Development of a helical coordinate system and its applications to analysis of polymer flow in screw extruders. Part II: A helical channel model for single screw extruders

Abstract Because of its simplicity and originality, the parallel plates model (PPM) is often used to analyze flow in a single screw extruder. This model is developed in a rectangular coordinate frame and approximates the geometry of the screw as a hollow rectangle. As such, the geometrical features of the screw channel (curvature and helicity) are lost. In this paper, we present a helical channel model (HCM). It is developed in a helical coordinate frame that takes the real screw geometry into full consideration. A comparison is made between the HCM and PPM to better appreciate the effects of these inherent geometrical parameters of a screw channel on flow in terms of velocity profile, flow rate and shape factors. In order to obtain analytical solutions, a one‐dimensional flow of an isothermal, incompressible and Newtonian fluid is considered. It is concluded that the PPM is a special case of the HCM. In other words, the HCM reduces to the PPM when the channel depth‐to‐screw diameter ratio approaches zero.