*Article* **Beam Shaping in Laser Powder Bed Fusion: Péclet Number and Dynamic Simulation**

**Sergey N. Grigoriev, Andrey V. Gusarov, Alexander S. Metel, Tatiana V. Tarasova, Marina A. Volosova, Anna A. Okunkova \* and Andrey S. Gusev**

> Department of High-Efficiency Processing Technologies, Moscow State University of Technology STANKIN, 127055 Moscow, Russia; s.grigoriev@stankin.ru (S.N.G.); a.gusarov@stankin.ru (A.V.G.); a.metel@stankin.ru (A.S.M.); tarasova952@mail.ru (T.V.T.); m.volosova@stankin.ru (M.A.V.); gusev.angrey@bk.ru (A.S.G.)

**\*** Correspondence: a.okunkova@stankin.ru; Tel.: +7-909-913-12-07

**Abstract:** A uniform distribution of power density (energy flux) in a stationary laser beam leads to a decrease in the overheating of the material in the center of the laser beam spot during laser powder bed fusion and a decrease in material losses due to its thermal ablation and chemical decomposition. The profile of the uniform cylindrical (flat-top) distribution of the laser beam power density was compared to the classical Gaussian mode (TEM00) and inverse Gaussian (donut) distribution (airy distribution of the first harmonic, TEM01\* = TEM01 + TEM10). Calculation of the Péclet number, which is a similarity criterion characterizing the relationship between convective and molecular processes of heat transfer (convection to diffusion) in a material flow in the liquid phase, shows that the cylindrical (flat-top) distribution (TEM01\* + TEM00 mode) is effective in a narrow temperature range. TEM00 shows the most effective result for a wide range of temperatures, and TEM01\* is an intermediate in which evaporation losses decrease by more than 2.5 times, and it increases the absolute laser bandwidth when the relative bandwidth decreases by 24%.

**Keywords:** energy excess; heat diffusion; laser beam mode; laser powder bed fusion; numerical simulation; profiling; power density distribution; thermal conductivity
