Abstract
The occurrence of backflow events, defined as negative wall-shear stress, is rare in turbulent flows. It is found that these backflow events are further suppressed in a toroidal flow when compared to a straight pipe flow at a nominally similar Reynolds number. The reduction of backflow is due to the secondary flow of Prandtl's first kind occurring in the toroidal flow.
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 [1,2,3,4,5]
The comparison between the toroidal pipe and its straight counterpart shows fewer backflow events and critical points in the torus. This is attributed to the secondary flow of Prandtl’s first kind present in the toroidal pipe, which is responsible for the convection of momentum from the inner to the outer bend through the core of the pipe, and back from outer bend to the inner bend along the azimuthal direction
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 pipe flow at Reτ 500
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 [1,2,3,4,5]. The transport phenomena [6] present close to the wall, which can be characterized in terms of the wall-shear-stress vector field, are relevant to understand a wide range of applications, including cardiovascular flows [7] (e.g., in the context of Lagrangian wall-shear stress structures [8]) and heat transfer [9,10]. The presence of regions of instantaneous reverse flow (denoted in the present work as backflow events) in wall-bounded turbulence is a topic of relevance for the understanding of separation mechanisms, both in steady [11] and unsteady [12] aerodynamic applications. Backflow events and the topology of the wall-shear stress have been used to further understand the separation mechanisms from the perspective of dynamical systems [14], control theory [15], and reduced-order
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