# Altering the Supply of Shielding Gases to Fabricate Distinct Geometry in GMA Additive Manufacturing
## 2 Results and Discussion
### Mathematical Model
Figure 11: Melt region of the weld pool at 2 s for oxygen concentration, (**a**) 310 ppm, (**b**) 420 ppm, and (**c**) 500 ppm. The increase in the weld depth with oxygen activity was further investigated by considering the weld pool velocity distribution. Figure 13a shows the weld pool velocity in the \(y\)-\(z\) plane for 420 ppm of oxygen at the time of melting and droplet impingement. Figure 13b show the weld pool velocity distribution for 500 ppm of oxygen at the same time. There was an oscillation in the melt pool, and the velocity in the \(z\)-direction was higher in the melt with 500 ppm, compared to 420 ppm. In the case of the 500 ppm simulation, there was an inward flow at the surface with a velocity of 1.6 cm/s in the \(z\)-direction and 1.0 cm/s in the \(y\)-direction, consistent with the surface tension coefficient remaining positive over a higher temperature range. The inward flow increases the downward flow velocity, giving a higher depth of the weld. Figure 12: Change in weld depth and width with respect to oxygen concentration. Figure 13: Weld pool velocity distribution in the \(x\)-\(z\) plane for identical heat input for (**a**) 420 ppm oxygen concentration and (**b**) 500 ppm oxygen concentration. The velocity in the \(z\)-direction is indicated by the color, and the length and direction of the arrow. **Case 3: Different heat fluxes with different surface tensions. **  
The heat flux for binary and ternary shielding gases was calculated using Equation (2). Some assumptions were made while calculating the heat flux for the two blends, as discussed below. 1. The radiative loss in GMAW arcs is dominated by metal vapor. The net radiative emission coefficient for the ternary and binary blends, and for 50 mol% mixtures of each blend with iron vapor, are shown in Figure 14. Although the binary blend radiates more strongly, the addition of iron vapor means that both blends radiate essentially the same amount. However, the ternary blend arc is shorter (Figure 2), so the radiative loss will be smaller. Therefore, the heat transferred to the workpiece will be larger for the ternary blend arc. However, since the radiative loss is in the order of 10-20% of the total power, this will result in a difference of at most 10%. 2. A substantial fraction (30-50%) of the heat transferred to the workpiece is carried by droplets [33]. The wire feed speed is the same for both gas blends, so the volume of metal transferred is the same. However, the droplet temperature is likely to be higher for the ternary blend case (with more, smaller droplets). The higher detachment rate is consistent with a lower surface tension, which indicates a higher liquid metal temperature. If 40% of the heat is transferred by droplets and there is a 20% higher droplet enthalpy for the ternary blend, then the heat transferred will be about 10% higher. Both the lower radiative loss, due to the shorter arc, and the higher droplet temperature will increase the heat transfer to the workpiece when the ternary blend is used, but the increase will only be about 20%. Thus, we assume that the efficiency of the ternary welding arc is 20% higher than that of the binary blend. An estimate of the effect of the plasma gas on the arc cross-sectional area A can be given by an equation for the total power flowing towards the workpiece at an axial position z.  
\[IV(z)\approx\overline{\rho(z)h(z)v_{z}(z)}A(z) \tag{5}\]  
where \(V(z)\) is the arc voltage drop from the electrode to the position z, \(I\) is the arc current, \(\rho\) is the mass density of the plasma, \(h\) is the specific enthalpy of the plasma, and \(v_{z}\) is the axial  
Figure 9:0 Net emission coefficient for the ternary and binary blends and for 50 mol% mixtures of each blend with metal vapor as a function of temperature [19; 20; 21]. speed; these are averaged over the area A [34].