Subfilter-scale transport model for hybrid RANS/LES simulations applied to a complex bounded flow

The partially integrated transport modeling (PITM) method viewed as a continuous approach of hybrid Reynolds-averaged Navier-Stokes equations/large eddy simulations (RANS/LES) with seamless coupling is first recalled. In the present work, the subfilter stress model derived from the PITM method is considered and developed in a general formulation valid for free as well as bounded flows. Numerical simulations of the well-known, fully turbulent channel flows are first performed on coarse and medium grids for assessing the subfilter model and for studying the sharing out of the energy when the filter width is changed. The practical flow over two-dimensional periodic hills is then simulated on coarse and medium grids for illustrating the performances of the subfilter stress model. As a result, it is found that the subfilter stress model reproduces fairly well this complex flow governed by interacting turbulence mechanisms associated with separation, recirculation, reattachment, acceleration and wall effects. Overall, it provides velocity and turbulent stresses in good agreement with the reference data for both the grids. The effects of the grid refinement are also investigated in detail. The solution trajectories projected onto the plane formed by the second and third invariants allow to analyze the realizability of the turbulent stresses and to assess the flow anisotropy. Moreover, the simulation using the subfilter stress model reveals the detail of the instantaneous flow structures. For comparison purposes, the channel flow over two-dimensional hills is also predicted using a statistical Reynolds stress model (RSM) developed in the RANS methodology. In contrast to the subfilter stress model used in the LES methodology, it appears that the Reynolds stress model provides inaccurate results in spite of being one of the most advanced RANS model. This failure seems to be attributed to the inability of the RANS models to capture the large-scale dynamics in the separated shear layer.