###### Abstract  
The compressor is a key component in the supercritical carbon dioxide (SCO\({}_{2}\)) Brayton cycle. In this paper, the authors designed a series of supercritical CO\({}_{2}\) compressors with different parameters. These compressors are designed for 100 MWe, 10 MWe and 1 MWe scale power systems, respectively. For the 100 MWe SCO\({}_{2}\) Brayton cycle, an axial compressor has been designed by the Smith chart to test whether an axial compressor is suitable for the SCO\({}_{2}\) Brayton cycle. Using a specific speed and a specific diameter, the remaining two compressors were designed as centrifugal compressors with different pressure ratios to examine whether models used for air in the past are applicable to SCO\({}_{2}\). All compressors were generated and analyzed with internal MATLAB programs coupled with the NIST REFPROP database. Finally, the design results are all checked by numerical simulations due to the lack of reliable experimental data. Research has found that in order to meet the [PERSON] stall criterion, axial compressors require a considerable number of stages, which introduces many additional problems. Thus, a centrifugal compressor is more suitable for the SCO\({}_{2}\) Brayton cycle, even for a 100 MWe scale system. For the performance prediction model of a centrifugal compressor, the stall predictions are compared with steady numerical calculation, which indicates that past stall criteria may also be suitable for SCO\({}_{2}\) compressors, but more validations are needed. However, the accuracy of original loss models is found to be inadequate, particularly for lower flow and higher pressure ratio cases. Deviations may be attributed to the underestimation of clearance loss according to the result of steady simulation. A modified model is adopted which can improve the precision to a certain extent, but more general and reasonable loss models are needed to improve design accuracy in the future. Keywords:SCO\({}_{2}\); compressor design; loss model; numerical simulation +
Footnote †: journal: Applied  
Among various working fluids, supercritical carbon dioxide attracts more attention due to its unique advantages: (1) SCO\({}_{2}\) is one of the most common supercritical fluids with relatively low critical pressure and temperature (7.3773 MPa, 304.13 K). (2) The high density and convective heat transfer coefficient of SCO\({}_{2}\) make it able to reduce the volume of turbomachines and heat exchangers. Compared with steam turbines, SCO\({}_{2}\) turbines are only about 1/100 of the size, so the SCO\({}_{2}\) Brayton cycle has an obvious advantage regarding construction costs. (3) The low viscosity and strong mobility of SCO\({}_{2}\) can reduce the flow resistance. (4) Compression works are largely reduced due to the low compressibility factor, accounting for about 20-30% of the turbine output power, which would improve the efficiency of thermal cycle. Compared to the helium Brayton cycle and the conventional Rankine steam cycle, the same net efficiency can be achieved by the SCO\({}_{2}\) cycle at a lower temperature, which means that it is less expensive than the others. Furthermore, the net efficiency of the SCO\({}_{2}\) cycle was shown to be significantly less sensitive to penalties from core bypass flow and cycle pressure drops than the helium Brayton cycle [4]. However, because the working pressure is so high and the size is so small, decent efficiency of the equipment is difficult to achieve, which leads to much lower experimental cycle efficiency than is expected. Due to the large density of SCO\({}_{2}\), the compressor's volume flow rate is so small that the blade height is much shorter than that of an air compressor. Narrow flow channels will cause high friction losses and leakage losses. Meanwhile, as the compressor operates near the critical point, the fluid properties are very different from those under normal temperature and pressure. Therefore, it is necessary to study the design method for supercritical CO\({}_{2}\) compressors. [PERSON] et al.