# Performance of a Supercritical CO2 Bottoming Cycle for Aero Applications
## 3 Results
### Closed Cycle Recuperator  
The overall geometry of the counter-flow recuperator matrix is defined through the height, weight and length of its cuboid. The recuperator is calculated as one component, but it would be easy to split into multiple smaller units that achieve the same overall performance and can be arranged circumferentially around the RBC's shaft. The fourth and fifth main parameters are the channel diameters for the two fluid flows. The individual parameter studies for the recuperator were conducted based upon the initial design assumptions stated in Appendix A. The \"full\" study, which varied all the main recuperator design parameters together, improved on the previously identified best MHX design. Figure 7a illustrates, that while the module height has little influence on the component pressure ratios above a value of 0.15 m, it does have a strong influence on the component's relative weight, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Cycle Parameter** & **Value** & **MHX Parameter** & **Value** \\ \hline \(\hat{m}_{\text{air}}\) & 32 kg/s & \(MN_{fr,h}\) & 0.11 \\ \(T_{air,in}\) & 615 K & \(N_{columns}\) & 4 \\ \(P_{air,in}\) & 36.1 kPa & \(a_{tube}\) & 0.005 m \\ PRRBC & 3.5 & RBC shaft power & 0.80 MW \\ \(\hat{m}_{\text{S-CO2}}\) & 20 kg/s & MHX weight & 269.7 kg \\ \(T_{cmp,in,S-CO2}\) & 305.15 K & \(\Delta\)fuel burn & +0.53\% \\ \(P_{cmp,in,S-CO2}\) & 7.5 MPa & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Parameters of the final MHX design at cruise. Figure 6: Parametric studies of the MHX of: (**a**) the hot-side inlet Mach number; (**b**) the number of columns per pass; and (**c**) the tube dimensions. The range of simulated module heights in the \"full\" parametric study was reduced to 0.2 to 0.4 m in order to achieve a reasonably compact, yet efficient design. The trends for module width were almost identical and are not illustrated, since both parameters affect the number of channels and thus the total free-flow areas very similarly. The recuperator length defines the length of all of the channels in the PCHE, so it has a big influence on the heat transfer, as is shown in Figure 7b. The pressure losses on either side of the recuperator are low due to the low flow velocities inside the channels of typically less than 10 m/s. The relative weight increases with increasing recuperator length and is the primary parameter counteracting longer flow channels for improved heat transfer. Typically, a recuperator has little effect on the shaft power generated in a bottoming cycle, but is a means to increase the cycle's thermal efficiency. In a scenario where weight and shaft power are primary design constraints, the weight penalty of the recuperator outweighs the small increases in shaft power that originate from higher MHX temperature levels on the S-CO\({}_{2}\) side. However, these studies revealed that recuperation is favourable, not only because of the slightly higher shaft power output, but because there is less temperature reduction in the exhaust gases. This increases the specific and net thrust of the core, making the engine more efficient for a fixed specific thrust design of the combined cycle. The fuel-burn difference between the recuperated and non-recuperated options is relatively small (\(\sim\)0.2-0.3 percentage points) and probably within the margin of error of the current models. Nonetheless, the trend is assumed to be qualitatively representative and a recuperated design is therefore preferred. The different inlet conditions to either side of the recuperator cause an imbalance in heat transfer coefficients With the cold-side HTC approximately twice as high as the hot-side HTC. Having smaller (but more closely spaced) flow channels on the hot-side will increase their HTC, but because hot and cold flow plates alternate during stacking, smaller diameter channels give a smaller total free flow area for that side relative to the other and increase the flow velocities, raising the pressure losses on that side.