Two-relaxation-time lattice Boltzmann model of the velocity profiles and volumetric flow rate of generalized Newtonian fluids in a single-screw extruder

Single-screw extruders and injection molding machines are essential equipment in polymer processing. It is of great importance for the optimization of operating parameters and the design of extrusion screw to predict the throughput of an extruder and the metering time of an injection molding machine according to the geometric parameters of the screw, operating parameters, and the rheological behavior of materials. Most polymer melts exhibit non-Newtonian behavior. The lattice Boltzmann method has many advantages in simulating the flow of non-Newtonian fluids. Herein, the dimensionless velocity profiles and dimensionless volumetric flow rate of generalized Newtonian fluids in a screw channel have been studied using the two-relaxation-time lattice Boltzmann method (TRT–LBM). The numerical results of power-law fluids are in good agreement with the analytical solutions, which verifies the validity of TRT–LBM. Through research, the change rule of the dimensionless volumetric flow rate of Bingham fluids with dimensionless pressure gradient has been obtained. It was found that the rheological properties of polymer melts and the dimensionless pressure gradient significantly affect the dimensionless velocity profiles and dimensionless volumetric flow rate. The dimensionless volume flow rate has some unexpected changes with the increase of the dimensionless pressure gradient. This study can provide theoretical guidance for the optimization of operating parameters and the design of extrusion screws.