Vortex-structure of secondary flows with effects of strong curvature on unsteady solutions through a curved rectangular duct of large aspect ratio

Due to engineering application and its intricacy, flow in a curved duct has become one of the most challenging research fields of fluid mechanics. In this paper, a computational numerical study is presented for the flow through a curved rectangular duct of aspect ratio 4 with strong curvature δ = 0.5 for the pressure gradient, the Dean number, 100 ≤ Dn ≤1000. A spectral method is employed as the basic tool to solve the system of nonlinear partial differential equations while function expansion and collocation method as the secondary tools. First, solution structure of the steady solutions is investigated. As a result, three branches of symmetric/asymmetric steady solutions with multi-vortex solutions are obtained by the path continuation technique. Then, in order to investigate non-linear behavior of the unsteady solutions, time evolution calculations as well as their phase portraits are obtained, and it is found that typical transition occurs from a steady flow to a chaotic state through periodic or multi-periodic flows if Dn is increased no matter what the curvature is. Finally, distribution of the time dependent solutions is shown in the Dean number vs. curvature (Dn ∓ δ) plane with vortex structure of secondary flows.