Contribution to the study of second order turbulence models
This work is devoted to one-point turbulence modelling for incompressible turbulent flows. The behaviour of classical second-order closures for homogeneous turbulence was first observed in the case of flows with superimposed rotation. This study was foccussed on pressure-strain modelling and allowed a discussion of objectivity and realisability constraints and of verification of rapid distorsion limit. The closure models were performed on classical homogeneous flows and compared to direct numerical simulations. The difficulty of predicting strongly rotating flows with classical models lead to the development of an homogeneous model based on a transport equation for the pressure-strain correlation. This equation was obtained with the help of a spectral description of turbulence. Three closure hypotheses were formulated for the corresponding dissipative, slow and rapid terms, according to the classical terminology for Reynolds-stress equations. The model's performances were compared to those of more classical ones on the same homogeneous test case as before, as well as on rapidly distorted flows. The calculations show better behaviour than classical models especially as for as rapid approximation is concerned. The influence of walls and inhomogeneous mecanisms are nevertheless two relevant effects one has to take into account for predicting realistic flows. The second part of the work is devoted to their analysis. The model presented earlier was then adapted to the fully-developed channel flow. The unusual level of this type of closure makes its application difficult to three-dimensional flows. Therefore the last part of this work is concerned with the validation of classical low-Reynolds closures to simulate flows in complex geometries. One of the second order closure previously examined in the case of the channel flow is validated in a three-dimensional test case characterized by a strong streamline vortex.