A systematic DNS approach to isolate wall-curvature effects in spatially developing boundary layers

Abstract

A methodology to numerically assess wall-curvature effects in boundary layers is introduced. Wall curvature, which directly induces streamline curvature, is associated with several changes in boundary-layer flow. By necessity, a local radial pressure gradient emerges to balance mean flow turning. Moreover, a streamwise (wall-tangential) pressure gradient can appear for configurations with non-constant wall curvature or a particular freestream condition; zero pressure gradient is a special case. In laminar concave flow, the Görtler instability and the associated Taylor-Görtler vortices destabilize the flow and promote laminar-turbulent transition, whereas in the fully turbulent regime, unsteady coherent structures formed by the centrifugal instability mechanism dramatically redistribute turbulent shear stress. One difficulty of assessing centrifugal effects on boundary layers is that they often appear simultaneously with other phenomena, such as a streamwise pressure gradient, making their individual evaluation often ambiguous. For numerical studies of transitional and turbulent boundary layers, it is therefore beneficial to understand the interactive nature of such coupled effects for generic configurations. A methodology to do so is presented, and is verified using the case of a subsonic, compressible turbulent boundary layer. Four direct numerical simulations have been computed, forming a 2×2matrix of turbulent boundary-layer states; namely with and without concave wall curvature, each having a zero and a non-zero streamwise-pressure-gradient realization. The setup and accompanying procedures to determine appropriate boundary conditions are discussed, and the methodology is evaluated through analysis of the mean flow fields. Differences in mean flow properties such as wall shear stress and boundary-layer thickness due to either streamwise pressure gradient or wall curvature are shown to be remarkably independent of one another.