Turbulence is an unsteady three-dimensional phenomenon. Its nature is such that large eddies are generated by the mean flow. Generally, the energy from these is dissipated by successively smaller eddies (note, reverse energy cascades, i.e. transfer from smaller to larger scales, can also occur in complex turbulent flows). This is called the turbulence energy cascade. The larger eddies (integral length scales) are a strong function of the local geometry and flow system, but the smaller eddies (near the Kolmogorov scale) are more universal in nature. The time scales relating the integral length scales are approximately equal to the ratio of the flow system characteristic size, L, to a characteristic velocity scale \( {U_0}\left( {i.e.t = L/{U_0}} \right) \) The Kolmogorov time scale can be evaluated as \( \sqrt {{\mu /\rho \varepsilon }} \), where ε is the viscous dissipation. Most engineering turbulence models, based on solving the RANS (Reynolds Averaged Navier-Stokes) equations, try to model both the effects of the unsteady larger and smaller turbulence scales. Since the dynamics of the larger scales are not so universal, their success is highly flow dependent. This lack of universality of such models has resulted in the availability of a wide range of turbulence models and modelling strategies. These will now be reviewed in an unsteady flow-modelling context. After this, the unsteady RANS models used in the Case Studies to be shown later will be presented.


Turbulence Model Large Eddy Simulation Integral Length Scale Stagnation Region RANS Region 
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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Paul G. Tucker
    • 1
  1. 1.Fluid Dynamics Research CentreThe University of WarwickUK

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