On the relation between centrifugal force and radial pressure gradient in flow inside curved and S-shaped ducts

Swirl flow in a curved duct and S-duct is governed by a centrifugal force and radial pressure gradient force between the sidewalls. In the present work, we introduce a dimensionless parameter that relates the ratio of these two forces and the duct’s center-line distance and show how the parameter is related to other more familiar dimensionless terms such as the pressure coefficient, Reynolds number, and Dean number. By using published data as well as our own measurements, it is shown that the data collapse reasonably well on a curve when the proposed parameter is plotted against dimensionless distance along the duct. The existence of collapsed curves for ducts of different curvature ratios indicates that the proposed parameter can be used to characterize the flow, although some scatter in the data exists, due to the presence of flow separation and streamwise vortices along the wall of the curved ducts. An attempt to suppress flow separation by using vortex generators in the S-duct leads to some improvement in the collapsed curve at the first bend of the duct. The results reported here are mainly focused on square and circular constant cross-sectioned 90° curved ducts and S-shaped ducts of different curvature ratios.