Excitation and evolution of subsonic Gortler vortices induced by free-stream vortical disturbances

We study the nonlinear development of subsonic Gortler vortices which are excited by free-stream vortical disturbances (FSVD) in compressible boundary layers over concave walls. The free-stream Mach number is assumed to be of O(1) and the FSVD are strong enough for compressibility and nonlinearity to be taken into account. The focus is on low-frequency (long-wavelength) components of FSVD, which excite the Gortler vortices in the boundary layers. The formation and evolution of Gortler vortices are governed by the compressible nonlinear boundary-region equations, supplemented by appropriate initial and boundary conditions that characterise the impact of the FSVD on the boundary layer. The numerical computations are performed for parameters typical of flows over pressure surfaces of high-pressure turbine blades, where the Gortler number and the turbulence Reynolds number are both of order-one quantities. For low-intensity FSVD, increasing the Gortler number or intensifying the FSVD render the boundary layers more unstable, while increasing the Mach number or frequency of the FSVD stabilizes the flows. Raising the FSVD level deactivates the effects of the studied parameters. In particular, the deactivation effect of high-level FSVD leads to the formation of streaks over a convex wall. The theoretical prediction captures well the experimental measurement of the enhancement of the wall-heat transfer and the skin friction. The mean-flow distortion is found to play a crucial role in the nonlinearly generated extra drag and heat transfer.