Hybrid RANS/LES simulations of the turbulent flow over periodic hills at high Reynolds number using the PITM method

International audienceWe apply the partially integrated transport modeling (PITM) method with a stress transport subfilter model [Chaouat B, Schiestel R. A new partially integrated transport model for subgrid-scale stresses and dissipation rate for turbulent developing flows. Phys Fluids 2005:17] to perform continuous hybrid non-zonal RANS/LES numerical simulations of turbulent flows over two-dimensional periodic hills at high Reynolds number Re = 37,000 on coarse and medium meshes. The fine scale turbulence is described using a subfilter scale stress transport model deduced from PITM. This work extends the previous simulations of the turbulent flow over periodic hills performed at the lower Reynolds number Re = 10,595 [Chaouat B. Subfilter-scale transport model for hybrid RANS/LES simulations applied to a complex bounded flow. J Turbul 2010:11] to the higher value 37,000 considering that studying the effects of the Reynolds number on the turbulence field constitutes a new material that deserves interest in CFD. So that, the aim of this paper is to explore the extension of a PITM subfilter model to high Reynolds numbers where conventional LES is not any more accessible because of the highly consuming cost. The effects of the grid refinement at Re = 37,000 are investigated in detail through the use of different mesh sizes with a very coarse grid and with a several medium grids. For comparison purposes, the channel flow over 2D hills is also computed using a full statistical Reynolds stress transport model developed in RANS methodology. As a result of the simulations, it appears that the PITM simulations, although performed on coarse meshes, reproduce this complex flow governed by interacting turbulence mechanisms associated with separation, recirculation, reattachment, acceleration and wall effects with a relatively good agreement. The mean velocity and turbulent stresses are compared with reference data of this experiment at the flow Reynolds number Re = 37,000 [Rapp Ch, Manhart M. Flow over periodic hills – an experimental study. Exp Fluids 2011:51]. Some discrepancies are observed in the immediate vicinity of the lower wall for the coarse simulations but as it could be expected, the simulation performed on the medium mesh provides better results than those performed on the coarse meshes thanks to the higher resolution due to the grid refinement in the streamwise and spanwise directions that allows a better account of the three-dimensional character of the flow. As usual in LES calculations, the instantaneous large flow structures are investigated in detail providing some interesting insights into the structures of the present turbulent flow. Comparatively to the PITM simulation results, it is found that the RANS Reynolds stress model based on second moment closures fails to predict correctly this flow in several respects, although being one of the most advanced model in RANS methodology. Important discrepancies with the experimental data are noticed. This work suggests that the present subfilter-scale stress model derived form the PITM method is well suited for simulating complex flows at high Reynolds numbers, with a sufficient accuracy from an engineering point of view, even if the grids are not as so fine as those used in conventional LES, while at the same time allowing a drastic reduction of the computational cost. Beside, these calculations give some ideas on the influence of the Reynolds number on the flow