[Objective] To improve the smoothness of the meridional flow passage and thereby enhance the flow efficiency of centrifugal compressors, this study develops a quasi-three-dimensional (quasi-3D) aerodynamic design methodology for CO₂ centrifugal compressors, based on a novel meridional passage design algorithm with high-order smooth curvature. The meridional passage is a critical geometric feature of a centrifugal compressor because it directly governs the through-flow velocity distribution, blade loading and internal losses. The design procedure consists of three steps. 

[Methods] First, a supercritical carbon dioxide (S-CO₂) centrifugal compressor is designed and optimized at the one-dimensional (1D) level, through which the key aerodynamic and geometric parameters, such as the specific speed, the flow coefficient and the impeller diameter ratio, are determined. Second, based on the obtained 1D parameters, a meridional flow passage design algorithm with high-order smooth curvature is developed. In this algorithm, the hub and shroud meridional contours are constructed so that the curvature varies continuously from the inlet to the outlet. Compared with the conventional multi-arc meridional contours, which exhibit discontinuous curvature at the arc junctions, the proposed contours are smoother. A discontinuity of curvature causes abrupt changes in the wall curvature and undesirable near-wall flow disturbances, which may promote boundary-layer separation and increase losses; the continuous curvature distribution, in contrast, suppresses such disturbances and yields a more uniform flow and a higher flow efficiency. Third, on the basis of the curvature-smooth meridional passage and the S1/S2 stream surface method, a quasi-3D blade profile design approach for the CO₂ compressor is developed. The S1/S2 method decomposes the three-dimensional flow into blade-to-blade (S1) and through-flow (S2) stream surfaces solved in a coupled manner, enabling an efficient and physically sound design of the blade camber lines and thickness distributions. Applying this methodology yields the impeller design scheme for the recompressor of a 300 MW-class CO2 power generation system with a split-flow recompression cycle. 

[Results] Numerical simulations of the designed compressor show that the total-to-total isentropic efficiencies of the impeller and the diffuser reach 93%~97% or above, fully validating the effectiveness of the proposed method. The stage-to-stage efficiency variation is mainly caused by the decrease in the specific speed of the last stage: as the pressure rises, the CO2 density increases and the volumetric flow rate decreases, which lowers the specific speed and degrades the efficiency of the final stage. 

[Conclusion] The proposed meridional passage and quasi-3D design methods are therefore expected to significantly promote the aerodynamic design research and engineering application of CO2 compressors.