Numerical analysis of Taylor-Dean flow through a curved duct of rectangular cross-section

The Taylor-Dean flow through a curved duct of rectangular cross-section is investigated numerically by use of the spectral method. The calculation covers a wide range of the pressure gradient (Dean number) and the rotational speed (Taylor number) of the duct. In the present calculation, two types of aspect ratio, γ = 2 and 3 are considered. Steady flow patterns of the induced secondary flow are obtained. Especially, multiple solutions appear in some ranges of the Taylor number when the secondary flows show very complicated behavior. In the case of γ = 2, there appear four-vortex or six-vortex secondary flow patterns. For γ = 3, flows having many secondary vortices, such as eight vortices or asymmetric flows appear. Finally, time evolution calculations of the solutions are performed. It is found that an unstable solution approaches a stable solution if it exists, while the flow oscillates periodically if there exists no stable steady solution.