**6. Conclusions and Future Work**

In this paper, the viscous flow field inside a grooved rotating-disk system was studied quantitatively. A 3D CFD model considering two-phase flow and heat transfer was utilized to simulate phase distributions and heat dissipation. Visualization tests were conducted to validate the flow pattern and the parametric effect on the flow field. Several conclusions were drawn as follows.

(1) The viscous flow field of the grooved rotating-disk system was identified to be an air–oil two-phase flow. A stable interface between the continuous oil phase and the two-phase area could be formed and observed in the flow field. The proposed 3D CFD model with VOF model and heat transfer consideration was validated by the comparison of simulation with the visualization test result of the flow field.

(2) The effects of angular velocity, inlet volumetric flow rate of oil, and disk spacing on the oil volume fraction along the radial direction were analyzed and compared with the visualization test results. In general, the interface between the continuous oil phase and the two-phase flow moved outwards with smaller angular speed, more inlet flow of oil, or decreasing disk spacing. Besides, for the whole flow field, the average oil volume fraction decreased with increasing angular speed, less inlet flow rate of oil, or increasing disk spacing.

(3) The local Nusselt number was remarkably affected by the air–oil volume fraction and the flow velocity distributions in this two-phase flow. The local Nusselt number was much higher near the disk edge—both the inner and the outer ones. Fluctuations of the local Nusselt number appeared near the two-phase interface due to the flow speed changes. At higher angular velocity, the area of fluctuation expanded. The variation of average Nusselt number over the whole flow field could be divided into three stages resulting from the variation of fluid volume fraction and fluid speed.

The results can be used to optimize the design of the grooved rotating-disk system disk fluid machine. The energy transfer characteristics of the air–oil two-phase flow need more study. Work on these topics is currently underway in the National Key Laboratory of Vehicular Transmission at the Beijing Institute of Technology.

**Author Contributions:** Conceptualization, C.L. and W.W.; Methodology, W.W.; Validation, C.L., W.W. and Y.L.; Formal Analysis, J.Z.; Investigation, C.H.; Writing—Original Draft Preparation, W.W. and Y.L.; Writing—Review & Editing, C.L.; Project Administration, C.L.; Funding Acquisition, C.L. and W.W.

**Funding:** This work is supported by the National Natural Science Foundation of China (Grant No. U1864210 and 51975045) and National Key R&D Program of China (Grant No. 2018YFB2001300).

**Acknowledgments:** The authors thank referees for improving the quality of the paper. If readers are interested in this paper, please contact the authors. It's our pleasure to provide readers with relevant model, grid and setup files.

**Conflicts of Interest:** The authors declare no conflict of interest.
