## 3 CFD Modeling  
It had been verified that the CFD simulation method was an effective means to accurately analyze the fluid characteristics of hydrostatic bearings [13; 22; 23; 24; 25]. Hence, the CFD simulation method is employed to investigate the effects of varied OLDRs on the performance of the hydrostatic thrust bearing. The CFD simulation model of the hydrostatic thrust bearing is constructed under conditions of the following assumptions:  
1. Isothermal flow occurs in the fluid field of the hydrostatic thrust bearing. Circulating water cooling is applied to the bearing, which keeps the temperature field of the hydrostatic thrust bearing constant. 2. The oil viscosity is mainly affected by the temperature and the oil flows out of the sealing lands in a very short time, so the oil temperature can be considered constant. Then, the oil viscosity is assumed to be constant. 3. The geometric tolerances of the hydrostatic thrust bearing are not considered in this paper. 4. The fluctuation of the supply oil pressure of the bearing is ignored. In this study, the 3D Navier-Stokes equations are solved for numerical simulations. According to the dimensional parameters and the operating conditions of the hydrostatic thrust bearing, the realizable \(k\)-\(\epsilon\) turbulence model is employed in the CFD model. The realizable \(k\)-\(\epsilon\) turbulence model has shown substantial improvements where the flow features include strong streamline curvature, vortices, and rotation, which is suitable to investigate the streamline and vortices in this paper [26; 27]. The governing equations are solved in steady state, which take no account of rotational velocity and gravity force [28]. The maximum y+ of the working wall of the oil film (\(S\), shown in Figure 1) is about 3.33. The enhanced wall treatment is employed as a near-wall modeling method in this paper, which can be used with coarse meshes and possesses the accuracy of the standard two-layer approach for fine near-wall meshes [26]. The ambient pressure (\(p_{o}\)) is 101,325 Pa, which is set as the operating pressure. The boundary conditions for the inlets and outlets are pressure inlet and pressure outlet,  
Figure 1: Schematic configuration of the orifice-compensated hydrostatic thrust bearing. (**a**) The hydrostatic thrust bearing; (**b**) local enlarged view of I.  
respectively. The inlet gauge total pressure (\(p_{in}\)) is set to 25 times that of the \(p_{o}\) and the outlet gauge pressure (\(p_{out}\)) is set to 0 Pa. The working wall of the oil film (\(S\), shown in Figure 1) is modeled as a \"stationary wall\". The No. 2 spindle oil is specified for the hydrostatic thrust bearing, of which the oil density is 799.47 kg/m\({}^{3}\) and the dynamic viscosity is 0.00223 Pa-s. The pressure-based solver is chosen for the numerical analysis in this study, and the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm is used to obtain a converged solution and the others are default. The residual convergence criteria is assumed to be achieved [29] when: (i) the net flow rate of fluid entering and leaving the model is less than 7.5 \(\times\) 10\({}^{-6}\) L/min; (ii) the averaged force of the wall \(S\) reaches a stable level. To ensure the accuracy of the numerical solution, a comparative check on grid independence is conducted for the CFD model. The OLDR of 2 is selected as a case study. Two different meshing schemes are conducted for the CFD model. Specifically, scheme 1 has 1,822,043 cells and 2,021,829 nodes, and scheme 2 has 4,227,466 cells and 4,596,011 nodes.