Series solutions for viscous and viscoelastic fluids flow in the helical rectangular channel of an extruder screw
Résumé
The flow of a viscous Newtonian and of a viscoelastic (upper-convected Maxwell) fluids in the helical rectangular channel of a screw have been solved using a series expansion on dimensionless torsion and curvature. At any given power of curvature or torsion, the velocity and stream function are solved using series of orthogonal eigenfunctions. Back pressure driven flow and drag driven flow have been both considered for Newtonian fluids, while only pressure driven flow can be studied for viscoelastic fluids. Contrary to common knowledge in polymer processing based on the Parallel Plate Model, we found that, in the case of cross-sections with large aspect ratio, torsion effects can be significant. Specific viscoelastic effects triggered by curvature and torsion have also been modelled. Our analytical model has been precisely validated by three-dimensional finite elements calculations