The outer layer dynamics of a high-Reynolds-number boundary layer recovering from non-equilibrium is studied utilising the multi-resolution approach of zonal detached eddy simulation mode 3. The non-equilibrium conditions are obtained from a boundary layer separation over a rounded step enhancing the turbulent production, and recovery happens during redevelopment after reattachment at high Reynolds numbers ( $Re_{\theta,max}\approx 24{,}000$ ). Most of the outer layer turbulence is resolved by the simulation, which reproduces accurately the experimental boundary layer relaxation. The spectral analysis of streamwise velocity fluctuations and turbulent kinetic energy (TKE) production evidences the different turbulent content distribution at separation and within the redevelopment region, at which very large-scale motions are identified with streamwise wavelengths up to $\lambda _x = 9\delta$ , where $\delta$ is the boundary layer thickness. The redevelopment of the boundary layer is analysed in terms of the persistence of a secondary peak in the TKE production and the evolution of the wall-shear stress statistics. The skewness and probability density function of the skin friction show a slower relaxation than the downstream flow fraction. This confirms the long-lasting impact of perturbations of the outer layer in high-Reynolds-number wall-bounded flows. This persistent non-equilibrium state is suggested to be the reason for the reported lack of accuracy of the considered Reynolds-averaged Navier–Stokes models in the relaxation region.
Two test cases for the assessment of ZDES mode 3 (WMLES approach) in both pressure gradient conditions and mild boundary layer separation are presented. For both of them, the confinement effects of side wall boundary layers from the reference experiments are non negligible and they are taken into account in two dimensional simulations by means of a top wall geometry modification. A better agreement in the pressure coefficient with experimental data results from this manipulation. Results from the first test case evidence the advantage of resolving turbulence. A more physical flow is predicted in such a case and more in depth analysis of turbulence is possible, for instance spectral analysis as presented in this work. RANS results for the boundary layer separation case are presented showing the improvement on the pressure coefficient prediction thanks to the top wall geometry modification. At the time of the redaction of this manuscript, ZDES results for the boundary layer separation case are not available yet. However, the initial run of the ZDES simulation is very encouraging and suggests that a significant improvement over RANS predictions might be achieved.
The aim of this work is to contribute to the understanding of sensitivity of boundary layers to the upstream boundary condition and history effects for both laminar and fully turbulent states in equilibrium conditions as well as some nonequilibrium turbulent boundary layers. Solutions of the two-dimensional boundary layer equations are obtained numerically for this study together with the Reynolds-averaged Navier-Stokes approach for turbulence modeling. The external pressure gradient is imposed through an evolution of the external velocity of the form Ue∝(x−x0)m, and boundary layers are initialized from a profile giving a perturbed shape factor. It is found that laminar boundary layers require very long distances for convergence toward the nondisturbed profiles in terms of the initial boundary layer thickness (∼104δin) and that this distance is dependent on m. In turbulent boundary layers, much shorter distances, although still large (∼102δin), are observed and they are also dependent on m. The maximum adverse pressure gradient for which convergence to a reference solution is possible is also studied finding that there is no limit for attached laminar boundary layers, whereas turbulent boundary layers do not converge once they are out of equilibrium. The convergence distances in turbulent boundary layers are also studied in terms of the turnover length (δUe+) because it has been shown to be more appropriate to refer the convergence distance to this length rather than the boundary layer thickness. The values for convergence using this criterion are extended to pressure gradient boundary layers. Moreover, an equivalent criterion is proposed and studied for laminar boundary layers based on the viscous characteristic time.
A robust hybrid Reynolds-Averaged Navier–Stokes (RANS)/Large Eddy Simulation (LES) strategy is proposed for a treatment of attached turbulent boundary layers with the RANS Menter Shear Stress Transport (SST) k–ω model irrespective of the grid density and pressure gradient and a quick RANS/LES switching after separation which is automatic, i.e., without shielding-related meshing constraints for the user. This formulation of Zonal Detached Eddy Simulation (ZDES) mode 2 (2020) initially based on the Spalart–Allmaras RANS model relies on local flow quantities providing a RANS shielding identified as a critical limitation of most popular RANS/LES models. The flow sensors are adapted for the SST context and calibrated on RANS boundary-layer-equation solutions over a wide Reynolds-number and pressure-gradient range approaching flow separation and on full Navier–Stokes RANS solutions with separations. The Reynolds-invariant protection includes the outer part of the boundary layer profile, crucial in adverse pressure gradients but ignored by older protection functions such as fd of Delayed Detached Eddy Simulation (DDES) (2006). The shielding resistance to infinite mesh refinement is demonstrated in a flat-plate boundary layer. A second test case involving a backward-facing step shows that the enhanced protection has no detrimental impact on the quick RANS/LES switching thanks to the efficient detection of separation and reinforced destruction of eddy viscosity in gray areas. This indicates that the proposed ZDES mode 2 (2020) Menter SST k–ω achieves safe and automatic RANS shielding of attached boundary layers and efficient RANS/LES switching in massive flow separations, paving the way for its application.
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.
