# Modelling of a Non-Transferred Plasma Torch Used for Nano-Silica Powders Production
## 4 Results and Discussion
### Flow of Plasma in the Torch  
In Figure 3, the distribution of plasma temperature is presented in the torch under the fixed gas flow rate \(Q_{in}=78\) sccm and for different current values. When the cold plasma forming gas passes through the anode column, it will be strongly heated and accelerated, so there is a fast increase in the temperature and velocity. Indeed, when the current rose from 100 A to 200 A the maximum temperature was increased from 5200 K to 5500 K.  
To show with greater clarity the effect of increasing current on plasma temperature changes, the temperature distributions, in front of the cathode tip, are represented in Figure 4. It can be clearly seen that the region area of the plasma temperature higher than 5000 K expands when the current increases. This can be explicated by the effect of the Joule heat produced, namely:  
\[Q_{joule}=\overrightarrow{J}\cdot\overrightarrow{E}=\frac{\left| \overrightarrow{J}\right|^{2}}{\sigma} \tag{18}\]  
Indeed, the rising of the current leads to an increase in the current density responsible for Joule heating. Although the electric conductivity of nitrogen gas presents a slow raise as the temperature increases, its influence remains insignificant compared to the current density. Then, the plasma temperature increases with increasing current. A small temperature variation was observed at the torch exit (from 5200 K to 5500 K), when the current rose from 100 A to 200 A. This was because the energy benefit of joule \begin{table}
\begin{tabular}{c c} \hline
**Item** & **Description** \\ \hline Working gas & Nitrogen \\ Reactor pressure & 400 kPa \\ Nitrogen flow rate & (78–240) sccm \\ Power range & 10–30 kW \\ Current plasma & 100–200 A \\ Plasma voltage & 80–200 V \\ Cathode material & Thoriated tungsten \\ Anode material & High-purity copper \\ Interelectrode gap & 1.8–2 mm \\ Overall length & 250 mm \\ Outlet electrode diameter & 17.2 mm \\ Temperature of exit gas & 2400–4800 \({}^{\circ}\)C \\ \hline \end{tabular}
\end{table} 
Table 3: Operation conditions used to synthesis nano-silica. heating that contributed to the current growth was practically offset by the energy loss due to the length reduction in the electric arc. This effect consequently leads to a trivial dependance of the arc current on the average temperature at the torch exit [33]. A temperature above 3000 K was observed at the electrode tip, indicating that a melt could occur at the electrode tip. This high temperature was generally compensated by  
Figure 4: Distribution of the temperature of plasma at the nozzle exit for different current value ((**a**) 100 A, (**b**) 150 A, (**c**) 200 A). Figure 3: Distribution of plasma temperature for different current values ((**a**) 100 A, (**b**) 150 A, (**c**) 200 A) in the torch. the cooling water of the cathode that causes thermal power loss through it, which can be calculated by:  
\[Cathode_{loss}=\frac{Q_{cathode}}{I.V_{arc}} \tag{19}\]  
where \(Cathode_{loss}\) represents the thermal power loss through cathode cooling water. However, sometimes after several hours we could observe erosion in the cathode tip [34]. This indicates that cooling of the cathode was not sufficient in this case. In Figure 5, the distribution of the velocity magnitude field is presented in the torch under the fixed gas flow rate \(Q_{in}=78\) sccm and for different current values. The results show that the highest plasma velocities within the torch were approximately 90, 110, and 150 m/s for current values of 150, 200, and 200 A, respectively. The augmentation of working current led to the increase in velocity magnitude. This axial acceleration of plasma flow was simultaneously influenced by the Lorentz force and by the rise in temperature driven by the joule heating effect [35], which reduces the gas density and reinforces the expansion of the plasma. Figure 6 shows the variation in plasma voltage versus current at different nitrogen mass flow rates (Q).