Entry flow in weakly curved ducts

The properties of the flow in the entry region of curved ducts at large Dean numbers and small but finite ratios of curvature K(0) are studied using an integral method. The results show that a singularity develops at the inner generator at a finite value of a suitable axial distance, and that the location of the singularity shifts to larger distances as K(0) increases. At the outer generator the velocity profiles assume the form of the similarity solution derived by Weiss (1975) in the limit of infinite distances from the inlet. Here, finite values of K(0) tend to increase the asymptotic value of the displacement thickness. Evaluation of the results for arbitrary generators shows that the deviations of the axial velocities from the Blasius profile are small except in the neighborhood of the singularity.