## 1 Introduction
It was found that the feasible blade height is in the range of 1.74 to 2.47 mm for a given turbine diameter of 30 mm. Furthermore, it was concluded that a low degree of reaction is preferred for single-stage turbines resulting in supersonic conditions at the rotor inlet. However, a higher degree of reaction is suitable for two-axial stage turbine leading to subsonic rotor inlet conditions. Besides the aforementioned research work in the field of sCO\({}_{2}\) turbo-machines designs, a large amount of work has been conducted for micro-scale organic Rankine cycle (ORC) turbine design, using the same design methodology for novel working fluids, including refrigerants such as R134a, R1234 yf and R152a. [PERSON] et al. [12] developed a design tool that included a loss model to examine the performance of a 50 kW radial turbine operating with various working fluids. The results of the study demonstrated that an efficiency ranging from 78-85 % can be achieved with a highest value (85%) for R134a and lowest value (78%) for R1234 yf. [PERSON] et al. [13] developed two preliminary designs for a five-stage transonic and eight stage supersonic radial-outflow 10 kW ORC turbine. It was found that the transonic turbines outperform the supersonic turbine during the partial-load operations thus resulting in enhanced efficiency. [PERSON] et al. [14] proposed a mean-line model integrated with both an optimisation algorithm and a real-gas formulation for a 15 kW radial turbine. The design model resulted in a turbine efficiency ranging from 82.4-84% with a maximum value found for R152a. [PERSON] et al. [15] integrated both mean-line design with loss correlations, developed previously for radial gas turbines, for examining turbine size, working conditions and predicting the efficiency of radial-inflow turbine operating with R245 fa. The study revealed that the turbine size has a noticeable effect on the efficiency, and thus an efficiency of 85 to 90% at high expansion ratio has been attained at an output power greater than 50 kW. Radial turbines are known to be an effective and compact machine for small-scale applications with a power ranging from 50 kW to 5 MW, allowing for the expansion of the working fluid in one single stage [12]. Thus, the radial-inflow turbine configuration has been the main candidate for small-sizeturbomachinery design in most of the aforementioned researches. Alternatively, a feasible single-stage axial turbine design could be achieved for micro-scale applications allowing for better heat transfer control, as the hot blades are far from the shaft, and subsequently prolongs the life of the bearing. In the current study, a mean-line approach is used to address the design of a single-stage 100 kW sCO\({}_{2}\) axial turbine design through identifying optimal turbine design parameters from both mechanical perspectives, owing to the significant axial thrust loads, high rotational speeds and high operating pressures, and aerodynamic performance perspectives. Additionally, the design tool implemented in the current study is refined by introducing [PERSON]'s and [PERSON] and Mathieson's loss correlations, which allows the loss within the rotor and stator to be estimated based on loading coefficient, tip clearance and blade geometry. The designs were evaluated at three different speeds of 150k, 200k, 250k RPM respectively,to achieve an overall turbine efficiency greater than 80% and keep low centrifugal stresses on the rotor blades, for turbine inlet conditions of 923 K, 170 bar, expansion ratio of 3. For the given inlet conditions, a single-stage design is proposed due to the low power rating and low volume ratio of the machine. The novelty in this current work lies in presenting a design of sCO\({}_{2}\) micro-scale single-stage axial turbine, alongside with defining the optimal turbine design parameters from both mechanical and aerodynamic performance perspectives. This paper is structured as follows: an overview of turbine design methodology and assumptions are presented in Section 2.