Taylor-Dean flow through a curved duct of square cross section

The Taylor-Dean flow through a curved duct of square cross section, in which walls of the duct except the outer wall rotate around the center of curvature and an azimuthal pressure gradient is imposed, is investigated numerically using the spectral method. The calculation covers a wide range of pressure gradient and duct rotational speed. The steady flow patterns of the induced secondary flow and flux through the duct are obtained. It is found that the secondary flow consists of two vortices in a cross section when the rotation of the duct is large and opposite to the negative pressure gradient. When the rotation is in the same direction as the negative pressure gradient, the secondary flow shows more complicated behavior. There appear four-vortex, eight-vortex or even non-symmetric secondary flow patterns with respect to the center line of the cross section. An analysis of linear stability is also carried out.