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

Abstract

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 ΠV < 2.0, implying minimum dimensionless pressure gradients Πp,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 (Πp,z ≥ -1.0, and t/Db ≤ 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 Πp,z, (ii) the power-law exponent n, and (iii) the screw-pitch ratio tDb. 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.

Application of Network Analysis to Flow Systems with Alternating Wave Channels: Part B. (Superimposed Drag-Pressure Flows in Extrusion)

“…In this part, we incorporated the influence of screw rotation into the modeling procedure. To this end, two- and three-dimensional melt-conveying models, presented in [ 30 , 31 , 32 ], were used in the network calculation, replacing the governing pressure-flow equation in the original theory. Moreover, the structure of the flow network was modified to additionally include leakage flow over the main flights.…”

Numerical Simulation of Polymer Solutions in a Single-Screw Extruder

“…Sci. 2019, 9, 5423 2 of 12 the helical screw channel is unwound and considered as a flat rectangular channel [4,[17][18][19][20][21][22]. Thus, plane-parallel fluid flow in a channel of infinite width is considered instead of direct 3D modeling.…”

“…Also, the principle of reversed motion is often used (tube rotation is considered at the fixed screw) [4,[17][18][19][20][21][22]. In all works, polymers are considered as shear-thinning fluid [4,[17][18][19][20][21][22].The main functional zones of the extruder are feeding (solids conveying), melting, and metering. The metering zone is the simplest for modeling in a single-screw extruder, since the flow laws of viscous fluids can be applied to the polymer melt flow [23].…”

“…Besides, it is the metering zone that determines the extruder performance [23].Work [4] describes a simple numerical method for solving the problem of the polymer melt flow in the metering zone of the single-screw extruder. The 2D mathematical model takes into account the presence of circulating motion, non-Newtonian behavior of the processed material, and heating of the polymer due to viscous dissipation.In [3,18,19,21,22,25], numerical solutions obtained in a 2D and 3D formulation are approximated by symbolic regression models. The heuristic approach for predicting the main characteristics of the polymer melts flow in the extruder channel is based on genetic programming.…”

“…In [3,18,19,21,22,25], numerical solutions obtained in a 2D and 3D formulation are approximated by symbolic regression models. The heuristic approach for predicting the main characteristics of the polymer melts flow in the extruder channel is based on genetic programming.…”