Numerical solution of fiber suspension flow through a complex channel

Abstract

Both numerical simulations and fiber orientation observations were carried out to investigate two-dimensional fiber orientations in a Newtonian flow through a 1:4 backward-facing step channel. Furthermore, the flows of suspensions with high aspect-ratio fibers in a Newtonian solvent through a 1:4 backward-facing step channel were computed rigorously by coupling the flow field with fiber orientation. In the numerical simulations, a statistical scheme (number of fibers N=1800) was used. In a recirculating flow, all fibers completely align along the streamlines for large aspect-ratio fibers ( r a=10 000), while complete alignment can be achieved, however, the preferred angle lies obliquely to the streamlines for small aspect-ratio fibers ( r a=5). On the other hand, in a main flow, the preferred angle lies obliquely to the streamlines in the central region of the channel, and furthermore, the fibers are less oriented and their preferred angles tilt away largely from the streamlines as the Reynolds number (Re) decreases. In the computations of flows of suspensions with high aspect-ratio fibers, co-linear alignment of fibers was used in a recirculating flow, while a complete alignment condition was adopted in a main flow. The relation between the fiber parameter φμ/ η and vortex length L v* follows a linear trend and its gradient decreases as Re increases, i.e. when inertia dominates the flow, the effect of fiber additives on flow structure becomes insignificant in an expansion flow. In an expansion flow of fiber suspensions for the complete alignment case, the worst orientation of fibers can be predicted clearly as a band-like pattern both near the vortex boundary and in the upper region of the expanding part. It can be supposed that fluid anisotropy near the vortex boundary is a key factor for the vortex enhancement in a complex flow.