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

Published online by Cambridge University Press:  07 April 2011

P. BOHORQUEZ ,
E. SANMIGUEL-ROJAS ,
A. SEVILLA ,
J. I. JIMÉNEZ-GONZÁLEZ  and
C. MARTÍNEZ-BAZÁN
P. BOHORQUEZ
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Mecánica y Minera, Universidad Jaén, Campus de las Lagunillas, 23071 Jaén, Spain
E. SANMIGUEL-ROJAS
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Mecánica y Minera, Universidad Jaén, Campus de las Lagunillas, 23071 Jaén, Spain
A. SEVILLA
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Térmica y de Fluidos, Universidad Carlos III de Madrid, 28911 Leganés, Spain
J. I. JIMÉNEZ-GONZÁLEZ
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Mecánica y Minera, Universidad Jaén, Campus de las Lagunillas, 23071 Jaén, Spain
C. MARTÍNEZ-BAZÁN*
Affiliation:
Área de Mecánica de Fluidos, Departamento de Ingeniería Mecánica y Minera, Universidad Jaén, Campus de las Lagunillas, 23071 Jaén, Spain
*
†Email address for correspondence: cmbazan@ujaen.es
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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∞.

JFM classification

Flow Control: Flow Control Flow Control: Instability control Wakes/Jets: Wakes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 676 , 10 June 2011 , pp. 110 - 144
Copyright
Copyright © Cambridge University Press 2011

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Bohorquez supplementary material

Plan view of streamwise vorticity contours, ωz = ± 0.05, during the single-frequency vortex shedding process observed in our numerical simulations close to criticality for Re = 415, highlighting the temporal features of Fig. 7

Download Bohorquez supplementary material(Video)
Video 7.7 MB

Bohorquez supplementary material

Plan view of streamwise vorticity contours, ωz = ± 0.05, during the single-frequency vortex shedding process observed in our numerical simulations close to criticality for Re = 415, highlighting the temporal features of Fig. 7

Download Bohorquez supplementary material(Video)
Video 7.6 MB

Bohorquez supplementary material

Plan view of streamwise vorticity contours, ωz = ± 0.05, illustrating the low frequency shedding of vortices shown in Fig. 10 for Re = 500.

Download Bohorquez supplementary material(Video)
Video 5.7 MB

Bohorquez supplementary material

Plan view of streamwise vorticity contours, ωz = ± 0.05, illustrating the low frequency shedding of vortices shown in Fig. 10 for Re = 500.

Download Bohorquez supplementary material(Video)
Video 4.1 MB