Large-eddy simulation of subcritical transition in an attachment-line boundary layer

Abstract

The large-eddy simulation (LES) technique is applied to the subcritical transition to turbulence of a finite-amplitude instability in the attachment-line boundary layer of a swept wing. The three-dimensional swept Hiemenz solution is used to model the base laminar flow along the leading edge of a swept wing. The filtered Navier-Stokes equations are solved numerically using a localized dynamic eddy-viscosity model to parameterize the unresolved scales. Outflow conditions are imposed using the buffer-domain technique, and initial disturbances are introduced through a blowing/suction strip. The linear stage of transition is bypassed due to the finite-amplitude perturbation. The instability growth rate is found to be significantly higher than in previous two-dimensional results, due to the commonly-made Görtler-Hümmerlin assumption that the perturbation has the same spanwise structure as the base flow; this assumption is not supported by our results, most probably due to the finite spanwise length of the blowing/suction strip. As the flow propagates downstream, energy is fed into the spanwise modes, and turbulence generated on the attachment line is transported to other spanwise locations by the mean motion in this direction. The shape factor on the attachment line matches the turbulent boundary layer estimates, while the turbulent mean-velocity profiles on the attachment line deviate from the universal logarithmic behavior due to the appearance of inflectional points, which make the flow susceptible to inviscid instabilities.