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Appl. Sci. 2020, 10, 5069 9 of 20 over the range from 150 to 250 kRPM for the loading and flow coefficient domains specified in Table 1. The lowest flow coefficient, over the range from 0.2 to 1.0, results in the highest efficiency level, as confirmed in Figure 4. However, a low flow coefficient results in larger turbine annulus area and a larger deflection angle. A loading coefficient of 1.6 results in the maximum efficiency at a fixed flow coefficient and degree of reaction of 0.2 and 0.5 respectively. At a loading coefficient of 1.6, the swirl angle is kept close to the recommended value, which is recommended not to exceed 20◦ [26], whilst the optimum difference in the whirl velocity components at the inlet and exit of the rotor is achieved, which enables a high efficiency to be achieve. Thus, for this design, the flow coefficient and loading coefficient are set to 0.2 and 1.6 respectively to achieve the maximum efficiency at a degree of reaction of 0.5. The corresponding turbine power output is 116 kW, with a total-to-total isentropic efficiency of 78%. In the following set of results, Figure 5a–d, φ and Λ have been set to 0.2 and 0.5 respectively, whilst ψ is varied from 0.8 to 3.0. Increasing the loading coefficient from 0.8 to 3.0 results in an increase in both rotor absolute and relative inlet flow angles, α2 & β2, from 74 to 81◦ and -60 to 60 ◦ 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 (Um) 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 Ma2 and Ma3, at the inlet and outlet of the rotor blades respectively, as shown in Figure 5b; where Ma2 and Ma3 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 ψ ranging between 1.6 to 1.7 for the three rotational speeds. It’s worth mentioning the ψ 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 α3 close to the recommended value, which is recommended not to exceed 20o [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 ψ 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 b2 and b3 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 b2 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, ψ 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 μm, can be achieved [42]. Similar to this design scale, Korea institute of energy research (KIER) developed a prototype for sCO2 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].PDF Image | Mean-Line Design of a Supercritical CO2 Micro Axial Turbine
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