Onset of instability in hypersonic cone/flare laminar separation bubble

Predicting instability onset in hypersonic boundary layers is crucial due to steep increases in heat flux and skin friction. In cone/flare flows, laminar separation and shock/fan interactions complicate the computation of steady base states and their instabilities. For these reasons, the 39\% scaled ROTEX-T model is investigated under well-known parametric conditions found in wind-tunnel experiments (Davami \textit{et al}, AIAA Paper 2024), namely $M = 6$, $T_0 = 550$ K and $P_0 = 335$ to $486$ kPa. In order to do so, the high-order numerical discretization methods in 3D4S (Assis \textit{et al}, Fluids 2024) are used to generate axisymmetric steady-states that are grid converged and disturbance-free, i.e. with machine precision zero residues. These solutions are subsequently used as base flows for linear and biglobal modal stability analyses using MONALISA (Freitas \textit{et al} Fluids 2025--\textit{submited}), which employs high-order finite difference schemes with shock-capturing capabilities. Main results are: i) an excellent agreement between axisymmetric DNS and global stability predictions, in terms of both damping ratios and mode shapes, ii) multiple unstable modes are found above the critical Reynolds number, iii) a shift of the dominant wavenumber to higher wavenumbers occurs when instability ensue.