Regularization Of Solution Area Of 3D Model Of Twin Screw Extruder And Its Application

The twin-screw extruders are widely applied in production of polymers.The numerical simulation for fluid flow in a twin-screw extruder is a hot issue.The fluid flow area is a complex area with sections of two inner boundaries rotating over time.It is the difficulty in calculation and results in it is difficult to simulate the fluid flow with high precision by the traditional algorithms.In this paper,for the difficult,by a conformal mapping,the section regions are mapped into a circle-bound region that does not change with time,so that the flow area is mapped into an area independent of time.As a numerical example,a heat conduction problem with a solution region similar to the flow section of the twin-screw extruder and known exact solution,is numerically solved with application of the conformal mapping,and the numerical result is compared with the exact solution.The comparison result shows that this mapping method is feasible and can be applied to numerical simulation for fluid flow in a twin-screw extruder.The specific content of this thesis is as follows:1.The physical model of the twin-screw extruder,the N-S equations,the finite element solution method and a conformal mapping algorithm from a three connected region to a circle-bound region by variational method,are introduced.2.In order to find a conformal mapping that can map the section regions into a three-connected region independent of time,the conformal mapping algorithm is modified.3.As a numerical example,a heat conduction IB VP problem with solution region of a circumference as outer boundary and two elliptical boundaries rotating over time as inner boundaries,and known exact solution,is numerically solved.By the modified conformal mapping algorithm,first the solution region maps into a three connected region with circular boundaries and independent of time,and second the transformed problem is solved numerically by the finite element method on the mapped region with the triangular mesh obtained when the conformal mapping is computed.The small error between the numerical solution and the exact solution shows at this mapping method is feasible.