Symbolic regression models for predicting viscous dissipation of three-dimensional non-Newtonian flows in single-screw extruders

Roland, Wolfgang; Marschik, Christian; Krieger, Michael; Löw-Baselli, Bernhard; Miethlinger, Jürgen

doi:10.1016/j.jnnfm.2019.04.006

Cited by 26 publications

(41 citation statements)

References 35 publications

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“…The part of the extruder under investigation is presented in the form of a channel with a screw twisted counterclockwise ( Figure 1). Mathematical modeling was performed under the assumption that gravity force is negligible and the fluid is incompressible [21]. In this regard, the distributions of hydrodynamic characteristics are identical in areas #1 and #2.…”

Section: Geometric Representation Governing Equations and Boundary mentioning

confidence: 99%

“…Sci. 2019, 9, 5423 2 of 12 the helical screw channel is unwound and considered as a flat rectangular channel [4,[17][18][19][20][21][22]. Thus, plane-parallel fluid flow in a channel of infinite width is considered instead of direct 3D modeling.…”

mentioning

confidence: 99%

“…Also, the principle of reversed motion is often used (tube rotation is considered at the fixed screw) [4,[17][18][19][20][21][22]. In all works, polymers are considered as shear-thinning fluid [4,[17][18][19][20][21][22].The main functional zones of the extruder are feeding (solids conveying), melting, and metering. The metering zone is the simplest for modeling in a single-screw extruder, since the flow laws of viscous fluids can be applied to the polymer melt flow [23].…”

mentioning

confidence: 99%

“…Besides, it is the metering zone that determines the extruder performance [23].Work [4] describes a simple numerical method for solving the problem of the polymer melt flow in the metering zone of the single-screw extruder. The 2D mathematical model takes into account the presence of circulating motion, non-Newtonian behavior of the processed material, and heating of the polymer due to viscous dissipation.In [3,18,19,21,22,25], numerical solutions obtained in a 2D and 3D formulation are approximated by symbolic regression models. The heuristic approach for predicting the main characteristics of the polymer melts flow in the extruder channel is based on genetic programming.…”

mentioning

confidence: 99%

“…In [3,18,19,21,22,25], numerical solutions obtained in a 2D and 3D formulation are approximated by symbolic regression models. The heuristic approach for predicting the main characteristics of the polymer melts flow in the extruder channel is based on genetic programming.…”

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confidence: 99%

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Numerical Simulation of Polymer Solutions in a Single-Screw Extruder

2019

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Single-screw extruders are the most common equipment used for polymer extrusion. The study of the hydrodynamics of a polymer melts flow in the extruder channel is the basis for modeling and understanding the extrusion process. In general form, the extruder includes a straight section with a screw installed in it. In this study, the three-dimensional mathematical modeling of the polymer solutions flow in the metering zone of a single-screw extruder is performed. The influences of the screw geometry (L/D 2 = 1 . . . 3) on the flow structure and the pressure drop are analyzed under a speed rotation up to 60 rpm. Aqueous solutions of 0.5% polyacrylamide (0.5% PAA) and 1.5% sodium salt of carboxymethyl cellulose (1.5% CMC) are considered as the working fluid. Appl. Sci. 2019, 9, 5423 2 of 12 the helical screw channel is unwound and considered as a flat rectangular channel [4,[17][18][19][20][21][22]. Thus, plane-parallel fluid flow in a channel of infinite width is considered instead of direct 3D modeling. Also, the principle of reversed motion is often used (tube rotation is considered at the fixed screw) [4,[17][18][19][20][21][22]. In all works, polymers are considered as shear-thinning fluid [4,[17][18][19][20][21][22].The main functional zones of the extruder are feeding (solids conveying), melting, and metering. The metering zone is the simplest for modeling in a single-screw extruder, since the flow laws of viscous fluids can be applied to the polymer melt flow [23]. In this zone, the polymer is completely molten [24]. Besides, it is the metering zone that determines the extruder performance [23].Work [4] describes a simple numerical method for solving the problem of the polymer melt flow in the metering zone of the single-screw extruder. The 2D mathematical model takes into account the presence of circulating motion, non-Newtonian behavior of the processed material, and heating of the polymer due to viscous dissipation.In [3,18,19,21,22,25], numerical solutions obtained in a 2D and 3D formulation are approximated by symbolic regression models. The heuristic approach for predicting the main characteristics of the polymer melts flow in the extruder channel is based on genetic programming. Speaking about the evolutionary computation in general, it should be noted that they, like any method using an element of randomness, do not guarantee the detection of a global extremum of the objective function (or optimal solution) for a certain time. Their main advantage is that they allow finding a "better" solution to a difficult task in less time than other methods.In contrast with the standard flat-plate model of the unwound screw channel (2D), this hydrodynamic problem is solved in a three-dimensional formulation in [17,26]. Authors of the papers consider mathematical modeling of the flow in the metering zone of a plasticizing extruder. The objective of the study was the melting of the polymer composition based on polyethylene.Work [27] presents the results of three-dimensional numerical simulation of the polymer mel...

