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

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.