Characterization of the secondary flow in hexagonal ducts

In this work we report the results of DNSs and LESs of the turbulent flow through hexagonal ducts at friction Reynolds numbers based on centerplane wall shear and duct half-height Re τ,c ≃ 180, 360, and 550. The evolution of the Fanning friction factor f with Re is in very good agreement with experimental measurements. A significant disagreement between the DNS and previous RANS simulations was found in the prediction of the in-plane velocity, and is explained through the inability of the RANS model to properly reproduce the secondary flow present in the hexagon. The kinetic energy of the secondary flow integrated over the cross-sectional area 〈K〉 yz decreases with Re in the hexagon, whereas it remains constant with Re in square ducts at comparable Reynolds numbers. Close connection between the values of Reynolds stress u w ¯ on the horizontal wall close to the corner and the interaction of bursting events between the horizontal and inclined walls is found. This interaction leads to the formation of the secondary flow, and is less frequent in the hexagon as Re increases due to the 120∘ aperture of its vertex, whereas in the square duct the 90∘ corner leads to the same level of interaction with increasing Re. Analysis of turbulence statistics at the centerplane and the azimuthal variance of the mean flow and the fluctuations shows a close connection between hexagonal ducts and pipe flows, since the hexagon exhibits near-axisymmetric conditions up to a distance of around 0.15DH measured from its center. Spanwise distributions of wall-shear stress show that in square ducts the 90∘ corner sets the location of a high-speed streak at a distance z v + ≃ 50 from it, whereas in hexagons the 120∘ aperture leads to a shorter distance of z v + ≃ 38 . At these locations the root mean square of the wall-shear stresses exhibits an inflection point, which further shows the connections between the near-wall structures and the large-scale motions in the outer flow.