  The simulation of fibre orientation in dilute suspension with a front moving
is carried out using the projection and level set methods. The motion of fibres
is described using the Jeffery equation and the contribution of fibres to the
flow is accounted for by the configuration field method. The governing
Navier-Stokes equation for the fluid flow is solved using the projection method
with finite difference scheme, while the fibre-related equations are directly
solved with the Runge-Kutta method. Our findings indicate that the fibre motion
has strong influence on the distributions of the streamwise and transverse
velocities in the fountain flow. Fibre motion produces strong normal stress
near the wall which leads to the reduction of transversal velocity as compared
to the Newtonian flow without fibres and in turn the streamwise velocity near
the wall is increased. Thus, the fibre addition to the flow weakens the
strength of the fountain flow. It is also found that the fibre orientation is
not always along the direction of velocity vector in the process of mold
filling. In the region of the fountain flow, the fibre near the centerline is
more oriented cross the streamwise direction comparing to that in the region
far behind the flow front. This leads to that the fibre near the centreline in
the region of fountain flow is more extended along the transverse direction.
Since fibre orientation in the suspension flow and the shape of the flow front
have great bearing on the quality of the product made from injection molding,
this study has much implications for engineering applications. These results
can also be useful in other field dealing with fibre suspensions.
