Abstract
A study of the back flow events and critical points in the flow through a toroidal pipe at friction Reynolds number Reτ ≈ 650 is performed and compared with the results in a turbulent channel flow at Reτ ≈ 934. The statistics and topological properties of the back flow events are analysed and discussed. Conditionally-averaged flow fields in the vicinity of the back flow event are obtained, and the results for the torus show a similar streamwise wall-shear stress topology which varies considerably for the spanwise wall-shear stress when compared to the channel flow. The comparison between the toroidal pipe and channel flows also shows fewer back flow events and critical points in the torus. This cannot be solely attributed to differences in Reynolds number, but is a clear effect of the secondary flow present in the toroidal pipe. A possible mechanism is the effect of the secondary flow present in the torus, which convects momentum from the inner to the outer bend through the core of the pipe, and back from the outer to the inner bend through the pipe walls. In the region around the critical points, the skin-friction streamlines and vorticity lines exhibit similar flow characteristics with a node and saddle pair for both flows. These results indicate that back flow events and critical points are genuine features of wall-bounded turbulence, and are not artifacts of specific boundary or inflow conditions in simulations and/or measurement uncertainties in experiments.
Highlights
A detailed assessment of the near-wall region in turbulent flows is a very complex problem, which involves a number of interesting fundamental questions including its modulation by the flow in the outer region [1, 2, 3, 4]
I.e. regions of reverse flow, were characterised in the torus and compared with the ones obtained in a direct numerical simulations (DNSs) of turbulent channel flow at Reτ 934
Our results show that back flow events are less numerous in the toroidal pipe than in the channel, with probabilities of occurrence of 0.006% and 0.06% in both cases, respectively
Summary
A detailed assessment of the near-wall region in turbulent flows is a very complex problem, which involves a number of interesting fundamental questions including its modulation by the flow in the outer region [1, 2, 3, 4]. The transport phenomena [5] present close to the wall, which can be characterised in terms of the wall-shear stress vector field, are relevant to understand a wide range of applications, including cardiovascular flows [6] (and as discussed by Arzani et al [7] in the context of Lagrangian wall-shear stress structures) and heat transfer (see for instance the studies by Dairay et al [8] and Wu et al [9]). The presence of regions of instantaneous reverse flow (denoted in the present work as back flow events) in wallbounded turbulence is a topic of relevance for the understanding of separation mechanisms, both in steady [10] and unsteady [11] aerodynamic applications.
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