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Accounting for wall effects in explicit algebraic stress models

LABORATOIRE D’ETUDES AERODYNAMIQUES (LEA) Université de Poitiers , CNRS , ENSMA. Progress in Wall Turbulence: Understanding and modelling Lille, France, April 21-23, 2009. Accounting for wall effects in explicit algebraic stress models. Thomas GATSKI.

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Accounting for wall effects in explicit algebraic stress models

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  1. LABORATOIRE D’ETUDES AERODYNAMIQUES (LEA) Université de Poitiers , CNRS , ENSMA Progress in Wall Turbulence: Understanding and modelling Lille, France, April 21-23, 2009 Accounting for walleffects in explicit algebraic stress models Thomas GATSKI Rémi MANCEAU Abdou Gafari OCENI

  2. Outline • Introduction of wall effects into Explicit Algebraic Stress Models • Explicit Algebraic Methodology • Introduction of the wall effects • Choice of the basis • Results • Channel Flows and boundary layer • Couette – Poiseuille Flows • Shear – free turbulent boundary layer • Conclusion

  3. Explicit Algebraic Methodology • Anisotropy tensor : Rodi 1976 • Weak Equilibrium : • Implicit algebraic equation :

  4. Accounting for the blocking effect of the wall Introduction of the Elliptic Blending into EASM • Explicit algebraic Model (EASM ) : Galerkin Projection :

  5. Blending function α orientation of the wall n : pseudo wall – normal vector EllipticBlending Reynolds stress model ( Manceau&Hanjalic,2002 ) • Based on elliptic relaxation concept of Durbin , 1991 • Numerical robustness and reduction of the number of equations • EB-RSM • obtained from elliptic relaxation equation : • At the wall • Far from the wall

  6. Standard EASM

  7. EllipticBlending EASM

  8. Choice of the basis • Incomplete representation unavoidable (even in 2D) • Several possibilities investigated • Selected Models Nonlinear EB-EASM #1 b= β1S+β2(SW-WS)+β3(S²-1/3{S²}I) • Exact representation in 1D • Exact representation in 2D (singularities possible) • Approximate representation in 3D Linear EB-EASM #2b= β1S+β2M • Approximate representation

  9. Galerkine Projection solutionof the form : New invariants introduced by the near-wall model Impingement Invariant Boundary layer Invariant Impinging jet Channel flow

  10. Results in channel flows and boundary layer EB-EASM#1 : b= β1S+β2(SW-WS)+β3(S²-1/3{S²}I) Channel flow at Reτ= 590 (Moser et al.) y+

  11. Boundary layer at Re= 20800 Lille experiment ij+ y+

  12. Channel flows (Moser et al.; Hoyas & Jimenez) y+

  13. EB-EASM#2 : b= β1S+β2 M Channel flow at Reτ= 590 y+

  14. y+

  15. Couette-Poiseuille Flows (DNS: Orlandi) y x h -h Uw y/h PT : Poiseuille-type flow IT : Intermediate-type flow CT : Couette-type flow

  16. Couette- type (CT) at Reτ= 207 Intermediate- type (IT) at Reτ= 182 y/h y/h Poiseuille- type (PT) at Reτ= 204 PT : Uw = 0.75 Ub IT : Uw = 1.2 Ub CT : Uw = 1.5 Ub

  17. Shear free turbulent boundary layer Nonlinear models : EB-EASM#1 b= β1S+β2(SW-WS)+β3(S²-1/3{S²}I) S=W= 0 everywhere in the boundary layer b= 0

  18. Linear models : EB-EASM#2 : b= β1S+β2 M b= 0 • Far from the wall : • at the wall :

  19. CONCLUSION • Introduction of wall blocage: • Through invariants involving • Implications in terms of tensorial representation • Polynomial representation is not possible with less than 6-term bases • Singularities may be faced • Applications to channels flows, boudary layers, Couette-Poiseuille flows: • No singularities faced • Accurate representation of the anisotropy • Simplified model (2-term basis) • Linear model • Partial representation of the anisotropy • 2-component limit • Similar to the V2F model, but with more physics • More complex flows

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