*3.2. Computational Model*

Since the flow was assumed to be axisymmetric, one single-groove section (a 36◦ section) of disk was selected, and a periodic boundary condition was adopted in the simulation. In terms of boundary conditions, the moving disk was the rotating wall surface, and the static disk was the stationary wall surface. The standard wall function method was adopted to deal with the flow near the wall surface. The model inner diameter was the inlet of the flow field and was set as the mass-flow-inlet condition. The outer diameter was the outlet of the flow field. Since the outlet of the flow field was connected with the atmosphere, it was set as the pressure-outlet, and the pressure was the standard atmospheric pressure. In order to better simulate the flow details of the disk clearance flow field, the mesh needed to be encrypted near the disk wall and the radial slot wall. The flow field was discretized by a structured mesh scheme. The Green Gauss node-based method was used for the evaluation of gradients. The momentum and the energy equations were solved by the QUICK scheme [42]. The PRESTO! (Pressure staggering option) scheme was employed for the discretization of the pressure. A continuum surface force model proposed by Brackbill et al. [43] was applied in this calculation. Interface reconstruction was performed using the explicit piecewise linear interface construction (PLIC) scheme [44]. To handle the two-phase flow condition, it was assumed that the inlet was filled with oil, thus the oil volume fraction was one at the inlet. In this paper, the convergence of the calculation was determined by monitoring the residual error and the flow parameters. The numerical results were obtained when the drag torque, the volume average oil phase, and the area average wall surface heat transfer coefficient were stable. To ensure the accuracy and the validity of numerical results, a careful check for the grid independence of the numerical solutions was conducted. Three sets of mesh resolutions were adopted for the flow field with 307,644 (Mesh 1), 365,796 (Mesh 2), and 439,432 (Mesh 3). In Table 1, the calculated results of the average oil volume fraction with different angular velocities are given. The differences between the mesh density of 307,644 elements and the other two were smaller than 5%, indicating that a higher resolution of mesh than Mesh 1 limited improvement on the calculation result. Mesh 1 basically satisfied the requirement of accuracy. Considering the reduction of computational time consumption, Mesh 1 was selected in the simulation model.


**Table 1.** Oil volume fraction results under different mesh resolutions and speeds.

#### **4. Experimental Apparatus**

A flow field test platform for the grooved rotating-disk system was built based on the Bruker's Universal Mechanical Tester, as shown in Figure 2. The platform consisted of a rotating grooved disk, a stationary ungrooved disk, a peristaltic oil pump, a data acquisition system, and a control system. The rotating disk was driven by an electric motor, and the precision of the controlled disk speed was 1.0 r/min. The gap between the stationary disk and the rotating disk could be adjusted continuously with the precision of 10 μm. In the test, the gap was set to be zero at first. The measured force in the axial direction was used to detect the zero-gap position. Then, the gap was increased gradually from zero position to a prescribed position. The pump could supply a maximum volumetric flow rate of 1000 mL/min with the accuracy of 1.0 mL/min. When the flow field became uniform and stable, the visualized image of the flow field was captured. The specifications of the grooved rotating-disk system in the test are shown in Table 2.

**Figure 2.** Test apparatus of the grooved rotating-disk system.

**Table 2.** Specifications of the grooved rotating-disk system model.

