Simulation of Multifilament Semicrystalline Polymer Fiber Melt-Spinning
Simulation of Multifilament Semicrystalline Polymer Fiber Melt-Spinning
Simulation of Multifilament Semicrystalline Polymer Fiber Melt-Spinning
Correspondence to:
Christopher L. Cox, email: clcox@clemson.edu
INTRODUCTION
Fiber melt spinning is one of the most common
industrial polymer processes. In multifilament
spinning, the molten polymer exits from a forming
die, or spinneret, into the quench zone where cooling FIGURE 1. Schematic of fiber spinning process
air is blown across fibers (often numbering in the
thousands) and the fibers solidify as they cool and are
stretched (see Figure 1). Extreme changes in process Most commodity polymers are semi-crystalline,
conditions (e.g. temperature and axial velocity) occur meaning that both crystalline and amorphous regions
during this stage resulting in large changes in fiber exist together in the solid state. Flow-enhanced
properties at the macro level (diameter, temperature) (flow-induced, or stress-induced) crystallization is
and molecular or structure level (polymer orientation, known to occur as a result of high tensile stresses in
degree of crystallinity for semi-crystalline polymers. the fibers. One of the more recent FEC models is the
Quench conditions strongly influence the structure, one developed by McHugh, et al [6-9]. Their
which is directly linked to final properties. experimentally validated approach, which combines a
Experimental data confirm that variations in quench viscoelastic constitutive model for the melt with a
properties across a multifilament bundle create rigid rod model for the crystalline phase, is able to
nonuniformities in fiber properties [1]. predict the location along the spinline of the necking
phenomenon associated with rapid phase change
Predictive models have the ability to provide a under high-stress conditions.
GOVERNING EQUATIONS
The McHugh FEC model accurately predicts effects
of viscoelasticity and phase change for a melt-spun
fiber [9]. We encapsulate the FEC equations for a
single fiber within a simple algorithm which accounts
for convective heat transfer between the quench air FIGURE 2. Overview of multifilament simulation
and the fibers. The conservation equations for the
quench environment, in discrete form, are similar to
those in [4] and [5]. The overall algorithm is The zero-shear-rate viscosity of the melt used in our
illustrated in Figure 2. version of the model takes the form of the Arrhenius
equation,
In this section we provide a brief description of the
FEC model and a more detailed discussion of the
0 (T ) A exp B (1)
equations governing the quench air. T
dT dvz (3)
vz C1(D,v z)h c(T Tair) C (v
2 z, ,c ,c ,x)
dz dz zz rr
[4] and Zhang et al. [5], consisting of conservation is the area of the cell border perpendicular
is air cross-flow
to the
equations for mass and energy. We assume that all primary direction of the quench air flow. Dutta
fibers in a row transverse to the quench air cross-flow calculates q using the equation
experience the same air velocity and temperature, and Reff
that the fibers are arranged in a rectangular array as q 2 air
rv dr (5)
shown in Figure 3. d
rf
1
CD ReD
FIGURE 3. Spinneret geometry vd v z1 2 (1 2 2 1/ 2 d (7)
[
) ]
Consider the computational cell in Figure 4 for one where is a dimensionless radius ( rf / r ), ReD
filament cross-section.
is the Reynold's number (ReD = D v/ ), CD is the
drag coefficient (CD 1.22K 0.78Re D0.61 and K = 0.22),
and is a constant being related to Prandtl's mixing
eff 1
1 CD ReD (8)
q 4 air f r2 *5
1 2
d d *
vz [ (1 2)2]1/2
1 *
air R eff
2 air e 10k r e 10k Reff 10k rf(i,j) e 10k r T( air , ) T( air, )
( i 1, j)C p( i 1, j) i 1j 1 i 1j
vd(i 1,j) T e rdr (12)
e rf(i,j) e Reff (i,j) 2
rf
R eff R
eff
2 (iair
1,j)Cp(iair
1,j) T(aii r1,j 1) T(i 1,j)
vd(i 1,j)e 10k rrdr T(iair1,j 1) T(iair
1,j) e 10k rf(i,j) T e 10k Reff
air
T(i,j) T ij air vd(i 1,j)rdr
2 ( i ,j )
e 10k rf(i,j) e 10k R eff ( , ) 2
rf(i,j)
rf(i,j)
R R
eff eff
air air
2 (i,j)Cp(i,j) air air 1) e 10k rf(i 1,j)
T(i,j 10k Reff
T(i,j 1) 10k r
T (i 1,j) vd(i,j)e rdr T(i 1,j)e vd(i,j)rdr
10k rf(i 1,j) e 10k R 2 2
e eff rf(i 1,j) rf(i 1,j)
R
eff 10krf(i 1,j) e 10kr
air air
air air air
2 (i,j)Cp(i,j)
vd(i,j) e
(14)
(i,j)Cp(i,j) c(i,j)Ac(i,j) rdr
v e rf(i 1,j) e Reff 2
rf(i 1,j)
CONCLUSIONS
We have presented a versatile melt spinning
simulation based on the McHugh et al. FEC single-
fiber model and a variation on the multifilament
quench zone model of Zhang et al. First we
demonstrated the correlation of the quench air
ACKNOWLEDGEMENT
This work was supported by the ERC program of the
National Science Foundation under Award Number
EEC-9731680. The authors gratefully acknowledge
Fred Travelute from Wellman Inc. for providing on-
line quench air data.
REFERENCES