# Performance of a Supercritical CO2 Bottoming Cycle for Aero Applications
## 3 Results
### Pre-Cooler  
The pre-cooler again uses the involute spiral design from [PERSON] et al. [30]. The three most influential parameters of the pre-cooler therefore are the cold-side inlet Mach number, the number of columns and the length of the tube minor axis. The aspect ratio of the tubes is again constant for all designs so the major axis of the tube changes along with the minor axis. A further design parameter is the inner annulus diameter of the pre-cooler bypass duct. The pre-cooler is likely to be positioned axially near the main engine's combustor or HPT. The inner annulus diameter alone has little effect on the performance of the pre-cooler, but together with the minor axis of the tubes, it influences the number of tubes in a module and hence the hot-side free-flow area. It is obvious in Figure 8a that cold-side inlet Mach numbers above 0.2 give unacceptable pressure losses. Analogously to the trends observed for the MHX, the hot-side (S-CO\({}_{2}\)) pressure losses are larger for low cold-side inlet Mach numbers, due to the longer tubes. The longer tubes also add weight, but the relative difference between the high and low Mach number designs is much smaller than it is for the MHX. Another noteworthy observation from Figure 8a is that the necessary cold-side air mass flow is smaller for the low Mach number designs. The lower air flow velocities in the pre-cooler and the lower heat transfer coefficients are more than off-set by the increased heat transfer surface areas of the tubes. The final pre-cooler will likely be designed for the smallest cold-side inlet Mach number compatible with the geometric and weight considerations. The sensitivity of the pre-cooler's thermal performance to its hydraulic performance can be observed in Figure 8b. Larger numbers of tube columns lead to increased cold-side pressure losses, while the cold-side temperature effectiveness of the pre-cooler design increases considerably when adding more columns. However, the component weight rises significantly with larger tube counts, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Recuperator Parameter** & **Value** & **Recuperator Parameter** & **Value** \\ \hline \(H\) & 0.2 m & \(d_{c,h}\) & 0.0015 m \\ \(L\) & 0.7 m & RBC shaft power & 0.81 MW \\ \(W\) & 0.3 m & recuperator weight & 133.4 kg \\ \(d_{c,c}\) & 0.001 m & \(\Delta\)fuel burn & +0.47\% \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Parameters of the final recuperator design at cruise. Figure 7: Parametric studies of the recuperator’s performance dependent on: (**a**) the module height; and (**b**) module length; and (**c,d**) the effects of the hot- and cold-side channel diameters. so the final design is unlikely to feature more than four outboard and inboard tube columns. It is very unlikely that the pre-cooler would feature only one pair of tube columns, as the tubes would have to be very long to achieve the necessary heat transfer. This would increase the hot-side pressure losses dramatically, as can be seen in Figure 8b. Excessive hot-side pressure losses have an immediate detrimental effect on the performance of the whole RBC cycle, as they reduce the possible expansion ratio of the turbine, and thus the shaft power produced by the RBC. Figure 8c illustrates the expected trend that smaller tube diameter designs perform better thermally. However, the hot-side pressure losses increase noticeably for a tube minor axis below one millimetre, making a tube minor axis up to 1.4 mm more favourable from a cycle perspective. A larger tube minor axis, and therefore major axis, means that the pre-cooler will need more air mass flow and longer tubes to off-set the reduced heat transfer coefficients, if all other input parameters such as the inlet Mach numbers are kept constant. This is why component weight and relative air mass flows increase considerably with increasing tube size.