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The hybrid Large-Eddy/Reynolds-Averaged Navier-Stokes (LES/RANS) and RANS simulations are used to investigate the properties of subsonic flow over NACA 0012 airfoils undergoing static and dynamic stall conditions (M=0.1, α=16.7°, Rec=1.0×10 6 ). In the simulations of NACA 0012 airfoil at static stall case, Menter’s SST model predicts an attached flow at the leading edge, whereas the Gieseking’s LES/RANS model on a coarser mesh predicts a massively separated flow characterized by the stabilization of a detached leading edge vortex near the trailing edge. The predictions by Gieseking’s model on a coarse mesh agree closely with PIV measurements of mean velocity, the Reynolds axial stress and the Reynolds normal stress, but over-predict the magnitude of the Reynolds shear stress. However, Gieseking’s model on a fine mesh predicts a more attached flow because the under-resolved LES on the fine mesh (but not fine enough as required in a wall-resolved LES) fails to reproduce the cascade process at the smaller scale and results in an overlyenergetic boundary layer near leading edge which resists and delays the separation. In 3D simulations of dynamic stall case where the NACA 0012 airfoil is dynamically pitching about its quarter-chord at a reduced frequency, kr=0.1, Gieseking’s model on a coarse mesh in spanwise direction correctly predicts response of the massive separation at static stall angle of 16.7° during downstroke pitching, but it also predicts some leading edge separation which is not present in the experiment during upstroke pitching. Mesh refinement in the spanwise direction helps reducing the level of leading edge separation during upstroke pitching, but results in an under-separated flow solution for downstroke response, which is consistent with what happens in the static stall case and the reason is also similar. By introducing a grid correction function in the definition of outer layer turbulence length scale, Salazar’s fix takes grid resolution into consideration while determining the RANS to LES transition. The inclusion of Salazar’s fix to Gieseking’s model delays the leading edge separation during upstroke pitching, but it also introduces a too-attached flow for downstroke response.

This work presents results from Reynolds-averaged Navier-Stokes and hybrid Largeeddy/Reynolds-averaged Navier-Stokes (LES/RANS) simulations of two flow cases: a turbulent flow past an Aerospatiale A-Airfoil near stall at a chord Reynolds number, ( , , ), and a flow past NACA 0012 airfoil under static and dynamic stall conditions ( , , ). In the flow past the A-Airfoil, the suction side boundary layer is complex: it includes a laminar separation bubble by an adverse pressure gradient, a turbulent reattachment and a turbulent separation near trailing edge. Comparisons with surface skin-friction coefficient and pressure coefficient distribution are generally in good agreement with experimental measurements. Comparisons with experimental velocity profile data and Reynolds-stress data are also generally favorable. Leading-edge laminar separation and turbulent reattachment is predicted when the Menter-Langtry correlation-based transition model is used in combination with either RANS or LES/RANS strategies, but the level of trailing-edge separated is under-predicted, relative to experimental data and to results obtained without the transition model. In the flow past NACA 0012 airfoil case, the airfoil was dynamically pitched about its quarter-chord at a reduced frequency, . Computational results from RANS simulations show that the flow remains attached in the leading edge region above the static stall angle during upstroke, whereas it remains separated below the static stall angle during downstroke. These results match the experimental measurement well. For static stall case of flow past NACA 0012 airfoil, results from the LES/RANS simulation are in much better agreement with the experimental data compared with those from RANS simulations. The RANS models predict flow attachment at the leading edge, whereas the LES/RANS model predicts leading edge flow separation, with the leading-edge vortex stabilized upstream of the trailing edge.

Leading edge vortex (LEV) formation, which is initiated by separation at the leading edge, depends on airfoil shape, Reynolds number, rate of translation/rotation, amplitude of motion and the pitch axis location. The Leading Edge Suction Parameter (LESP) derived from inviscid theory, serves to predict the onset LEV formation for any unsteady motion using a critical value that depends on the airfoil shape and Reynolds number of operation. In this paper, the critical LESP value is determined for different airfoils over a range of Reynolds numbers. The SD7003 airfoil was used as a baseline and modified airfoils were derived by altering the leading edge radius, keeping maximum thickness unchanged. Increasing the leading edge radius resulted in higher critical LESP values, demonstrating that separation is delayed for flow over a more rounded leading edge since it can support more suction. The effect of Reynolds number was more complicated, with the critical LESP decreasing from Re = 5,000 to Re = 100,000, and increasing after. Hence conditions which promote and suppress leading edge vortex formation were identified, and the critical LESP values were made available over a broad range of parameters, which can be used for low-order prediction and modeling of complicated, vortex-dominated flows.