Abstract
The flow topology of the wake behind a circular cylinder at the super-critical Reynolds number of Re=7.2×105 is investigated by means of large eddy simulations. In spite of the many research works on circular cylinders, there are no studies concerning the main characteristics and topology of the near wake in the super-critical regime. Thus, the present work attempts to fill the gap in the literature and contribute to the analysis of both the unsteady wake and the turbulent statistics of the flow. It is found that although the wake is symmetric and preserves similar traits to those observed in the sub-critical regime, such as the typical two-lobed configuration in the vortex formation zone, important differences are also observed. Owing to the delayed separation of the flow and the transition to turbulence in the attached boundary layer, Reynolds stresses peak in the detached shear layers close to the separation point. The unsteady mean flow is also investigated, and topological critical points are identified in the vortex formation zone and the near wake. Finally, time-frequency analysis is performed by means of wavelets. The study shows that in addition to the vortex shedding frequency, the inception of instabilities that trigger transition to turbulence occurs intermittently in the attached boundary layer and is registered as a phenomenon of variable intensity in time.
Highlights
Massoudi and Ivette RodríguezThe flow past a circular cylinder has been the subject of many investigations, as the complexity of the flow—which involves a laminar boundary layer, separation of the flow, the transition to turbulence and the development of a turbulent wake with a periodic vortex shedding—is present in a wide range of engineering applications
The main observations of these studies regarding the super-critical wake can be summarized as follows. (i) The separated shear layers are bent toward the wake centerline, where they interact with each other; the vortex shedding frequency rises up to St ≈ 0.44. (ii) The super-critical wake is symmetric with two symmetric separation bubbles on each side of the cylinder rear. (iii) Drag and lift fluctuations decrease by about an order of magnitude with respect to the values reported for the sub-critical regime and the onset of the critical one
These observations are in agreement with the results obtained from large eddy simulations (LES) computations by Rodríguez et al [16], where the wake was described to be coherent with a narrow band energy peak in the spectrum of the lift fluctuations centered at the the vortex shedding frequency of St = f vs Ure f /D ≈ 0.44
Summary
The flow past a circular cylinder has been the subject of many investigations, as the complexity of the flow—which involves a laminar boundary layer, separation of the flow, the transition to turbulence and the development of a turbulent wake with a periodic vortex shedding—is present in a wide range of engineering applications. The mesh used was coarser than that used in Rodríguez et al [16], the topological characteristics presented, as well as the pressure distribution and aerodynamic coefficients, were in good agreement with those reported in the literature. Another point of discussion is whether vortex shedding exists in the super-critical regime. Even though different authors measured a coherent vortex shedding frequency in this regime (see, for instance, the experimental works of [3,4,17]), the super-critical wake has traditionally been described as incoherent [2,5,18,19], with turbulent transition at separation. The coherent vortex motion is resolved by using the phase-averaging technique, and it is compared to those reported in the sub-critical regime
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