An indicator of the dominant instability in transition on an extended correlation based transition model

The extended γ-Re_θt model with crossflow transition criterion can predict transition due to Tollmien-Schlichting (TS) instability or crossflow (CF) instability, but it doesn’t tell which instability induces the transition, in other words, which instability is the dominant one in the transition process. Such information of how TS and CF instabilities relate to the occurrence of transition is important in aerodynamic design and laminar flow control as the two instabilities require different controlling measures. On this problem, this article proposed an indicator of the dominant instability using the transition onset factor (F_TS and F_CF), which is the ratio of local Reynolds number and transition Reynolds number over a correlation parameter. The transition position is predicted based on the extended γ-Re_θt model coupled with crossflow transition criterion. Additionally, the dominant instability in the transition process is inspected by extracting a series of TS and CF transition onset factors along the boundary layer and comparing their maximum values at the predicted transition position. If the maximum (F_TS)_xtr is larger than the maximum (F_CF)_xtr, the transition is induced by TS instability. If not, the transition is induced by CF instability. As a verification, transition prediction and analysis are performed in the infinite swept wing case and the sickle-shaped wing case with varied swept angles. For the infinite swept NACA64₂A015 wing, the transition onset factors indicate that the transition process is dominated by TS instability at the swept angle of 20° and by CF instability at the swept angle of 50°, which is as expected. The indicator also works well for the sickle-shaped wing, showing that the transition is induced by CF instability on the upper surface of the wing.