Abstracts - KTH Mechanics

Modelling Shear Flow Effects on the Fibre Orientation
Distribution Function in a Planar Contraction
M. Hyensjö ∗ and Anders Dahlkild †
The effect of turbulence generating vanes and its location in a planar contraction
on fibre orientation anisotropy was studied by mathematical modelling. We use single
phase CFD modelling as an input for the fibre orientation dispersion model to study
the effect of shear flow and turbulence in an accelerated fluid flow on fibre orientation
anisotropy. The fibre dispersion model is based on a Fokker-Planck equation 1 ,which
describes the evolution of the fibre orientation probability distribution function in a
flow field. We consider a plane case, for one orientation angle in the symmetry plane 2
of the contraction, and also the case of a 3D fibre orientation described with two
orientation angles. The rotational angular velocities are based on the flow around a
fibre with high aspect ratio, but without spatial extension 3 . The two models have
been compared to experimental data 4 . For different streamlines in the contracting
channel, the fibre orientation distribution function is obtained numerically, and the
fibre orientation anisotropy could be studied along streamlines near the vane wall
and vane tip and further away downstream. In figure 1 (a), (b) and (c) example on
outlet fibre orientation distributions are shown for a wake, a undisturbed region and
a wall boundary layer respectively. A higher degree of orientation can be seen in the
undisturbed region, i.e. cf. figure 1 (b). In the wake region, cf. figure 1 (a), for a
plane γ=0, the preferred orientation angle is shifted towards β values smaller than π
/2, i.e. fibres are oriented upwards, the opposite effect is shown for the wall boundary
layer, cf. figure 1 (c). For the wake region of the outlet profile of the contraction
the fibre orientation anisotropy was decreased by moving the vane tip closer to the
outlet.
Figure 1: (a) The wake region. (b) The undisturbed region. (c) The boundary layer
∗ Metso Paper Karlstad AB, SE-651 15 Karlstad, Sweden.
† KTH Mechanics OB 18, SE-100 44 Stockholm, Sweden.
1 Advani and Tucker, Journal of Rheology, 31(8) (1987).
2 Hyensjö, Krochak, Olson, Hämäläinen and Dahlkild, In Proc. ICMF’04, Yokohama, (2004).
3 Jeffrey, Proc. R. Soc., 102(A) (1922).
4 Asplund and Norman, Journal of Pulp and Paper Science, 30(8) (2004).
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