam. separation. • Use of internally computed lam. BL data can lead to numerical instabilities when laminar separations are treated  interaction between different separations can occur  interaction of separation points and transition points: oscillation of separation can lead to oscillation of transition  automatic shut down of transition iteration individually for each wing section or component of the configuration necessary

  35. Conclusion • In the nearest future: • Much, much more test cases • generic aircraft case: - a variation - different N factors - transition on all wings of the aircraft - inclusion of fuselage • transonic cases • physical validation, e.g. F4, F6 (AIAA drag prediction workshop) • complex high lift configurations, e.g. from European EUROLIFT projects • Setup of Best Practice guidelines

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