Extended melt-conveying models for single-screw extruders: Integrating domain knowledge into symbolic regression

The literature provides several analytical approximation methods for predicting the flow of non-Newtonian fluids in single-screw extruders. While these are based on various flow conditions, they were developed mostly for extruder screws with standard geometries. We present novel analytical melt-conveying models for predicting the flow and dissipation rates of fully developed flows of power-law fluids within three-dimensional screw channels. To accommodate a broad range of industrial screw designs, including both standard and high-performance screws, the main intention of this work was to significantly extend the scope of existing theories. The flow equations were first rewritten in a dimensionless form to reduce the mathematical problem to its dimensionless influencing parameters. These were varied within wide ranges to create a set of physically independent modeling setups, the flow and dissipation rates of which were evaluated by means of a finite-volume solver. The numerical results were then approximated analytically using symbolic regression based on genetic programming. To support the regression analysis in finding accurate solutions, we integrated domain-specific process knowledge in the preprocessing of the dataset. We obtained three regression models for predicting the flow and dissipation rates in melt-conveying zones and tested their accuracy successfully against an independent set of numerical solutions.