On the excitation of Görtler vortices by distributed roughness elements

Abstract

Gortler vortices evolve in boundary layers over concave surfaces as a result of the imbalance between centrifugal effects and radial pressure gradients. Depending on various geometrical and flow conditions, these vortices can significantly distort the baseline flow and lead to secondary instabilities and ultimately to transition. In this study, the growth of Gortler vortices excited by distributed roughness elements is analyzed using the solution to the nonlinear boundary region equations with upstream boundary conditions derived previously via an asymptotic analysis applied in the vicinity of the roughness elements. Generalized Rayleigh pressure equation derived based on the assumption that the baseline flow is a function of the transverse coordinates only is used to determine the growth rates associated with the secondary instabilities. Within the analysis, the roughness shape, height and diameter as well as the spanwise separation between the roughness elements are varied in the linear regime, while keeping the same Gortler number. It is found that bell-shaped distributed roughness elements are more likely to excite the Gortler instabilities than sharp-edge-type (e.g., cylindrical) roughness elements, and by increasing the roughness diameter, the strength of Gortler vortices associated with the bell-shaped roughness elements increases as expected, but the strength of Gortler vortices associated with cylindrical-shaped roughness elements decreases.