# Altering the Supply of Shielding Gases to Fabricate Distinct Geometry in GMA Additive Manufacturing
## 2 Results and Discussion
### Mathematical Model  
The equations of conservation of mass, momentum, and energy were solved in a three-dimensional domain using the volume-of-fluid method to generate and predict the weld pool geometry. The flow was considered laminar. A more detailed description of this model has been presented in the literature ([PERSON] and [PERSON], 2018)([PERSON] and [PERSON], 2018). For the GMAW surface tension transfer process, the mass droplets with energy and momentum were considered. The heat flux and surface tension were used as boundary conditions. The heat and mass loss due to conduction, convection, radiation, and vaporization were considered as boundary conditions. \[\gamma=1.943-4.3\times 10^{4}(T-1811)-RT2.03\times 10^{8}ln[1+1.38\times 10^{-2}a _{i}e^{-(\frac{-143.3\times 10^{8}}{RT})}] \tag{2}\]  
where \(T\) is in Kelvin (\(K\)), \(R\) is in J K\({}^{-1}\) mol\({}^{-1}\), and \(\gamma\) is in N m\({}^{-1}\). The equation above was used to calculate the surface tension coefficient for the varied concentrations of oxygen in the Fe-O system. Heat loss due to various modes of heat transfer and heat loss through vaporization was also considered in this model by  
\[K\frac{\partial T}{\partial\overrightarrow{n}}+h(Ts-T)+q_{vap}+q_{rad}=q(r) \tag{3}\]  
where \(K\) is the thermal conductivity, \(n\) is the normal vector, \(Ts\) is the surface temperature, \(q_{vap}\) is the heat loss through vaporization, and \(q_{rad}\) is heat loss through radiation. The base metal and droplets were assumed to be stainless steel, and their thermophysical properties are listed in Table 2([PERSON], 2018). Three cases were simulated: Case 1--the heat flux input was varied for the same surface tension coefficient; Case 2--the surface tension coefficient was varied for the same heat flux; and Case 3--both heat flux and surface tension were varied. **Case 1: Same surface tension with different heat fluxes inputs**  
The simulation was performed with three different cases of input heat fluxes: first with the actual heat flux, second with a three-fold increase of the heat flux, and third with a six-fold increase. In all cases, the oxygen concentration was 310 ppm. The heat flux distribution was calculated using Equation (4):  
\[q(r)=\frac{\eta VI}{2\pi\sigma^{2}}\exp-\left(\frac{r^{2}}{\sigma^{2}}\right) \tag{4}\]  
where \(V\) and \(I\), respectively, are the average welding voltage and current, \(r\) is the radius, \(\eta\) is the efficiency, and \(\sigma\) is the heat distribution parameter, usually taken as the radius of the arc [26] ([PERSON], [PERSON], and [PERSON], 2008). Although many previous models assume an identical heat flux in numerical modeling, even with different shielding gases, it is clearly evident from the outcome of our research that there are significant changes in the bead characteristics. The droplet parameters (droplet size, droplet heat, velocity, and frequency) were assumed constant for all cases and were derived from the AM parameters and the literature [27; 28]. Figure 9 shows the simulation results of the melt pool region for the three different heat flux inputs; an identical surface tension-to-temperature relationship was used. It can be seen that, with all the parameters kept constant, the higher heat flux caused greater penetration in the welding material. There was a significant change in the dimensions of the weld bead, as shown in Figure 9. There was also a sharp change in the weld depth--a 32% increase using the three-fold heat flux and a 114% increase using the six-fold flux. The width of the weld bead increased slightly: a 9% increase in the three-fold case and a 14% increase in the six-fold case. The abrupt change in the depth of the weld pool is associated with the Gaussian distribution of the heat flux, which is peaked at the center and reduces rapidly with the change in radius; to increase the heat flux, the parameter in the numerator (\(q\prime\)) was increased. Obviously, the results would be different if the parameter in the denominator (\(\sigma\)) were reduced to increase the heat flux.