## 3 Results and Discussions
### Discussion about Nucleation Characteristic and Inlet Flow
#### 3.2.2 Interaction of Fluid Field and Ice Phase
The part that is not occupied by the ice phase in the computational domain is filled with liquid water at beginning with a temperature of 283.15 K (10 \({}^{\circ}\)C). Simulation Results  
Firstly, in case 3 at the initial stage (\(t\) = 0.0 s), there is no ice in the computational domain. By the method of this paper, the process of n-hexanol driving water and ice developing is numerically simulated, and then the distributions of cryogenic fluid, water, and ice at different moments are presented in Figure 11. The red zone represents the cryogenic fluid and ice, and the blue zone represents the water phase. From the figure, it is seen that the numerical simulation method could simulate the process of ice expansion and two-phase fluid flow. At the initial phase of t = 0.2 s, due to the low temperature and high rate of crystallization on the wall boundary, there are respective ice layers on the upper and lower boundaries. Then the cryogenic fluid of n-hexanol from the left velocity-inlet \begin{table}
\begin{tabular}{c c} \hline \hline
**Boundary** & **Conditions** \\ \hline Left & \(u_{l}=0\), \(v_{l}=0\), \(T_{l}=283.15\), \(u_{s}=0\), \(v_{s}=0\), \(T_{s}=283.15\), \(\alpha_{s}=0\) \\ Right & \(\frac{\partial u_{l}}{\partial x}=0\), \(\frac{\partial v_{l}}{\partial x}=0\), \(\frac{\partial T_{l}}{\partial x}=0\), \(\frac{\partial u_{l}}{\partial x}=0\), \(\frac{\partial v_{s}}{\partial x}=0\), \(\frac{\partial T_{s}}{\partial x}=0\), \(\frac{\partial u_{s}}{\partial x}=0\) \\ Upper & \(u_{l}=0\), \(v_{l}=0\), \(T_{l}=253.15\), \(u_{s}=0\), \(v_{s}=0\), \(T_{s}=253.15\), \(\frac{\partial u_{s}}{\partial m}=0\) \\ Lower & \(u_{l}=0\), \(v_{l}=0\), \(T_{l}=253.15\), \(u_{s}=0\), \(v_{s}=0\), \(T_{s}=253.15\), \(\frac{\partial u_{s}}{\partial m}=0\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The settings of the boundary conditions (Case ex). Figure 10: Ice formation and development on the wall boundary with time advancing (case ex) (**a**) 50 s, (**b**) 100 s, and (**c**) 150 s.  
boundary flows around the ice layers and drives the water in the middle domain. Furthermore, the low temperature of n-hexanol affects the growth of ice on the wall boundaries and causes the left of the ice layer to be thicker. With time advancing (t = 0.4 s, 0.6 s, and 0.8 s), the ice layers gradually grow and further block the inflow of cryogenic fluid. Then the n-hexanol flows through the narrow channel due to the formed ice and then spreads towards the whole water area. The flow fields distribution at various moments are shown in Figure 12. The influences of the ice layer on the flow state are reflected in the flow velocity changing (a value of up to about 0.014 m s\({}^{-1}\) is obtained in the simulation, which is higher than the inlet velocity of 0.01 m s\({}^{-1}\), indicating the fluid acceleration due to the presence of ice layer). For the fluid in the right domain with the thinner ice layers, the fluid velocity gradually decreases and becomes relatively stable. The velocity distribution shown in Figure 12 indicates that the simulated result obeyed the basic conservation law of mass and momentum. Thus, the present method can correctly simulate the propagation of the ice phase and its effect on the flow state. In order to study the effect of the initial distribution of the ice phases on the convection process, the distributions of three phases (cryogenic fluid, water and ice) at \(t\) = 0.5 s are plotted in Figure 13. Therein, case 3 is without initial ice and the initial ice phase distributions in case 4, case 5, and case 6 are presented in Figure 10a-c, respectively. It is obviously seen from Figure 13 that the initial ice phase distribution has significant influence on the convection of cryogenic fluid and water. With the initial ice phase composition increasing, the cryogenic fluid spreads more rapidly. Figure 14 shows the vector graph of fluid velocity of water and n-hexanol at \(t\) = 0.5 s under different initial conditions of ice phase composition.