## 1 Introduction  
The supercritical carbon dioxide (sCO\({}_{2}\)) cycle enables higher thermal efficiency than the conventional steam Rankine cycle, resulting in reduced fuel cost and greenhouse gas production [1]. Thus, the sCO\({}_{2}\) cycle is extensively applied in various power-conversion systems, including concentrated solar thermal and nuclear power [2; 3; 4; 5], waste heat recovery from large engines [6], and geothermal [1]. The high density of sCO\({}_{2}\) at high-pressure can cause compact turbomachinery, critical equipment in circulatory systems for the sCO\({}_{2}\) thermodynamic cycle, at low capital costs [2]. To achieve commercial viability, various types of bearings have been investigated to support the rotors of such high-speed turbomachinery. [PERSON] et al. [2] replaced angular contact ball bearings initially installed in a turbocompressor for the sCO\({}_{2}\) Brayton cycle with gas-foil bearings (GFBs). The GFBs lubricated with sCO\({}_{2}\), enabled a simple configuration without the sealing mechanism to prevent oil contamination and ensured a long bearing life. During preliminary tests, the authors found that high-pressure sCO\({}_{2}\) in the foil thrust bearing generates significant power loss, which is attributed to the rotational speed. [PERSON] et al. [7] employed GFBs to support the shaft in their 10-kWe-class unrecuperated sCO\({}_{2}\) Brayton cycle [7]. Preliminary operations were successfully conducted at 30 kppm and at a turbine inlet temperature and pressure of 83 \({}^{\circ}\)Cand 8500 kPa, respectively. [PERSON] et al. [8] also reported a 60-kWe-class recuperated Brayton cycle facility with turbomachinery supported on oil-lubricated tilting-pad bearings. To prevent oil contamination of the process fluid (sCO\({}_{2}\)), carbon ring-type mechanical seals are fixed between the turbine and the bearing unit, resulting in a long shaft. The above-cited studies focused on cycle analysis rather than the constituents. Although [PERSON] et al. [9] and [PERSON] et al. [10] studied the design of the experimental loop for sCO\({}_{2}\) power cycles, they did not detail the bearings employed for turbomachinery. To achieve the desired performance of turbomachinery for sCO\({}_{2}\) power cycles, the performance of their bearings is an important design consideration [10]. Thus, researchers have developed computational models to predict the performance of various types of sCO\({}_{2}\)-lubricated bearings. [PERSON] [11] used an isothermal and real gas model to investigate the static performance of a sCO\({}_{2}\)-lubricated gas-foil thrust bearing (GFTB). The author used the thermodynamic properties of sCO\({}_{2}\) reported in Ref. [12] and showed that GFTB has a larger load capacity and power loss when lubricated with sCO\({}_{2}\) than with air. [PERSON] et al. [13; 14] investigated the static performance of sCO\({}_{2}\)-lubricated GFTBs using computational fluid dynamics (CFD). [PERSON] and [PERSON] [15] studied a plain sCO\({}_{2}\)-lubricated journal bearing using a density model linearized with pressure. The isothermal model considers pressure-dependent density on only the Reynolds equation's left-hand side (Poiseuille terms). The overly simplified compressible model predicted a greater load capacity of the bearing than did the incompressible model. [PERSON] et al. [16] assumed sCO\({}_{2}\) as an isothermal ideal gas and analyzed a gas-foil journal bearing (GFJB) with the same diameter and length as the journal bearing reported in Ref. [15]. The authors predicted a comparable load capacity of GFDB for the plain journal bearing. In addition, they reported that the load capacity obtained using the compressible model is higher than that obtained using the incompressible model, which is inconsistent with the results reported in Ref. [15]. [PERSON] and [PERSON] [17] studied sCO\({}_{2}\)-lubricated tilting pad journal bearings (TPJBs).