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Subgrid-Scale Stress Modelling Based on the Square of the Velocity Gradient Tensor

Abstract

A new subgrid scale model is proposed for Large Eddy Simulations in complex geometries. This model which is based on the square of the velocity gradient tensor accounts for the effects of both the strain and the rotation rate of the smallest resolved turbulent fluctuations. Moreover it recovers the proper y 3 near-wall scaling for the eddy viscosity without requiring dynamic procedure. It is also shown from a periodic turbulent pipe flow computation that the model can handle transition.

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References

  1. Lilly, D.K., A proposed modification of the germano subgrid-scale closure method. Phys. Fluids A 4(3) (1992) 633-635.

    Google Scholar 

  2. Wray, A.A. and Hunt, J.C.R., Algorithms for classification of turbulent structures. In: Proceedings of the IUTAM Symposium Topological Fluid Mechanics (1989) pp. 95-104.

  3. Metais, O. and Lesieur, M., Spectral large-eddy simulation of isotropic and stably stratified turbulence. J. Fluid Mech. 239 (1992) 157-194.

    Google Scholar 

  4. Lesieur, M. and Métais, O., New trends in large-eddy simulations of turbulence. Ann. Rev. Fluid Mech. 28 (1996) 45-82.

    Google Scholar 

  5. Lund, T.S. and Novikov, E.A., Parameterization of subgrid-scale stress by the velocity gradient tensor. In: Center for Turbulence Research, Annual Research Briefs (1992) pp. 27-43.

  6. Van Driest, E.R., On turbulent flow near a wall. J. Aero. Sci. 23 (1956) 1007-1011.

    Google Scholar 

  7. Moin, P. and Kim, J., Numerical investigation of turbulent channel flow. J. Fluid Mech. 118 (1982) 341-377.

    Google Scholar 

  8. Comte, P., Ducros, F., Silvestrini, J., David, E., Lamballais, E., Métais, O. and Lesieur, M., Simulation des grandes échelles d'écoulements transitionnels. In: AGARD Conference Proceedings 551 (1994) pp. 14/1-14/11.

  9. Ducros, F., Comte, P. and Lesieur, M., Large-eddy simulation of transition to turbulence in a boundary layer spatially developing over a flat plate. J. Fluid Mech. 326 (1996) 1-36.

    Google Scholar 

  10. Germano, M., Piomelli, U., Moin, P. and Cabot, W.H. A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3(7) (1991) 1760-1765.

    Google Scholar 

  11. Meneveau, C., Lund, T. and Cabot, W., A Lagrangian dynamic subgrid-scale model of turbulence. J. Fluid Mech. 319 (1996) 353-385.

    Google Scholar 

  12. Ghosal, S., Lund, T., Moin, P. and Akselvoll, K., A dynamic localization model for large-eddy simulation of turbulent flows. J. Fluid Mech. 286 (1995) 229-255.

    Google Scholar 

  13. Jansen, K., Unstructured-grid large-eddy simulation of flow over an airfoil. In: Center for Turbulence Research, Annual Research Briefs (1994) pp. 161-173.

  14. Nicoud, F., Ducros, F. and Schönfeld, T., Towards direct and large eddy simulations of compressible flows in complex geometries. In: Friedrich, R. and Bontoux, P. (eds), Notes on Numerical Fluid Mechanics, Vol. 64. Vieweg, Braunschweig (1998) pp. 157-171.

    Google Scholar 

  15. Ducros, F., Nicoud, F. and Schönfeld, T. Large-eddy simulation of compressible flows on hybrid meshes. In: Proceedings of the Eleventh Symposium on Turbulent Shear Flows, Grenoble, France, Vol. 3 (1997) pp. 28-1, 28-6.

    Google Scholar 

  16. Schönfeld, T. and Rudgyard, M., A cell-vertex approach to local mesh refinement for 3d Euler equations. AIAA Paper 94-0318 (1994).

  17. Eggels, J.G.M., Unger, F., Weiss, M.H., Westerweel, J., Adrian, R.J., Friedrich, R. and Nieuwstadt, F.T.M., Fully developed turbulent pipe flow: A comparison between direct numerical simulation and experiment. J. Fluid Mech. 268 (1994) 175-209.

    Google Scholar 

  18. Lele K.S., Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103 (1992) 16-42.

    Google Scholar 

  19. Schönfeld, T. and Rudgyard, M., Steady and unsteady flows simulations using the hybrid flow solver AVBP. AIAA J. 37(9) (1999) to appear.

  20. Nicoud, F.C., Poinsot, T.J. and Ha Minh, H., Direct numerical simulation of turbulent flow with massive uniform injection. In: Proceedings of the Tenth Symposium on Turbulent Shear Flows, The Pennsylvania State University, Vol. 3 (1995) pp. 29-13, 29-18.

  21. Comte-Bellot, G. and Corrsin, S., Simple Eulerian time correlation of full-and narrow-band velocity signals in grid generated, ‘isotropic’ turbulence. J. Fluid Mech. 48 (1971) 273-337.

    Google Scholar 

  22. Moin, P., Squires, K., Cabot, W. and Lee, S., A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids A 3(11) (1991) 2746-2757.

    Google Scholar 

  23. Dubois, T., Jauberteau, F. and Temam, R., Incremental unknowns, multilevel methods and the numerical simulation of turbulence. Comput. Methods Appl. Mech. Engrg. 159 (1998) 123-189.

    Google Scholar 

  24. Schlichting, H., Boundary Layer Theory. McGraw-Hill, New York (1979).

    Google Scholar 

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Nicoud, F., Ducros, F. Subgrid-Scale Stress Modelling Based on the Square of the Velocity Gradient Tensor. Flow, Turbulence and Combustion 62, 183–200 (1999). https://doi.org/10.1023/A:1009995426001

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  • DOI: https://doi.org/10.1023/A:1009995426001

  • turbulence
  • large eddy simulations
  • wall-bounded flow
  • unstructured mesh
  • transition