A local correlation-based transition model is developed for high-speed transitional flows. Through an analysis of self-similar solutions for compressible boundary layers, a new correlation for the ...

Complete transition to turbulence via first- and second-mode oblique breakdown in a high-speed boundary layer at Mach 4.5 is studied by direct numerical simulations (DNS) and linear stability theory (LST). The initial frequency and spanwise wavenumbers for both types of oblique breakdown are determined from LST. Then, DNS is employed to study the main features of the two oblique breakdown types in detail, which has rarely been discussed in previous studies. This includes the main flow structures and evolution of various modes during the linear, nonlinear, and breakdown stages, and both different and similar features for the two oblique breakdown types are summarized. Compared with only one type of low-speed streak existing for first-mode oblique breakdown, two types occur in the second-mode oblique breakdown, and the generation mechanism, evolution process, and role of the low-speed streaks are studied. Subsequently, the generation mechanism of both the heat transfer and skin-friction overshoot during both oblique breakdowns is illustrated with emphasis on the heat transfer overshoot for the second mode, which occurs at the laminar stage. Finally, both types of oblique breakdown are the likely path to a fully developed turbulent flow, although the unstable region for the second-mode oblique waves is short and for the first-mode oblique waves is amplified slowly.

Discrete roughness-induced transition in Mach flow controlled by two-dimensional wall blowing is studied using direct numerical simulation. Spectral analysis and flow freezing operations reveal that the main source of unsteadiness in the case without blowing is the separated shear layer/counter-rotating vortex system: the shear layer is bent by the vortex pair, and this interaction induces disturbance growth at the shear layer. With the existence of weak wall blowing, the transition is delayed. Flow visualization demonstrates that upstream-positioned blowing achieves this by lifting the inflow boundary layer and decreasing the roughness Reynolds number. In contrast, downstream-positioned blowing takes effect by weakening the counter-rotating vortex pair and inhibiting the interaction. Vorticity transportation analysis suggests that this result is accomplished by increasing dissipation for streamwise vorticity and converting some of it into spanwise vorticity. In cases with strong wall blowing, the control effect is reversed, as wall blowing with enough strength can induce unsteadiness and promote transition. In upstream-positioned strong blowing cases, a new unstable mode is observed in spectral results throughout the near-roughness region, and further analysis indicates that this mode originating from the separation zone upstream of the blowing is the key factor for transition. With regard to downstream-positioned strong blowing cases, a very low-frequency mode is generated from the separation bubble between the roughness element and the blowing, but it only provides an initial disturbance for the transition process. The transition that occurs downstream is due to the distortion of the boundary layer in the wake.

Oblique breakdown in a Mach 2.0 supersonic boundary layer controlled by a local cooling strip with a temperature jump is investigated using direct numerical simulations and linear stability theory. The effect of temperature on the stability of the fundamental oblique waves is first studied by linear stability theory. It is shown that the growth rate of fundamental oblique waves will decrease monotonically as the temperature decreases. However, the results of the direct numerical simulations indicate that transition reversal will occur as the growth rate of the fundamental oblique waves of cooled case becomes faster compared with that of baseline case downstream of the cooling strip. When the cooling strip is in the linear region, the transition is delayed due to the suppression effect of the cooling strip on the fundamental oblique waves. When the cooling strip is located in the early nonlinear region, the fundamental oblique waves will be suppressed by higher spanwise wavenumber steady modes generated by the mutual and self-interaction between the fundamental oblique waves and harmonic modes, which is first called the self-suppression effect (SSE) in the present study. Further research indicated that the meanflow distortion generated by steady modes plays an important role in the SSE. Compared with the stabilization effect of the cooling strip, the SSE is more effective. Moreover, the SSE might provide a new idea on the instability control, as it is observed that the SSE works three times leading to the growth rate of fundamental oblique waves slowing down at three different regions, respectively.