The supercritical carbon dioxide (S-CO₂) Brayton cycle efficiency increases as the compressor inlet condition approaches the critical point. However, the thermodynamic properties of CO₂ vary dramatically near the critical point, and phase change is most likely to happen. Both cavitation and condensation bring about significant adverse effects on the performance of compressors. In this paper, the quantitative effects of nonequilibrium condensation and cavitation on the performance of an S-CO₂ centrifugal compressor with different inlet-relative entropy values are investigated. The properties of CO₂ were provided by the real-gas property table, and the nonequilibrium phase-change model was adopted. The numerical simulation method with the nonequilibrium phase-change model was validated in the Lettieri nozzle and Sandia compressor. Furthermore, simulations were carried out in a two-stage centrifugal compressor under conditions of various inlet-relative entropy values. The type of nonequilibrium phase change can be distinguished by inlet-relative entropy. Cavitation makes the choke mass flow rate decrease due to the drop in the speed of sound. Condensation mainly occurs on the leading edge of the main blade at a large mass flow rate, but cavitation occurs on the splitter. The condensation is more evenly distributed on the main blade, but the cavitation is mainly centered on the leading edge.

Since the beginning of the 21st century, the supercritical carbon dioxide (sCO₂) Brayton cycle has emerged as a hot topic of research in the energy field. Among its key components, the sCO₂ compressor has received significant attention. In particular, axial-flow sCO₂ compressors are increasingly being investigated as power systems advance toward high power scaling. This paper reviews global research progress in this field. As for performance characteristics, currently, sCO₂ axial-flow compressors are mostly designed with large mass flow rates (>100 kg/s), near-critical inlet conditions, multistage configurations with relatively low stage pressure ratios (1.1–1.2), and high isentropic efficiencies (87–93%). As for internal flow characteristics, although similarity laws remain applicable to sCO₂ turbomachinery, the flow dynamics are strongly influenced by abrupt variations in thermophysical properties (e.g., viscosities, sound speeds, and isentropic exponents). High Reynolds numbers reduce frictional losses and enhance flow stability against separation but increase sensitivity to wall roughness. The locally reduced sound speed may induce shock waves and choke, while drastic variation in the isentropic exponent makes the multistage matching difficult and disperses normalized performance curves. Additionally, the quantitative impact of a near-critical phase change remains insufficiently understood. As for the experimental investigation, so far, it has been publicly shown that only the University of Notre Dame has conducted an axial-flow compressor experimental test, for the first stage of a 10 MW sCO₂ multistage axial-flow compressor. Although the measured efficiency is higher than that of all known sCO₂ centrifugal compressors, the inlet conditions evidently deviate from the critical point, limiting the applicability of the results to sCO₂ power cycles. As for design and optimization, conventional design methodologies for axial-flow compressors require adaptations to incorporate real-gas property correction models, re-evaluations of maximum diffusion (e.g., the DF parameter) for sCO₂ applications, and the intensification of structural constraints due to the high pressure and density of sCO₂. In conclusion, further research should focus on two aspects. The first is to carry out more fundamental cascade experiments and numerical simulations to reveal the complex mechanisms for the near-critical, transonic, and two-phase flow within the sCO₂ axial-flow compressor. The second is to develop loss models and design a space suitable for sCO₂ multistage axial-flow compressors, thus improving the design tools for high-efficiency and wide-margin sCO₂ axial-flow compressors.