# Numerical Study on Single-Bubble Contraction-Rebound Characteristics in Cryogenic Fluids
## 3 Comparison of Bubble Collapse in Different Fluids
The comparison results are shown in Figure 7. The dimensionless pressure inside the bubble was reduced. This result indicated that the impact caused by bubble collapse was strong under low operating pressure. The temperature variation at the bubble boundary with time is shown in Figure 8. The initial and final temperature at the bubble boundary were upraised at higher operating pressure, but the amplitude decayed. With increment of supercooling degree, the lower initial temperature at the bubble boundary led to larger temperature undulation. However, the influence of supercooling degree on the final bubble boundary temperature was not significant. Figure 6: Pressure inside liquid hydrogen bubbles under different operating pressures (**a**) and different supercooling degrees (**b**) during collapse. Figure 7: Dimensionless pressure inside liquid hydrogen bubbles under different operating pressures. Different from the liquid temperature at the bubble boundary, there was a larger undulation in vapor temperature due to its small heat capacity. Moreover, the oscillation of temperature inside the bubble was enhanced due to the vapor compression process. As shown in Figure 9a, the initial temperature inside the bubble increased under higher operating pressure. Under different operating pressures, the peak value of the temperature remained almost the same during the first few periods. The influence of the supercooling degree on the bubble temperature is shown in Figure 9b. The equilibrium temperature inside the bubble was almost unaffected by the supercooling degree. The temperature peak increased with the supercooling degree. In order to compare the temperature inside the bubble and that at the bubble boundary, the condition was selected with the operating pressure equal to 3 atm and supercooling degree equal to 1 K. The two temperatures are shown in Figure 10. The temperature peak inside the bubble was much larger than that at the bubble boundary. As the thermal conductivity of the vapor phase was much lower than that of the liquid phase, the temperature inside the bubble accumulated gradually, and its valley value gradually separated from the temperature at the bubble boundary. Figure 5.0 Temperature at liquid hydrogen bubble boundaries under different operating pressures (**a**) and different supercooling degrees (**b**) during collapse. Figure 5.1 Temperature inside liquid hydrogen bubbles under different operating pressures (**a**) and different supercooling degrees (**b**) during collapse. Based on the investigation of bubble collapse in liquid hydrogen, the effect of fluids' properties on bubble collapse was studied. The comparison of the bubble radius and bubble growth rate in different fluids is shown in Figure 11a,b, respectively. The oscillation frequency and amplitude of the liquid hydrogen bubble were much larger than those in the other three fluids. The radius and growth rate of the bubble in liquid nitrogen and liquid methane had similar peak values. The bubble radius in liquid nitrogen had a relatively lower valley value. Due to the great differences in standard boiling points among different fluids, it was meaningless to compare temperature inside the bubble and that at the bubble boundary directly. Therefore, the bubble temperature was nondimensionalized with the fluid critical temperature. As shown in Figure 12, the amplitude and frequency of the dimensionless temperature and the equilibrium temperature of the bubble in liquid hydrogen were larger than those in the other fluids. Moreover, it is worth noting that only the peak temperature inside the liquid hydrogen bubble was higher than the critical temperature during temperature oscillation. Additionally, the bubble oscillation time of liquid hydrogen was much smaller than that in the other fluids. Figure 5.2 Bubble radius (**a**) and radius growth rate (**b**) in different fluids under 3 atm operating pressure and 5 K supercooling degree during collapse.