Delayed detached-eddy simulations of NACA wing sections using spectral elements

We develop hybrid RANS–LES strategies within the spectral element code Nek5000 based on the (Formula presented.) SST turbulence model. We chose airfoil sections with chord-based Reynolds number on the order of (Formula presented.), in both attached and stalled conditions, as our target problem to comprehensively test the solver accuracy and performance. Verification and validation of the (Formula presented.) SST model are performed for two reference cases: for the zero-pressure gradient boundary layer developing on a flat plate and for mild adverse-pressure gradient boundary layers developing on suction side of NACA0012. The (Formula presented.) SST model shows good grid convergence characteristics, at par or better in comparison to existing reference results. The results also show good corroboration with existing experimental and numerical datasets for low incoming flow angles. A small discrepancy appears at higher angle in comparison with the experiments, which is in line with our expectations from an RANS formulation. Building on this foundation, we construct a hybrid RANS–LES framework based on the Delayed Detached-Eddy Simulation (DDES) approach. DDES captures both the attached and separated flow dynamics well when compared with available numerical datasets. We demonstrate that for the hybrid approach a high-order spectral element discretization converges faster (i.e. with less resolution) and captures the flow dynamics more accurately than representative low-order approaches. We also revise some of the guidelines on sample size requirements for statistics convergence for massively separated flow within the current numerical framework. Finally, we analyse some of the observed discrepancies of our unconfined DDES at higher angles with the experiments by evaluating the ‘blocking’ effect of wind tunnel walls. We carry out additional simulations for confined domains and assess the observed differences as a function of Reynolds number.