A COMPUTATIONAL APPROACH FOR THE MODELING OF SHORT-FIBER ORIENTATION IN A VISCOUS FLOW DURING THE MOLD-FILLING PROCESS USING DIFFERENT CLOSURE APPROXIMATIONS

The last half century has seen an increase in the use of fiber composites in
many areas. One such class of composites is Short Fiber Reinforced Thermoplastics
(SFRT), well known for their versatility in various applications. However, the
physical properties of the finished molding are highly dependent upon the fiber
orientation, which in turn is heavily influenced by the processing conditions. It is
thus of interest to model the mold-filling process and compute the resulting fiber
orientation due to the flow field that develops within the mold. This was done in this
research in three stages. In the first stage, the mold-filling flow was modeled as a
non-isothermal, incompressible, non-Newtonian fluid in a three-dimensional flow.
The flow equations were solved numerically using the commercial Computational
Fluid Dynamics (CFD) code, FLUENT 6.3. The simulation setup was validated by
means of comparison with a numerical test case from literature. In the second stage,
the fiber orientation evolution equation was discretized and numerically solved in
Matlab, utilizing coefficients obtained from data imported from FLUENT. The third
stage included a comparison of the performances of three closure models; linear,
quadratic and hybrid, used to complete the fiber orientation evolution equation. The
experimental data set was obtained from literature and it consisted of fiber
orientation measurements from an injection molded, film-gated rectangular strip. For
all three closure models, the dominant orientation component was directed along the
flow direction – the a11 orientation tensor. The numerically computed a11 orientation
tensor produced results which agreed well with the experimental data where the
typical deviation range observed was about 45%. For the non-dominant components:
a22, a33 and a13 the simulation results demonstrated better agreement with the
experimental data set, however there was a broader range of deviation among the
three closures than was observed with the a11 component. From an analysis of the
deviation trends for all three closure models, it was concluded that for the film-gated
mold geometry simulated here, the linear closure model performed best.
A qualitative comparison of the numerical and experimental data trends showed that
the hybrid closure model demonstrated over-prediction of the a11 orientation in
regions of high shear rate in the flow. In regions of low shear rate, near the midplane
of the flow, all three models demonstrated significant under-prediction of the
a11 orientation. The highest degree of agreement between the numerically obtained
a11 orientation and experimental data occurred in regions of high shear for all three
closures. From the analyses performed it is clear that the simulation results were in
qualitative agreement with the experimental data. Nevertheless the observed
deviations between simulation and experiment highlight the importance of coupling
effects between the fluid momentum and fiber orientation as well as the necessity of
accurate closure models.