A Tailored Modeling Approach to Predict the Three-Dimensional Flow of Polymer Melts in Helical Screw Channels

The use of high-performance single screws, such as barrier and wave-dispersion screws, is steadily increasing in polymer processing operations. In these screw types, regions with deep channels are found, where the polymer melt flow is markedly affected by channel curvature. Aiming for an accurate prediction of the flow rate and viscous dissipation rate, the governing equations for three-dimensional viscous fluid flow were developed in a helical reference frame. In contrast to previous modeling approaches, two helical coordinates in down- and cross-channel direction were introduced, which allows a more direct comparison with the flat plate theory. To reduce the complexity of the problem, focus was placed on an isothermal and fully developed flow of a power law fluid in fully confined channels of unit length. After conversion into a dimensionless form, the equations reveal five influencing parameters on the flow: (i) the channel depth ratio, (ii) the screw pitch ratio, (iii) the channel aspect ratio, (iv) the power law index, and (v) the dimensionless down-channel pressure gradient. The effect of channel curvature is described by the channel depth ratio and appears threefold: (i) net forces and deformations due to the locally changing orientation of the channel, (ii) additional flow coupling due to the twisted channel cross-section, and (iii) variable curvature radius and down-channel arc length across the channel depth. The resulting mathematical framework can be implemented into various numerical solution techniques to investigate and optimize the melt conveying behavior of single screw pumps.