Title page for ETD etd-06062008-164249
|Type of Document
||Hartt, William H.
||Flow of viscoelastic fluids through banks of cylinders :an experimental and numerical investigation
|Baird, Donald G.
|Davis, Richey M.
|Kriz, Ronald D.
|Loos, Alfred C.
|Wilkes, Garth L.
|Date of Defense
In this research it is attempted to determine whether the pressure drop for a
polymer melt flowing transversely through a square array of cylinders can be predicted
using purely viscous models or whether a viscoelastic constitutive equation is required.
To predict these pressure drops, finite element calculations were performed using the
generalized Newtonian fluid (GNF) model with the Bird-Carreau viscosity function, as
well as two viscoelastic constitutive equations, the Phan-Thien and Tanner (PTT)
model and the Rivlin-Sawyers (RS) model with the Pap ana sta siou, Scriven, and
Macosko (PSM) damping :function. The constitutive equations were fit to the steady
shear viscosity of a LLDPE melt and a LDPE melt. The PTT and RS models were also
fit to uniaxial extensional stress growth data for each melt. The predictions of the
pressure drop by means of the finite element calculations and a capillary model based
on Darcys Law were compared to pressure drops from experiments performed with
the two polymer melts. The agreement between experimental data and theoretical
predictions was best for the calculations using the PTT model. The calculations using
the PTT model as the constitutive equation indicate that time dependent fluid
properties and extensional rheology must be correctly predicted by the constitutive
equation used if accurate pressure drops of viscoelastic fluids flowing through banks
of cylinders are to be calculated.
This research is also concerned with the comparison of the results of numerical
simulation of confined flow past a cylinder to birefringence data for two polymer
melts. The Phan-Thien and Tanner (PTT) constitutive equation and the Rivlin-Sawyers
constitutive equation with the Papanastasiou, Scriven, and Macosko (PSM) damping
function were each fit to the shear viscosity and extensional viscosity data of both
linear low-density polyethylene (LLDPE) and low-density polyethylene (LDPE) melts
to determine the values of the model parameters. Finite element calculations were
carried out using the 4x4SUPG and 4x4SU methods for the PTT model and the
method developed by Dupont et al. for the RS model. Isochromatic birefringence
patterns calculated from the predicted stress field and the stress-optic law were
compared to birefringence data. Agreement was found between the birefringence data
and the numerical predictions, except in the immediate vicinity of the cylinder surface.
Large extensional stresses were observed and predicted along the centerline
downstream of the cylinder for LDPE. This behavior was not observed or predicted
for LLDPE. Stress fields obtained from birefringence measurements for LDPE
flowing past three cylinders in a channel indicate an effect of deformation history on
the flow behavior of LDPE. It is shown that the PTT model does not correctly predict
the rheological behavior of LDPE as a function of shear history because the time scale
of structural recovery is much longer than the relaxation time associated with
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