Generalized predictions of the pumping characteristics and viscous dissipation of single‐screw extruders including three‐dimensional curvature effects

• Published in: Polymer engineering and science 2024-11, Vol.64 (11), p.5566-5587
• Main Authors: Herzog, Daniel, Roland, Wolfgang, Marschik, Christian, Berger‐Weber, Gerald Roman
• Format: Article
• Language: English
• Subjects: Approximation; Computational fluid dynamics; Continuous extrusion; Curvature; Design analysis; Dimensional analysis; Dissipation; Error analysis; Extruders; Extrusion rate; flow simulation; Flow velocity; Fluid dynamics; Fluid flow; Genetic algorithms; Helical flow; hybrid modeling; Laws, regulations and rules; melt conveying; Metering zone; power‐law fluid; Regression models; Similarity theory; Simulation methods; single‐screw extrusion; Stokes flow; Stokes law (fluid mechanics); Systematic errors; Troubleshooting
• ISSN: 0032-3888; 1548-2634
• DOI: 10.1002/pen.26934

Reliable predictions of the flow rate and viscous dissipation in the melt conveying zone of single‐screw extruders are crucial for designing high‐quality and efficient extrusion processes. Full‐scale computational fluid dynamics simulations offer deep insights into the process, but they cover only specific use cases. Conversely, state‐of‐the‐art analytical approximation models suffer from a systematic error by neglecting channel curvature. To overcome these limitations, we employed a hybrid modeling approach that efficiently combines analytical, numerical, and data‐based techniques. First, the mathematical problem was formulated for a three‐dimensional, isothermal Stokes flow of power‐law fluids in curved channel segments of unit length, and the theory of similarity was applied to render it in a dimensionless form. Using the finite‐volume method, the flow problem was then solved numerically for a wide range of extrusion setups. Finally, by means of symbolic regression and genetic programming, three dimensionless approximation equations were derived from the numerical dataset. These regression models provide continuous and remarkably accurate predictions  of both flow rate and viscous dissipation rate, and clearly outperform existing approximations due to the included effects of channel curvature. Implemented within screw design software, our novel regression models will enable faster progress in screw design and process troubleshooting. Highlights Three‐dimensional flow of power‐law fluids in helical screw channels Generalized problem description using dimensional analysis Melt conveying simulations considering both curvature and flight effects Integration of process knowledge into symbolic regression modeling Analytical screw characteristic curves with extended scope of validity New analytical models were developed to predict the pumping characteristics and viscous dissipation of single‐screw extruders. For the first time, these models fully capture the three‐dimensional screw channel curvature alongside the shear‐thinning behavior of polymer melts, without the need for time‐consuming numerical simulations.