Calculation Of 3D Melting Section Model Of Single Screw Extruder Using Geometric Transformation Algorithm

This paper studies the calculation of the three-dimensional melting zone model of the single-screw extruder using geometric transformation algorithm.The single-screw extruder is the main facility for the production of polymer products,so the numerical simulation of the fluid flow in its melting section is a practical research.The melting zone of the single-screw extruder is very complicated,and the fluid flow zone in the extruder changes continuously with the rotation of the screw.In this regard,we use the geometric transformation algorithm to transform it into a fixed area that does not change with time,and further solve the numerical simulation problem.However,the transformed equation is still a complicated three-dimensional equation,and it is difficult to solve.Aiming at this problem,in this paper the projection algorithm,finite difference method,speed-up method and other methods are used to solve the problem numerically in the transformed cuboid area.The main content of this article is:1.Introduce the main structure of the single screw extruder and the specific process of extrusion,the mathematical model of the geometric transformation algorithm,the Navier-Stokes equations,the finite difference method,the speedup method and the projection algorithm.2.For the equations converted by the geometric transformation algorithm,it is calculated by the projection algorithm.First of all,the equations we seek are discretized into first-order precision in the time direction,and a semidiscrete format with first-order precision is obtained according to the Helmholtz-Hodge decomposition theorem.Then an intermediate velocity variable u*is introduced and a Poisson equation of pressure p is obtained.After the Poisson equation is solved numerically,we can get the velocity u at next time through the coupling relationship between velocity and pressure.3.Detailed derivation of the equation system transformed by the geometric transformation algorithm through the projection algorithm,and calculating the equation system through matlab programming.The numerical results show the geometric transformation algorithm is practicable.