# Performance of a Supercritical CO2 Bottoming Cycle for Aero Applications
## 2 Materials and Methods
### Closed Circuit Recuperator  
S-CO\({}_{2}\) cycles profit strongly from the addition of a recuperator to enhance their efficiency. In many instances more than half of the total heat energy input to the compressor exit flow is achieved in the recuperator and more than 60% is not uncommon (e.g., see [37]). Although the standalone thermal efficiency is not the primary focus of the bottoming cycle, it will still have a considerable effect on the shaft power output. A secondary incentive for a recuperator is that the flow on both sides is S-CO\({}_{2}\). This means the heat transfer coefficients are high and the imbalance between the two sides is much less. Not only would the S-CO\({}_{2}\) cycle be less efficient if no recuperator were employed, and the pre-cooler would need to be considerably larger. This would increase the installation dimensions and weight of the bottoming cycle, as well as the flow distortion of the main engine bypass flow. The recuperator's influence on the S-CO\({}_{2}\) cycle performance is greater for cycles with higher turbine entry temperatures, these cause larger gaps between the compressor and turbine outlet temperatures. During cruise, the design point of the bottoming cycle, the LPT exhaust gas temperatures (EGT) of the TF2050 only reach about 615 K. Because this gives relatively low TET in the bottoming cycle, the parametric studies included a scenario without a recuperator. Table 5 states the ranges of all the investigated parameters. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Units** & **Range** & **Remarks** \\ \hline \(MN_{fr,h}\) & - & 0.1–0.2 & \begin{tabular}{c} Mach numbers below 0.12 would be more efficient, but lead to excessive MHX dimensions \\ \end{tabular} \\ \hline \(N_{columns}\) & - & 4–10 & \begin{tabular}{c} One column always encompasses the staggered column behind the first as well (see Figure 3(b)) \\ \end{tabular} \\ \hline \(a_{tube}\) & m & 0.005–0.013 & Major internal axis of the elliptical tubes \\ \hline \(x\) & - & 0.6–1 & \
\begin{tabular}{c} Percentage of the LPT exit inner annulus diameter, used to calculate inner annulus diameter of hot-side frontal area \\ \end{tabular} \\ \hline \(\rho_{mat}\) & kg/m\({}^{3}\) & 4330 & Ti-6 Al-4V Grade 5 [36] assumed, to minimise weight \\ \hline \(tube_{th}\) & m & 0.0002 & Tube wall thickness assumed at 0.2 mm, according to [5] \\ \hline \(d_{duct,in}\) & m & 0.3 &
\begin{tabular}{c} Inner annulus diameter of cold-side inlet duct, second order influence on pressure losses \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Main heat exchanger (MHX) design parameters. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Units** & **Range** & **Remarks** \\ \hline \(H\) & m & 0.2–0.4 & Height \\ \(L\) & m & up to 1 & Length \\ \(W\) & m & 0.2–0.4 & Width \\ \(d_{c,c}\) & m & 0.001–0.004 & Cold-side channel diameter \\ \(d_{c,h}\) & m & 0.001–0.004 & Hot-side channel diameter \\ \(e_{abs,c}\) & \(e_{abs,h}\) & m & \(1\times 10^{-5}\) & Hot- and cold-side absolute surface roughness \\ \(\rho_{mat}\) & kg/m\({}^{3}\) & 4330 & Ti-6 Al-4V Grade 5 [36] assumed, to minimise weight \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Recuperator design parameters. In an effort to minimise the footprint of the recuperator and therefore maximise the benefits arising from having two high density fluids, the recuperator is designed as a printed circuit heat exchanger (PCHE) [38]. Diffusion bonding stacks of corrugated plates makes PCHEs easy to customise and they feature great thermo-mechanical strain tolerances. Due to their very small flow channels, PCHEs also deliver high effectiveness for small size. The small flow channels limit access to the core of the component for inspection, but fouling should not be a problem in the closed-circuit system. PCHEs are the most commonly used design for recuperators in S-CO\({}_{2}\) application at the moment, with only plate fin heat exchangers (PFHE) offering similar qualities.