Structure of turbulence in the flow around a rectangular cylinder

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.

An almost subharmonic instability in the flow past rectangular cylinders

“…In this case, the vortices shed from the LE shear layer that foster the 3-D instability result from a Kelvin-Helmholtz instability of the shear layer (Chaurasia & Thompson 2011). In the flow past elongated rectangular cylinders, a Kelvin-Helmholtz instability of the LE shear layer is not observed at the Reynolds number here considered, although it becomes a key feature of the flow at larger Re, as described by Chiarini et al (2022a) at Re = 3000 in the turbulent regime. A further difference between the two flows is that for the blunt flat plate, the 3-D instability is exactly subharmonic, since the base flow does not satisfy the present spatio-temporal symmetry.…”

“…The rectangular cylinder with A = 5 defines the benchmark of the aerodynamics of a rectangular 5 : 1 cylinder or BARC (see https://www.aniv-iawe.org/barc-docs), which aims to characterise the flow and set the standards for simulations and experiments in the turbulent regime. At large Reynolds numbers, the small-scale velocity fluctuations associated with the turbulent motions coexist and interact with the large-scale motions due to the flow instabilities, giving rise to a self-sustaining cycle (Cimarelli, Leonforte & Angeli 2018;Moore, Letchford & Amitay 2019;Chiarini et al 2022a). Hence the study of the flow instabilities at low Reynolds numbers and the comprehension of their triggering mechanisms is crucial also to understand the complex and multiscale flow dynamics in the turbulent regime.…”

“…At large Reynolds numbers, the small-scale velocity fluctuations associated with the turbulent motions coexist and interact with the large-scale motions due to the flow instabilities, giving rise to a self-sustaining cycle (Cimarelli, Leonforte & Angeli 2018; Moore, Letchford & Amitay 2019; Chiarini et al. 2022 a ). Hence the study of the flow instabilities at low Reynolds numbers and the comprehension of their triggering mechanisms is crucial also to understand the complex and multiscale flow dynamics in the turbulent regime.…”

Structure function tensor equations with triple decomposition

“…Extension and intensity of these sinks change with ϕ, according to the evolution of p cs 33 , π s 33 and d s 33 . A cut-off scale r z,min (Chiarini et al 2022a) can also be plotted to quantify the minimal scale where (spanwise) energy is always dissipated, regardless of the wall distance.…”

“…Arun et al (2021) derived the budget equation for the derivative of the two-point velocity correlation for compressible flows, and identified the effects of variable density and dilatation on the energy cascades. The more recent AGKE, instead, have been first demonstrated in a plane channel flow (Gatti et al 2020), and then used to investigate the ascending/descending and direct/inverse cascades of the Reynolds stresses in a turbulent Couette flow (Chiarini et al 2022b) and to characterise the structure of turbulence in the flow past a rectangular cylinder (Chiarini et al 2022a).…”