Linear modal instabilities around post-stall swept finite wings at low Reynolds numbers

Abstract

Linear modal instabilities of flow over untapered wings with aspect ratios$AR=4$and 8, based on the NACA 0015 profile, have been investigated numerically over a range of angles of attack,$\alpha$, and angles of sweep,$\varLambda$, at chord Reynolds numbers$100\le Re\le 400$. Laminar base flows have been generated using direct numerical simulation and selective frequency damping, as appropriate. Several families of unstable three-dimensional linear global (TriGlobal) eigenmodes have been identified and their dependence on geometric parameters has been examined in detail at$Re=400$. The leading global mode A is associated with the peak recirculation in the three-dimensional laminar separation bubble formed on the wing and becomes unstable when recirculation reaches$\textit {O}(10\,\%)$. On unswept wings, this mode peaks in the midspan region of the wake and moves towards the wing tip with increasing$\varLambda$, following the displacement of peak recirculation; its linear amplification leads to wake unsteadiness. Additional amplified modes exist at nearly the same and higher frequencies compared to mode A. The critical$Re$has been identified and it is shown that amplification increases with increasing sweep, up to$\varLambda \approx 10^\circ$. At higher$\varLambda$, all global modes become less amplified and are ultimately stable at$\varLambda =30^\circ$. An increase in amplification of the leading mode with sweep was not observed over the$AR=4$wing, where tip vortex effects were shown to dominate.