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Structure of turbulence in the flow around a rectangular cylinder

Published online by Cambridge University Press:  11 August 2022

Alessandro Chiarini Open the ORCID record for Alessandro Chiarini [Opens in a new window] ,
Davide Gatti Open the ORCID record for Davide Gatti [Opens in a new window] ,
Andrea Cimarelli Open the ORCID record for Andrea Cimarelli [Opens in a new window]  and
Maurizio Quadrio Open the ORCID record for Maurizio Quadrio [Opens in a new window]
Alessandro Chiarini*
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
Davide Gatti
Affiliation:
Institute for Fluid Mechanics, Karlsruhe Institute of Technology, Kaiserstr. 10, 76131 Karlsruhe, Germany
Andrea Cimarelli
Affiliation:
DIEF, University of Modena and Reggio Emilia, 41125 Modena, Italy
Maurizio Quadrio
Affiliation:
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, via La Masa 34, 20156 Milano, Italy
*
†Email address for correspondence: [email protected]
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Abstract

The separating and reattaching turbulent flow past a rectangular cylinder is studied to describe how small and large scales contribute to the sustaining mechanism of the velocity fluctuations. The work is based on the anisotropic generalised Kolmogorov equations, exact budget equations for the second-order structure function tensor in the space of scales and in the physical space. Scale-space energy fluxes show that forward and reverse energy transfers occur simultaneously in the flow, with interesting modelling implications. Over the longitudinal cylinder side, the Kelvin–Helmholtz instability of the leading edge shear layer generates large spanwise rolls, which get stretched into hairpin-like vortices and eventually break down into smaller streamwise vortices. Independent sources of velocity fluctuations act at different scales. The flow dynamics is dominated by pressure–strain: the flow impingement on the cylinder surface in the reattachment zone produces spanwise velocity fluctuations very close to the wall, and at larger wall distances reorients them to feed streamwise-aligned vortices. In the near wake, large von Kármán-like vortices are shed from the trailing edge and coexist with smaller turbulent structures, each with its own independent production mechanism. At the trailing edge, the sudden disappearance of the wall changes the structure of turbulence: streamwise vortices vanish progressively, while spanwise structures close to the wall are suddenly turned into vertical fluctuations by the pressure–strain.

JFM classification

Turbulent Flows: Shear layer turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 946 , 10 September 2022 , A35
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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