Laminar secondary flows in curved rectangular ducts

The occurrence of secondary flow in curved ducts due to the centrifugal forces can often significantly influence the flow rate. In the present work, the secondary flow of an incompressible viscous fluid in a curved duct is studied by using a finite-volume method. It is shown that as the Dean number is increased the secondary flow structure evolves into a double vortex pair for low-aspect-ratio ducts and roll cells for ducts of high aspect ratio. A stability diagram is obtained in the domain of curvature ratio and Reynolds number. It is found that for ducts of high curvature the onset of transition from single vortex pair to double vortex pair or roll cells depends on the Dean number and the curvature ratio, while for ducts of small curvature the onset can be characterized by the Dean number alone. A comparison with the available theoretical and experimental results indicates good agreement. A correlation for the friction factor as a function of the Dean number and aspect ratio is developed and is found to be in good agreement with the available experimental and computational results for a wide range of parameters.