Laminar flows through a curved rectangular duct over a wide range of the aspect ratio

The laminar flow in a curved rectangular duct for a range of the aspect ratio 1 less than or equal to l less than or equal to 12 is investigated by use of the spectral method. The steady solutions are obtained using the Newton-Raphson method with the symmetry condition. As a result, five branches of steady solutions are found. Linear stability characteristics are also investigated for all the steady solutions. It is found that one steady solution is linearly stable for most of 1, but two linearly stable steady solutions exist for a region of small 1 and there are several intervals of 1 where there is no linearly stable steady solution. We performed time-evolution calculations with and without the symmetry condition, and observed periodic oscillations with the symmetry condition and aperiodic time evolutions without the symmetric condition. Finally, the present results numerically suggest that what determines which solution is realizable may be the maximum of the momentum transfer in the cross section. (C) 2002 Published by The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.