This work invesigates the two-dimensional fiber orientation in a recirculating flow within a salient corner of an abrupt expansion channel in order to elucidate the fiber orientation state in a recirculating flow as a fundamental study on anisotropic channel flow.
Orientation of a large number of fibers (N=1, 800) with aspect ratio r
a = 5 and 100, which are injected with a random initial orientation, can be evaluated by computing the Jeffery's equation along two streamlines. Then, the second-order orientation tensor and orientation ellipse, which are suitable and concise ways of describing the orientation distribution of fibers, can be determined using this statistical scheme. The effects of aspect-ratio of fibers and location of streamlines along which fibers circulate on the evolution of the second-order orientation tensor and the orientation ellipse are discussed in detail. Furthermore, orientation visualization experiments of large aspect-ratio fibers were carried out in a recirculating flow which occurs within a salient corner of a backward-facing step channel, and the observed fiber orientations are compared with the computed ones.
For large aspect-ratio fibers, steady orientation state of fibers can be obtained after several circulation, and furthermore, all fibers almost completely align along the streamlines. This result is obseved in both the experiments and computations.
On the other hand, the computations predict that for small aspect-ratio fibers, steady and almost complete orientation state can be observed along streamlines, however, preferred angle of fibers lies obliquely to the streamlines even in such an orientation state.
Therefore, fiber suspension flows through a complex channel, where recirculating flows occur, can be rigorously computed by taking account of fiber orientation distribution as follows :
(1) Fiber orientation distribution has to be computed in a main flow regime.
(2) In a recirculating flow regime, large aspect-ratio fibers completely align along the streamlines. On the otherhand, for small aspect-ratio fibers, steady and complete orientation state can also be attained, however, preferred angle of fibers has to be computed.
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