## 5 Conclusions  
In this study, to design a pump-drive turbine for sCO\({}_{2}\) cycle application, the performance of hydrostatic bearings using liquid CO\({}_{2}\) as lubricant was analyzed and the dynamic characteristics of the rotor were predicted. To demonstrate the viability of the designed pump-drive turbine, an operating test was performed, and the rotor vibration was measured during the test. The following conclusions were obtained from this study. Figure 14: Measured and predicted rotor vibration at the turbine side bearing. Figure 13: Rotor vibration measurement results. (**a**) x-direction; (**b**) y-direction. 1. The results predicted using the hydrostatic bearing analysis program of this study were similar to those of previous research, and the reliability of the developed analysis model was confirmed;
2. Under the design conditions, a pressure ratio existed that maximized the stiffness of the radial bearing, in consideration of which the orifice diameter was determined;
3. Based on the rotordynamic analysis, it was predicted that no critical speed would be presented below the rated speed and no instability would occur, indicating a wide range of operating speeds;
4. Tests performed on the manufactured pump-drive turbine in the sCO\({}_{2}\) test facility confirmed that successful operation is possible for the designed sCO\({}_{2}\) cycle, and the measured rotor vibration was 2 \(\upmu\)m at the rated speed;
5. The test results showed that hydrostatic bearing with liquid CO\({}_{2}\) as the lubricant can be successfully applied to the sCO\({}_{2}\) turbomachinery. Conceptualization, D.L., M.P. and E.Y. ; methodology, B.K. and M.P. ; software, D.L. and H.L. ; validation, M.P., H.L. and E.Y. ; formal analysis, D.L. and B.K. ; writing--original draft preparation, D.L. ; writing--review and editing, M.P. ; project administration, E.Y. ; funding acquisition, E.Y. All authors have read and agreed to the published version of the manuscript. This work was supported by the Korea Ministry of Land, Infrastructure and Transportation. It was also supported by the Korean Agency for Infrastructure Technology Advancement (Project No. : 19 HITP-B151621-01-00000). The work was partially supported by National Research Council of Science and Technology (NST) grant funded by the Ministry of Science and ICT, Korea (Grant No. KIMM-SC1270). The authors declare no conflict of interest. * (3) [PERSON]; [PERSON] Supercritical carbon dioxide Brayton power cycle development overview. In Proceedings of the Turbo Expo 2012, Copenhagen, Denmark, 11-15 June 2012. * (4) [PERSON]; [PERSON]; [PERSON] Steady-State power operation of a supercritical carbon dioxide Brayton cycle with thermal-hydraulic control. In Proceedings of the Turbo Expo 2016, Seoul, Korea, 13-17 June 2016. * (5) [PERSON] [PERSON]; [PERSON] Transient Modeling of a Supercritical CO2 power Cycle and Comparison with Test Data. In Proceedings of the Turbo Expo 2017, Charlotte, NC, USA, 26-30 June 2017. * (6) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Development of a 250-kWe class supercritical carbon dioxide ranking cycle power generation system and its core components. In Proceedings of the Turbo Expo 2019, Phoenix, AZ, USA, 17-21 June 2019. * (7) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Scale dependencies of supercritical carbon dioxide Brayton cycle technologies and the optimal size for a next-step supercritical CO2 cycle demonstration. In Proceedings of the SCO2 Power Cycle Symposium, Boulder, CO, USA, 24-25 May 2011. * (8) [PERSON]; [PERSON]; [PERSON] Investigation of magnetic journal bearing instability issues in supercritical CO2 turbomachinery. In Proceedings of the ASME-JSME-KSME 2019 Joint Fluids Engineering Conference 2019, San Francisco, CA, USA, 28 July 2019. * (9) [PERSON]; [PERSON]; [PERSON] Optimisation of externally pressurized bearings for minimum power and low temperature. _Tribol. Int._**1970**, \(3\), 153-157.