Flow Through a Rotating Curved Duct with Square Cross-Section

The incompressible viscous steady flow through a curved duct of square cross-section driven by a pressure gradient along the duct is considered. The rotation of the duct about the centre of the curvature is imposed to investigate the combined effects of rotation (Coriolis force) and curvature (centrifugal force) on the flow. The numerical calculations covering a wide range of rotational speed are carried out for the Dean numbers, D_n, of 400, 642 and 800. When the rotation is in the same as the main flow direction, multiple solutions with 2-cell and 4-cell secondary flow patterns are obtained in case of D_n = 400 and 642, while only 4-cell solution is obtained in case of D_n = 800. When the rotation is opposite to the main flow direction, the 6-cell secondary flow pattern is obtained for D_n = 400, 642 and D_n = 800 with increasing the rotational speed gradually. For all cases, the total flux through the duct has a sharp peak, where the 6-cell pattern appears.