# Numerical Study on Single-Bubble Contraction-Rebound Characteristics in Cryogenic Fluids
## 1 Introduction
Different from ordinary fluids, the temperature drop of the bubble growth process cannot be ignored in cryogenic liquids. The existing isothermal hypothesis is not viable. Therefore, for cryogenic fluids, thermodynamic effects must be considered on cavitation development and bubble growth. [PERSON] et al. [27] modified the cavitation model for ordinary fluids considering thermal effects and used it to study cavitation in liquid nitrogen. The application of the cavitation model for cryogenic fluids was improved in prediction. Comparing to the experimental results, the numerical results were within the error limits. Recently, a large number of numerical studies popped up focusing on cryogenic fluid cavitation. [PERSON] et al. [28] used the modified cavitation model with thermodynamic effects to compare the cavitation process of water and liquid nitrogen. The numerical results indicated that thermal effects could inhibit the cavitation in liquid nitrogen but had almost no suppression effect for water. Moreover, the particularity of liquid hydrogen cavitation, which is different from other cryogenic fluids, was further investigated by [PERSON] et al. [29]. The empirical evaporation and condensation constant in liquid hydrogen was obviously higher than that in other fluids. In addition to the modification of the cavitation model, [PERSON] et al. [30] also used the modified model to study the cavitation model of liquid oxygen in turbopumps. Cavitation was mainly distributed in the leading edge of the inlet of the inducer and the central blade head of the impeller. In most of the existing cavitation models, modifications have focused on the influence of the thermal effect. There are relatively few models which have been proposed for single-bubble growth and collapse. [PERSON] [31] considered the equation of heat conduction outside the bubble and used it to calculate the phase transition in the thermal boundary layer. In addition, this model was also used to study the bubble development process in liquid hydrogen, liquid nitrogen and liquid oxygen. The growth process of bubbles in the inducer was studied numerically based on this model [32]. However, the temperature difference between the center and boundary of the bubble was not considered. During the growth and collapse of a single bubble, the temperature and pressure of the vapor inside the bubble vary greatly [33]. Nevertheless, most of the existing bubble growth and collapse models assume that the temperature inside the bubble is the same as that of the fluid at the bubble boundary. For the more accurate prediction of the growth-collapse process of single bubbles in cryogenic fluids, existing bubble models should be modified. In this paper, based on the existing bubble model, a single-bubble collapse model was proposed for cryogenic fluids. The modified Rayleigh-Plesset equation, heat balance equation, heat diffusion equation and state equation were solved simultaneously in various cryogenic fluids. By comparing the tendency of bubble bursting and rebound in different fluids, the influence of the physical properties of cryogenic fluids on bubbles was analyzed. In addition, the influence of the bubble internal temperature on the bubble collapse and rebound process was considered and calculated. The bubble contraction-rebound process in liquid hydrogen was selected as the main research object. The oscillations of the bubble radius, radius growth rate, temperature at the bubble boundary and temperature and pressure inside the bubble were studied using the model. The amplitude, attenuation rate and period of bubble collapse were analyzed under different supercooling degrees and operating pressures.