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Section: Geometric Representation Governing Equations and Boundary mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Numerical Simulation of Polymer Solutions in a Single-Screw Extruder

2019

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Modeling melt conveying and power consumption of co‐rotating twin‐screw extruder kneading blocks: Part B. Prediction models

Stritzinger

Roland

Berger‐Weber

et al. 2023

Polymer Engineering & Sci

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Intermeshing co‐rotating twin‐screw extruders are very versatile because their screw configurations can be tailored both to the application and to the properties of the materials used. Finding the best screw configuration is one of the main purposes of twin‐screw extrusion modeling, and requires models that accurately predict conveying and power consumption. The better the process can be predicted, the better the requirements of the final product can be met. We present novel prediction models of the conveying and power‐consumption behaviors of intermeshing co‐rotating twin‐screw extruder kneading blocks for Newtonian fluids. These are based on numerical simulations and therefore consider the complex three dimensional (3D) geometry of this element type without the need for common simplifications. Our models are thus capable of including all leakage flows and gap influences, which are usually ignored, for example, by the flat‐plate model. Since our models are derived by symbolic regression based on genetic programming, they consist of algebraic functions and are low‐threshold. They can be used to calculate various process parameters for individual kneading blocks or entire screw configurations, as illustrated by a use case.

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Correction factors for the drag and pressure flows of power‐law fluids through rectangular ducts

Marschik

Roland

2023

Polymer Engineering & Sci

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There are many industrial examples of low Reynolds number non-Newtonian flows through rectangular ducts in polymer processing. They occur in all types of manufacturing processes in which raw polymeric materials are converted into products, ranging from screw extrusion to shaping operations in dies and molds. In addition, they are found in numerous rheological measurement systems. The literature provides various mathematical formulations for non-Newtonian flows through rectangular ducts, but-if not simplified furthertheir solution usually requires use of numerical techniques. Removing the need for these time-consuming techniques, we present novel analytical correction factors for the drag and pressure flows of power-law fluids in rectangular flow channels. We approximated numerical results for a fully developed flow under isothermal conditions using symbolic regression based on genetic programming. The correction factors can be applied to the analytical theory that describes the flow of power-law fluids between parallel plates to include effects of the side walls in the prediction of flow rate and viscous dissipation.

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Symbolic regression models for predicting viscous dissipation of three-dimensional non-Newtonian flows in single-screw extruders

Cited by 26 publications

References 35 publications

Numerical Simulation of Polymer Solutions in a Single-Screw Extruder

Numerical Simulation of Polymer Solutions in a Single-Screw Extruder

Modeling melt conveying and power consumption of co‐rotating twin‐screw extruder kneading blocks: Part B. Prediction models

Correction factors for the drag and pressure flows of power‐law fluids through rectangular ducts

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