# Performance of a Supercritical CO2 Bottoming Cycle for Aero Applications
## 2 Materials and Methods  
All simulations were carried out in the commercially available \"Propulsion Object Oriented Simulation Software\" (PROOSIS 3.6.14, Empresarios Agrupados Internacional, Madrid, Spain) [25]. PROOSIS does not feature S-CO\({}_{2}\) as a working fluid by default, so the fluid property tables and the related real gas fluid functions had to be integrated. Following compression of the S-CO\({}_{2}\), it is pre-heated in the recuperator, utilising the heat from the S-CO\({}_{2}\) turbine's exhaust flow. Thereafter, the high pressure flow temperature is further raised in the main heat exchanger (MHX), recovering part of the main engine's low pressure turbine exhaust heat. Subsequently the S-CO\({}_{2}\) is expanded in the turbine and cooled in the recuperator. Finally, the pre-cooler rejects the remaining heat energy to a part of the bypass flow of the main engine, to restore the compressor inlet conditions and close the cycle. Standard PROOSIS simulation tools include quasi-1D representations of turbomachinery components through component maps, but do not include geometric representations of the heat exchangers. To improve the fidelity of the simulations, S-CO\({}_{2}\)-specific maps were implemented for the compressor and turbine, and the heat exchanger's component codes were extended to include geometric calculations to better represent the thermodynamic performance. The overall installation weight of the bottoming cycle is likely to be greater than 400 kg. To maximise the fuel burn benefits that arise from the TSFC reductions, the shaft power generated in the RBC is transferred to the low pressure shaft of the geared turbofan engine (TF2050) via a reduction gearbox. The TF2050 was also modelled in PROOSIS, so the potential fuel burn benefit of adding a bottoming cycle to it could be estimated. The cycle parameters of the TF2050 were projected forward to an assumed State of the Art in 2050 as listed in Table 2.  
In order to avoid the complexity and resulting stability problems of a combined cycle model, engine trade factors were derived to quantify the TSFC changes due to the interaction of the bottoming cycle with the TF2050. The following parameters were considered:  
* Pressure losses and temperature reductions in the core exhaust gases due to the MHX
* Pressure losses and temperature increases in the pre-cooler bypass duct air
* Provision of additional power to the low pressure turbine (LPT) shaft  
By changing the optimum core cycle, the RBC will facilitate the design of lower specific thrust engines without needing a larger LPT or smaller high pressure compressor (HPC) blades. The lower specific thrust design option has not been captured in a trade factor as of yet, possibly leading to an underestimation of the fuel burn benefit. The evaluation of possible lower specific thrust designs will be part of later combined cycle optimisation studies. Mission fuel burn benefits are calculated by utilising aircraft trade factors that relate the TSFC and weight changes to fuel burn. Power transmission losses are not accounted for, but assuming an efficiency of 99%, the losses will be of the order of 10 kW and will have very little effect on overall performance. A dedicated transmission model is being developed for the bottoming cycle and will be applied in future studies. To reduce the computational effort associated with this investigation, the procedure to determine the RBC's design was split into three distinct stages. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Altitude & 10,668 m & \(\eta_{\text{fan,BP}}\) & 0.95 \\ Mach number & 0.82 & \(\eta_{\text{HPC}}\) & 0.92 \\ F\({}_{\text{n}}\) & 49 kN & \(\eta_{\text{HPC}}\) & 0.91 \\ BPR & 20.7 & \(\eta_{\text{HPT}}\) & 0.91 \\ OPR & 64.4 & \(\eta_{\text{LPT}}\) & 0.95 \\ T\({}_{\text{4}}\) & 1580 K & TSFC & 12.88 g/(kN-s) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Cruise performance parameters of the reference TF2050. 1.