Effect of small surface deformations on the stability of tollmien-schlichting disturbances

The effect of a small Gaussian shaped deformation on the development and growth of Tollmien-Schlichting disturbances on an unswept airfoil is investigated. A broad range of gap depths and widths is modeled that can be sufficient to generate localized pockets of reverse flow. Boundary-layer profiles are computed using a Navier-Stokes solver, permitting a thorough investigation of all configurations considered. The linear stability of Tollmien-Schlichting waves is then examined using parabolized stability equations and linearized Navier-Stokes formulations, with the former method giving excellent agreement with the latter for all disturbances studied, including within separated boundary layers. Tollmien-Schlichting disturbances are amplified by deeper and wider gaps, with a correlation derived by relating the increase in the N factor with the gap dimensions and freestream Reynolds number.