ZDES Simulation and Spectral Analysis of a High-Reynolds-Number Out-of-Equilibrium Turbulent Boundary Layer

A test-case for the assessment of Zonal Detached Eddy Simulation (ZDES) mode 3 [which corresponds to a Wall-Modelled Large Eddy Simulation approach (WMLES)] for turbulent boundary layers in pressure gradient conditions is presented. The demanding test-case corresponds to an experiment at high Reynolds number, reaching up to \(Re_\theta \approx 13000\), probably too expensive for Direct Numerical Simulation or Wall-Resolved Large Eddy Simulation, but still affordable using ZDES mode 3 (WMLES). At the considered station, the boundary layer is in out-of-equilibrium conditions. The presented results prove the advantage of the scale-resolving approach, the ZDES mode 3, with respect to the RANS approach, as evidenced by the better representation observed for the mean velocity and Reynolds stress profiles, in particular in the outer layer where non-canonical effects are more evident. Thanks to the resolved turbulence, a more physically realistic flow is predicted by ZDES mode 3 and more in depth analysis of turbulence is accessible. In particular, spectral analysis of turbulence is performed in this study, and a scale-dependent convection velocity is also assessed for the first time with a hybrid RANS/LES approach in out-of-equilibrium conditions. Such analysis allow to identify some features of the turbulent scales distribution within the boundary layer, which seem responsible for some uncommon features observed in the present mean flow.