| This project, suggested by the IMI of NRC focuses on the simulation of thermohydrodynamic instabilities causing manufacturing defects during metal powders injection molding processes. At present time, 30% of the manufactured parts are defective. We can found inhomogeneities, empty spaces or debilitating parts when operating conditions are poorly controlled or poorly known. An understanding of the phenomenon will enable manufacturers to reduce or even eliminate defects and improve their competitiveness. The elimination of these effects involves a study and a rigorous fundamental analysis based on CFD ("Computational Fluid Dynamics") and sensitivity analysis. We use a T-shape geometry, typical of injectors that are found in systems of metallic powders casting. The metallic powders is injected at the basis of the T, and then leave by the two ends of the T.;We modeled this problem by using the equations of motion (Navier-Stokes) coupled with the heat transfer equation and a generalized Newtonian viscosity model. Our equations are then solved by the finite elements method which provides the velocity (u and v), pressure and temperature as functions of space and time. The calculation of sensitivities will establish a causal relationship between the different ranges of parameter values that cause instability. The stability or instability depends on the value of two rheological parameters, the Graetz number (ratio of thermal conduction time to fill time) and B, a dimensionless ratio measuring the importance of the effects of temperature on the viscosity. For some values of Graetz and B numbers, the flow becomes unstable and asymmetrical. However, in some cases, this asymmetry is growing to the point where the fluid is forced to leave the injection channel by a single exit. This eventually lead to a complete cessation of the flow in one branch of the T, as if it was obstructed. The instabilities are due to changes in viscosity, itself driven by temperature gradients which can be found at the entrance to the injector. We can see an exponential growth in the temperature difference between the two exits (symmetrical point at the injectors exits). The sensitivity analysis will establish rigorously which of the two parameters trigger instability. Moreover, this analysis will indicate in what regions and at what times the parameters are critical to stability.;After assuring ourself that the implementation in the computer code has been verified by the method of manufactured solutions, we built with the help of numerical solutions the stability chart of the flow in terms of the dimensionless number Gz and B. The chart allows to define the border separating the region where the flow is stable from the one where the flow is unstable. Finally, in connection with the calculation of neighbouring solutions, sensitivity analysis shows that it is possible to anticipate and predict the behaviour of fluid when parameters of the flow (i.e. Gz et B) are disrupts. These results suggest that it is possible to control and even eliminate manufacturing defects in processes related to metal powders injection molding. |
