## 4 Results  
### The First Cycle  
After deposition of the titanium alloy powder (the layer thickness is about 32 \(\upmu\)m), the laser beam moves along three parallel tracks and creates the first level of the product. Figure 7 presents the simulation stages of the first cycle of laser treatment. Untreated particles of titanium alloy are shown in olive color, a laser beam is shown in green, a liquid phase with blue, and solidified material is shown in brown. The laser beam moves forward in Figure 7. After the beam reaches the end of the track, the model simulates cooling till all the material transits into the solid state. Then, the next track begins. The pause between the tracks can be varied.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Properties** & **Ti-6 Al-V** & **Glass** & **Air (Nitrogen)** \\ \hline Melting temperature, \(T_{m}\) (K) & 1922 & 1336 & - \\ Boiling temperature \(T_{b}\), (K) & 3560 & 2503 & - \\ Heat capacity, \(C_{p}\) (J kg\({}^{-1}\) K\({}^{-1}\)) & 560 & 500 & 1 \(\div\) 1.25 \\ Specific latent heat, \(L\) (J g\({}^{-1}\)) & 360 \(\div\) 370 & - & - \\ Thermal diffusivity, \(\mu\) (m\({}^{2}\) s\({}^{-1}\)) & 2.9 \(\times\) 10\({}^{-6}\) & 37 \(\div\) 67 \(\times\) 10\({}^{-6}\) & 200 \(\div\) 300 \(\times\) 10\({}^{-6}\) \\ Convective heat transfer coefficient, \(h\) & 50 & 50 & - \\ (Wm\({}^{-2}\) K\({}^{-1}\)) & 4420 & 2700 & 0.6 \(\div\) 0.35 \\ Density, \(\mu\) (Pa s) & 4.42 \(\times\) 10\({}^{-3}\) & 0.1 \(\div\) 500 & 30 \(\div\) 55 \(\times\) 10\({}^{-6}\) \\ Kinematic viscosity, \(\
u\) (m\({}^{2}\) s\({}^{-1}\)) & 10\({}^{-6}\) & 3.75 \(\times\) 10\({}^{-5}\) \(\div\) 0.2 & 20 \(\div\) 250 \(\times\) 10\({}^{-6}\) \\ The surface tension of the liquid–gas & 1.55 & 0.25 & - \\ interface, \(\gamma\) (N m\({}^{-1}\)) & 6.5 \(\times\) 10\({}^{-5}\) & 8.5 \(\times\) 10\({}^{-6}\) & 1.22 \(\times\) 10\({}^{-3}\) \\ Thermal expansion coefficient, \(\alpha_{l}\) (K\({}^{-1}\)) & 6.5 \(\times\) 10\({}^{-5}\) & 8.5 \(\times\) 10\({}^{-6}\) & 1.22 \(\times\) 10\({}^{-3}\) \\ Rayleigh number, Ra & 676 & 0.2 \(\div\) 2.5 \(\times\) 10\({}^{-6}\) & 0.005 \(\div\) 0.1 \\ Bond (Eötvös) number, Bo(Eo) & 11.4 \(\times\) 10\({}^{-6}\) & 43.2 \(\times\) 10\({}^{-6}\) & - \\ \hline \hline \end{tabular}
\end{table}
Table 1: Properties of the materials.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Properties** & **Ti-6 Al-V** & **Glass** \\ \hline Melting temperature \(T_{m}\), (-) & 1.0 & 0.614 \\ Boiling temperature \(T_{b}\), (-) & 2.031 & 1.358 \\ Temperature decrement \(\Delta T\), (K) & 452.3 & 645.1 \\ Temperature decrement \(\Delta T\), (-) & 0.288 & 0.411 \\ Specific latent heat (enthalpy) \(L\) (-) & 0.415 & - \\ Convective heat transfer coefficient, \(h\) (-) & \(5.05\times 10^{-6}\) & 7.72 \(\times\) 10\({}^{-5}\) \\ Relaxation time for fluid flow \(\tau_{\text{F}}\), (-) & 0.55 & 25.5 \\ Relaxation time for heat flow \(\tau_{\text{T}}\), (-) & 0.75 & 0.53 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulation parameters.  
Figure 8a presents the temperature distribution in the cross-section across the movement immediately following the laser beam. The temperature scale is presented in Figure 8d, and it is the same in all the following figures. Blue represents low temperature and red represents high. Black, pink, and light blue correspond to the melting temperature of the titanium alloy and are somewhat higher and lower (about 10%) than the melting temperature. Figure 8b,c show the state of the material at the beginning and end of the track in the cross-section along the laser movement. Melting is seen to continue for a short time after the laser passes. The melting pool expands and deepens as a result of the heat accumulated in the liquid phase.