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Combined effects of centrifugal and coriolis instability of the flow through a rotating curved duct with rectangular cross section have been studied numerically by using a spectral method, and covering a wide range of the Taylor number for a constant Dean number. The rotation of the duct about the center of curvature is imposed in the positive direction, 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 multi-vortex solutions are obtained. To investigate the non-linear behavior of the unsteady solutions, time evolution calculations as well as power spectrum of the unsteady solutions are performed, and it is found that the unsteady flow undergoes through various flow instabilities in the scenario “chaotic → multi-periodic → periodic → steady-state”, if Tr is increased in the positive direction. The present results show the characteristics of both the secondary flow and axial flow distribution in the flow.

Recently, great attention has been paid for the study of flows and heat transfer through rotating curved ducts and channels because of its practical application in chemical, mechanical, bio-mechanical and biological engineering. A quantitative analogy between flows in stationary curved pipes and orthogonally rotating straight pipes has been reported by Ishigaki [

One of the interesting phenomena of the flow through a curved duct is the bifurcation of the flow because generally there exist many steady solutions due to channel curvature. An early complete bifurcation study of two-dimensional (2-D) flow through a curved duct with square cross section was performed by Winters [

It is well known that, fluid flowing in a rotating curved duct is subjected to two forces: the Coriolis force, caused by the rotation of the duct, and centrifugal force caused by the curvature of the duct. These two forces affect each other, as a result complex behavior of the secondary flow and the axial flow can be obtained (Wang and Cheng [

Time dependent analysis of fully developed curved duct flows was first initiated by Yanase and Nishiyama [

In the present study, a comprehensive numerical result is presented for fully developed bifurcation structure of two-dimensional (2D) viscous incompressible fluid flow through a rotating curved rectangular duct. Flow characteristics are investigated over a wide range of Taylor number

Consider that the flow is viscous and incompressible which is streaming through a rotating curved duct with rectangular cross section. Let 2h and 2l be the height and the width of the cross section.

Momentum equations

where

where