Viscous Behaviours Of Each Phase And Wall Slip In Bi-Phase Simulation Of The MIM Injection

In the processes of metal injection moulding (MIM), the effect of powder segregation may be induced by the filling process of injection. The mixture feedstock homogeneously mixed by metallic powder and plastic binder may change locally their proportion. This is a special and important factor that may affect final quality of the MIM products. The technology of numerical simulation, based on the use of computors, is then very important in simulation of the injection processes and prediction of the segregation effect. The simulation and prediction of segregation effect requires the introduction of bi-phase flow model. The flow of metallic powder and plastic binder are regarded as the flows of two distinct phases. Variation of the volume fractions for each phase in the injection process is used to represent the segregation caused by injection. Two coupled Navier-Stokes equations are used to describe the flow of powder phase and binder phase, with a term of the momentum exchange to represent the interaction between two phases.To carry out the simulation based on a bi-phase model, the viscous behaviours of each phase should be provided. However, only viscosity of the mixture feedstock can be measured. Based on the analytical model for capillary tests of the viscosity values, the model of bi-phase flow for capillary tests is built. Its analytical solution, and the solution by finite difference method, is achieved by the present research. By the relationship of mass conservation between the flows of bi-phase model and the flow of a mono-phase model, the analytical model is established to determine the viscosities for each phase based on the measurement on mixture feedstock.The classic model for capillary tests supposed the sticking on wall of the tested fluid, while there is the slip phenomenon for the mixture flow on wall. The slip phenomenon will certainly affect the determination of viscosity for measured material. In the practical analysis and simulation, the slip effect of injected feedstock on wall of the mould cavities has also the significant influence on injection process and the injected results. It is in fact an important fact that should not be negligible in the modelling and simulation. The present research developed hence a special tool for the analysis of capillary test by a bi-phase model. This numerical tool is based on the finite difference method. It provides the facility to impose different boundaryconditions for the flows of distinct phases, including the slip wall condition. Such a useful tool will provide the convenient and effective way for the further and more profound research on the influence of slip effect inside the mould cavities by multi-phase simulation. It provides also the feasible way for determination of the calibrating method on parameters of the capillary tests that will be involed in the further research.The main objective of present research is to determine the viscous behaviours for each phase and the slip parameter inside the mould cavities for bi-phase simulation. The suitable method for experimental calibration and modelling for analysis should be searched to realize the reasonable and reliable simulation. Based on such an objective, the slip effect is introduced into the analytical model for capillary test. By the tests with different diameters of the capillaries, the slip quantity and viscosity of the mixture feedstock can be determined. Furthermore based on the bi-phase model analysis including the slip condition, the viscous behaviours for each phase can be determined for numerical simulation. It is proved that, by the analytical analysis and reasonable numerical method, the determination of slip velocity on wall and the viscosities for each phase can be made individually in the bi-phase flow model with slip effect. The interaction parameter for momentum exchange between two phases can be determined individually by experiments, after the determination of other parameters.On the basis of above mentioned work and previous development on algorithm of the simulation, the function to introduce the slip boundary condition has been implemented into the developed software for MIM injection simulation. The solution s of velocity fields in software are modified by reasonable treatment of new boundary and initial conditions. The influence of slip phenomenon can be then evaluated. The modified software is used to analyze the influence of slip phenomenon on the process of MIM injection moulding, as well as to predict its influence on segregation effect. The results are compared with the simulation results without taking into account the slip boundary effect. The numerical examples prove well the influence of slip phenomenon on simulation of the injection process and in prediction of the segregation effect. The importance to introduce the boundary slip condition in simulation software is then proven evident.