Non-equilibrium turbulent boundary layer with adverse pressure gradient and convex wall curvature

Direct numerical simulations (DNS) of flows over an airfoil (suction side) and a flat plate are compared to characterize the effect of wall curvature on a turbulent boundary layer and generate data for acoustic model development for fan applications. The two cases have matched adverse pressure gradient (APG) quantified by the acceleration parameter ($K=(ν/U_∞²)(dU_∞/dx_s)$). For the airfoil flow, an existing DNS carried out by Wu et al. {Journal of Fluid Mechanics}, 868:584-610 (2019) of the flow around a controlled-diffusion (CD) airfoil is used.  For the flat-plate flow, a separate simulation that matches the $K$ distribution in the APG region of the airfoil flow is carried out.

The differences between the two cases constitute the mild convex curvature effects found in a boundary layer on a CD airfoil. Specifically, in the region of weak APG, the curvature effect dominates and yields a lower friction coefficient. In the high-APG region (near the airfoil trailing edge) the effects of wall curvature and APG appear to interact.

Overall, the comparison between the two flows shows that the boundary layer developments are qualitatively similar, indicating that a flat-plate boundary layer can serve as a low-cost surrogate of an airfoil boundary layer in numerical studies of important features of an airfoil flow for fan applications