| Summary: | Recently, the CO<sub>2</sub> power cycle has attracted attention because of tightening environmental regulations. The turbine is a factor that greatly affects the efficiency of the cycle. The radial outflow turbine is a turbomachine with the various advantages of an axial flow turbine and a radial inflow turbine, but the design theory for the turbine is uncertain. In this study, a preliminary design algorithm for a radial outflow turbine with a multi-stage configuration is presented. To verify the preliminary design algorithm, a preliminary design for a two-stage radial outflow turbine for a CO<sub>2</sub> power cycle was carried out, and a computational fluid dynamic analysis was performed. Consequently, values close to the target performance were obtained, but blade optimization was performed to obtain more satisfactory results. The final geometry of the radial outflow turbine was obtained through optimization considering the blade exit angle related to the deviation angle, blade maximum thickness-true chord ratio, and incidence angle. In the final geometry, the error rates of power (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>W</mi><mo>˙</mo></mover></semantics></math></inline-formula>), efficiency (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>η</mi><mrow><mi>t</mi><mi>s</mi></mrow></msub></mrow></semantics></math></inline-formula>), and pressure ratio (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><msub><mi>R</mi><mrow><mi>t</mi><mi>s</mi></mrow></msub></mrow></semantics></math></inline-formula>) between target performance and computational fluid dynamic results were improved to 5.0%, 4.8%, and 1.8%, respectively. The performance and flow characteristics of the initial and final geometries were analyzed.
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