The Study On The Geometric Transformation Algorithm Of Single Screw Extuder In The 3-Dimensional Space

The single screw extruder has been widely used in polymer processing, and researches on numerical simulation for the fluid flow in its metering section are playing important role. Due to the complexity and time-dependence of the solution domain, numerical computation for its 3-dimensional mathematical model is quite difficult and little work in this area has done. In this paper, a new numerical algorithm easy to compute is developed for the 3-dimensional model of fluid flow in the metering section by using the rotating spiral rectangular coordinate transformation, conformation mapping and projection algorithm. A numerical simulation for the model is performed, and the result demonstrates the new algorithm is stable and efficient.The specific content of this thesis is as follows:1. The geometry of the single screw extruder, the Navier-Stokes equations, the numerical conformation mapping and the projection algorithm are briefly introduced.2. The solution domain is transformed into a fixed cylindrical one by considering the screw channel is composed of a bunch of spiral curves and setting a rotating spiral rectangular coordinate system. Then a conformal mapping to transform the cross section of the cylinder into a rectangle is constructed by using Symm’s method and composite Schwarz-Christoffel transformation. With these transformations the solution domain is transformed into a cuboid domain in which the model is easier to be computed.3. A numerical simulation is performed for the incompressible fluid flow in the metering section of a single screw extruder by using the projection algorithm and the above transformations. The numerical result shows that the new algorithm is reliable and efficient.