Assessment of spanwise domain size effect on the transitional flow past an airfoil

In most large-eddy and direct numerical simulations of flow past an isolated airfoil, the flow is assumed periodic in the spanwise direction. The size of the spanwise domain is an important geometrical parameter determining whether the turbulent flow is fully developed, and whether the separation and transition patterns are accurately modeled. In the present study, we investigate the incompressible flow past an isolated NACA0012 airfoil at the angle of attack of 5 degrees and Reynolds number 5 × 104. The spanwise domain size Lz, represented by the aspect ratio AR=Lz/C where C is the airfoil chord length, is varied in the range 0.1−0.80.1−0.8. The effect of varying the normalized spanwise domain size AR is examined via direct numerical simulation (DNS) on several aspects of the turbulent flow quantities including the time-averaged and time-dependent behavior as well as the spanwise variation of the selected statistical quantities. DNS results reveal that different aspect ratios result in close predictions of the time-averaged aerodynamic quantities, and the velocity field except for a slight difference in the separation bubble. Smaller aspect ratios tend to underpredict the turbulent fluctuations near the separation point but overpredict them inside the separation bubble. Large differences are observed for multiple statistical quantities near the reattachment point, especially the turbulent kinetic energy budget terms. The leading edge separation is notably three-dimensional for simulation at AR=0.8, while remaining quasi-2D for smaller aspect ratios. The spanwise two-point correlation coefficient shows significant dependence on the position of the probe and the velocity component analyzed: small aspect ratios do not produce uncorrelated results for all the velocity components. The simulation results demonstrate that examining only a few statistical quantities may result in a misleading conclusion regarding the sufficiency of the spanwise domain size. Reliable metrics to establish the sufficiency of spanwise domain size require thorough analysis of the turbulent statistics, and are necessary for three-dimensional simulation of turbulent flow in similar configurations.