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Turbulence and Its Modelling

  • Chapter
Unsteady Computational Fluid Dynamics in Aeronautics

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 104))

Abstract

Averaging procedures used to form the Unsteady Reynolds Averaged Navier-Stokes (URANS) and Large Eddy Simulation (LES) equations are outlined. Also, turbulence modelling hierarchies for unsteady flows are presented. These range from URANS to DNS (Direct Numerical Simulation). The grid requirements for different approaches are also discussed. The LES models that are used for results in later chapters are given, along with details of others. Different types of LES filters are outlined. Their potential strong impact on results is discussed. A hierarchy of key elements for industrial LES is proposed. Notably, for flows without transition, the actual explicit LES model comes low down. More the key element is the numerical schemes discussed in Chap. 3. Key hybrid RANS-LES approaches are given. The advantages and disadvantages of these are outlined. The discussion shows that considerable expertise is needed to safely use hybrid RANS-LES techniques. Hence, the need for best practice guidelines is proposed. Methods for generating turbulence inflow are outlined. It is shown that many of these have limited applicability to complex engineering systems and so suitable strategies proposed.

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Notes

  1. 1.

    For hypersonic and highly compressible flows, where the turbulent fluctuations lead to substantial density fluctuations, it can be necessary to use Favre averaged RANS equations. This involves making density weighted averages. Hence, with this process, for example, \(\bar{\phi} = \frac{\int_{\tiny{-t_{l}/2}} ^{\tiny{t_{l}/2}} \rho (t ) \phi (t )dt }{\int_{\tiny{-t_{l}/2}} ^{\tiny{t_{l}/2}} \rho (t )dt } = \frac{\overline{\rho\phi }}{\bar{\rho}} \).

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Tucker, P.G. (2014). Turbulence and Its Modelling. In: Unsteady Computational Fluid Dynamics in Aeronautics. Fluid Mechanics and Its Applications, vol 104. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7049-2_3

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