Numerical simulation of contraction and expansion flows of fiber suspensions

Abstract

Flow patterns and fiber orientations in the two‐dimensional contraction and expansion flows of fiber suspensions are calculated using Dinh–Armstrong model. The assumption that all fibers lie tangent to a streamline is excluded from the present calculation. Therefore the Jeffery’s equation is integrated along a streamline to obtain the fiber orientation. The flow pattern of fiber suspension is different from that of Newtonian fluid: a vortex near the corner in the suspension flow becomes larger than that in the Newtonian flow. The dependence of the vortex length on a parameter a, which is a characteristic parameter of fiber suspensions,, and on Reynolds number is discussed. In the contraction flow, fibers lie tangent to a streamline in the main flow, but not in the vortex region. In the expansion flow, however, fibers rotate along a streamline, so fibers do not lie tangent to a streamline even in the main flow. Furthermore, stress‐relief‐mechanism causes increase of the vortex in both flows.