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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