## 3 Results
### Cycle Modelling
#### 3.1.2 Modified Cycle  
As discussed in Section 1, supercritical CO2 cycles, regardless of whether they employ cooling or not, have the beneficial characteristics of small turbomachinery components due to the high fluid density. Suggestions from literature limit the applicability of radial turbines to cycles of up to 30 MW\({}_{e}\)[30]. The criteria for that power level was proposed on the basis of closed sCO2 cycles with lower operating pressures and temperature compared to conditions witnessed in cycles similar to the Allam cycle. The numerical value of a turbine specific speed is used as an index of power output and passage size [31]; the dimensionless parameter is used by designers to determine turbine type and efficiency. [PERSON] shows that for a specific speed \(\left(n_{s}=\frac{\omega\sqrt{Q_{5}}}{\left(\Delta h_{id}\right)^{0.75}}\right)\) in the narrow range of 0.3-1.0, where this span corresponds to small turbine passage areas, a 90\({}^{\circ}\) inward-flow radial (IFR) turbine can reach high efficiencies in contrast with the conventional axial turbines which have a much broader spectrum of peak performance [31]. A larger-scale turbine--higher volumetric (\(\dot{Q}\)) or mass flow rate (\(\dot{m}\))--corresponds to a higher specific speed value for fixed ideal heat drops (\(\Delta h_{id}\)) and rotational speeds (\(\omega\)). Thus, taking a within-the-range recommended value of n\({}_{s}\) = 0.7 [18; 31] and knowing the ideal enthalpy drop from the cycle model (\(\Delta h_{id}\) = 284,370 J/kg), plus having performed some calculations on possible rotational speeds being in the range of 25,000 rpm, through initial turbine sizing (i.e., \(\omega\) = 2618 rad/s) the corresponding maximum allowable mass flow rate is:  
\[\dot{m}_{max}=\dot{Q}_{max}\cdot\rho_{out}=\left(\frac{0.7\Delta h_{id}^{0.75} }{\omega}\right)^{2}\cdot\rho_{out}\approx 354\text{ kg/s} \tag{1}\]  
where \(\rho_{out}\) is the density of the flow at turbine outlet and is around 33.2 kg/m\({}^{3}\) from the cycle model. The limit obtained for the largest size of a radial turbine operating under the conditions of a dense working environment, at TIT = 900 \({}^{\circ}\)C, turbine inlet pressure (TIP) = 297 bar and pressure ratio \begin{table}
\begin{tabular}{l l l l} \hline \hline  & **Unit** & **Results of This Work** & **Results of [10] Optimised Cycle** \\ \hline Thermal energy of feedstock (LHV) & MW\({}_{th}\) & 768.21 & 768.31 \\ Turbine power output & MW\({}_{e}\) & 610.55 & 609.74 \\ Recycle flow compressors & MW\({}_{e}\) & 88.00 & 97.81 \\ Natural gas compressor & MW\({}_{e}\) & 3.97 & - \\ Air separation unit & MW\({}_{e}\) & 85.51 & - \\ Storage compressor & MW\({}_{e}\) & 0.25 & - \\ Net electric power output & MW\({}_{e}\) & 432.82 & 421.06 \\ Turbine outlet temperature & \({}^{\circ}\)C & 830.53 & 783.81 \\ Turbine inlet flow rate & kg/s & 1567.7 & 1513.7 \\ Net electric efficiency (LHV) & \% & 56.34 & 54.80 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of optimised cycle between [10] and uncooled turbine model. (II) = 4.95, is used to assign the scale of the cycle and assess the applicability of such a size. The cycle model is altered with the selection of \(\dot{m}_{max}\) and an assumed medium-value turbine isentropic efficiency of 85%, and the final modified cycle performance parameters are listed in Table 3. Although the net electric power output of 67.33 MW\({}_{e}\) is not within the scale range of the suggested 700 MW NET Power plans, the net work of this cycle is in the scale of gas turbines used in small industrial and commercial applications by major OEMs. The market for turbines in the range of less than or equal to 70 MW\({}_{e}\) is believed to grow considerably in the near future [32]. To summarise, Table 4 offers the turbine boundary conditions which are used to design, size and assess a radial expander that could be fit for use. The obtained turbine fluid components is comparable to the NET Power working environment reported in literature [9] with a slightly higher CO\({}_{2}\) mole fraction.