The multidimensional output-pressure behavior of non-Newtonian fluids in single-screw extrusion can only be determined by using numerical methods. We present two methods which employ mathematical models building on analytic equations developed using an evolutionary heuristic optimization algorithm. Both allow fast and stable calculation of the 2-dimensional throughput–pressure gradient relationship of single-screw extruders, rendering cost-intensive CFD simulations of the output-pressure behavior redundant. A performed error analysis showed that our methods yield good approximations of the numerically determined data.
This paper addresses the use of heuristic optimization algorithms to generate generally valid analytic equations for estimating the initial pressure drop of square and Dutch woven screens in polymer recycling. We present a mathematical description of the isothermal initial pressure drop of non-Newtonian polymer melt flows through woven screens without the need for numerical methods. We first performed numerical CFD simulations to create a set of 9,000 physically independent modeling set-ups as a basis for heuristic modeling. Then, we applied symbolic regression based on genetic programming to develop pecScreen models, achieving coefficients of determination R 2 > 0.9995. For verification of our models, we performed experiments using both virgin and slightly contaminated in-house and postindustrial recycling materials. The experimentally determined data are in good agreement with the approximation results, which yielded a coefficient of determination R 2 of 0.926. Our modeling approach, the accuracy of which we have proven, allows fast and stable computational modeling of the initial pressure drop of polymer melt flows through 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.
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