# TEG Design for Waste Heat Recovery at an Aviation Jet Engine Nozzle
## Appendix A  
In order to get a more comprehensive overview on simulations and to allow readers to establish correlations between simulation results and different application boundary conditions and thermocouple designs further information is given within this supplementary information. This comprises the temperature dependent courses of transport properties (thermal conductivity, electrical conductivity and Seebeck-coefficient) considered for the p- and n-type thermoelectric materials within the simulation. The gravimetric power density in dependence of the cold side heat transfer coefficient is shown additionally, which is not discussed in the publication due to the difficulty to improve the cold side convective heat exchange without losing the positive effect on the fuel consumption by acceleration of the bypass flow. Although the potential for further improvement on the convective heat transfer at the cold bypass flow and possibly connected repercussions on the engine operation still have to be investigated in detail, these results confirm a significant positive impact on the gravimetric power density of the TEG, and might be helpful for prospective considerations. Additionally simulations results on the evolution of the thermocouple mass and the hot side heat flow and heat flux density, respectively, are shown as the function of the hot side heat transfer coefficient for different filling factors. Though, these results are not discussed extensively throughout the publication, they reflect central key figures of the particular TEG designs, and shall therefore be displayed within the supporting information for the sake of completeness. Since operation parameters are obtained for a uni-couple configuration, but scaled to an TE module and finally projected to a TEG at the engine nozzle, governing relations are given within this appendix in order to support the understanding (see Table A1). In order to increase the confidence level of the FEM-based numerical simulations, a validation of the operation parameter has been conducted by means of a comparison to an analytical constant property model (CPM). Results are displayed in Table A2 and confirm a maximum deviation of all relevant operation parameters to be less than 2%.  
Figure 17: The \(m_{\rm TC}\) at the respective optimal leg length as a function of the hot side heat transfer coefficient \(\alpha_{\rm H}\) for different filling factors \(F\) of the thermocouple.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Property** & **CPM** & **ANSYS** & **Deviation** \\ \hline Electrical resistance R [m\(\Omega\)] & 182.389 & 185.386 & 1.64\% \\ Thermal conductance [\(10^{-3}\) W/K] & 0.835 & 0.83 & 0.59\% \\ Effective Seebeck coefficient [\(\mu\)V/K] & 401.1 & 402.325 & 0.30\% \\ Optimum current \(\eta_{\text{max}}\) [A] & 0.39 & 0.385 & 1.28\% \\ Optimum current \(P_{\text{max}}\) [A] & 0.439 & 0.434 & 1.13\% \\ Maximum power \(P_{\text{max}}\) [\(10^{-3}\) W] & 35.283 & 34.925 & 1.01\% \\ Incident heat flow \(Q_{\text{in}}\) [\(10^{-3}\) W] & 442.142 & 438.756 & 0.76\% \\ Maximum efficiency \(\eta_{\text{max}}\) [\%] & 7.98 & 7.96 & 0.25\% \\ \hline \hline \end{tabular}
\end{table}
Table 10: Relation between operation parameters obtained for a uni-couple configuration and corresponding values for a TE module (TEM) and a TEG. \(N\) denotes the number of uni-couples in a series connection within a TEM, whereas \(M\) denotes the number of TEM in a series connection within a TEG.