Modeling of flow in an extruder with radial clearance as a distributed feedback system described by a delay differential equation

Abstract

A model used to calculate leakages through the radial clearance in screw extruders is considered. The primary disadvantage of most widely used models is that the leakage flow is carried outside the boundaries of the channel, whereas in reality the material migrates from one flight of the extruder channel to the other conjugated via the flight land. The developed approach to the numerical modeling of the flow in the channel is based on the idea that the balance of mass discharges through the main channel and clearance can be expressed as an additional differential relationship, and the intensity of the leakage flow, with allowance for pressure distribution throughout the channel length, is defined by a delay differential equation. We present here an algorithm and its implementation to examine the isothermal flow of linear viscous flow fluid in a straight - flow extruder. The proposed surface equation allows us to estimate the orientation of structural parameters and the degree of their influence on the flow pattern in screw machines.