# Numerical Study on Single-Bubble Contraction-Rebound Characteristics in Cryogenic Fluids
## 3 Comparison of Bubble Collapse in Different Fluids  
According to the open literature [40], the pressure of 0.1 MPa\({}^{-}\)0.51 MPa and the temperature of 20-27.4 K are often used in liquified hydrogen storage and delivery. Therefore, in this section, the operating pressure of 1-3 atm and the supercooling degree of 1-5 K were selected for calculation. The effects of operating pressure and supercooling degree on the radius of a single bubble, bubble growth rate, temperature and pressure inside a bubble were investigated. In order to study the particularity of bubble behavior in liquid hydrogen, the bubble collapse process of liquid nitrogen, liquified methane and water were introduced and compared. In the process of bubble collapse, there is a bubble period with rapid contraction and rebound. In the collapse process, the variation in the bubble radius with time under different operating pressures and supercooling degrees is shown in Figure 4a,b, respectively. Under the condition of low operating pressure, the liquid hydrogen force acting on the bubble was small, so the bubble growth rate was slow. Therefore, the bubble contraction-rebound period increased with higher operating pressure. Moreover, the amplitude of the bubble radius increased with lower operating pressure because of the small kinetic energy attenuation. When the operating pressure of the bubble remained the same, the velocity of bubble contraction increased greatly with the supercooling degree. Therefore, the period of the bubble radius decreased with the supercooling degree. Meanwhile, due to the fast contraction of the bubble, the bubble radius became larger with the same kinetic energy attenuation. Figure 3: Comparison of the calculation results of the growth–collapse model with the experimental results (**a**) and the calculation results of the Yukio [39] model (**b**). In addition to the bubble radius, the bubble growth rate over time was also investigated. The bubble growth rate under different operating pressures and supercooling degrees is shown in Figure 5. As analyzed above, the maximum bubble growth rate was not significantly correlated with operating pressure. Initially, the peak and valley values of the bubble growth rate were almost the same under the same supercooling degree. However, the bubble growth rate was affected by the high operating pressure and the attenuation rate was rapidly accelerated. In contrast, the amplitude of the bubble growth rate increased greatly with the supercooling degree of liquid hydrogen. The peak value and attenuation rate of the bubble growth rate were affected by the operating pressure and the supercooling degree. The period of the bubble growth rate decreased with the operating pressure and the supercooling degree. During contraction-rebound, the pressure and temperature of the bubble also varied greatly. The pressure inside the bubble during oscillation is shown in Figure 6. The peak and equilibrium of the pressure inside the bubble was promoted under larger operating pressure. Similarly, the peak in pressure inside the bubble was also enlarged sharply with supercooling degree. Accompanied with the variation in bubble radius, rapid contraction led to the fast compression of hydrogen inside the bubble. The period of the bubble pressure  
Figure 4: Radius of liquid hydrogen bubbles under different operating pressures (**a**) and different supercooling degrees (**b**) during collapse. Figure 5: Radius growth rate of liquid hydrogen bubbles under different operating pressures (**a**) and different supercooling degrees (**b**) during collapse. was almost the same as the bubble radius period. The fluctuation of pressure inside the bubble was possibly caused by the variation in the bubble radius. Due to the different operating pressures, the absolute value of the peak pressure inside the bubble did not reflect the impact intensity during bubble collapse clearly. Therefore, the pressure inside the bubble was nondimensionalized using the operating pressure of infinity.