A Sodium cooled-Fast Reactor (SFR) has receiving attention as one of the promising next generation nuclear reactors because it can recycle the spent nuclear fuel produced form the current commercial nuclear reactors and accomplish higher thermal efficiency than the current commercial nuclear reactors. However, after shutdown of the nuclear reactor core, the accumulated fission products of the SFR also decay and release heat via radiation within the reactor. To remove this residual heat, a new decay heat removal system (DHRS) with supercritical $CO_2$ as the working fluid is suggested with a turbocharger system which achieves passive operational capability. However, for designing this system an improved $S-CO_2$ turbine design methodology should be suggested because the existing methodology for designing the $S-CO_2$ Brayton cycle has focused only on the compressor design near the critical point.
To develop a $S-CO_2$ turbine design methodology, the non-dimensional number based design and the 1D mean line design method were modified and suggested. The design methodology was implemented into the developed code and the code results were compared with attainable turbine experimental data. The data were collected under air and $S-CO_2$ environment. The developed code in this work showed a reasonable agreement with the experimental data. Finally using the design code, the turbocharger design for the suggested DHRS and prediction of the off design performance were carried out. As further works, the generated performance maps will be utilized for evaluating the capability to remove varying residual heat. Furthermore, collecting more $S-CO_2$ turbine test data for validating the design code and methodology will be pursued.