Extended Regression Models for Predicting the Pumping Capability and Viscous Dissipation of Two-Dimensional Flows in Single-Screw Extrusion

Generally, numerical methods are required to model the non-Newtonian flow of polymer melts in single-screw extruders. Existing approximation equations for modeling the throughput-pressure relationship and viscous dissipation are limited in their scope of application, particularly when it comes to special screw designs. Maximum dimensionless throughputs of Pi(V) < 2.0, implying minimum dimensionless pressure gradients Pi(p,z) >= -0.5 for low power-law exponents are captured. We present analytical approximation models for predicting the pumping capability and viscous dissipation of metering channels for an extended range of influencing parameters (Pi(p,z) >= -1.0, and t/D-b <= 2.4) required to model wave- and energy-transfer screws. We first rewrote the governing equations in dimensionless form, identifying three independent influencing parameters: (i) the dimensionless down-channel pressure gradient Pi(p,z), (ii) the power-law exponent n, and (iii) the screw-pitch ratio t/D-b. We then carried out a parametric design study covering an extended range of the dimensionless influencing parameters. Based on this data set, we developed regression models for predicting the dimensionless throughput-pressure relationship and the viscous dissipation. Finally, the accuracy of all three models was proven using an independent data set for evaluation. We demonstrate that our approach provides excellent approximation. Our models allow fast, stable, and accurate prediction of both throughput-pressure behavior and viscous dissipation.