Understanding the instability-wave selectivity of hypersonic compression ramp laminar flow

Abstract

The hypersonic flow stability over a two-dimensional compression corner is studied using resolvent analysis, linear stability theory (LST) and parabolised stability equation (PSE). The authors find that the interaction between upstream convective-type disturbances and the laminar separation bubble can be divided into two regimes, whose behaviour can be well explained by comparative research. First, two-dimensional (2-D) high-frequency Mack modes neutrally oscillate with the presence of alternating stable and unstable regions inside the separation bubble. These discontinuous unstable regions are generated by repeated synchronisations between discrete modes with evolving branches. Through a modal sychronisation analysis, we report that the second modes upstream and downstream of the separation bubble can be essentially different from each other, since they originate from different branches of discrete modes due to flow separation. Second, the 2-D low-frequency `shear-layer mode' is found to be stable in the separation bubble by LST, whereas multiple unstable three-dimensional (3-D) eigenmodes are identified by LST. In general, three significant modes are dominant successively near the separation point, in the separation bubble and near the reattachment point. These modes are found to be sensitive to the streamline curvature effect. The locally dominant modes agree with the resolvent response in terms of the disturbance shape and the growth rate of energy. Thus, a combination of global and local analyses demonstrates that the separation bubble tends to selectively amplify low-frequency 3-D disturbances and `freeze' high-frequency Mack-mode disturbances in an explainable manner. These findings facilitate the understanding of the early evolution of low- and high-frequency instabilities in hypersonic separated flows.