Adverse-pressure-gradient turbulent boundary layer on convex wall

Abstract

Direct numerical simulations (DNSs) of an incompressible turbulent boundary layer on an airfoil (suction side) and that on a flat plate are compared to characterize the non-equilibrium turbulence and the effect of wall curvature on the flow. The two simulations effectively impose matching streamwise distributions of adverse pressure gradient (APG) quantified by the acceleration parameter ( K). For the airfoil flow, an existing compressible DNS carried out by Wu et al. [“Effects of pressure gradient on the evolution of velocity-gradient tensor invariant dynamics on a controlled-diffusion aerofoil at Rec = 150,000,” J. Fluid Mech. 868, 584–610 (2019)] of the flow around a controlled-diffusion airfoil is used. For the flat-plate flow, a separate simulation is carried out with the aim to reproduce the flow in the region of the airfoil boundary layer with zero to adverse pressure gradients. Comparison between the two cases extracts the effect of a mild convex wall curvature on velocity and wall-pressure statistics in the presence of APG. In the majority part of the boundary layer development, curvature effect on the flow is masked by that of the APG, except for the region with weak pressure gradients or a thick boundary layer where the effect of wall curvature appears to interact with that of APG. High-frequency wall-pressure fluctuations are also augmented by the wall curvature. Overall, the boundary layers are qualitatively similar with and without the wall curvature. This indicates that a flat-plate boundary layer DNS may serve as a low-cost surrogate of a boundary layer over the airfoil or other objects with mild curvatures to capture important flow features to aid modeling efforts.