Backflow events under the effect of secondary flow of Prandtl's first kind

A study of the backflow events in the flow through a toroidal pipe at friction Reynolds number Re-tau approximate to 650 is performed and compared with the results in a straight turbulent pipe flow at Re-tau approximate to 500. The statistics and topological properties of the backflow events are analysed and discussed. Conditionally averaged flow fields in the vicinity of the backflow event are obtained, and the results for the torus show a similar streamwise wall-shear stress topology which varies considerably for the azimuthal wall-shear stress when compared to the pipe flow. In the region around the backflow events, critical points are observed. The comparison between the toroidal pipe and its straight counterpart also 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. These results indicate that backflow events and critical points are genuine features of wall-bounded turbulence, and are not artefacts of specific boundary or inflow conditions in simulations and/or measurement uncertainties in experiments.