Mathematical modeling of the melt flow in the cone-ring channel of the extruder matrix

Abstract

The peculiarity of the work is to develop a mathematical model of the melt flow in the cone-annular channel of the extruder die, which will allow you to choose the optimal geometric shape of the annular channel, as well as the angular rotation speed of the extruder screw. The object of the study is the cone-ring channel of the extruder matrix. To solve the three-dimensional problem of turbulent and laminar unsteady motion, the FlowVision software package was used, which allows solving partial differential equations using the finite volume method. The correct choice of the geometric shape of the annular gap made it possible to change the molecular structure of the product by creating a maximum pressure value. The optimally selected angular rotation speed of the extruder screw made it possible to carry out deep melting of the product due to the conversion of the mechanical energy of the screw into thermal energy. In the process of designing the forming of the cone-ring channel, the three volumes of the changing geometry of the stamp were selected, at the borders of the transition of which extreme points were observed. Deviations between the analyzed and experimental values of velocity and pressure were found in the limits of 9–12 % and 17–22 %, respectively. Based on the analysis of the obtained results of modeling, the optimal geometric shape of the annular gap and the recommended angular rotation speed of the extruder screw were revealed. The mathematical model proposed formed the basis of the developed design of the six-zone extruder. In the extruder, the geometric characteristics of the screw (variable pitch of the turns) were substantiated and selected, which provide the maximum effect of dissipation, i.e. autogenous mode of operation