## 3 Results
### Preliminary Design  
The design phase that builds on the results of the cycle analysis and the meanline code consists of the definition of three-dimensional geometries which are then further investigated using higher fidelity tools. The tool employed in this phase is the preliminary design solution generator, which is part of the AxSTREAM design suite, is initiated with defined settings (working fluid, loss models, number of stages), boundary conditions and geometry constraints. The boundary conditions required to obtain \begin{table}
\begin{tabular}{l l l} \hline \hline
**Data** & **Unit** & **Value** \\ \hline Inter temperature (T) & \({}^{\circ}\)C & 900 \\ Inlet pressure (P) & bar & 297 \\ Mass flow rate & kg/s & 354.2 \\ Outlet pressure & bar & 60 \\ Thermal power output (\(\dot{W}\)) & MW\({}_{th}\) & 100.7 \\ \hline \multicolumn{3}{c}{**Fluid Component Mode Fractions**} \\ \hline CO\({}_{2}\) & \% & 94.06 \\ H\({}_{2}\)O & \% & 4.13 \\ N\({}_{2}\) & \% & 1.14 \\ Ar & \% & 0.55 \\ O\({}_{2}\) & \% & 0.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Radial turbine boundary conditions from cycle model. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Data** & **Unit** & **Value** \\ \hline HTHE heat duty & MW & 242.92 \\ LTHE heat duty & MW & 43.42 \\ Thermal energy of feedstock (LHV) & MW\({}_{th}\) & 137.18 \\ Turbine power output & MW\({}_{e}\) & 99.31 \\ Vapor phase compressors & MW\({}_{e}\) & 3.96 \\ Dense phase compressors & MW\({}_{e}\) & 8.86 \\ Oxidant compressor & MW\({}_{e}\) & 3.09 \\ Total flow compressors & MW\({}_{e}\) & 15.91 \\ Natural gas compressor & MW\({}_{e}\) & 0.74 \\ Air separation unit & MW\({}_{e}\) & 15.29 \\ Storage compressor & MW\({}_{e}\) & 0.045 \\ Net electric power output & MW\({}_{e}\) & 67.33 \\ Net electric efficiency (LHV) & \% & 49.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Modified cycle performance parameters. 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 solutes 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\({}^{\circ}\) (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.  
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.