Direct numerical simulation of the flow around a wing section at moderate Reynolds number

Abstract

A three-dimensional direct numerical simulation has been performed to study the turbulent flow around the asymmetric NACA4412 wing section at a moderate chord Reynolds number of Rec=400,000, with an angle of attack of AoA=5∘. The mesh was optimized to properly resolve all relevant scales in the flow, and comprises around 3.2 billion grid points. The incompressible spectral-element Navier–Stokes solver Nek5000 was used to carry out the simulation. An unsteady volume force is used to trip the flow to turbulence on both sides of the wing at 10% of the chord. Full turbulence statistics are computed in addition to collection of time history data in selected regions. The Reynolds numbers on the suction side reach Reτ ≃ 373 and Reθ=2,800 with the pressure-gradient parameter ranging from β ≈ 0.0 to β ≈ 85. Similarly, on the pressure side, the Reynolds numbers reach Reτ ≈ 346 and Reθ=818 while β changes from β ≈ 0.0 to β≈−0.25. The effect of adverse pressure gradients on the mean flow is consistent with previous observations, namely a steeper incipient log law, a more prominent wake region and a lower friction. The turbulence kinetic energy profiles show a progressively larger inner peak for increasing pressure gradient, as well as the emergence and development of an outer peak with stronger APGs. The present simulation shows the potential of high-order (spectral) methods in simulating complex external flows at moderately high Reynolds numbers.