# TEG Design for Waste Heat Recovery at an Aviation Jet Engine Nozzle
## 2 Materials and Methods
However, room for further improvement on the heat exchange at the hot side is indicated by a certain insensitivity of the propulsive efficiency of the engine to the fluidic conditions at the core stream boundary layer [25]. The situation is significantly different at the cold bypass flow and it seems to give apparently much less space for heat exchange optimization. In order to maintain the detected positive effect on the propulsive efficiency from the acceleration of the bypass boundary layer, the HTC on the cold side is set to \(\alpha_{\mathrm{C}}\) = 64 WK\({}^{-1}\)m\({}^{-2}\) for all discussed cases in this work. This value represents a flat surface design at the cold bypass flow, as it was assumed in the CFD calculations, which shall not impose a restriction for further optimization of heat exchange by e.g., vortex-generating or lamellar surface structures. Additional studies are needed to quantify the potential of an improved convective heat exchange at the bypass flow of the nozzle with minimal repercussions on the engine operation, but the conservation of positive effects on the propulsive efficiency due to the TEG. For the sake of completeness, further simulation results for a model with higher cold side HTC can be found in the supporting information in the appendix (Figure 10). Summarizing, Table 2 gives a survey on the cases and their respective parameter ranges, which will be discussed later on. For the determination of the TEG performance, the thermocouples are supposed to be connected to TE modules (TEM) with a footprint of 50 \(\times\) 50 mm\({}^{2}\). With the given cross section of 1 mm\({}^{2}\) of each TE leg the footprint of one thermocouple equals \(A_{\mathrm{TC}}\) = 8 mm\({}^{2}\) (1 mm spacing between each leg), according to \(F\) = 25%. With this filling factor, 312 thermocouples can be connected within one TEM, yielding a total area covered by the TE legs of \(A_{\mathrm{TE}}\) = 624 mm\({}^{2}\) per TEM (Table 3). \begin{table}
\begin{tabular}{c c c c c} \hline
**Case** & \(\alpha_{\mathrm{H}}\) [WK\({}^{-1}\)m\({}^{-2}\)] & \(\alpha_{\mathrm{C}}\) [WK\({}^{-1}\)m\({}^{-2}\)] & \(F\) [\%] & \(I_{\mathrm{TE}}\) [mm] & \(\Delta\)PF [\%] \\ \hline
1 & 100–500 & 64 & 25 & 1–25 & 0 \\
2 & 100–500 & 64 & 25 & 1–25 & +10/20/30 \\
3 & 100–500 & 64 & 3–25 & 1–25 & 0 \\ \hline \end{tabular}
\end{table} 
Table 2: Simulation cases with their considered parameter ranges for different model properties: Hot and cold side heat transfer coefficient \(\alpha_{\mathrm{H}}\) and \(\alpha_{\mathrm{C}}\), filling factor \(F\), leg length \(I_{\mathrm{TE}}\) and \(\Delta\)PF as the change of the power factor as compared to the baseline material properties of the high performance virtual material (HPVM). \(\Delta\)PF = 0 indicates the use of the HPVM, as defined in Figures 1 and 10 in the supporting information, respectively. The coverage by TEM was extrapolated to the full nozzle surface (Figure 5) by a linear scaling of extensive performance key figures, as calculated for the uni-couple configuration. The relation between operation parameters of a single leg, a uni-couple, TE module, and TEG, respectively, is given in Table A1. According to the GasTurb engine design, a total surface \(A_{\text{noz}}\cong 1.1\) m\({}^{2}\) is available for the TEG installation at the nozzle, which gives space for 442 TEM of 50 \(\times\) 50 mm\({}^{2}\) per engine. A possible implementation encompasses a TEM alignment within 13 rings around the nozzle body, each with 34 modules. Simulations of the thermal conditions at the nozzle revealed a radial symmetric temperature distribution. However, a minor axial temperature variation along the nozzle, which is confirmed to be \(<\)11 K for cruise conditions, was not considered for the simulations on the TEG design and the resulting power of the overall system at the nozzle.