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

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.