Stability and dynamics of the laminar wake past a slender blunt-based axisymmetric body

Abstract

We investigate the stability properties and flow regimes of laminar wakes behind slender cylindrical bodies, of diameter D and length L, with a blunt trailing edge at zero angle of attack, combining experiments, direct numerical simulations and local/global linear stability analyses. It has been found that the flow field is steady and axisymmetric for Reynolds numbers below a critical value, Recs (L/D), which depends on the length-to-diameter ratio of the body, L/D. However, in the range of Reynolds numbers Recs(L/D) < Re < Reco(L/D), although the flow is still steady, it is no longer axisymmetric but exhibits planar symmetry. Finally, for Re > Reco, the flow becomes unsteady due to a second oscillatory bifurcation which preserves the reflectional symmetry. In addition, as the Reynolds number increases, we report a new flow regime, characterized by the presence of a secondary, low frequency oscillation while keeping the reflectional symmetry. The results reported indicate that a global linear stability analysis is adequate to predict the first bifurcation, thereby providing values of Recs nearly identical to those given by the corresponding numerical simulations. On the other hand, experiments and direct numerical simulations give similar values of Reco for the second, oscillatory bifurcation, which are however overestimated by the linear stability analysis due to the use of an axisymmetric base flow. It is also shown that both bifurcations can be stabilized by injecting a certain amount of fluid through the base of the body, quantified here as the bleed-to-free-stream velocity ratio, Cb = Wb/W∞.

Low-dimensional dynamics of a turbulent axisymmetric wake

“…The intensity of the axisymmetric pulsation increases as the axis of the body is approached. The frequency and shape of this mode is very close to the low frequency oscillation of the wake observed by Bohorquez et al (2011) and Bury & Jardin (2012) for a body of similar geometry in the transitional regime at low Reynolds numbers.…”

“…The symmetry-breaking instabilities of the transitional wake observed at Re D < 1000 (Bohorquez et al 2011;Bury & Jardin 2012) before the chaotic regime, persist at high Reynolds numbers (here Re D ∼ 2 × 10 5 ). Although the wake is turbulent, the large-scale coherent structures associated with it retain the structure of the laminar instabilities in a statistical sense.…”

“…Bohorquez et al (2011) also reported a second peak appearing in the spectra of the axial velocity component at a frequency approximately one quarter of the shedding.…”

“…The flow past blunt-based axisymmetric bluff bodies has been considered in various direct numerical simulations (Sanmiguel-Rojas et al 2009;Bohorquez et al 2011;Bury & Jardin 2012). These studies showed that the wake undergoes two successive bifurcations at low Reynolds numbers from an axisymmetric steady state.…”

Transitions to chaos in the wake of an axisymmetric bluff body

“…Numerous studies focused on spheres, revealing transitions of the wake structure from 1) an axisymmetric steady state Email address: yannick.bury@isae.fr, thierry.jardin@isae.fr (Yannick Bury, Thierry Jardin) (corresponding to the base flow) to 2) a reflectional symmetry steady state (SS), 3) a reflectional symmetry preserving (RSP) oscillatory state, and 4) a reflectional symmetry breaking (RSB) oscillatory state [4,5]. Such transitions and resulting wake structures exhibit similarities with wakes that develop downstream blunt-based axisymmetric bluff bodies [6,7]. However this geometry is still poorly documented despite its practical interest and a lack of comprehension subsists regarding the scenario that leads to a chaotic state.…”