# Experimental Study on Geysers Induced by the Release of Trapped Air in Storage Tunnel Systems
## 4 Data Analysis and Discussion
In this paper, the \(\overline{v}_{1}\) value is statistically analyzed from \(h_{w}=0.15\) m to \(h_{w}=0\) with no geyser conditions. Through regression analysis, one excellent fitting curve with high consistency was obtained (as shown in Figure 7). The corresponding index values were \(\alpha=0.008\), \(\alpha 1=1.5\), \(\alpha 2=0.5\), and \(\alpha 3=-2.5\). The \(Fr\) of free surface is expressed as:  
\[Fr=\frac{\overline{v}_{1}}{\sqrt{gD}}=0.008\frac{H_{0}^{*}{}^{1.5}V^{*0.5}}{D^ {*2.5}} \tag{4}\]  
where \(H_{0}^{*}=H_{0}/D_{0}\), \(V^{*}=V/\pi{D_{0}}^{3}/4\), \(D^{*}=D/D_{0}\). When considering the influence of water column height, under the geyser condition, the air column is not broken in the shaft, the \(\overline{v}_{1}\) value is obtained by extrapolation according to the velocity variation trend. Vast data on free surface velocity, including geyser cases and no geyser cases, were analyzed, and the fitting curve was obtained as shown in Figure 8. The corresponding equation is expressed as:  
\[Fr=\frac{\overline{v}_{1}}{\sqrt{gD}}=0.009\frac{H_{0}^{*}{}^{1.5}V^{*0.5}}{D^ {*2.5}h_{w}^{*}{}^{0.5}} \tag{5}\]  
where \(h_{w}^{*}=h_{w}/D_{0}\). However, when the height of the water column is greater than the external pressure head, the free surface cannot be moved upward, so the formula is inappropriate. When the height of the water column is relatively small, the disturbance of the water column is enhanced. This may increase the deviation of the free surface velocity. For the average interface net velocity, \(\overline{v}_{net}\), which is mainly dominated by the flow characteristics of the liquid film, its value floats at a fixed constant during the gas-flow geyser. The influencing factors are relatively complex, the free surface velocity (\(v_{1}\)) and the value of \(D\) have the most significant influence. Figure 9 shows the relation between the Froude number of average interface net velocity, \(Fr_{net}\), and the Froude number of free surface velocity, \(Fr_{1}\). The corresponding equation is defined by data fitting as:  
\[Fr_{net}=\frac{\overline{v}_{net}}{\sqrt{gD}}=0.025 Fr_{1}+0.39 \tag{6}\]  
Figure 8: Expanded fitting curve for the Froude number of average free surface velocity. Figure 6:0 Fitting curve for the Froude number of average free surface velocity. Figure 6:1 Comparison between \(Fr_{net}\) and \(Fr_{1}\). According to the expressions of \(\overline{v}_{1}\) and \(\overline{v}_{net}\), when the vertical shaft diameter is large, then the free surface velocity will be small, and the net velocity of the interface will be large, and it will be more difficult to form a gas-flow geyser. Meanwhile, by comparing the relative relation of the \(\overline{v}_{1}\) value, \(\overline{v}_{net}\) value, the height of shaft \(H\), and the initial height of the water column \(h_{0}\), the occurrence conditions of gas-flow geyser can be obtained as follows:  
Figure 6:2  
Figure 10 shows the relation between \(\frac{Fr_{1}}{Fr_{net}}\) and \(\frac{H}{h_{0}}-1\) based on fitting Formulas (5) and (6). The results are in good agreement with the experimental results. The upper part of the figure is the geyser region, the bottom part is the no-geyser region, the middle part between dotted lines is the transition region, the calculation value in the transition region may have a certain degree of error because of the unstable characteristic of the geyser, and the deviation was between 10% and 20%. However, in this paper, the tunnel diameter of the experiment device was fixed at 0.15 m, the effect of tunnel diameter on the geyser was not determined, and the conclusions presented in this paper still need to be further verified. In addition, the \(v_{net}\) value was extremely unstable; the shape of the air column had a great influence on the \(v_{net}\) value. When the air column head has a defective or unsteady interface, the \(v_{net}\) value increases significantly, so the measured data becomes more random and less regular.