Numerical Solution of Fiber Orientation in a Backward-Facing Step Channel

Abstract

As a fundamental study on anisotropic channel flow, two-dimensional fiber orientation was investigated in a main flow as well as in a recirculating flow within a salient corner of a backward-facing step channel. For a large number of fibers (N=1800, aspect ratio γa=5 and 10000) having a random initial orientation, the orientation distribution after injection was computed with the Jeffery's equation along streamlines in Newtonian flows. This distribution, which was described by the second-order orientation tensor and the orientation ellipse determined on a statistical basis, was compared with the actual distribution found from experiments.For large γa, both experiments and computations indicated that steady orientation was achieved after several circulation and all fibers aligned almost completely along the streamlines in a recirculating flow. For small γa, the computations predicted that almost complete orientation was achieved at steady state but a preferred orientation angle lay obliquely to the streamlines. When fibers almost completely aligned along the streamlines flowed into an expanding part of a channel, this orientation state remained in a main flow at high Reynolds numbers Re, because of gradual divergence of main flow, but their preferred orientation angle lay obliquely to the streamlines in the central region of the channel. In contrast, for low Re that resulted in the main flow abruptly diverging at the expanding part, the fibers were less oriented and their preferred orientation angle in the central region increased just at downstream side of the expansion entrance. This worse orientation was expected to remain in a wider downstream region for lower Re.All above results provided a clue for rigorous computation of fiber suspension flows, which is carried out by coupling flow field with fiber orientation state, through a complex channel often inducing a recirculating flow.