Characteristics of Velocity Profile and Pressure Fluctuation in Curved Turbulent Boundary Layers

Direct numerical simulations at a low Mach number (𝑀 = 0.085) are conducted to investigate the complex interplay between near-wall turbulence and wall pressure fluctuations in curved turbulent boundary layers. The study focuses on two forward-facing chamfered step geometries with distinct curvatures, each characterized by an upstream concave wall blending into a downstream convex wall. The curvature-induced pressure gradient influences Reynolds shear stress distributions and leads to deviations of mean velocity profile from the classical logarithmic law. The generalized wall function is then evaluated and demonstrates a relatively good performance in concave regions; however, its accuracy diminishes with increasing convex curvature. Building on these fundamental observations of mean flow and turbulence statistics, the curvature effects on wall pressure fluctuations are further examined. Space-time correlations show that the convection velocity of wall pressure fluctuations first increases and then decreases, correlating with pressure gradient variations. A quantitative evaluation of seven recently developed semi-empirical models of wall pressure spectrum reveals varying predictive performance across frequency bands, with accuracy significantly affected by curvature changes. The results suggest that only taking pressure gradients into account is not sufficient to accurately model the wall pressure spectrum in curved turbulent boundary layers.