Selected Topics of Modeling Transport Phenomena in Single-Screw Extrusion Viscous Dissipation, Melt Conveying, and Mixing

Single-screw extruders are among the most important processing machineries in the polymer industry. They are used in continuous production lines of semi-finished products (e.g., films, sheets, pipes, profiles, and fibers) and in recycling extrusion lines. Additionally, single-screw extruders are used as plasticizing unit in injection- and blow-molding machines. As a result of the economic challenges, polymer processing companies are forced to run the processing units with increased throughput. Nevertheless, the required melt quality must be guaranteed. In order to meet the increased requirements on the processing machinery an improved understanding of the extrusion process, physical processes, and transport phenomena is needed. The main goal of this work is the development of improved, novel, innovative, and enhanced models for describing and modeling functional processes of single-screw extrusion for scientific and industrial use. The focus in model development lies not only on accuracy, but also on numerical stability for application in digital twins and model-based predictive control. Additionally innovative and novel concepts are investigated that deepen and extend the understanding of screw extrusion in theory and practice. This thesis deals with modeling transport phenomena with special consideration of viscous dissipation which is mainly responsible for the melt temperature development. Additionally melt-conveying and pumping, as well as mixing, are investigated. The main focus of this thesis is related to analyzing the viscous dissipation of polymer melt flows in single-screw extruders, and the development of universal symbolic regression models that accurately predict viscous dissipation. Viscous dissipation models are developed for a one-, two-, and three-dimensional modeling framework. The non-Newtonian flow behavior is considered by the power-law model. By applying the theory of similarity the characteristic dimensionless influencing parameters are derived. Based on these independent influencing parameters, comprehensive sets of design points have been generated and its flow equations have been solved numerically. Approximation models for viscous dissipation have been developed based on the numerically derived results by applying symbolic regression based on genetic programming. Models are presented for both given pressure gradient and given throughput rate. These developed models allow fast, stable, and accurate prediction of viscous dissipation for pressure-generating and pressure-consuming (overridden) melt-conveying zones without the need of further time-consuming and computationally expensive numerical simulations. Additionally extended regression models for predicting the pumping capability of two- and three-dimensional flows in single-screw extrusion are developed. The one-, two-, and three-dimensional models predicting viscous dissipation and pumping capability are based on the flat-plate model. This widely accepted modeling approach does not consider the influence of the channel curvature. As part of this thesis, the effect of the channel curvature on flow rate and viscous dissipation is investigated for a two-dimensional power-law flow in metering channels. The obtained results allow estimating the application limits for the flat-plate model.