Numerical Prediction of Dean-Taylor Flow and Unsteady Solutions through a Rotating Curved Duct

The fluid flowing in a rotating curved duct is subjected to both the Coriolis force due to rotation and the centrifugal force due to curvature of the duct. In this paper, the combined effects of the two forces on the fluid flows in a rotating curved duct have been examined numerically by using a spectral method, and covering a wide range of the Dean number and the Taylor number. Numerical results are obtained for both the positive and negative rotation of the duct. First, steady solutions are obtained by the Newton Raphson iteration method. As a result, multiple branches of steady solutions with two-, four- and six-vortex solutions are obtained. Linear stability of the steady solutions is then investigated. When there is no stable steady solution, time evolution calculations as well as their phase orbits show that the flow undergoes through various flow instabilities, if the Dean number or the Taylor number is increased. Secondary flow patterns and axial flow distributions are also obtained for the both cases