Quantification of flows in a rectangular channel of a single-screw extruder with a small helix angle based on the energy dissipation rate

In this work, a systematic approach is proposed for quantifying the effective viscosity, effective shear rate, and screw characteristics of non-Newtonian fluids in an unwound rectangular channel screw flow of a metering zone of the single-screw extruder. The analyses are limited to a small helix angle case (less than 6.7 degrees), where the cross-sectional drag velocity component is small enough. We begin by separating the flow within the channel into two individual flows (the drag-driven flow and the adverse pressure-driven flow). Both the correlations between drag velocity and drag force in the drag flow and between flow rate and pressure buildup in the pressure-driven flow are investigated separately. Then, we propose mixture rules for shear rate and energy dissipation for the combined drag and (adverse) pressure-driven flows in the rectangular channel. The flow quantification approach of the combined flow is established by incorporating the correlations observed in the individual flows with a velocity ratio (the ratio of the drag velocity to the flow rate). The flow quantification method was validated using three non-Newtonian fluids (power law fluid models, a Carreau fluid model, and a regularized Herschel–Bulkley fluid model), through extensive numerical simulations with a 2.5D hybrid scheme. The proposed quantification method can be applied for estimating the relationship between torque, pressure buildup and throughput in the single-screw process with a small helix angle. Theoretical predictions agree well with numerical simulations, with maximum relative errors of 3.3%, and 11% for drag force and pressure buildup, respectively.