SUMMARYAnnular pressure-tooling extrusion is simulated for a low density polymer melt using a Taylor-PetrovGalerkin ÿnite element scheme. This represents industrial-scale wire-coating. Viscoelastic uids are modeled via three forms of Phan-Thien=Tanner (PTT) constitutive laws employed for short-die and full speciÿcation pressure-tooling. E ects of variation in Weissenberg number (We) and polymeric viscosity are investigated. Particular attention is paid to mesh reÿnement to predict accurate results. The impact of variation in shear-thinning and strain-softening properties is considered upon the modelling predictions. For the short-die ow, the in uence of the lack of strain softening is identiÿed. For the full-die ow and more severe deformation rates, the linear PTT model failed to converge. In contrast, the exponential PTT model is found to be more stable numerically and to adequately re ect the material response. Comparing short-die and full-die pressure-tooling results, shear rates increase 10-fold, while strain rates increase one hundred times.
Numerical solutions of viscoelastic flows are demonstrated for a time marching, semi‐implicit Taylor–Galerkin/pressure‐correction algorithm. Steady solutions are sought for free boundary problems involving combinations of die‐swell and stick‐slip conditions. Flows with and without drag flow are investigated comparatively, so that the influence of the additional component of the drag flow may be analysed effectively. The influence of die‐swell is considered that has application to various industrial processes, such as wire coating. Solutions for two‐dimensional axisymmetric flows with an Oldroyd‐B model are presented that compare favourably with the literature. The study advances our prior fixed domain formulation with this algorithm, into the realm of free‐surface viscoelastic flows. The work involves streamline‐upwind/Petrov–Galerkin weighting and velocity gradient recovery techniques that are applied upon the constitutive equation. Free surface solution reprojection and a new pressure‐drop/mass balance scheme are proposed. Copyright © 2001 John Wiley & Sons, Ltd.
This work is concerned with the numerical prediction of wire coating flows. Both annular tube-tooling and pressure-tooling type extrusion-drag flows are investigated for viscous fluids. The effects of slip at die-walls are analysed and free surfaces are computed. Flow conditions around the die exit are considered, contrasting imposition of no-slip and various instances of slip models for die-wall conditions. Numerical solutions are computed by means of a time-marching Taylor Galerkin/pressure-correction finite element scheme, that demonstrate how slip conditions on die walls mitigate stress singularities at die exit. For pressure-tooling and with appropriate handling of slip, reduction in shear rate at the die-exit may be achieved. Maximum shear rates for tube-tooling are about one quarter of those encountered in pressure-tooling. Equivalently, extension rates peak at land entry, and tube-tooling values are one third of those observed for pressure-tooling. With slip and tube-tooling, peak shear values at die-exit may be almost completely eliminated. Nevertheless, in contrast to the pressure-tooling scenario, this produces larger peak shear rates upstream within the land region, than would otherwise be the case for noslip.
A semi-implicit Taylor Galerkin/pressure-correction finite element scheme (STGFEM) is developed for problems that manifest free surfaces associated with the incompressible creeping flow of Newtonian fluids. Such problems include stick-slip and die-swell flows, both with and without a superimposed drag flow, and for plane, axisymmetric and annular systems. The numerical solutions are compared with available analytical and numerical solutions, both in the neighbourhood of singularities and elsewhere. Close correspondence in accuracy is extracted to the literature for both stick-slip and die-swell flows. Stick-slip flow is used as a precursor study to the more complex free surface calculations involved for die-swell in extrudate flow. Two different free surface techniques are reported and results are analysed with mesh refinement and varying structure.
This article focuses on the comparative study of annular wire-coating flows with polymer melt materials. Different process designs are considered of pressure-and tube-tooling, complementing earlier studies on individual designs. A novel mass-balance free-surface location technique is proposed. The polymeric materials are represented via shear-thinning, differential viscoelastic constitutive models, taken of exponential Phan-Thien/Tanner form. Simulations are conducted for these industrial problems through distributed parallel computation, using a semiimplicit time-stepping Taylor-Galerkin/pressure-correction algorithm. On typical field results and by comparing short-against full-die pressure-tooling solutions, shear-rates are observed to increase ten fold, while strain rates increase one hundred times. Tube-tooling shear and extension-rates are one quarter of those for pressure-tooling. These findings across design options, have considerable bearing on the appropriateness of choice for the respective process involved. Parallel finite element results are generated on a homogeneous network of Intel-chip workstations, running PVM (Parallel Vitual Machine) protocol over a Solaris operating system. Parallel timings yield practically ideal linear speed-up over the set number of processors.
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