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Appl. Sci. 2018, 8, 2038 8 of 16 Table 2. Range of design space. Loading Coefficient [-] Flow Coefficient [-] Range 0.7–1.1 0.1–0.4 Rotational Speed [r/min] 10,000–130,000 The results of the validation design for T-100 and T-100re optimization design are summarized in Table 3, and the T-100 original data is also listed as a comparison. The loading coefficient of the T-100 turbine is 0.91 [27], and the flow coefficient is selected as 0.22 by trial and error method to reach the main known parameters of the original T-100 turbine. It can be seen that the result is quite close to the T-100 original data, which verifies the correctness and accuracy of the present mean line design method. Table 3. Results of the validation design and optimization design. Parameters Loading Coefficient Flow Coefficient Rotational Speed Rotor Inlet Radius Inlet Blade Height Inlet absolute Flow Angle Inlet relative Flow Angle Axial Clearance Radial Clearance Backface Clearance Number of Rotor Blades Outlet Hub Radius Outlet Shroud Radius Outlet Blade Height Outlet Absolute Flow Angle Outlet Relative Flow Angle Chord Length Trailing Edge Thickness Nozzle Inlet Radius Blade Height Outlet Radius Outlet Absolute Flow Angle Chord Length Trailing Edge Thickness Number of Nozzle Vanes Nozzle Loss Incidence Loss Passage Loss Tip Clearance Leakage Loss Exit Energy Loss Windage Loss Total-to-static Efficiency Unit [-] [-] [r/min] [mm] [mm] [◦] [◦] [mm] [mm] [mm] [-] [mm] [mm] [mm] [◦] [◦] [mm] [mm] [mm] [mm] [mm] [◦] [mm] [mm] [-] [kJ/kg], [%] [kJ/kg], [%] [kJ/kg], [%] [kJ/kg], [%] [kJ/kg], [%] [kJ/kg], [%] [%] T-100 (Original) 0.91 - 106,588 58.2 6.35 76.8 −31.8 0.25 0.22 0.46 16 15.2 36.8 21.6 −0.03 −57.4 45.7 0.76 74.0 6.35 63.5 77.8 22.9 0.51 19 - - - - - - 86.4 Verification 0.91 0.22 106,588 57.3 6.35 76.6 −22.5 0.25 0.22 0.46 16 15.2 36.3 21.1 0 −64.2 40.9 0.50 74.0 6.35 63.5 77.8 22.9 0.51 19 11.63, 19.88 0.19, 0.33 26.06, 44.55 8.88, 15.18 9.64, 16.48 2.09, 3.58 86.4 T-100re (Optimization) 0.90 0.21 114,185 54.1 6.84 77.0 −27.0 0.3 0.3 0.3 14 14.2 37.5 23.4 0 −66.7 40.5 0.43 69.0 6.84 59.1 77.0 20.0 0.36 17 10.81, 19.64 0.03, 0.06 25.66, 46.62 7.67, 13.93 8.89, 16.15 1.98, 3.60 87.4 The T-100re optimization is obtained using the present GA assisted preliminary design procedure. The GA configuration has a population size of 15, an elite number of 1, a mutation rate of 0.15 and a maximum generation number of 200. The convergence curve of the total-to-static efficiency is shown in Figure 6 and the T-100re turbine has a total-to-static efficiency of 87.4%. It can be found that the convergent speed is quite fast and the design process costs only a few minutes. Some key parameters like rotor inlet radius and blade number, etc. can be easily optimized through the empirical correlations in the preliminary design optimization, but hard to be optimized in the later three-dimensional (3D)PDF Image | Design and Optimization Approach for Radial Inflow Turbines
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