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Appl. Sci. 2020, 10, 4168 9 of 26 the preliminary design solutions are based on design specifications from the cycle requirements that are fixed, whereas all other parameters obtained from an initial meanline calculation are specified as a range of values. The particular range employed is defined based on the survey of literature together with outcomes of the sensitivity analysis from the initial calculations step. The inlet total temperature and outlet total pressure are used as boundary conditions and the criterion against which output designs are selected is based on the total-to-static efficiency. A vaned nozzle is used and based on results not shown in this paper, cases without volutes are selected which means that an annular collector would be required to gather the inlet flow to the turbine. The rotor inlet metal angle is set to 90◦ (i.e., straight radial blades at inlet) for manufacturability and structural reasons. Full input data generated from the meanline design code is found in Table 5. Table 5. Input data for preliminary turbine design. Variable Unit Value Boundary Conditions Inlet total pressure Inlet total temperature Outlet total pressure Mass flow rate Inlet rotor metal angle Shaft rotational speed bar 297 K 1173 bar 60 kg/s 354.2 ◦ 90 rpm 17,000–24,000 Geometric Parameters and Constraints Stator outlet mean diameter m Rotor blade height ratio - Rotor diameter ratio - Rotor inlet height m Hub reaction - Stator inlet diameter m Inlet flow angle ◦ Rotor outlet hub diameter m 0.4–0.6 2–3 1.5–3 0.01–0.04 0.3–0.5 0.4–0.8 1–179 0.05–0.3 The preliminary design space allows the visualisation of the estimated set of turbine solutions for the given input data. An example of a generated design space with 130 possible solutions is shown in Figure 2 with each point corresponding to a particular turbine design. The total-to-static efficiency is represented by the colour of each point for both plots. Higher efficiency values coincide with the lower range of flow coefficients and higher velocity ratios (faster rotational speeds). In some cases, a qualification between efficiency and velocity ratio is needed to limit the induced rotor tip speed from high rotational speeds because of permissible material limits. Greater power is produced from the designs with higher efficiencies as expected. From the preliminary design space, designs are filtered through firstly by imposing general constraints within the design space explorer that automatically discards points, followed by manually selecting the turbines and assessing geometries and velocity triangles. The design space explorer is used to set constraints to narrow down the selection process, and to compare designs that meet the turbine requirements. Filter limits are specified to automatically and rapidly remove unsatisfactory points;theimposedcriteriaistodiscardanyturbinesthathaveW ̇ <100MWandefficiencies<80%. 78 out of the 130 solutions do not meet the imposed criteria and are removed from the selection process. The remaining solutions are individually selected for further assessment of the general geometric features and velocity triangles in order to ensure that the restrictions on tip speeds and flow angles are applied.PDF Image | Radial Turbine Design for a Utility-Scale Supercritical CO2 Power
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