Level Set Method Solved By Precise Time Integration And Its Application In Filling Process Of Molding

Plastic is being applied more and more widely in every field of our national economics with its many excellent properties. Injection molding, as one of the most effective plastic processing methods, has the following technical steps: to inject the melt polymer into the cavity of the mold with specific velocity, to fill the whole cavity, to wait for the melt polymer to solidify, to open the mold and fetch the plastic product and then to repeat and make the next product. Conventional technique of the injection molding depends on the limited experiences of engineers, the relative simple calculation formula as well as the great diversity of the melt polymer's flow property and the huge variety of the products and molds' structure, which induce repeated trials and modifications of the molds, long manufacture period, high manufacture cost and even no guarantee of the products' quality.To improve the products' quality and the manufacture efficiency, it is crucial to develop efficient numerical analysis tools for this complicated technique process to replace the conventional time-consuming and labor-consuming trails and modifications of the molds, to predict potential flaws in the practical injection, to optimize structural design of the mold, to adjust technical parameters and to design specific solutions in order to reduce raw material waste and the manufacture cost and to improve the products' quality and market competitiveness. In the past decades, although the numerical simulation of the injection molding process has attracted more and more wide attention, there are still many open problems to be solved, such as to capture the moving interface accurately and to solve the kinetic governing equations of the melt polymer fluid in a stable, efficient and accurate manner and so on.The existing work of the capturing moving interface accurately is based on the interface tracking method and the mesh generation-remeshing models in a fashion of the Arbitrary Lagrangian Eulerian method. However, when severe topological changes of the melt polymer fluid flow take place, the implementation of the ALE method will encounter some difficulties. Level set method is employed in the Eulerian manner in this paper, which shifts the viewpoint of the moving interface tactically and uses a continuous scalar level set function to describe and capture the evolution of the moving interface. Six-noded triangle finite element is employed in the spatial discretization and the precise time integration method with the accurate solution on computer is employed in the temporal resolution when solving the purely convective governing equation of the level set function. When solving the velocity and pressure of the melt polymer fluid, an iterative stabilized fractional step algorithm is employed to solve the corresponding Navier-Stokes equations. To employ the u-p element with different order interpolation functions satisfying the LBB restriction as well as introduce the iterative procedure of the convective term implicitly to satisfy the incompressibility condition of the Newtonian fluid, the algorithm can augment the time step to a great extent and guarantee a high precision. In the numerical examples, the accuracy and stability of the level set function update algorithm is verified by the straight, curve and circle moving interfaces under the uniform and nonuniform flow fields. A coupled numerical simulation algorithm for an Isothermal Newtonian flow of the injection molding is implemented in a simple straight cavity mold filling simulation.