Influence of the geometry on the two- and three-dimensional dynamics of the flow in a 180° sharp bend

An analysis of the successive regimes of the two-dimensional (2D) flow through a sharp 180° bend is performed by means of parametric numerical simulations where the Reynolds number Re and the opening ratio ? (defined as the ratio of bend opening to the inlet width) vary in the respective ranges [0-2500] and [0.1-10]. In the outlet, the sequence of flow regimes is found to bear similarities with the flow behind a two-dimensional cylinder, despite being asymmetric by nature: when Re was increased, we found a laminar flow, then a flow with a first recirculation attached to the inside boundary, then one with a second recirculation attached to the top boundary. The onset of unsteadiness occurs through instability of the main stream and vortex shedding from the inside boundary. For ? ? 0.2, the flow is characterised by the dynamics of the jet generated at the very small turning part whereas for ? ? 0.3, it behaves rather like the flow behind an obstacle placed in a channel. This difference is most noticeable in the unsteady regimes where the vortex shedding mechanisms differ. While the former generates a more turbulent flow rich in small scale turbulence, the latter produces large structures of the size of the channel. In the turning part, further series of recirculation develop in each corner, akin to those identified by Moffatt ["Viscous and resistive eddies near a sharp corner," J. Fluid Mech.18, 1 (1964)10.1017/S0022112064000015]. For ? > 1 corresponding eddies merge to form a series of alternately rotating recirculating cells, which occupy the whole width of the turning part. We find that for ? > 1, the effective opening ratio ?*, which correspond to the area occupied by the mainstream while passing from the inlet to the outlet, tends towards a value of ?0.7. The combination of regimes in the outlet and the turning part yields a wealth of flow regimes, which open interesting possibilities to tailor the design of 180° bends to suit particular applications involving mixing, heat, and mass transfer. Selected 3D simulations show that with a few noticeable exceptions, 2D dynamics determine the main features of the flow (drag and recirculation length), even in a wide bend, while 3D structure tends to slow down the shedding mechanism. 2D simulations are thus not only relevant to configurations where the flow is expected to be 2D (thin bend, MHD flows), but also to 3D flows where they can predict some of the global flow features at a low computational cost. This abstract contains mathematical symbols which do not display correctly on this platform - please see the attached published version or the abstract on the publisher's website http://dx.doi.org/10.1063/1.4807070