Flow through a Rotating Curved Square Duct: The Case of Positive Rotation

Abstract

In this paper, a comprehensive numerical study is presented for the flow characteristics through a rotating curved duct with square cross section. Numerical calculations are carried out by using a spectral method and covering a wide range of the Taylor number 0 ≤ Tr ≤ 3000 for two cases of the Dean numbers, Case I: Dn =1000 and Case II: Dn = 2000 . A temperature difference is applied across the vertical sidewalls for the Grashof numberGr = 500 , where the outer wall is heated and the inner one cooled. In this paper, the positive rotation of the duct about the center of curvature is imposed, and the effects of rotation (Coriolis force) on the flow characteristics are investigated. As a result, multiple branches of asymmetric steady solutions with two-, three- and four-vortex solutions are obtained. Time evolution calculations as well as phase spaces of the unsteady solutions are obtained, and it is found that in the unstable region the flow undergoes in the scenario “periodic → chaotic → multi-periodic → periodic → steady-stable”, if Tr is increased.