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Physical Analysis of an Anisotropic Eddy-Viscosity Concept for Strongly Detached Turbulent Unsteady Flows

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IUTAM Symposium on Unsteady Separated Flows and their Control

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 14))

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A tensorial eddy-viscosity turbulence model is developed in order to take into account of the structural anisotropy appearing between the mean strain-rate tensor and the Reynolds turbulent stresses in strongly detached high Reynolds number flows. In the framework of the Organised Eddy Simulation, a physical investigation of the misalignment of these two tensor principal directions is performed by means of phase-averaged 3C-PIV measurements in the near-wake of a circular cylinder at Reynolds number 1.4 × 105. Considering the stress—strain misalignment as a local sign of the turbulence non-equilibrium, anisotropic criteria are derived. This leads to a tensorial eddy-viscosity concept which is introduced in the turbulent stress constitutive law. Additional transport equations for the misalignment criteria are derived from a degenerated SSG second order closure scheme. A two-dimensional version of the present model is implemented in the NSMB solver on the basis of a two-equation k−ε isotropic OES model. Numerical simulation results are compared to an experimental dataset concerning the incompressible flow past a NACA0012 airfoil at 20 degrees of incidence and Reynolds number 105.

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References

  1. A. BOUHADJI, S. BOURDET, M. BRAZA, Y. HOARAU, P. RODES and G. TZABIRAS. Turbulence modelling of unsteady flows with a pronounced periodic character. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 81:87–96, Springer, 2002.

    Google Scholar 

  2. M. BRAZA, R. PERRIN and Y. HOARAU. Turbulence properties in the cylinder wake at high Reynolds number. J. Fluids Struct., 22:755–771, 2006.

    Article  Google Scholar 

  3. R. PERRIN, M. BRAZA, E. CID, S. CAZIN, A. SEVRAIN, M. STRELETS, M. SHUR, Y. HOARAU, A. BARTHET, G. HARRAN and F. MORADEI. 3D circular cylinder. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 94:299–312, Springer, 2006.

    Article  Google Scholar 

  4. J. BOUSSINESQ. Théorie de l'écoulement tourbillant. Mém. prés. par div. Sav. à l'Acad. Sci., Paris, 23:46–50, 1877.

    Google Scholar 

  5. P.S. KLEBANOFF. Characteristics of Turbulence in a Boundary Layer with Zero Pressure Gradient. NACA Technical Note, 3178, 1954.

    Google Scholar 

  6. P.A. DURBIN and B.A. PETTERSSON REIF. Statistical Theory and Modeling for Turbulent Flow. Wiley, Chichester, 2001.

    Google Scholar 

  7. G. JIN and M. BRAZA. A two-equation turbulence model for unsteady separated flows around airfoils. AIAA J., 32(11):2316–2320, 1994.

    Article  ADS  Google Scholar 

  8. S.B. POPE. A more general effective-viscosity hypothesis. J. Fluid Mech., 72:331–340, 1975.

    Article  MATH  ADS  Google Scholar 

  9. T.B. SHIH, J. ZHU and J.L. LUMLEY. A realizable Reynolds stress algebraic equation model. NASA TM 105993, ICOMP-92-27, CMOTT-92-14, 1993.

    Google Scholar 

  10. T. JONGEN and T.B. GATSKI. General explicit algebraic stress relations and best approximation for three-dimensional flows. Int. J. Engr. Sci., 36:739–763, 1998.

    Article  Google Scholar 

  11. C.G. SPEZIALE and X.H. XU. Towards the development of second-order closure models for non-equilibrium turbulent flows. Int. J. Heat Fluid Flow, 17:238–244, 1996.

    Article  Google Scholar 

  12. T.B. GATSKI and C.G. SPEZIALE. On explicit algebraic stress models for complex turbulent flows. J. Fluid Mech., 254:59–78, 1993.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. S. WALLIN and A.V. JOHANSSON. An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows. J. Fluid Mech., 403:89, 2000.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  14. W. HAASE, V. SELMIN and B. WINZELL. Progress in computational flow-structure interaction. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 81, Springer, 2002.

    Google Scholar 

  15. W. HAASE, B. AUPOIX, U. BUNGE and D. SCHWAMBORN. FLOMANIA — A European initiative on flow physics modelling. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 94, Springer, 2006.

    Google Scholar 

  16. R. BOURGUET, M. BRAZA, R. PERRIN and G. HARRAN. Anisotropic eddy-viscosity concept for strongly detached unsteady flows. AIAA J., 45(5):1145–1149 2007.

