Growth of Tollmien-Schlichting Waves on Airfoils with Surface Roughness

摘要

Surface roughness can enhance the growth rate of unsteady Tollmien-Schlichting (T-S) waves, and thus even small-amplitude surface roughness can change the boundary layer transition location in aerodynamic applications. For example, an experiment in the Virginia Tech Stability Wind Tunnel showed that adding paint roughness to a DU96-W-180 airfoil moved transition upstream by 2-6% chord. This work describes a linear stability approach to calculate the growth rates of T-S waves in variable pressure gradient boundary layers with surface roughness. Airfoil boundary layer profiles are calculated using an in-house two-dimensional boundary layer solver; this boundary layer is the starting point for a linearized Navier-Stokes calculation to determine how the roughness affects the time-averaged boundary layer. This modified boundary layer is then used as the input for linear stability calculations of unsteady disturbances. This methodology was used to calculate the growth rates of T-S waves on an airfoil with two-dimensional, small-amplitude surface waviness. The results show two-dimensional roughness destabilizes T-S waves upstream of the minimum pressure point, leading to increased T-S wave growth.