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With industrial modernity and its multiple advantages over global industry. The use of 3D printers has become a primary necessity for the industry. The laser melting process (SLM) is one of the most widely used processes for the manufacture of metal parts from a powder. Thanks to laser fusion manufacturing, very complex structures and geometries can be produced with very good quality. The materials used in SLM are metals that come in the form of granules. During the manufacture of the parts, the metal powder cannot be compacted as much during the process. It is therefore necessary to use supports for cantilevered structures. The interest of our research is to model the suspension mechanism of Ti-6Al-4v granules in a turbulent flow of Newtonian fluid due to the fusion of granules in a powder bed. We will start with a mathematical study based on the transport equation for Ti-6Al-4v granules and the Navier-Stokes equations. Then the mathematical and numerical discretization of the equations is done by using the finite volume method, for the resolution of the equations we use the Gauss-Seidel method. And finally, we built a numerical code for the resolution of the fluid velocity equations and the concentration profile of the granules in the FORTRAN language.
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