## 3 Results
### Computational Fluid Dynamics Analyses
#### 3.3.4 Isolated Rotor Analysis  
An isolated rotor model is primarily developed for use in stress calculations but is also utilised for examination of the rotor performance without the inclusion of the stator effects. The boundary conditions are taken as dictated by the main project database of AxSTREAM with P0\({}_{in}\) = 270 bar, T0\({}_{in}\) = 1173 K at an absolute flow angle of 73.93\({}^{\circ}\) and P\({}_{out}\) = 54.0 bar. Performance results of the rotor only model at design point are listed in Table 11. The computed total-to-static pressure drop is lower than the defined value of with the CFD value of P0\({}_{in}\) being 256 bar. The mass flow rate is very close to the design 354.6 kg/s rate along with much better efficiencies compared to the full turbine cascade. The power output is around 14% lower than the 100 MW because of the lower pressure ratio (absence of stator means no static pressure drop there). The solution indicates that a large portion of losses arise in the stator-rotor passage and the incorrect flow conditions supplied by the nozzle. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Variable** & **Unit** & **Value** \\ \hline \(\dot{m}\) & kg/s & 356.3 \\ \(\dot{W}\) & MW & 86.38 \\ \(\eta_{tt}\) & \% & 87.80 \\ \(\eta_{ts}\) & \% & 80.46 \\ \(\psi\) & - & 1.21 \\ \(\phi\) & - & 0.423 \\ R & - & 0.406 \\ \(\Pi_{ts}\) & - & 4.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 11: 3D CFD performance results for the isolated rotor. Figure 12: Off-design relative Mach number distribution at mid-span from 3D CFD simulations: (a) 23,550 rpm & \(\Pi_{ts}\) = 3, (b) 19,268 rpm & \(\Pi_{ts}\) = 7. The visualisation of several parameters is seen in Figure 13 where two blade passages are set side by side at mid-span. At the rotor leading edge, the flow experiences, as expected, an acceleration on the suction side and a slowing down on the pressure side with the corresponding pressure changes. There still exists a rise in entropy on the blade suction surface with the diffusion of the flow. However, relative velocity and total pressure distributions do not indicate full flow separation or reversal. In addition to that, the absence of the incidence loss region and the excessive nozzle acceleration allow for a more uniform flow distribution on the rotor blade. The isolated rotor model gives better performance characteristics than the full turbine passage (stator and rotor). However, the power output is 86.38 MW which is lower than the target 100 MW range meaning that either a greater pressure drop is required, or a new design of an integrated nozzle is needed. In the former case, the higher pressure ratio can be obtained via higher velocities (increasing rpm or changing blade angles) however, it is important to maintain the speeds imposed by material limits. A generic Nickel-based alloy (IN 718), typically employed in gas turbine applications is used in the stress simulations of the rotor disk. Although the known materials are not used for sufficient yield strengths at temperatures exceeding 760 \({}^{\circ}\)C [37], assumed properties are employed to investigate the range and areas of stress concentrations on a non-optimised rotor wheel design. The static stress analysis performed signals a concern for the insufficient material strength at certain areas of the radial turbine. The aerodynamic part of the turbine itself (the designed rotor), even at higher loading than design point conditions, is mostly limited to stresses that are lower than the defined allowable von-Mises stress (400 MPa); the distribution of von Mises stresses is displayed using Figure 14. For better visualisation of the areas of high stress concentration, the contour limits of the displayed von Mises stress is set to the maximum 400 MPa; the grey regions are areas with stress over the permissible ceiling. The areas of stress concentration are defined as the disc root and the blade root both of which belong to the mechanical design aspect of the turbine.