A numerical investigation of developing flow in an eccentric curved annulus in the presence of gravity

In this article developing incompressible viscous flow in an eccentric curved annulus in the presence of gravity is numerically studied using a second order finite difference method based on the projection algorithm to solve the governing equations including the continuity and full Navier–Stokes equations. The equations written in a bipolar–toroidal coordinate system are discretized in a three dimensional staggered grid. The effects of governing non-dimensional parameters including the eccentricity, non-dimensional curvature ratio, Dean number, Froude number, aspect ratio, and the Reynolds number on the flow field in the entrance and fully developed region are investigated. The numerical results indicate that at the small Froude numbers, the flow field distorts from the symmetrical condition due to the larger body force effect and the axial velocity formation mostly takes place at the lower half of the annulus. In addition, at the constant Froude number, by decreasing the curvature radius, the peak axial velocity and its sharp gradient appear on the outer curvature region due to the larger centrifugal forces and by increasing the eccentricity the flow rate intensifies at the wider region and weakens at the narrower region due to the larger flow resistance. Furthermore, the friction factor increases by decreasing the Froude number and increasing the Dean number.

► Developing flow in an eccentric curved annulus in the presence of gravity for the first time.
► Deriving governing equations in bipolar–toroidal coordinates system.
► Study of mutual effect of eccentricity and curvature on the flow field pattern.
► Study of friction factor dependence on the curvature, eccentricity, Dean number, and Froude number.