Fully Developed Flow in Curved Channels of Square Cross Sections Inclined

Abstract

The fully developed viscous flow in curved channels of obliquely oriented square cross section with angle of inclination is analyzed for an incompressible fluid. A nonorthogonal helical coordinate system is introduced to study the flow field for various angles of inclination. To obtain a stationary numerical solution, a primitive-variable formulation of the pressure-velocity finite-difference scheme is formulated based on an ADI method. The results for the channel at zero angle are compared with data available in the literature. Detailed predictions of secondary-flow streamlines, axial velocities and friction factor ratios show that there are significant changes at inclination angles 0, 15, 30, 45, 60, and 75 deg. At a certain Dean number, it is found that no additional pair of vortices appears near the outer wall, except for angle of inclination 0 deg. If the Dean number is less than 125 the friction factor ratio has a minimum value at zero angle. If the Dean number is greater than 125, the minimum value of the friction factor ratio occurs at the angles of rotation 15 and 75 deg.