Continuum Mechanics and Thermodynamics

, Volume 12, Issue 2, pp 79–94 | Cite as

Balance equation of the generalised sub-grid scale (SGS) turbulent kinetic energy in a new tensorial dynamic mixed SGS model

  • F. Gallerano
  • E. Napoli
Original Articles

A new dynamic model is proposed in which the eddy viscosity is defined as a symmetric second rank tensor, proportional to the product of a turbulent length scale with an ellipsoid of turbulent velocity scales. The employed definition of the eddy viscosity allows to remove the local balance assumption of the SGS turbulent kinetic energy formulated in all the dynamic Smagorinsky-type SGS models. Furthermore, because of the tensorial structure of the eddy viscosity the alignment assumption between the principal axes of the SGS turbulent stress tensor and the resolved strain-rate tensor is equally removed, an assumption which is employed in the scalar eddy viscosity SGS models.

The proposed model is tested for a turbulent channel flow. Comparison with the results obtained with other dynamic SGS models (Dynamic Smagorinsky Model, Dynamic Mixed Model and Dynamic K-equation Model) shows that the tensorial definition of the eddy viscosity and the removal of the local balance assumption of the SGS turbulent kinetic energy considerably improves the agreement between results obtained with Large Eddy simulation (LES) and Direct Numerical Simulations (DNS), respectevely.


Large Eddy Simulation Direct Numerical Simulation Eddy Viscosity Turbulent Channel Flow Smagorinsky Model 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • F. Gallerano
    • 1
  • E. Napoli
    • 2
  1. 1.Dipartimento di Ingegneria Idraulica, Trasporti e Strade. Università di Roma “La Sapienza”. Via Eudossiana 18, Roma, ItalyIT
  2. 2.Dipartimento di Ingegneria Idraulica ed Applicazioni Ambientali. Università di Palermo. Viale delle Scienze, Palermo, ItalyIT

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