## 2 Method
### Simulation of Molybdenum Powders in the LPBF Process  
To model the physical structure of the powder bed as accurately as possible, the powder geometry created via DEM simulation was converted into STL format. This approach enabled a more detailed analysis of the laser melting process, allowing the microstructure of the powder bed to be realistically represented in the simulation environment. Furthermore, to ensure the accuracy of thermal distribution and fluid dynamics calculations in the simulation, the substrate thickness was set to 4 mm. This thickness allows for the realistic simulation of temperature differences that arise during the laser melting process, ensuring balanced heat distribution across the substrate. Additionally, using a 10 \(\upmu\)m mesh resolution enabled more precise modeling of the dynamic behavior of the melt pool and surface tension effects. As a result, the temperature distribution, phase changes, and fluid movements in the laser-treated area were analyzed in detail, enhancing the physical realism of the simulation. For the simulation, the temperature-dependent physical and thermal properties of Molybdenum (Mo) were integrated into the model using data obtained from the Thermo-Calc software. To accurately model the laser melting process, LPBF parameters such as laser power, laser spot diameter, and scanning speed were defined based on actual system conditions. Boundary Conditions:  
* The initial system temperature was set to 200 \({}^{\circ}\)C;
* The length of a single scan path was adjusted to 10,000 \(\upmu\)m to ensure a homogeneous and consistent melt track. These parameters facilitated a detailed analysis of the laser melting behavior of Molybdenum powders in the LPBF process. In the simulation study, the effects of parameters \begin{table}
\begin{tabular}{c c} \hline
**Particle Radius (\(\upmu\)m)** & **Particle Number Density Percentage (\%)** \\ \hline
9.835 & 34.78 \\
14.4 & 44.33 \\
19.465 & 17.95 \\
22.4 & 2.94 \\ \hline \end{tabular}
\end{table} 
Table 4: Group particle sizes and numerical ratios are defined for the CFD. Figure 2: (**a**). Temperature-dependent density (Kelvin, g/cm\({}^{3}\)) (**b**). Temperature-dependent viscosity (Kelvin, g/cm\(\cdot\)s) (**c**). Temperature-dependent specific heat (Kelvin, 10\({}^{-7}\) J/g\(\cdot\)K) (**d**). Temperature-dependent thermal conductivity (Kelvin, 10\({}^{-7}\) W/cm\(\cdot\)K). such as laser power, laser spot diameter, scanning speed, and powder layer thickness on the melt pool were thoroughly analyzed. For the simulation, the following software tools were used:  
* FLOW-3D WELD 3.0.1.1.8 Release 7 and FLOW-DEM 3.0.1.1.6 Release 7;
* Particle to STL Converter 3.0.0.0 Release 7 Update 3 was used to convert the particle geometry into STL format;
* HEEDS software was used to optimize the inputs for FLOW-3D WELD simulation within the parameter ranges specified in Table 5.  
Additionally, the scanning strategy was set as unidirectional and cross-scanning. The optimization of the LPBF process was conducted using HEEDS, a design exploration platform that incorporates the SHERPA (Simultaneous Hybrid Exploration that is Robust, Progressive, and Adaptive) algorithm. SHERPA is a hybrid, adaptive search method that dynamically blends global and local optimization strategies, allowing for efficient navigation of complex, nonlinear, and high-dimensional parameter spaces. Within the scope of this study, SHERPA was utilized to identify a parameter set that ensures melt pool stability and strengthens the mechanical integrity of the printed material. HEEDS systematically varied the input parameters within predefined bounds and executed a series of high-fidelity simulations. From these simulations, key performance indicators--including melt pool volume, surface area, and micro-porosity--were derived and assessed based on the defined optimization objectives.