## 3 Verification of Automated Preliminary Design Methodology
### Mean Line Design
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **Unit** & **T-100 (Original)** & **Verification** & **T-100 re (Optimization)** \\ \hline Loading Coefficient & [-] & 0.91 & 0.91 & 0.90 \\ Flow Coefficient & [-] & - & 0.22 & 0.21 \\ Rotational Speed & [r/min] & 106,588 & 106,588 & 114,185 \\
**Rotor** & & & & \\ Inlet Radius & [mm] & 58.2 & 57.3 & 54.1 \\ Inlet Blade Height & [mm] & 6.35 & 6.35 & 6.84 \\ Inlet absolute Flow Angle & [\({}^{\circ}\)] & 76.8 & 76.6 & 77.0 \\ Inlet relative Flow Angle & [\({}^{\circ}\)] & \(-31.8\) & \(-22.5\) & \(-27.0\) \\ Axial Clearance & [mm] & 0.25 & 0.25 & 0.3 \\ Radial Clearance & [mm] & 0.22 & 0.22 & 0.3 \\ Backface Clearance & [mm] & 0.46 & 0.46 & 0.3 \\ Number of Rotor Blades & [-] & 16 & 16 & 14 \\ Outlet Hub Radius & [mm] & 15.2 & 15.2 & 14.2 \\ Outlet Shroud Radius & [mm] & 36.8 & 36.3 & 37.5 \\ Outlet Blade Height & [mm] & 21.6 & 21.1 & 23.4 \\ Outlet Absolute Flow Angle & [\({}^{\circ}\)] & \(-0.03\) & 0 & 0 \\ Outlet Relative Flow Angle & [\({}^{\circ}\)] & \(-57.4\) & \(-64.2\) & \(-66.7\) \\ Chord Length & [mm] & 45.7 & 40.9 & 40.5 \\ Trailing Edge Thickness & [mm] & 0.76 & 0.50 & 0.43 \\
**Nozzle** & & & & \\ Inlet Radius & [mm] & 74.0 & 74.0 & 69.0 \\ Blade Height & [mm] & 6.35 & 6.35 & 6.84 \\ Outlet Radius & [mm] & 63.5 & 63.5 & 59.1 \\ Outlet Absolute Flow Angle & [\({}^{\circ}\)] & 77.8 & 77.8 & 77.0 \\ Chord Length & [mm] & 22.9 & 22.9 & 20.0 \\ Trailing Edge Thickness & [mm] & 0.51 & 0.51 & 0.36 \\ Number of Nozzle Vanes & [-] & 19 & 19 & 17 \\ Nozzle Loss & [kJ/kg], [\%] & - & 11.63, 19.88 & 10.81, 19.64 \\ Incidence Loss & [kJ/kg], [\%] & - & 0.19, 0.33 & 0.03, 0.06 \\ Passage Loss & [kJ/kg], [\%] & - & 26.06, 44.55 & 25.66, 46.62 \\ Tip Clearance Leakage Loss & [kJ/kg], [\%] & - & 8.88, 15.18 & 7.67, 13.93 \\ Exit Energy Loss & [kJ/kg], [\%] & - & 9.64, 16.48 & 8.89, 16.15 \\ Windage Loss & [kJ/kg], [\%] & - & 2.09, 3.58 & 1.98, 3.60 \\ Total-to-static Efficiency & [\%] & 86.4 & 86.4 & 87.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the validation design and optimization design. numerical optimization, which indicates that it is strongly necessary to perform an optimization at the preliminary design stage. For the T-100 re turbine, the axial, radial and back face clearance is set to be 0.3, respectively, which is a minimum reasonable clearance. The six loss terms of the T-100 re design are all lower than those of the verification design, which results in a higher total-to-static efficiency of 87.4%. The T-100 re design has a smaller rotor inlet radius than that of the verification design, thus having a lower passage loss and nozzle loss. Though the rotor tip clearance of the T-100 re design is a little bit larger than that of the verification design, the tip clearance loss is lower due to the smaller size too. Figure 7 shows a comparison of the meridional contours of these two turbines. It can be seen that the T-100 re turbine has a lower inlet radius and shorter axial length of the rotor than the T-100 turbine. Therefore, the T-100 re rotor weighs much lighter than the T-100, and the turbine's total weight will also reduce due to the lower radial geometry size of rotor, nozzle and the corresponding volume. It is of significance for APU of aerospace and turbine rotor of turbochargers. Therefore, the present automated preliminary design approach is quite effective to determine the main parameters for the preliminary design. In this approach, the GA helps the designer find the best combination of \((\psi,\phi,n)\) corresponding to the highest total-to-static efficiency under specified constraints and well-established loss models in a short time, thus making a good start for the later 3D numerical optimization work, which will be presented in Part II of this paper [34]. Figure 6: Convergence curve of the optimal design. Figure 7: Comparison of meridional contour.