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Two-Point Homogeneous Turbulence

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Turbulent Flows

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Abstract

The equations for mean moments as required for modeling have been investigated in Chapter 2 with eddy-viscosity type closures. Only the mean-flow equations were solved, together with transport equations for one or two scalar quantities (like K and ε) describing characteristic time and length scales of turbulence which are processed throughout the flow without requiring detailed forms adequate to a particular zone of the flow. The allowed unknowns were the mean pressure and the mean velocity, and the scalar quantities. Unfortunately, such models, although bringing significant results from an engineering point of view, suffer from serious drawbacks, most of them being due either to the eddy-viscosity hypothesis or to the second equation for a turbulent quantity, that of e for instance. We must therefore consider classes of models which solve these unsatisfactory aspects, even though they are limited to particular situations. This is what is done in Chapter 3 where we assume the homogeneity of the mean flow, i.e. its translational invariance. In chapter 4 where the eddy-viscosity assumption of Chapter 2 will be removed, the information gathered in Chapter 3 will be used for the construction of Reynolds-stress-equation (also called second-moment) models (RSM).

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Piquet, J. (1999). Two-Point Homogeneous Turbulence. In: Turbulent Flows. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03559-7_3

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