Instabilities in compressible attachment–line boundary layers (original) (raw)

The hydrodynamic stability of the weakly compressible attachment-line boundary layer, with a sweep Mach number ranging from 0.1 to 1.3, is studied using a temporal compressible direct numerical simulation. A flow impinging non-normally onto an infinitely extended flat plate was computed. This complements the study of Hall et al. ͓Proc. R. Soc. London, Ser. A 395, 229 ͑1984͔͒ who investigated the linear stability of an incompressible attachment-line boundary layer under the assumption of Görtler-Hämmerlin perturbation modes. In the present work, the base flow is modeled starting from the incompressible swept Hiemenz flow. Using Rayleigh-Jansen Mach number expansions, we obtain a family of base flows parameterized with the sweep Mach number ranging from 0.1 to 1.3. The Reynolds number of the simulation is higher than the incompressible critical Reynolds number, and the plate is adiabatic. Small purely vortical stochastic perturbations are inserted in the boundary layer and followed in time. For Mach numbers up to 0.3, developed velocity and pressure modes are similar to the ones assumed by Görtler and Hämmerlin. The chordwise dependencies of the temperature mode are presented. When increasing the Mach number, the structure of the modes changes; for high Mach numbers, a significantly slower decay of the eigenfunction with wall-normal distance is observed. Above M = 0.5, the perturbations are exponentially decaying. This demonstrates the strong stabilizing effect of compressibility in the moderate Mach regime. Furthermore, for the same base flow, a higher exponential growth rate of the perturbation is obtained, if an isothermal wall boundary condition is applied instead of an adiabatic one.