## 3 Results and Discussion
### Impact of Liquid Nitrogen Boiling on the Stability of the DCM
#### 3.3.2 Gas-Liquid Two-Phase Flow Simulation  
Figure 15a illustrates the distribution of gas volume fraction in the cooling loop. Liquid nitrogen boiling begins at the inlet section of the cooling loop, forming a bubbly flow. Subsequently, during the secondary heating process in the cooling loop, the gas volume fraction gradually increases, forming slug flow [23] in the cooling loop of the first crystal. The development of a two-phase flow downstream in the heating loop results from the combined effects of superheated boiling and the decrease in saturation vapor pressure. The temperature cloud map of the cooling loop wall in Figure 15b shows that after liquid nitrogen flows out of the cooling loop of the first crystal, it still has a relatively high temperature, indicating that the liquid nitrogen is in a superheated state. Over time, the superheated liquid nitrogen continuously undergoes vaporization, gradually increasing the gas volume fraction downstream. The phase-change model used in this research is the Lee model, and the occurrence of boiling or condensation is related to the saturation temperature of liquid nitrogen. As shown in Figure 15c, the pressure gradually decreases with the extension of the flow path, causing the saturation temperature to drop. Therefore, gas continues to be generated inside the downstream loop. Based on the simulation results, when the gas-liquid two-phase flow passes through the bends in the pipeline, the fluid velocity slows down, and the bubbles in the fluid merge. Bubbles near the inner side of the bend entrance momentarily pause and merge with subsequent inflowing bubbles before entering the bend. This phenomenon was also observed by [PERSON] [24] in visual experiments on liquid nitrogen flow through bends, where bubbles seemed to be momentarily \"frozen\". This phenomenon occurs because the fluid behavior is complex at the bend, and there is significant local resistance at the bend entrance. The gas phase has low inertia during the flow process, and its kinetic energy is insufficient to overcome the resistance loss, leading to a rapid decrease in velocity. When it merges with subsequent bubbles into a much larger bubble, it hinders the liquid phase flow in the pipeline. Under the push of the liquid phase, the merged big bubble can then passively enter the bend. As liquid nitrogen flows to the two-crystal circuit, the gas-liquid two-phase flow in the pipeline evolves into slug flow. Slug flow is characterized by the alternating gas and liquid flow, representing a strongly turbulent gas-liquid two-phase flow phenomenon. Due to the significant difference in fluid density between the gas and liquid phases and speed differences between the gas and liquid phases, there is a significant difference in fluid energy within a unit volume. Under the action of centrifugal force, the liquid is \"thrown\" to the outside of the  
Figure 14: Temperature distribution. (**a**) The first crystal. (**b**) The wall of the U-shaped circuit of the first crystal. (**c**) Liquid nitrogen in the U-shaped circuit. pipe, squeezing the bubbles into the inside. The obstruction of the pipeline causes the direction of fluid motion to change continuously, leading to changes in fluid momentum. This results in the continuous impact of the alternating gas-liquid two-phase flow on the pipeline, causing the pressure field on each side of the pipeline wall to change continuously. Under the influence of centrifugal force, the pressure on the outer side of the bend wall is higher than the inner side, leading to continuous changes in pressure on both sides of the bend wall and ultimately causing pipeline instability. As shown in Figure 15a, after the slug flow exits the bend and reaches the straight pipe, due to the influence of gravity, the gas initially on the inside of the bend rises toward the top of the pipe. This process triggers intense oscillations in the flow field.