Numerical techniques for the prediction of flow induced orientation

Short fiber orientations are predicted from the mold processing conditions based on the dilute suspension theory. The velocity components and the stream function are, in general, solved by the finite element method. Fiber orientations within the flow are subsequently calculated in terms of the fluid kinematics. Three distinct numerical schemes are developed for the prediction of short fiber orientations; one method endeavors to track individual fiber motions within the flow to determine a particle trajectory. Secondly, random initial fiber orientation conditions imposed at the inlet sections of the mold are simulated by a statistical orientation distribution. A third technique utilizes the Galerkin finite element method which is applied directly to the system of orientation equations to obtain a piecewise continuous approximation to the fiber orientation state on a grid of triangular and/or quadrilateral quadratic elements.