## 3 Verification of Automated Preliminary Design Methodology
### Numerical Computation  
In 2012, [PERSON] [35] published a paper that intended to make the T-100 turbine an open benchmark for validation work and provided all the geometric data. In this study, an in-house blade design code for radial inflow turbines is developed in order to reconstruct the T-100 turbine based on the original data [27; 35] and initialize the T-100 re turbine design. Figures 8 and 9 show the T-100 nozzle profile and the T-100 rotor geometry, respectively. The rotor blade is defined by the beta-angle and thickness distribution. An initial back face profile is provided for both T-100 and T-100 re rotors so that the rotor weight can be evaluated. It turns out that the T-100 rotor weighs 1.31 kg and the T-100 re rotor weighs 0.96 kg. Although the rotor weight is not an objective in the preliminary design optimization, the rotor weight could be decreased due to its smaller rotor size obtained by the preliminary design optimization. In order to validate the precision of the present preliminary design method, 3D numerical simulations are carried out for both T-100 and T-100 re turbine under design and off-design conditions. Figure 10 shows the computational mesh of the T-100 turbine. A single passage of the nozzle and rotor flow path connected is considered as the computational domain. A long extension is provided in order to avoid the back-flow, and the rotor tip clearance is also considered. The T-100 re turbine is meshed using the same configuration with T-100 turbine. The mesh statistics information is shown in Table 4. The simulations are conducted using ANSYS-CFX commercial CFD software (ANSYS, Inc., Canonsburg, PA, USA). The ideal air is selected as the working fluid. The RANS coupled with the SST turbulence model is solved with the first layer y+ less than 2. It is worth mentioning that the mesh number and the turbulence model used were verified by mesh independenc  
Figure 8: T-100 nozzle profiles. Figure 9: T-100 rotor geometry. models provided in ANSYS-CFX, respectively. The details of verification can be found in Reference [19] published by our research group. The boundary conditions for validations are adopted using the design conditions in Table 1. It is noted that a modeling test was conducted with a T-100 turbine of a real geometry size (shown in Table 3), so the test boundary conditions are different from the design parameters. That is to say, the aerodynamic performance of T-100 turbine was tested under lower pressure and lower temperature at turbine inlet, and lower rotor rotational speed conditions (as shown in Table 5) according to similarity and modularization theory of turbomachinery. Table 6 shows the total-to-static efficiency under design condition. It can be seen that the CFD results are just a little higher than those of the preliminary design and the T-100 preliminary result is in good agreement with the experimental data. It is worth mentioning that the mass flow rate of CFD is a little lower than the given preliminary value, about less than 1%. In order to compare, the mass flow rate of the modeling test was transferred to the design condition according to the similarity and modularization theory of turbomachinery. The result shows that the experimental mass flow rate is a bit bigger about 1% than the design value. Figure 11 gives the comparison of total-to-static efficiency between the CFD and the experimental data under a range of velocity ratios, and it can be seen that the T-100 CFD results are a little higher than those of the experiment under each condition due to the ignorance of windage loss and flow non-uniformity at the volute outlet in the CFD simulations, but the changing trend of both results are in good agreement. It is worth mentioning that, through the mean line optimization, the optimal velocity ratio is 0.75 because the optimal rotation speed is higher than the original design speed.