Combined Effects of Centrifugal and Coriolis Instability of the Flow Through a Rotating Curved Duct of Small Curvature

In this paper, a comprehensive numerical study is presented for the fully developed two-dimensional flow of viscous incompressible fluid through a rotating curved rectangular duct of small curvature. Numerical calculations are carried out by using a spectral method, and covering a wide range of the Taylor number 0 ≤ Tr ≤ 2000 for the Dean numbers Dn = 500 and 1000. A temperature difference is applied across the vertical sidewalls for the Grashof number Gr = 100, where the outer wall is heated and the inner wall cooled. The rotation of the duct about the center of curvature is imposed, and the effects of rotation (Coriolis force) on the unsteady flow characteristics are investigated. It is found that the unsteady flow undergoes in the scenario ‘Chaotic→ multi-periodic→ periodic → steady-state’, if Tr is increased in the positive direction. Contours of secondary flow patterns and temperature profiles are also obtained at several values of Tr, and it is found that there exist two- and multi-vortex solutions for the unsteady flow if the duct rotation is involved in the present cases.