Theoretical analysis on the secondary flow in a rotating helical pipe with an elliptical cross section

In the present study, the flow in a rotating helical pipe with an elliptical cross section is considered. The axes of the elliptical cross section are in arbitrary directions. Using the perturbation method, the Navier-Stokes equations in a rotating helical coordinate system are solved. The combined effects of rotation, torsion, and geometry on the characteristics of secondary flow and fluid particle trajectory are discussed. Some new and interesting conclusions are obtained, such as how the number of secondary flow cells and the secondary flow intensity depends on the ratio of the Coroilis force to the centrifugal force. The results show that the increase of torsion has the tendency to transfer the structure of secondary flow into a saddle flow, and that the incline angle alpha increases or decreases the secondary flow intensity depending on the resultant force between the Corilois force and centrifugal force.