Three-dimensional fiber orientation of fiber suspensions flowing through a rotating curved expansion duct

Abstract

A complete three-dimensional Jeffery equation is solved through both analytical and numerical method to obtain the orientation evolution of a single fiber rotating in a shear flow. The orientation evolutions of a single fiber under different conditions are given. A more complete model for the simulation of fiber orientation is presented and combined with the Runge-Kutta algorithm to obtain the evolution of fiber orientation in the fiber suspensions through a rotating curved expansion duct. The numerical results show that the evolution of fiber orientation along the duct in different cross-sections is quite different. The fiber orientations change drastically in the vicinity of the inlet and then change slowly along the flow direction. The inlet velocity has little effect on the evolution of fiber orientation, but a great effect on the trajectory of the fiber. The effect of the initial fiber orientation on the evolution of fiber orientation is contrary to that of inlet velocity. The effect of rotation rate on the evolution of fiber orientation is much smaller than that of inlet velocity. Near the concave wall region the smaller the fiber aspect ratio is, the more drastically the fibers swing. The fibers near the centerline and the convex wall region do not show a swing. Studying such complex flow will beneficially contribute to reach a better understanding of flow properties in many important manufacturing processes to make composites.