Advanced simulations of turbulent boundary layers under pressure-gradient conditions

Abstract

A high-Reynolds-number turbulent boundary layer experiencing pressure gradients is simulated with Reynolds-averaged Navier-Stokes (RANS) and hybrid RANS/LES (Large Eddy Simulation) advanced turbulence modeling approaches, namely, two eddy viscosity models, two Reynolds Stress models (RSMs), and Zonal Detached Eddy Simulation (ZDES) mode 3 which corresponds to a wall-modeled LES approach. Such a study is the first of its kind to the authors’ best knowledge. The test-case considered is the experimental work of Cuvier et al. [“Extensive characterisation of a high Reynolds number decelerating boundary layer using advanced optical metrology,” J. Turbul. 18, 929–972 (2017)]. Some modifications of the top wall geometry have been proposed to take into account the blockage effect of the boundary layers developing over the wind tunnel side walls so that statistically two-dimensional simulations are possible. Comparisons have shown that there are some difficulties in properly predicting the mean skin friction and the Reynolds stresses in the adverse-pressure-gradient region for the ZDES and RSMs. The mean velocity profiles in this region are, however, poorly reproduced by all models. The atypical profiles experimentally observed at the beginning of the favorable-pressure-gradient region are well reproduced by RSMs, one eddy viscosity model, and ZDES for the mean velocity; however, only ZDES is able to satisfactorily predict the Reynolds stresses at this station. A spectral analysis of streamwise velocity fluctuations and Reynolds shear stress by means of ZDES has allowed us to identify external energetic turbulent structures at y ≈ 0.5δ and of size λx ≈ 3δ which are probably responsible for these atypical profiles. The present numerical test-case may constitute a development base for turbulence modeling under pressure gradient effects.