Vortex Patterns of the Flow in a Curved Duct

The vortex patterns of the secondary flow in a curved duct of square cross-section are numerically investigated. The flow is driven by the axial pressure gradient as well as the walls rotation of the duct except the outer wall around the center of curvature. When the rotation is in the same direction as the negative pressure gradient, the secondary flow shows complicated multiple patterns, which consists of two-vortex, four-vortex, eight-vortex or even non-symmetric secondary flow pattern. An analysis of linear stability on the flow is also carried out to distinguish possible flow patterns among multiple steady solutions.