## 2 Analysis of Smooth-Walled Radial Bearing Ignoring Cavitation Effects
### Governing Equations
It was first predicted by the physicist [PERSON] in 1873 that the high-speed relative motion between the propeller and the water would create a vacuum cavity that affects the performance of the propeller during the travel of the ship. Later, [PERSON] et al. [16]. However, cavitation is not the only disadvantage. Along with the cavitation process, the bubbles generated by the fluid and the moving wall reduce the macroscopic shear force during the movement. For example, supercavitation \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Calculation Scheme** & **Mesh Number** & **LCC** & **Error** \\ \hline FEM & 61,500 & 853.1 N & \\ Scheme 1 & 20,364 & 847.6 N & 0.65\% \\ Scheme 2 & 61,179 & 853.6 N & 0.05\% \\ Scheme 3 & 114,260 & 850.9 N & 0.26\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mesh independence verification. Figure 2: Pressure distribution of oil film on the journal hydrostatic bearing: oil pressure (MPa). technology is used to generate cavitation on the surface of the torpedo, so that the resistance of the torpedo can be reduced by 90% [17], among which the \"full cavitation model\" was studied by [PERSON] et al. It accounts for phase change, bubble dynamics, turbulent pressure fluctuations, and noncondensable gases. It is able to take into account multiphase flows or flows with multiphase transport of matter, the effect of sliding velocity between liquid and gas phases, as well as the thermal effects and compressibility of liquid and gas phases, establishing the Rayleigh-Plessset equation, also known as the Porisky equation, which is also a widely used cavitation model [18]. Since the negative pressure problem in the diverging wedge region needs to be solved in combination with the cavitation phenomenon, the bearing oil film model is divided into two simplified slider bearings, the convergent wedge and the diverging wedge, which are analyzed separately. With the multiphase cavitation modeling approach, a basic two-phase cavitation model consists of using the standard viscous flow equations governing the transport of mixture phases. In cavitation, the liquid-vapor mass transfer equation has the following form:  
\[\frac{\partial}{\partial t}(\alpha\rho_{v})+\
abla\cdot(\alpha\rho_{v}\vec{v }_{v})=R_{e}-R_{c} \tag{6}\]  
In the equations mentioned above, \(t\) is time, \(\alpha\) is volume fraction, \(\rho_{v}\) is vapor density, \(\vec{v}_{v}\) is vapor velocity, \(R_{e}\) and \(R_{c}\) are mass transfer source terms connect to the growth and collapse of the vapor bubbles. For different cavitation models, the definition of \(\alpha\) or other assumptions are different, resulting in different calculation methods of \(R_{e}\) and \(R_{c}\). However, several cavitation models can be written as similar formulas with different calculation methods of coefficients \(C_{vap}\) and \(C_{cond}\). \[\left\{ \begin{array}{l}R_{e}=C_{vap}\rho_{v}\rho_{l}\sqrt{\frac{3}{3}\frac{( p_{v}-p)}{p_{l}}}\\ R_{c}=C_{cond}\rho_{v}\rho_{l}\sqrt{\frac{2}{3}\frac{(p-p_{v})}{p_{l}}}\end{array} \right. \tag{7}\]  
The saturation pressure \(p_{v}\) is corrected by an estimation of the local values of the turbulent pressure fluctuations:  
\[p_{v}=p_{sat}+\frac{1}{2}(0.39\rho k)\]model needs to compare the mixture model and the Eulerian model. Pull the model to make trade-offs. The selection of the mixture model and Eulerian model is mainly based on the following principles. * The mixture model is used when the gas phase is widely distributed, and the Eulerian model is used when the gas phase is concentrated in a local area. * The mixture model is used when the stability and efficiency of the calculation are pursued, and the Eulerian model is used when the calculation accuracy is pursued. * When choosing the Eulerian model, the influence of the interphase drag force needs to be considered. If the interphase drag force rule is unknown, the mixture model is used. For the bearing oil film model with micro-texture on the wall surface, the flow field is more complicated.