Oscillatory momentum transport in cascade transitional boundary layer flows

Abstract

The generation and early evolution of boundary layer transitional instabilities, named Tollmien-Schlichting (T-S) waves, in airfoil cascade flows are studied. The energy exchange between the mean flow and the flow instabilities is computed by performing Direct Numerical Simulation of the fluid flow governing equations and by calculating the fluctuating kinetic energy (FKE) budget within the separated boundary layer. The driving role of the FKE production in the wavelength modulation process associated to the receptivity phenomenon, i.e., the generation of T-S waves, is demonstrated. The FKE production largely hastens the wavelength modulation around the inflection point of the mean velocity profile across the boundary layer. Above the inflection point, the fluctuating pressure field favors the energy transport and provides the energy necessary to convect the instabilities out of the boundary layer. The evolution of the T-S waves depicts an asymmetric distribution of the production term in the transverse direction, i.e., in the lower half of the boundary layer the mean flow provides energy to the instabilities while the opposite occurs in the upper half