# Spatiotemporal Evolution of Gas in Transmission Fluid under Acoustic Cavitation Conditions
## 1 Introduction  
Liquid transmission systems are mainly used for the precise transmission of pressure and are widely used in various types of machinery or equipment [1; 2]. Complex gas-liquid two-phase flow is often generated in the transmission systems due to factors such as air and high temperature [3; 4; 5; 6; 7]. Since the transmission fluid itself dissolves air and has low boiling-point components, cavitation occurs when the transmission fluid pressure induced by the pressure wave is lower than the air separation or saturated vapor pressure [8; 9]. This phenomenon is also known as acoustic cavitation. It is caused by air evolution, which forms bubbles or cavities by the low-boiling-point components evaporating around the tiny gas nucleus [10; 11; 12]. The gas bubbles affect the transmission characteristics; therefore, the ruptured bubbles damage the system, generate noise, and shorten the service life of the machinery [13; 14; 15; 16; 17]. The spatiotemporal evolution process of gas in liquid is complex, and it is worth studying with a mathematical model. The gas-liquid two-phase flow model can be divided into the separated flow model and homogeneous flow model. Concerning the separated flow model, [PERSON] et al. [18] divided the continuity equation into liquid and gas phases,considering that the gas and liquid were at the same speed. They coupled the gas-liquid two-phase continuity equation through the source term, and the model validity was verified by the experimental results. However, most researchers used the homogeneous flow model to simulate cavitation [9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24]. [PERSON] et al. [25] developed a new model of positive pressure cavitation based on partial differential equations controlling mass and momentum conservation. The results show that the flow discontinuity caused by the beginning and end of cavitation shows robustness. Furthermore, [PERSON] et al. [26] used a homogeneous flow model to avoid the calculation of slipping velocity between the gas and liquid phases. Thus, the gas and liquid phases were viewed as a single phase. The analytical data were compared with experimental data (the Moehwald-Bosch MEP2000-CA4000 high-performance test bench data). The results show that even in the case of discontinuity caused by cavitation, pressure wave propagation can be simulated with high accuracy [27]. The homogeneous flow model can be divided into the non-conservative and conservative homogeneous flow models. [PERSON] et al. [28] developed a set of fluid dynamics equations for a fuel injection system based on the non-conservative model and simulated the occurrence and time evolution of cavitation. However, [PERSON] et al. [29] compared the conservative and non-conservative homogeneous flow models. They ascertained the precision of the conservative homogeneous flow model in cavitation transient flow simulations by comparing the calculated pressure timescales and experimental results for two tube locations in the injection system. The non-conservative homogeneous flow model produced some errors in the analysis. [PERSON] et al. [30] proposed a comprehensive thermodynamic method to simulate acoustic cavitation considering the temperature change caused by the compression effect and the influence of vapor cavitation in the fuel injection system. The authors compared the isentropic and isothermal evolution of the pure liquid zone to assess the impact of temperature changes on the macroscopic results generated by the local pressure time history and compare them with experiments to verify the effectiveness and robustness at the beginning and end of acoustic cavitation. [PERSON] [31] analyzed and discussed the effect of frequency-dependent friction on the simulation of pressure wave dynamics under cavitation conditions and applied it to the momentum conservation equation. Their results showed that the equation provides an outstanding resolution in the time prediction of experimental pressure wave damping.