Flow of viscoelastic fluids through banks of cylinders: an experimental and numerical investigation
Hartt, William H.
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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 viscoelasticity.
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