    Article  ADS  Google Scholar 

  17. H.S. KANG and C. MENEVEAU. Effect of large-scale coherent structures on subgrid-scale stress and strain-rate eigenvector alignments in turbulent shear flow. Phys. Fluids, 17:055103, 2005.

    Article  ADS  Google Scholar 

  18. R. PERRIN, M. BRAZA, E. CID, S. CAZIN, F. MORADEI, A. BARTHET, A. SEVRAIN and Y. HOARAU. Near-wake turbulence properties in the high Reynolds incompressible flow around a circular cylinder by 2C and 3C PIV. 6th ERCOFTAC International Symposium on Engineering Turbulence Modelling and Measurements - ETMM6, proceedings, 2005, J. Flow Turb. Combustin print.

    Google Scholar 

  19. C.G. SPEZIALE, S. SARKAR and T.B. GATSKI. Modeling the pressure strain correlation of turbulence: an invariant dynamical systems approach. J. Fluid Mech., 227:245–272, 1991.

    Article  MATH  ADS  Google Scholar 

  20. J.C. HUNT, A. WRAY and P. MOIN. Eddies, stream, and convergence zones in turbulent flows. Center for Turbulence Research Report,CTR-S88, 1988.

    Google Scholar 

  21. A.J. REVELL, S. BENHAMADOUCHE, T. CRAFT, D. LAURENCE and K. YAQOBI. A stress-strain lag eddy viscosity model for unsteady mean flow. Eng. Turb. Model. Exp., 6:117– 126, 2005.

    Article  Google Scholar 

  22. J.B. VOS, E. CHAPUT, B. ARLINGER, A. RIZZI and A. CORJON. Recent advances in aerodynamics inside the NSMB (Navier–Stokes Multi-Block) consortium, In 36th Aerospace Sciences Meeting and Exhibit, AIAA Paper 0802, Reno, 1998.

    Google Scholar 

  23. A. BOUHADJI, S. BOURDET, M. BRAZA, Y. HOARAU, P. RODES and G. TZABIRAS. Turbulence modelling of unsteady with a pronounced periodic character. Progress in Computational Flow-Structure Interaction, Notes on Numerical Fluid Mechanics, 81:251–260, 2002.

    Google Scholar 

  24. K.Y. CHIEN. Predictions of channel and boundary-layer flows with a low-Reynolds-number turbulence Model. AIAA J 20(1) 33–38 1982.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  25. E. BERTON, D. FAVIER et C. MARESCA. Progress in computational flow-structure interaction. Notes on Numerical Fluid Mechanics, 81, Springer, 2002.

    Google Scholar 

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Acknowledgments

The numerical implementation was performed in collaboration with Dr. J.B. Vos (Computational Fluid and Structure Engineering, CFSE and Ecole Polytechnique Fédérale de Lausanne, EPFL) and Dr. Y. Hoarau (Institut de Mécanique des Fluides et des Solides, IMFS de Strasbourg) who are gratefully acknowledged. The calculations were performed at the Centre Informatique National de l'Enseignement Supérieur (CINES), the Institut du Développement et des Ressources en Informatique Scientifique (IDRIS) and the Centre Interuniversitaire de Calcul de Toulouse (CICT). The first author was financially supported by the Centre National de la Recherche Scientifique (CNRS) and the Délégation Générale pour l'Armement (DGA).

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Authors and Affiliations

  1. Institut de Mécanique des Fluides de Toulouse, Unité Mixte de Recherche CNRS 5502, Allée du Prof. Camille Soula, Toulouse, 31400, France

    M. Braza

  2. Institut de Mecanique des Fluides de Toulouse, UMR 5502 CNRS-INPT/UPS, Allee du Prof. Camille Soula, Toulouse, 31400, France

    R. Bourguet, M. Braza, R. Perrin & G. Harran

  3. Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA, 02139, USA

    R. Bourguet

Authors
  1. R. Bourguet
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  2. M. Braza
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  3. R. Perrin
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  4. G. Harran
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Editors and Affiliations

  1. Institut de Mécanique des Fluides de Toulouse, Unité Mixte de Recherche CNRS 5502, Allée du Prof. Camille Soula, Toulouse, 31400, France

    Marianna Braza

  2. Division of Biological Engineering, Monash University, Clayton VIC, 3800, Australia

    Kerry Hourigan

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Bourguet, R., Braza, M., Perrin, R., Harran, G. (2009). Physical Analysis of an Anisotropic Eddy-Viscosity Concept for Strongly Detached Turbulent Unsteady Flows. In: Braza, M., Hourigan, K. (eds) IUTAM Symposium on Unsteady Separated Flows and their Control. IUTAM Bookseries, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9898-7_33

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