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 α, 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.