Large-eddy simulation of airfoil flow near stall condition at Reynolds number 2.1 × 106

Abstract

This paper investigates an airfoil flow involving a turbulent transition and separations near the stall condition at a high Reynolds number Rec = 2.1 × 106 (based on the freestream velocity and the airfoil chord) and provides the wall-resolved large-eddy simulation (LES) database for near-wall models in LES. The present results are compared with the existing experimental and computational data. The wall-resolved LES with the finest mesh (Δξ+,Δη+,Δζ+: chordwise, wall normal, spanwise ≲25, 0.8, 13) and the widest spanwise extent (approximately 5% of the chord length) resolves the key phenomena of the flow (i.e., laminar separation, transition to turbulence, turbulent reattachment, turbulent boundary layer development, and turbulent separation) and well predicts turbulence statistics. The present LES also clarifies unsteady flow features associated with shear-layer instability: the high frequency unsteadiness of St ≃ 130 (based on the freestream velocity and the airfoil chord) at the laminar separation bubble near the leading edge and low frequency unsteadiness of St ≃ 2 at the turbulent separation near the trailing edge. The characteristic frequencies can be scaled to 0.035 and 0.033 by the local momentum thickness and the shear layer velocity which are similar to the natural frequency of the laminar and turbulent shear layer, respectively. With regard to the near-wall modeling in LES, the obtained database indicates that the pressure-gradient term in the mean streamwise-momentum equation is not negligible at the laminar and turbulent separated regions. This fact suggests that the widely used equilibrium wall model is not sufficient, and the inclusion of the pressure-gradient term is necessary for wall modeling in LES of such an airfoil flow. Additionally, influences of computational mesh resolution and spanwise extent on the computational results in wall-resolved LES are investigated.