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In the same logic as we do for Boussinesq's hypothesis, we directly check here the closure hypothesis which is at the heart of this equation.Ī large number of papers have been already devoted to the development, validation and application of such turbulence models. This equation is widely used, but since it uses an hypothesis considered as almost “natural”, it has almost never been directly checked, and is widely considered as the strongest part of eddy viscosity model equations. The classical K transport equation assumes only one modelling hypothesis: the sum of two fluxes is proportional to the kinetic energy gradient. We present here an overview of these results, and complete them with new databases.įor one and two equations turbulence models, the eddy viscosity is given as function of the kinetic energy K and a transport equation for K is introduced to model the spatio-temporal turbulent transport of this quantity (for 2 equations models, such as K-ε or K-ω a second transport equation is given for εand ω, see Kolmogorov, 1942 and Jones and Launder, 1972). We have already undertaken such direct test using experimental complex flow ( Schmitt and Hirsch, 2000 2001a) or DNS of simple shear flow ( Schmitt and Hirsch 2001a, b). Despite of this, it has been quite rarely directly checked using experimental or numerical databases. This hypothesis is at the heart of eddy viscosity turbulence models, being their first main symplifying assumption. For most models, such as K-ε model ( Jones and Launder, 1972 Launder and Spalding, 1974) this relation is linear, the traceless part of the Reynolds stress tensor being proportional to the mean strain tensor, with the eddy viscosity as proportionality factor: this is Boussinesq's hypothesis ( Boussinesq, 1877). They are based on a constitutive equation, giving a relation between the Reynolds stress tensor and the mean velocity gradient tensor.
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Hirsch, in Engineering Turbulence Modelling and ExperimeINTRODUCTIONĮddy viscosity turbulence models are widely used for industrial, aeronautical, meteorological and oceanographical applications, among others (see Wilcox (1998) and Pope (2000) for reviews).
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