## 5 Analysis of Experimental and Simulation Results
### Uniform Water Body Conditions
#### 5.1.1 Case 1 Working Conditions  
Under Case 1 conditions, the initial velocity of the jet is 0.1 m/s, the water depth is 0.26 m, and the temperature difference with the ambient water body is 10 \({}^{\circ}\)C. PLIF technology is used to measure the thermal jet in a uniform water environment at intervals of 5 s, 10 s, 15 s, 20 s, 25 s, and 30 s to observe changes in the temperature field distribution. The experimental results are shown in Figure 4.  
As depicted in Figure 4, at 5 s, the outflow distance of the thermal jet is slightly greater than 10 cm, with a floating height of no more than 5 cm. In the core area of the thermal jet, there remains a temperature difference of nearly 10 \({}^{\circ}\)C between the thermal jet and the environment; while in an area about 10 cm away from the outlet, it appears to float upwards, with a decreased temperature difference of about 4 \({}^{\circ}\)C. By 10 s, the outflow distance has increased to close to 20 cm, and the floating height is approximately 10 cm. The thermal jet appears more obvious in its upward stage after reaching a distance of around 10 cm from the outlet. During this stage, there is a gradual decrease in temperature difference between the thermal jet and the environmental water body from 4 \({}^{\circ}\)C to about 1 \({}^{\circ}\)C. At 15 s, the outflow distance exceeds slightly beyond 20 cm, and the floating height exceeds 10 cm. Compared with 10 s, the temperature field area of the temperature difference between the thermal jet and the environmental water body within 1 \({}^{\circ}\)C increases. At 20 s, the outflow distance of the thermal jet is about 25 cm, and the floating height is more than 15 cm. Compared with 15 s, the temperature field area of the temperature difference range of 2-4 \({}^{\circ}\)C is slightly reduced. At 25 s, the thermal jet outflow distance is close to 30 cm, and the rising height is more than 20 m. Compared with 20 s, the temperature difference range \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Case**} & **Time** & \multicolumn{5}{c}{(\(x\), \(z\))} \\ \cline{3-7}  & **Step/s** & **(0.05, 0.25) m** & **(0.1, 0.2) m** & **(0.15, 0.15) m** & **(0.2, 0.1) m** & **(0.25, 0.05) m** \\ \hline \(d\) & 0.01 & 299.928 K & 294.805 K & 292.419 K & 291.902 K & 290.855 K \\ \(e\) & 0.02 & 299.936 K & 294.813 K & 292.422 K & 291.894 K & 291.341 K \\ \(f\) & 0.05 & 300.121 K & 295.215 K & 291.688 K & 290.155 K & 299.155 K \\ \hline \end{tabular}
\end{table} 
Table 4: The temperature of the flow field at different positions of y = 0 section under the condition of different time steps. (\(K\) is thermodynamic temperature.) \begin{table}
\begin{tabular}{c c c c c c c} \hline \multirow{2}{*}{**Case**} & **Mesh** & \multicolumn{5}{c}{(\(x\), \(z\))} \\ \cline{3-7}  & **Numbers** & **(0.05, 0.25) m** & **(0.1, 0.2) m** & **(0.15, 0.15) m** & **(0.2, 0.1) m** & **(0.25, 0.05) m** \\ \hline \(a\) & 6.5 \(\times\) 10\({}^{5}\) & 300.016 K & 295.678 K & 291.451 K & 290.899 K & 290.872 K \\ \(b\) & 7.8 \(\times\) 10\({}^{5}\) & 299.911 K & 294.852 K & 292.416 K & 292.012 K & 291.164 K \\ \(c\) & 9.7 \(\times\) 10\({}^{5}\) & 299.936 K & 294.813 K & 292.422 K & 291.894 K & 291.341 K \\ \hline \end{tabular}
\end{table} 
Table 3: The temperature of the flow field at different positions of \(y\) = 0 section under the condition of different number of grids. (\(K\) is thermodynamic temperature.) \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Case**} & **Velocity (m/s)** & **Depth (cm)** & **TD (\({}^{\circ}\)C)** \\ \hline
1 & 0.1 & 26 & 10 \\
2 & 0.2 & 26 & 10 \\
3 & 0.1 & 26 & 20 \\
4 & 0.1 & 52 & 10 \\ \hline \end{tabular}
\end{table} 
Table 5: Hydrostatic-uniform water experimental conditions. of 1\({}^{\circ}\) continues to expand, the diffusion distance is 30 cm, the rising height is 21 cm, and the temperature difference dissipates in some areas at the back end of the rising stage.