Flow modeling in a metering section of a single screw extruder with a small helix angle based on the energy dissipation rate

In the present work, an approach based on energy dissipation rate was presented for quantifying the screw characteristics, effective Reynolds number, viscosity, and shear rate of non-Newtonian fluids in the metering zone of a single screw extruder, characterized by a small helix angle. The flow is separated into two individual flows: one induced by the screw rotation, known as rotational flow, and another driven by back-pressure from the die, known as pressure-driven flow. We start by investigating the individual flow problems separately, specifically focusing on the torque and rotation speed correlations in the rotational flow and exploring pressure buildup and flow rate correlations in the pressure-driven flow. Following this, a method to quantify the combined flow, which includes both rotational and pressure-driven flows, is formulated by blending the relationships from each of the individual flow, employing mixture rules to determine shear rate. The mixture rules involve a key parameter, the velocity ratio, to define the flow rate contribution of the two individual flows to the combined flow. The proposed method for quantifying flow is confirmed, by comparing the results with numerical simulations employing three different inelastic non-Newtonian fluids. The proposed method can be employed to predict the pressure buildup and the torque and to monitor the viscosity behavior of the material as a function of the shear rate. A comparison of the theoretical predictions and the numerical simulation results for the estimation of pressure buildup, torque, and shear-rate dependent viscosity revealed discrepancies of 11.7%, 3.6%, and 6.2%, respectively. Furthermore, we report that the commonly used relationship between dimensionless pressure number and dimensionless throughput number for a Newtonian fluid is applicable to that of non-Newtonian fluids, with the effective viscosity employed in the present study.Highlights Accurate estimation of representative viscosity of non-Newtonian fluids for the flow in a single screw. The flow in the screw is split into a rotating flow and a pressure-driven flow. Representative shear rates can be determined by rotational speed and flow rate.