Control of oblique breakdown in a supersonic boundary layer at Mach 2.0 using a local cooling strip is investigated by direct numerical simulation. Previous studies have indicated that wall cooling can stabilize first-mode disturbances, but no study has yet investigated the use of local cooling to control oblique breakdown in a supersonic boundary layer. In the present work, local cooling strips with various temperatures and widths are utilized at different locations to control oblique breakdown. Insight is obtained into the stabilizing effect of a cooling wall on the evolution of various disturbances in the streamwise direction. A local cooling strip controls oblique breakdown mainly by suppressing the amplification of the fundamental oblique waves in the streamwise direction, and it is found that this suppressive effect is enhanced by increasing the width and decreasing the temperature of the strip. The stabilizing effect of a local cooling strip on higher-harmonic modes is reinforced when the strip is located farther downstream, although this effect is negligible when compared with the stabilizing effect on the fundamental oblique waves. When the cooling strip is placed in the midstream area, where the steady vortex mode is amplified to the order of the fundamental oblique waves, outstanding performance in suppressing transition is found. Furthermore, in addition to the stabilizing effect of the cooling wall on the fundamental oblique waves, the boundary layer is stabilized by rapid growth of higher-spanwise-wavenumber steady modes. Eventually, oblique breakdown is suppressed and substantial improvements in the skin-friction coefficient are also obtained.

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.

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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.

Roughness-induced transition control is a key technology for aircraft design, and associated research is useful in practical applications as well as for understanding the mechanism of the roughness-induced transition. One practical approach involves the “shielding effect,” whereby the roughness-induced transition is shielded by smaller pockets of surrounding roughness. In this paper, we investigate the shielding effect of a two-dimensional downstream strip in the boundary layer disturbed by discrete smooth-edged roughness and focus on the shielding strip height kss and the distance between the two areas of roughness xss. Our results indicate that downstream shielding delays the transition by weakening the strongest streamwise vortices in the middle of the wake, thus inhibiting the “lift-up” effect that induces growth in the disturbance. The main mechanisms for reducing the streamwise vorticity are (a) enhanced dissipation of the streamwise vorticity and (b) conversion of streamwise vorticity into more stable spanwise vorticity. The strip suppresses the separation zone behind the roughness, thus affecting the receptivity process and reducing the initial disturbance. However, the strip strengthens other streamwise vortices in the wake. When kss exceeds a critical value, vortices closer to the wall will induce stronger lift-up than those in the middle of the wake, resulting in an earlier transition. Analysis of xss shows a simpler trend, whereby the onset position of the transition moves upstream as xss increases. This is because the shielding strip weakens the streamwise vortices earlier and the separation zone becomes smaller as the strip moves closer to the discrete roughness patch.