A seamless hybrid RANS-LES model based on transport equations for the subgrid stresses and elliptic blending

Atabak Fadai-Ghotbi (1) , Christophe Friess (1) , Remi Manceau (2, 1) , Jacques Borée (1)

1 PPrime [Poitiers] - Institut Pprime [UPR 3346]
2 CNRS - Centre National de la Recherche Scientifique

The aim of the present work is to develop a seamless hybrid Reynolds-averaged Navier-Stokes RANS large-eddy simulation LES model based on transport equations for the subgrid stresses, using the elliptic-blending method to account for the nonlocal kinematic blocking effect of the wall. It is shown that the elliptic relaxation strategy of Durbin is valid in a RANS steady as well as a LES context unsteady. In order to reproduce the complex production and redistribution mechanisms when the cutoff wavenumber is located in the productive zone of the turbulent energy spectrum, the model is based on transport equations for the subgrid-stress tensor. The partially integrated transport model PITM methodology offers a consistent theoretical framework for such a model, enabling to control the cutoff wavenumber c , and thus the transition from RANS to LES, by making the C 2 coefficient in the dissipation equation of a RANS model a function of c. The equivalence between the PITM and the Smagorinsky model is shown when c is in the inertial range of the energy spectrum. The extension of the underlying RANS model used in the present work, the elliptic-blending Reynolds-stress model, to the hybrid RANS-LES context, brings out some modeling issues. The different modeling possibilities are compared in a channel flow at Re = 395. Finally, a dynamic procedure is proposed in order to adjust during the computation the dissipation rate necessary to drive the model toward the expected amount of resolved energy. The final model gives very encouraging results in comparison to the direct numerical simulation data. In particular, the turbulence anisotropy in the near-wall region is satisfactorily reproduced. The contribution of the resolved and modeled fields to the Reynolds stresses behaves as expected: the modeled part is dominant in the near-wall zones RANS mode and decreases toward the center of the channel, where the relative contribution of the resolved part increases. Moreover, when the mesh is modified, the amount of resolved energy changes but the total Reynolds stresses remain nearly constant.

Domaines: Milieux fluides et réactifs

Atabak Fadai-Ghotbi, Christophe Friess, Remi Manceau, Jacques Borée. A seamless hybrid RANS-LES model based on transport equations for the subgrid stresses and elliptic blending. Physics of Fluids, 2010, 22 (5), pp.055104. ⟨10.1063/1.3415254⟩. ⟨hal-02132038⟩