The role of geometry on the global instability of wakes behind streamwise rotating axisymmetric bodies

Abstract

Abstract We perform direct and adjoint global stability analyses of the wake behind streamwise rotating axisymmetric bodies of hemispherical nose and cylindrical trailing edge of different length-to-diameter ratios, l , to evaluate the role of geometry on the unstable global modes. The study is limited to laminar Reynolds numbers, Re 500 , and moderate values of the rotation parameter, Ω ≤ 1 , defined as the ratio between the azimuthal velocity at the body’s surface and the freestream velocity. As the aspect ratio, l , is varied, important differences on the wake stability features are found as the rotation parameter Ω is increased. For short bodies such as hemispheres ( l = 0 ), axisymmetry breaking takes place through the destabilization of a low frequency (LF) mode, which is a modified version of the steady-state (SS) mode related to wakes without rotation, which becomes more unstable as Ω grows. This destabilizing effect of rotation vanishes for low Ω as the aspect ratio l increases (bullet-like bodies, l > 0 ), until a critical value is reached, l c 1 , from which the LF mode is stabilized as Ω grows. In addition, increasing l above two other critical thresholds, l c 2 and l c 3 , promotes, respectively, the destabilization of a high frequency (HF) mode, which is a modified version of the RSP mode at wakes without rotation, and a new medium frequency (MF) mode, whose origin remains unclear. Computation of sensitivity to base flow modifications shows that the LF mode is destabilized by rotation for short bodies (i.e. sphere or hemisphere) due to an increase in the shear along the separation line and a weakening of perturbation advection inside the recirculation bubble. Conversely, as l grows, the larger angular momentum stabilizes the LF mode by strengthening the advection of perturbations in the near wake. Destabilization of HF and MF modes are also discussed in terms of sensitivity to base flow modifications. Finally, an analysis of the structural sensitivity shows that the destabilization of the MF mode is analogous to that behind the spiral vortex breakdown, in terms of conservation of angular momentum, being it mainly driven by an inviscid mechanism whose origin lies at the rear stagnation point of the recirculation bubble.