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Particulars of the cross- and spanwise near-wake development of a short Semicircular-section Shell, through the TransitionRe-range (60 ≤Re ≤ 600)

Abstract

Within the fundamental context of quasi-2D bluff-body near-wake investigation, we analyse the way the initial wake vortices (primary and secondary vortices) form and develop with time behind a short (5.2∶1) cylindrical semicircular shell (hollow at the back), after an impulsive start in translation. The study includes the transition regime and non-usual cross-sectional shapes. The structure of the vortices is examined by means of precise visualizations both in the mid-cross and mid-span planes. The particulars induced by the hollow face are deduced from a comparison with the cases of analogous solid cylinders and more particularly with the full semicircular cylinder (Boisaubert et al., 1996; Coutanceau et al., 1998).

The crosswise analysis shows that, except some fundamental difference at the separation initiation and some differences in details, a similar development of the Bénard-Kàrmàn-vortices is observed, thus :

  • - the regime of the occurring structures changes beyond the first phase of development (i.e.t * ≥ 6) when Reynolds number is passing through a critical valueRe c (here 120 ≤Re c ≤ 140)

  • - Kelvin-Helmholtz instabilities are detected forRe = 600 in the rolled-up separated shear layers originating from the sharp body-edges.

On the contrary, the spanwise analysis reveals that the hollow face plays an important role in the time-development of the induced body-end three-dimensionalities (end-vortices and opposite spanwise currents) and intrinsic three-dimensionalities respectively. Thus, as opposed to solid bodies similarly limited in span, the emergence of clear patterns of secondary Taylor-Görtler-like vortices in the near wake have been experimentally proved for the first time whenRe passes beyond the transition value ofRe t ≊ 200. The consequence on the global structure of the flow is deduced.

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Correspondence to M. Coutanceau.

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Author Profile Madeleine Coutanceau: She was (up to 1995) Professor of Fluid Mechanics at the University of Poitiers, France, from which she received her Doctorat ès Sciences in 1971. She was at the head of a research group working mainly in the domain of flow visualization. Her main themes of research include the investigation of viscous flows around obstacles with rigid or free surfaces, such as drops and bubbles, in Newtonian and non-Newtonian liquids, and the time development of wakes around bluff bodies and aerodynamic profiles subjected to various motions after an impulsive start. She is currently an Honorary Professor of the University of Poitiers, a member of the Association Universitaire de Mécanique, of the Scientific Committee of the Colloque National de Visualisation et de Traitement d’Images en Mécanique des Fluides and of the International Organizing Board of the International Symposium on Flow Visualization.

Christophe Migeon: He received his master degree from the University of Poitiers, France, in 1995. He is currently about to get his Ph.D. in Aerodynamics and Fluid Mechanics from the same University. His theme of research is related to the two- and three-dimensional study of various lid-driven cavity-flows. At the same time, he is a lecturer at the Institut National de Sciences Appliquées (INSA) in Rennes, France.

Patrick Erhmann: He received his master degree (1992) and his Ph.D. (1996) from the University of Poitiers, France, in the domain of Aerodynamics and Fluid Mechanics. His theme of research was related to the comparative study of wake formation as function of the body shape. He is currently a manager in the french automotive branch of a US firm.

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Coutanceau, M., Migeon, C. & Ehrmann, P. Particulars of the cross- and spanwise near-wake development of a short Semicircular-section Shell, through the TransitionRe-range (60 ≤Re ≤ 600). J Vis 3, 9–26 (2000). https://doi.org/10.1007/BF03182437

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Keywords

  • three-dimensional formation
  • cylindrical shell
  • cross and spanwise visualization
  • primary and secondary instabilities