*5.2. Parametric Analysis*

The angular speed, the flow rate, and the disk spacing are sensitive system parameters. In the visualization test results, the radial position of the continuous oil film boundary (which indicates the air–oil interface) could be utilized to demonstrate the effect of each parameter on the phase distribution in the flow field. Figure 6 presents the effects of different angular velocities on the oil volume fraction along the radial direction. The horizontal value of the coordinate was a dimensionless radial location *r*/*r*2. It is noteworthy that the oil volume fraction at one radial position was the averaged value of all the cells at this same radius. The following figures with different parameters were obtained in the same approach. For a certain angular velocity, the oil volume fraction tended to be 1.0 near the inlet area, indicating a pure oil flow. Around the middle radius region, the oil volume fraction decreased rapidly, indicating that the oil phase was aerated and a two-phase flow existed. As the radial position approached the outlet, the decline slope of the oil volume fraction reduced, and an air phase flow played a dominate role near the outer edge.

**Figure 6.** Average oil volume fraction curves at different radial positions with different angular velocities.

For different angular velocities, it could be seen that the transition location of the full oil phase to two-phase flow in the radial coordinate became closer to the inner radius with the angular speed increasing. In the two-phase flow zone, the oil volume fraction of the flow field became lower with the increasing angular speed at the same radial position. Figure 7 shows the effect of angular velocity on the flow field in the visualization test. It was observed that the interface between the continuous oil phase and the aerated part moved radially inwards with the increasing angular velocity. The continuous oil film shrunk at higher angular speeds. Thus, the simulation results agreed well with those of the visualization test.

**Figure 7.** Comparison of the air–oil interface radial position at different angular velocities.

Figure 8 presents the variations of the oil volume fraction along the radial direction at different inlet volumetric flow rates. With the increase of the flow rate, the transition location of the full oil phase to two-phase flow in the radial coordinate moved gradually outwards to the outer radius. At the same radial location in the two-phase flow zone, the oil volume fraction became larger with higher flow rate. Furthermore, the decline slope of the average oil volume fraction was reduced with larger flow rate. As a validation, the visualization test results of various flow rates are shown in Figure 9. The boundary of the continuous oil phase area expanded with the increasing flow rate at the same speed. Since a larger flow rate is beneficial for heat dissipation in practical application, the flow rate is an important operating parameter. However, a larger flow rate requires a greater oil pump, leading to greater power consumption. Besides, it also results in higher drag torque at the same speed. Thus, a suitable flow rate needs to be confirmed according to the variation of the flow pattern.

**Figure 8.** Average oil volume fraction curves at different radial positions with different oil flow rates.

**Figure 9.** Comparison of the air–oil interface radial position with different inlet oil flow rates.

The effects of the disk spacing on the flow field are shown in Figure 10. The boundary of the continuous oil phase remarkably moved inwards with higher disk spacing. At the same radial position in the two-phase zone, the oil volume fraction became much smaller with a higher disk spacing. The visualization test results of different disk spacing are shown in Figure 11. The continuous oil phase area shrunk with larger disk spacing. The numerical simulation results agreed well with the experimental results. The disk spacing is also an important system geometric parameter, since it significantly influences the viscous drag. Thus, the disk spacing needs to be optimized according to the practical restriction.

**Figure 10.** Average oil volume fraction curves at different radial positions with different disk spacing.

**Figure 11.** Comparison of the air–oil interface radial position with different disk spacing.

For the flow field inside the grooved two-disk system, both the flow rate and the disk spacing had direct effects on the radial flow velocity. The variation of the flow rate or the disk spacing changed the radial flow velocity. A more detailed investigation on the radial flow velocity is necessary. Furthermore, the flow rate and the disk spacing mentioned above are usually applied as the control parameters in engineering.

The average oil volume fractions of the flow field within the whole calculation domain under different angular velocities, oil flow rates, and disk spacing are shown in Figure 12. The simulated and the measured values of the average oil volume fraction were compared. It seems that the average oil volume fraction became lower with the increase of the angular speed, as shown in Figure 12a. When the angular speed was relatively low, the average oil volume fraction decreased nearly linearly. At relatively high speed, the slope of the average oil volume fraction curve got smaller and tended to be a constant value. In Figure 12b, both the simulated and the measured average oil volume fractions increased linearly with the flow rate before the flow rate reached 50 mL/min, which filled the flow field between the two disks. Lastly, in Figure 12c, the average oil volume fraction decreased with the increase of the disk spacing in a linear way. In the application of the disengaged wet clutch, the oil phase distribution is of crucial importance, since it affects the heat dissipation and the drag loss significantly. Thus, the two-phase flow behavior should be considered carefully in the clutch disk design.

**Figure 12.** Parametric effects on the average oil volume fraction. (**a**) effect of the angular velocity; (**b**) effect of the inlet oil flow rate; (**c**) effect of the disk spacing.
