Reaserches On The Area Transformation Algorithm For Single Screw Extuder

The area transformation algorithm for fluid flow in a single screw extruder is researched in the thesis.The single screw extruder is a important equipment for polymer processing,etc,and the numerical computation for the fluid flow problems is a hot topics.The main difficulty in computation is that the fluid flow area is very complex with irregular double connected cross sections and rotating in time.For overcoming the difficulty in time-varying and complex solution region,first the cross section is transformed to a concentric ring by conformal mapping,and then a three-dimensional transformation based on the mapping is constructed such that the complex solution region is transformed to the regular circle cylinder region.The calculation of the problem can be greatly simplified with the transformations.The numerical results show that the method is simple and effective.In this paper,the main work is as follows:1.The geometric structure of a single screw extruder,the Navier-Stokes equations,the conformal mapping and the projection algorithm are introduced.2.Firstly the fluid flow area is transformed to a fixed area by a rotation transformation.Secondly a typical cross section of the fluid flow area is transformed to a concentric ring by a conformal mapping.And then a 3D transformation is constructed to transform the fluid flow area to a circle cylinder region by using the feature that a cross section of the area can be obtained by a rotation from the typical cross section,and further the circle cylinder region is transformed to a cuboid by the cylindrical coordinate transformation.The composite transformation can be computed easily and expressed by 3D spline functions.With the transformation the main difficulty in computation can be overcome and the calculation of the problem can be greatly simplified.3.Using the above transformation and the projection algorithm,the detail computational process for the fluid flow problems is derived and described.A Dirichlet boundary value problem of Poisson equation in the flow area with circular outer boundary curve and elliptic inner boundary curve of the cross sections is solved numerically,and the numerical solutions are compared with the exact solutions.The numerical results show that the transformation method is reliable and efficient.