Mathematical model of the flow of polymer melt in the extruder forming die

Abstract

Abstract. Steady creeping flow of viscoelastic fluid with the free surface which is realized when fluid polymer is entering the forming channel and leaving it is investigated. Fluid motion is described by equations conservation of mass and momentum supplemented by Metzner's determinative rheological constitutive equation of the fluid. On the basis of finite element method a stable numerical algorithm for solving the problem was developed. IntoductionThe continuous growth of the production of chemical fibers and yarns requires the solution for a number of issues, among which should be noted such as improving the continuity of technological processes and their intensification, creation of a new high-efficiency equipment, reducing labor intensity by mechanization and automation of production processes. One of the main directions of development of mechanical engineering for the production of the finished products from polymer melts is an increase of spinning rate and combination of technological operations, decrease of energy and metal intensity of the equipment, mechanization and automation of processes using microprocessor technology. When solving all the above problems the development of mathematical models, methods of computation and optimization of molding process by extrusion with subsequent verification and implementation of the obtained results into production is becoming particularly urgent [1,2]. Governing equationsMotion of an incompressible viscoelastic fluid is described by the equations of conservation of mass and momentum.In a cylindrical coordinate system creeping flow of a viscoelastic fluid in the absence of gravity is described by the system equations conservation of mass and momentum which are closed by the Giesekus determinative rheological constitutive equation [6, 7]: