In many extrusion processes, the metering section is the rate-controlling part of the screw. In this functional zone, the polymer melt is pressurized and readied to be pumped through the die. We have recently proposed a set of heuristic models for predicting the flow behavior of power-law fluids in two- and three-dimensional metering channels. These novel theories remove the need for numerical simulations and can be implemented easily in practice. Here we present a comparative study designed to validate these new methods against experimental data. Extensive experiments were performed on a well-instrumented laboratory single-screw extruder, using various materials, screw designs, and processing conditions. A network-theory-based simulation routine was written in MATLAB to replicate the flow in the metering zones in silico. The predictions of the three-dimensional heuristic melt-conveying model for the axial pressure profile along the screw are in excellent agreement with the experimental extrusion data. To demonstrate the usefulness of the novel melt-flow theories, we additionally compared the models to a modified Newtonian pumping model known from the literature.

Numerous analyses have modeled the flow of polymer melts in the melt-conveying zones of single-screw extruders. While initial studies mainly provided exact analytical results for combined drag and pressure flows of Newtonian fluids, more recently developed, numerical methods seek to deepen the understanding of more realistic flow situations that include shear-thinning and non-isothermal effects. With the advent of more powerful computers, considerable progress has been made in the modeling and simulation of polymer melt flows in single-screw extruders. This work reviews the historical developments from a methodological point of view, including (1) exact analytical, (2) numerical, and (3) approximate methods. Special attention is paid to the mathematical models used in each case, including both governing flow equations and boundary conditions. In addition, the literature on leakage flow and curved-channel systems is revisited.

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 ${\mathsf{\Pi }}_V<2.0$ , implying minimum dimensionless pressure gradients ${\mathsf{\Pi }}_{p,z}\ge -0.5$ 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 ( ${\mathsf{\Pi }}_{p,z}\ge -1.0$ , and $t/D_b\le 2.4$ ) 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 ${\mathsf{\Pi }}_{p,z}$ , (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.

Modeling the non-Newtonian flow of polymer melts in single-screw extrusion generally requires numerical methods. This study analyzes the viscous dissipation of the melt-conveying zone, which is mainly responsible for the axial melt temperature increase, in single-screw extruders for both one- and two-dimensional stationary, fully developed flows of a power-law fluid. Rewriting the flow equations and applying the theory of similarity revealed three independent parameters that influence the physics of the fluid flow: the dimensionless pressure gradient {\mathrm{\Pi }}_{\mathrm{p},z} , the power-law exponent n , and the screw-pitch ratio t/D_{\mathrm{b}} . Based on these parameters, we carried out a comprehensive numerical parametric study evaluating viscous dissipation and flow rate. Here, we present four heuristic models that predict the viscous dissipation of a power-law fluid in the melt-conveying zone of single-screw extruders. For one-dimensional and two-dimensional flows, we developed models for both a given pressure gradient and a given throughput. The approximation equations obtained allow fast and stable prediction without the need for numerical simulations of viscous dissipation. The accuracy of the heuristic models developed was validated in an error analysis, which showed that our approaches provide excellent approximations of the numerical results. POLYM. ENG. SCI., 2018. © 2018 The Authors Polymer Engineering & Science published by Wiley Periodicals, Inc. on behalf of Society of Plastics Engineers