Secondary instabilities of boundary layers

Abstract

Several aspects of the subharmonic instability of boundary layers are studied. First, the subharmonic instability of incompressible flows over a flat plate is investigated using the resonant triad model and the Floquet model. The primary wave is taken in the form of a two-dimensional (2-0) Tollmien-Schlichting (T-S) wave. The subharmonic wave is taken in the form of a three-dimensional (3-D) wave. Results from both models are presented and compared with the experimental data and numerical simulation. It is found that the results of the Floquet model are in good agreement with the experimental data and numerical simulation, whereas the results of the resonant triad model agree only qualitatively with the experimental data. Second, the subharmonic instability of incompressible flows over a 2-0 hump is studied using the Floquet model. The mean flow over the hump is calculated by using interacting boundary layers, thereby accounting for viscid/inviscid interactions. The results show that increasing the hump height results in an increase in the amplification factors of the primary and subharmonic waves. When the hump causes separation, the growth rates of both the primary and subharmonic waves are considerably larger than those obtained in the case of no separation. Third, the subharmonic instability of compressible boundary layers over a flat plate is studied using the Floquet model. Results are presented for adiabatic wall boundary conditions and subsonic, transonic, and supersonic flows. For supersonic flows results are presented for first- and second-mode primary waves. The effect of Mach number, spanwise wavenumber, primary-wave amplitude, Reynolds number, and frequency are studied. Fourth, results for the effect of heat transfer on the subharmonic instability of a two-dimensional compressible boundary layer over a flat plate are presented for different Mach numbers. For supersonic flows results are presented for first- and second-mode waves. The effect of different levels of heat transfer on changing the features of the subharmonic compressible instability is evaluated. Fifth, results for the effect of suction on the subharmonic instability of a two-dimensional compressible boundary layer over a flat plate are presented. It is found that when the primary wave is a first-mode merging with a second-mode, the subharmonic wave is strongly destabilized by suction. Sixth, the effect of a bulge on the subharmonic instability of compressible boundary layers is studied. It is found that the effect of compressibility on reducing the growth rate of the disturbances weakens as the hump height increases.