Instabilities and receptivities of turbulent aerospace flows

Turbulent flows in aerospace applications often exhibit unsteady dynamics that can be adequately studied using a global stability analysis based on a set of URANS equations. One of the objectives of this work is to develop a unified framework for solving linear stability problems for turbulent flows using both time-stepping and matrix-forming methods. Following a validation phase using canonical tests, two configurations of engineering interest are examined. Firstly, the transonic flow through a diffuser (Sajben model G) is investigated in both a strong shock (with flow separation) and a weak shock (without separation) configurations. The 2D global stability analysis reveals that the unsteadiness observed experimentally is not driven by a global instability. Through the resolvent analysis, a peak is observed at the same frequency, indicating that this is a receptivity mechanism. Extending the study to the spanwise direction by superimposing a 3D perturbation onto the 2D base flow reveals the emergence of a zero-frequency unstable mode for the strong-shock case; this is a centrifugal instability which, however, does not emerge in the weak-shock case. Secondly, the 3D jet with counter-current flow is analysed, which mimics the landing phase of reusable launch vehicles. Without an angle of attack, the flow is globally stable; with an angle of attack of theta=10°, the spectrum exhibits several unstable modes at the same frequency as the URANS PSD. Two families of modes can be distinguished: A lower-frequency modes whose peak activity lies in mixing layer and a higher-frequency modes whose peak activity lies in the wake region .