A Study Of The Secondary Instability And Oblique Mode Breakdown In The Supersonic Flat-plate Boundary Layers

In this paper, the evolutions of the disturbances in the supersonic flat-plate boundary layers were simulated by using parabolized stability equations.First, we investigated the evolutions of the disturbances with finite amplitude. Their evolutions obtain by using nonlinear parabolized stability equations agree reasonably well with those obtain by spatial mode direct numerical simulations. This is the foundation and preparation for calculating the nonlinear evolutions of the disturbances by using the nonlinear parabolized stability equations. Second, the nonlinear interaction of the disturbances with receptivity theory was studied. Third, an in-depth discussion of the secondary instability and oblique mode breakdown mechanisms is given for both a Mach 1.5 flat-plate boundary layer and a Mach 4.5 flat-plate boundary layer.The following conclusions are drawn:1. The second mode instability disturbances may be evoked by the first mode disturbances which were given by receptivity theory. The amplitude of the disturbances are concerned with the parameter of the initial disturbances. The disturbances with short span wise wavelength will grow faster than the disturbances with long span wise wavelength.2. Both secondary instability and oblique mode breakdown mechanism can lead to laminar – turbulent transition. Especially the physical characteristics of nonlinear stability of various harmonic waves in order to study and analysis the mechanism of the transition process for Mach 1.5 and Mach 4.5 are demonstrated.3. The dominant mechanism for transition at Mach 1.5 flat-plate boundary layer is oblique mode breakdown. The oblique mode breakdown mechanism appears to be a more likely route to transition than the secondary instability mechanisms. Conversely, secondary instability mechanisms should be the main mechanism lead to breakdown at Mach 4.5 flat-plate boundary layer. Only can a pair of oblique waves with equal but opposite angles result growth of instability waves due to nonlinear interaction.