A seamless hybrid RANS/LES model based on transport equations for the subgrid stresses and elliptic blending
Résumé
The aim of the present work is to develop a seamless hybrid RANS-LES model, using the elliptic blending method to account for the kinematic wall blocking effect. In order to reproduce the complex production and redistribution mechanisms when the cutoff wavenumber is located in the productive region of the turbulent spectrum, the model is based on transport equations for the subgrid stress tensor. The PITM (Partially Integrated Transport Model) methodology offers a consistent theoretical framework for such a model, enabling to control the cutoff wavenumber kappac, and then the transition from RANS to LES, by making the Ceps2 coefficient in the dissipation equation of a RANS model a function of kappac. The extension of the underlying RANS model used in the present work, the elliptic blending Reynolds-stress model (EB-RSM), to the hybrid RANS-LES context, brings out some modelling issues which are discussed in the paper. The different modelling possibilities are tested in a channel flow at Retau=395. The final model gives encouraging turbulent statistics. In particular, the anisotropy of turbulence in the near-wall region is satisfactorily reproduced, although it is far from perfectly matching the DNS results. The contribution of the resolved and modelled part to the Reynolds stresses behaves as expected: the modelled part is dominant in the near-wall zone (RANS mode) and decreases toward the centre of the channel, where the resolved part in turn becomes dominant (LES mode). Moreover, when the mesh is refined, more energy is resolved, but the total Reynolds stresses remain approximately constant. The mean velocity profile is satisfactorily reproduced and weakly dependant of the mesh, contrary to what is observed in LES with a dynamic Smagorinsky model.