# Optimization Design Study of Pipe Curtain Freezing Scheme for Sanya Estuary Submarine Channel
## 5 Optimal Design of Freezing Scheme and Analysis of Numerical Simulation Results
### Path Analysis
#### 5.4.2 Analysis of Observation Points  
(1) The graphs (a) and (b) of Figure 12 present the final temperatures at seven observation points for the 40 th day of freezing, measured at various distances from the central point under three distinct scenarios. The plots illustrate the relationship between the final temperatures and distance. It is evident that, for all three scenarios, the temperature increases \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Scheme** & **Original Plan** & **Scenario 1** & **Scenario 2** \\ \hline \(-1\) °C isotherm inter-circle time/(d) & 11 & 15 & 16 \\ \(-10\) °C isotherm inter-circle time/(d) & 14 & 23 & 24 \\ Thickness of permafrost curtain on west wall/(m) & 5.16 & 4.34 & 4.34 \\ Thickness of permafrost curtain on east wall/(m) & 5.22 & 4.4 & 4.17 \\ Thickness of permafrost curtain on top plate/(m) & 5.05 & 4.36 & 4.11 \\ Thickness of subgrade permafrost curtain/(m) & 4.67 & 4.33 & 4.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Comparison of freezing conditions of different schemes. Figure 11: Road map. with distance from the freezing tube, indicating a reduced freezing effect. Moreover, in each scenario, the final temperatures of observation points upstream are higher than those downstream, attributed to the enhanced seepage effect upstream and the groundwater flow carrying cold from upstream to downstream. Figure 12a,b depict the temperature changes of the outer sides of steel pipes for paths DJ\(-\)1 and DJ-2 under Scenario 1 and the original scenario, as well as the inner sides of pipes for paths DJ\(-\)1 and DJ-2 under Scenario 1 and Scenario 2, and the outer sides of pipes for paths DJ-3 and DJ-4 under all three scenarios. These observations show minimal temperature changes and nearly identical curves, reflecting the lack of optimization in the number of freezing pipes at these locations. Under Scenario 2, the optimization of the number of freezing tubes on the outer side of path DJ\(-\)1 results in higher final temperatures compared to the original scenario, with the temperature difference at the most distant observation points being only 6 \({}^{\circ}\)C. Similarly, the final temperatures of paths DJ-3 and DJ-4 under Scenario 1 and Scenario 2 are higher than those under the original scenario, attributable to the optimization of the number of freezing tubes on the inner side, with a temperature difference of only 8 \({}^{\circ}\)C between the optimized scenarios and the original scenario, which meets the design criteria. (2) The figure in Figure 12 presents the temperature changes over time for the three programs, based on the selection of four paths in both the upstream and downstream strong and weak freezing zones. The weighted average daily temperatures of the seven observation points on each path during the active freezing period for 40 days were mea  
Figure 12: Path analysis diagram. (**a**) Frozen final temperature map of the path observation point at the strong freeze zone. (**b**) Map of the frozen final temperature of the path observation point at the weak freeze zone. (**c**) Map of temperature change of path observation points at strong freezing areas. (**d**) Temperature change map of the path observation point at the weak frozen area. sured. The plots in Figure 12c,d indicate that during the initial 10 days of freezing and cooling, the cooling rates for the four paths under the three schemes were faster, and then they gradually leveled off after 10 days. This is attributed to the higher cooling rate of the brine cooling scheme during the first 10 days. From the average temperature change curve of the four paths under the original scheme, it can be inferred that the cooling effect in the downstream is superior due to the influence of the direction of groundwater seepage, which transports cold to the downstream area.