# Performance of a Supercritical CO2 Bottoming Cycle for Aero Applications
## 2 Materials and Methods
### Main Heat Exchanger  
The main heat exchanger (MHX) is positioned downstream of the LPT of the main engine and transfers parts of the otherwise largely wasted residual heat to the S-CO\({}_{2}\) bottoming cycle. The involute spiral heat exchanger design, developed by [PERSON] et al. at Chalmers University in the LEMCOTEC project, was implemented. Figure 4 shows schematically the U-bend design with continuous tubes, but the modelled design had separate inboard and outboard flowing tubes connected by cross-over ducts. Note, the involute spiral heat exchanger was originally designed as an intercooler and has been repurposed for this study. The detail available on the design and performance of the heat exchanger in [29; 30; 31] enabled it to be adapted for the MHX duty with turbine exhaust gases and S-CO\({}_{2}\). All correlations contained in [29; 30] were originally derived from CFD experiments featuring air as the medium on both sides. This makes them non-ideal for application to S-CO\({}_{2}\). However, all correlations have non-dimensional representations of the geometry and the Prandtl numbers of S-CO\({}_{2}\) in the investigated range do not differ too much from those of air in [PERSON]'s studies (0.8 to 1.5 for S-CO\({}_{2}\) vs. 0.8-0.9 for air). Furthermore, as Equation 3 is valid for a range of 0.5 < Pr < 2000 [17],  
Figure 4: Illustrations of the involute spiral two-pass cross flow intercooler concept in 3D, reproduced with permission from [32], [PERSON], 2017 (**a**); and the arrangement of the elliptical tubes in (**b**). Figure 3: Comparison of the compressor map of BNI: (**a**) reproduced with permission from [22], Barber Nichols Inc., 2016; and that in Propulsion Object Oriented Simulation Software (PROOSIS) (**b**). the correlations are assumed to be accurate enough for the current investigations. Care has to be taken during the design of the cold-side free flow area, to ensure the design adheres to the Reynolds number limits stated in [29]. From the designs investigated by [PERSON] et al. in [30], the option featuring a radial tube spacing of \(d_{b}=2b\) and an axial tube spacing of \(d_{a}=a\) was chosen, where \(a\) and \(b\) represent the large and small axes of the elliptic tube profile. The aspect ratio of the tube cross-section is fixed in all studies to \(\frac{a}{b}=8\) (see Figure 4 for reference). This high aspect ratio, combined with the high internal pressure, requires that the tubes have internal webs to stiffen them. The tube wall thickness is set to 0.2 mm, but this might need to be increased when a dedicated mechanical integrity model is in place. For now, the risk of weight increase due to thicker tube walls and webs is highlighted in the discussion section. Dedicated correlations define the pressure losses for the heat exchanger inlet, outlet and cross-over ducts, and inside the tubes. The heat transfer and pressure losses for each of the two passes of the MHX are calculated separately. The equations below reflect the most important correlations from [30], relating the non-dimensional flows inside and outside the tubes to their heat transfer coefficients (HTC) and pressure losses. For the correlations of the remaining sections of the MHX see [29].