## 5 Results and Discussion
Increasing the loading coefficient from 0.8 to 3.0 results in an increase in both rotor absolute and relative inlet flow angles, \(\alpha_{2}\) & \(\beta_{2}\), from 74 to 81\({}^{\circ}\) and -60 to 60 \({}^{\circ}\) respectively as shown in Figure 5a. In principle, low loading coefficients result in higher efficiency, though it results in higher blade speed and thus high mechanical stresses; at values of 1.0 and 3.0 the mean blade speed (U\({}_{\text{m}}\)) reaches approximately 522 and 306 m/s, and results in a total blade stresses of 160 MPa and 76 MPa respectively. Meanwhile, at high loading values a smaller number of rotor blades is needed. Therefore, the design decision should be made based on the selected material, the maximum allowable stress, along with the required number of blades. Furthermore, increasing the loading coefficient causes a slight decrease in both Ma\({}_{2}\) and Ma\({}_{3}\), at the inlet and outlet of the rotor blades respectively, as shown in Figure 5b; where Ma\({}_{2}\) and Ma\({}_{3}\) are the Mach numbers calculated with respect to the absolute and the relative velocity respectively. To achieve a subsonic flow at a flow coefficient of 0.2, the loading coefficient should be greater than 0.8. Additionally, it was found that increasing the loading coefficient results in an efficiency increase until a maximum is reached at values of \(\psi\) ranging between 1.6 to 1.7 for the three rotational speeds. It's worth mentioning the \(\psi\) has a limited effect on the efficiency at all rotational speeds for a flow coefficient of 0.2. The highest efficiency is achieved for the turbine designs that keep the swirl angle \(\alpha_{3}\) close to the recommended value, which is recommended not to exceed 20\({}^{\circ}\)[26], along with achieving the optimum difference in the whirl velocity components at the inlet and exit of the rotor. Increasing the exit circumferential velocity, owing to the increased swirl angle, results in an increase in centrifugal force which leads to an increased amount of flow reversal at the rotor outlet. Hence, higher losses and lower efficiencies are observed. Increasing \(\psi\) results in an increase in the blade height at the rotor inlet and outlet blade heights reaching, up to 2.1 and 3.7 mm for \(b_{2}\) and \(b_{3}\) respectively at a speed of 250 kRPM (Figure 5d). For feasible wheel manufacturing, it is hypothesised that inlet blade height and blade diameter should be designed to be above a minimum allowable rotor diameter of 30.00 mm and a minimum allowable blade height \(b_{2}\) of 1.25 mm [11]. Thus, according to these criteria, for a design with a flow coefficient of 0.2 and rotational speed of 250 kRPM, \(\psi\) should be above 1.7. Owing to the micro-scale design dimensions, it is anticipated that micro-electrical discharge machining (EDM) milling could be used for the manufacturing of the turbine components. EDM is already in use for micro-gas turbines where high accuracy features, in the order of several micrometres, and surface finishes, with roughness values as low as 0.4 \(\mu m\), can be achieved [42]. Similar to this design scale, Korea institute of energy research (KIER) developed a prototype for sCO\({}_{2}\) Brayton cycle in which a 60 kW axial impulse turbine was manufactured; this demonstrates the ability to manufacture the turbine and the applicability of an axial turbine configuration for micro-scale applications [43]. To investigate the effect of changing the degree of reaction on the performance of the axial turbine, \(\Lambda\) has been varied between 0.0 and 0.5 while fixing \(\phi\) to 0.2 and \(\psi\) to 1.6. Accordingly, the flow angle \(\beta_{2}\) decreased from 61 to \(-26^{\circ}\) and \(\alpha_{2}\) decreased from 82 to \(78^{\circ}\) as shown in Figure 5(a). In the same context, increasing the degree of reaction results in an increase in \(\text{Ma}_{3}\) from 0.50 to 0.92 and a decrease in \(\text{Ma}_{2}\) from 1.43 to 0.90 as shown in Figure 5(b).