A heuristic method for modeling three-dimensional non-Newtonian flows of polymer melts in single-screw extruders

Considering the non-Newtonian behavior of polymer melts in the flow analysis of single-screw extruders generally requires use of numerical procedures. We present a generalized heuristic relationship for predicting the isothermal conveying characteristics of power-law fluids in three-dimensional screw channels without the need for numerical methods. Applying the theory of similarity, we were able to rewrite the governing flow equations in a dimensionless form and identified the characteristic model parameters that define the physical conditions of the extruder flow. These dimensionless quantities were varied to create a set of 87,840 physically independent modeling set-ups, whose volume flow rates were evaluated numerically by means of a finite-volume solver. The numerical results were approximated employing a heuristic optimization algorithm, which yielded an algebraic output-pressure gradient relationship for power-law fluids in single-screw extruders. As a result of our three-dimensional modeling approach, the relationship takes the effects of both cross-channel flow and flight flanks on the conveying rate into account. This new analytical model, the accuracy of which we have proven, allows fast and reliable prediction of the pumping capability of single-screw extruders, thus contributing to the optimal design of extruder screws.