Heuristic analysis of viscous dissipation in single‐screw extrusion

Abstract

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 P p;z , the power-law exponent n, and the screw-pitch ratio t=D 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 powerlaw 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.

Numerical Simulation of Polymer Solutions in a Single-Screw Extruder

“…Therefore, further, area #1 is considered as the area under investigation ( Figure 2). In this paper, the screw rotation is simulated by the rotation of the outer pipe, this method is widely used for similar problems in the two-dimensional setting [19].…”

“…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.…”