Predicting the Non-Linear Conveying Behavior in Single-Screw Extrusion: A Comparison of Various Data-Based Modeling Approaches used with CFD Simulations

The traditional approach to modeling the polymer melt flow in single-screw extruders is based on analytical and numerical analyses. Due to increasing computational power, data-driven modeling has grown significantly in popularity in recent years. In this study, we compared and evaluated databased modeling approaches (i. e., gradient-boosted trees, artificial neural networks, and symbolic regression models based on genetic programming) in terms of their ability to predict – within a hybrid modeling framework – the three-dimensional non-linear throughput-pressure relationship of metering channels in single-screw extruders. By applying the theory of similarity to the governing flow equations, we identified the characteristic dimensionless influencing parameters, which we then varied to create a large dataset covering a wide range of possible applications. For each single design point we conducted numerical simulations and obtained the dimensionless flow rate. The large dataset was divided into three independent sets for training, interpolation, and extrapolation, the first being used to generate and the remaining two to evaluate the models. Further, we added two features derived from expert knowledge to the models and analyzed their influence on predictive power. In addition to prediction accuracy and interpolation and extrapolation capabilities, we evaluated model complexity, interpretability, and time required to learn the models. This study provides a rigorous analysis of various data-based modeling approaches applied to simulation data in extrusion.

Using Symbolic Regression Models to Predict the Pressure Loss of Non-Newtonian Polymer-Melt Flows through Melt-Filtration Systems with Woven Screens

When selecting a melt-filtration system, the initial pressure drop is a critical parameter. We used heuristic optimization algorithms to develop general analytical equations for estimating the dimensionless pressure loss of square and Dutch woven screens in polymer processing and recycling. We present a mathematical description – without the need for further numerical methods – of the dimensionless pressure loss of non-Newtonian polymer melt-flows through woven screens. Applying the theory of similarity, we first simplified, and then transformed into dimensionless form, the governing equations. By varying the characteristic independent dimensionless influencing parameters, we created a comprehensive parameter set. For each design point, the nonlinear governing equations were solved numerically. We subsequently applied symbolic regression based on genetic programming to develop models for the dimensionless pressure drop. Finally, we validated our models against experiments using both virgin and slightly contaminated in-house and post-industrial recycling materials. Our regression models predict the experimental data accurately, yielding a mean relative error of MRE = 13.7%. Our modeling approach, the accuracy of which we have proven, allows fast and stable prediction of the initial pressure drop of polymer-melt flows through square woven and Dutch weave screens, rendering further numerical simulations unnecessary.

Analyzing the Influence of Surface Renewal on Diffusive Mass Transport in Vented Single-Screw Extruders

We present a semi-numerical modeling approach to analyzing the role of surface renewal during bubble-free devolatilization in vented single-screw extruders. To demonstrate the significance of surface renewal in the mass transport of volatiles, we derived approximate analytical solutions for the two-dimensional circulatory flow in a partially filled screw channel, placing special emphasis on the melt pool that forms in front of the active flight. By applying the resulting velocity field to the governing conservation equation for the volatile concentration in the polymeric phase, the convective influence of the polymer flow on mass transport is taken into account. The resulting convection-diffusion equation, which is solved numerically using the finite-volume method, provides both qualitative and quantitative insights into how volatile depletion in the melt pool is related to the flow field developed. Thus, we clearly demonstrate that surface renewal improves mass transport efficiency considerably, even at very low screw speeds.