## 3 Results and Discussion
### Impact of Liquid Nitrogen Boiling on the Stability of the DCM
#### 3.3.3 Crystal Vibration Response  
Under the influence of gas-liquid two-phase flow, the amplitude response of the DCM is shown in Figure 16. From Figure 16a, it can be observed that, compared to velocity pulsation, the impact of gas-liquid two-phase flow on the stability of the crystal is significantly enhanced. Under the effect of slug flow, the system reaches relative stability at 0.27 s, followed by resonance. Through the frequency-amplitude diagram in Figure 16b, it can be found that the fundamental frequency of the response is 35.5 Hz, which is the first-order modal frequency of the DCM vibration.  
Figure 17 shows the change in liquid volume fraction at the x-z section of monitoring point p3. The figure shows that the curve of liquid volume fraction in the section has significant breaks at certain moments, exhibiting a low-frequency pulse signal. The energy of the fluid is intermittent, and the fundamental frequency of the pulse excitation is very close to the first-order modal frequency of the DCM, continuously impacting the outer wall of each bend in the pipeline. After the slug flow exits the bend, under the influence of gravity, the high-energy liquid phase will fall back to the bottom of the pipe and then impact the pipeline again. Moreover, for the pulse excitation signal, the response amplitude of the DCM is related to the integration of this pulse signal segment. Hence, the vibration of the DCM induced by slug flow is higher than the influence of harmonic signals.  
To avoid liquid nitrogen boiling, commonly used methods mainly include increasing the degree of undercooling, raising the flow rate, and elevating the saturation boiling point. [PERSON] [25] and others pointed out that increasing the degree of undercooling can lead to the crystal temperature field being in the \"cold expansion\" range, causing the crystal surface to cave in. Taking measures to increase the flow rate imposes higher requirements on the performance indicators of pumps and pulsation attenuators.  
Figure 16: The vibration response plot of the DCM under the action of gas–liquid. (**a**) Time domain feature. (**b**) Frequency domain feature two-phase flow.  
Figure 17: Liquid volume fraction at monitoring point 3.  
This can improve the turbulence intensity inside the pipeline, making designing an ultrastable DCM cooling system more challenging. [PERSON] and others carried out testing at the MAX IV laboratory in Sweden and found that high-pressure conditions are favorable for minimizing DCM vibration. Their test data showed that their pipeline withstood a pressure of 5.9 standard atmospheres, raising the saturation temperature of liquid nitrogen from the standard condition of 77.36 K to around 91.89 K. This ensures that heat is wholly absorbed before liquid nitrogen boils, preventing the occurrence of gas-liquid two-phase flow-induced vibration. Additionally, it is possible to reduce local resistance in the pipeline by increasing the curvature of the cooling pipeline and shortening the distance between the boiling point and the second crystal to avoid the transition from bubbly flow to slug flow.