# The Variation of Surface Shape in the Gas Jet Forming
## 6 Discussion
\begin{table}
\begin{tabular}{c c c c} \hline
**Parameters** & **Error** & **Parameters** & **Error** \\ \hline \(V_{0}=9.5\) m/s, \(H=20\) mm & 0.01164 & \(V_{0}=10.5\) m/s, \(H=20\) mm & 0.02202 \\ \(V_{0}=9.5\) m/s, \(H=22.5\) mm & 0.00086 & \(V_{0}=10.5\) m/s, \(H=22.5\) mm & 0.02211 \\ \(V_{0}=9.5\) m/s, \(H=25\) mm & 0.00826 & \(V_{0}=10.5\) m/s, \(H=25\) mm & 0.02522 \\ \(V_{0}=9.5\) m/s, \(H=27.5\) mm & 0.00130 & \(V_{0}=10.5\) m/s, \(H=27.5\) mm & 0.06659 \\ \(V_{0}=9.5\) m/s, \(H=30\) mm & 0.00561 & \(V_{0}=10.5\) m/s, \(H=30\) mm & 0.07670 \\ \(V_{0}=10\) m/s, \(H=20\) mm & 0.00824 & \(V_{0}=11\) m/s, \(H=20\) mm & 0.06482 \\ \(V_{0}=10\) m/s, \(H=22.5\) mm & 0.00323 & \(V_{0}=11\) m/s, \(H=22.5\) mm & 0.07881 \\ \(V_{0}=10\) m/s, \(H=25\) mm & 0.01480 & \(V_{0}=11\) m/s, \(H=25\) mm & 0.08948 \\ \(V_{0}=10\) m/s, \(H=27.5\) mm & 0.00882 & \(V_{0}=11\) m/s, \(H=27.5\) mm & 0.09778 \\ \(V_{0}=10\) m/s, \(H=30\) mm & 0.01875 & \(V_{0}=11\) m/s, \(H=30\) mm & 0.10790 \\ \hline \end{tabular}
\end{table} 
Table 4: Errors between the numerical simulations and experimental data for the principal curvature of the formed surface. \begin{table}
\begin{tabular}{c c c c} \hline
**Parameters** & **Error** & **Parameters** & **Error** \\ \hline \(V_{0}=9.5\) m/s, \(H=20\) mm & 1.8402 & \(V_{0}=10.5\) m/s, \(H=20\) mm & 1.4042 \\ \(V_{0}=9.5\) m/s, \(H=22.5\) mm & 1.8428 & \(V_{0}=10.5\) m/s, \(H=22.5\) mm & 0.7813 \\ \(V_{0}=9.5\) m/s, \(H=25\) mm & 1.5873 & \(V_{0 During the formation process, the difference in rate between the gas phase compared to the liquid phase is large. Differentiating the VOF method rate attributes \(\mathbf{U}_{\text{VOF}}\) and \(\mathbf{U}_{\text{lidq}}\) yields the following final formula:  
\[\mathbf{U}_{\text{\tiny error}}=\frac{\alpha_{\text{gas}}\rho_{\text{lidq}} \Big{(}\mathbf{U}_{\text{gas}}-\mathbf{U}_{\text{lidq}}\Big{)}}{\alpha_{\text{ gas}}\rho_{\text{gas}}+\alpha_{\text{lidq}}\rho_{\text{lidq}}}, \tag{22}\]  
In the VOF method, the gas and liquid phases must fill a certain grid. This means that the gas and liquid phases are in the control body, and the volume fraction sums to 1. The formula is as follows:  
\[\alpha_{\text{gas}}+\alpha_{\text{lidq}}=1, \tag{23}\]  
The mirror blanks were formed at a constant temperature of 20 \({}^{\circ}\)C, at which point the density of air is 1.225 kg/m\({}^{3}\) and the density of the liquid phase is 977 kg/m\({}^{3}\). Equation (24) was obtained by substituting the density data into Equation (22). \[\mathbf{U}_{\text{\tiny error}}=\frac{977\alpha_{\text{gas}}\Big{(}\mathbf{U }_{\text{gas}}-\mathbf{U}_{\text{lidq}}\Big{)}}{\alpha_{\text{gas}}1.225+ \alpha_{\text{lidq}}977}, \tag{24}\]  
In the VOF method, the accuracy of the subtype prediction in this test case is related to the difference between the mixed-phase rate property \(\mathbf{U}_{\text{VOF}}\) and the associated \(\mathbf{U}_{\text{lidq}}\). After deduction, the factors influencing \(\mathbf{U}_{\text{\tiny error}}\) include \(\alpha_{\text{gas}}\), \(\alpha_{\text{lidq}}\), and the difference in rate \(\mathbf{U}_{\text{gas}}-\mathbf{U}_{\text{lidq}}\) between the gas and liquid phases. Assuming that within a specific grid at a certain \(\alpha_{\text{gas}}\) and \(\alpha_{\text{lidq}}\) the time step is constant in this paper, the gas-liquid two-phase rate is the only factor that affects them. Since the liquid phase is a highly viscous fluid and the gas phase is air, the difference between the two phases is too significant, causing iterative errors.