ON THE ONSET OF DEAN VORTICES AND UNSTEADY SOLUTIONS THROUGH A CURVED RECTANGULAR DUCT OF LARGE ASPECT RATIO

Abstract

The present study covers a comprehensive numerical study on fully developed two-dimensional flow of viscous incompressible fluid through a curved rectangular duct of aspect ratio 4. Numerical calculations are carried out by using a spectral method, and covering a wide range of the Dean number,100 DnCase I: as formation of Dean vortices on unsteady solutions as the unsteady flow is steady-state, periodic, multi-periodic or chaotic, if the Dn is increased. Time evolution calculations show that the steady-state flow turns into chaotic flow through various flow instabilities, if Dn is increased no matter what the curvature is. It is found that the unsteady flow is a steady-state solution for small Dn`s, and it oscillates periodically or non-periodically (chaotic) between two-, four-, six-, eight- ten- and twelve-vortex solutions, if Dn is increased. In this study, we obtained multi-vortex solutions due to strong centrifugal force. It is found that the chaotic solution is weak for small Dn’s but strong as Dn becomes large. It is also found that the axial flow shifted to the outer wall of the duct as Dn increases

Keywords

• Curved duct, secondary flow, unsteady solutions, Dean number, aspect ratio

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