# TEG Design for Waste Heat Recovery at an Aviation Jet Engine Nozzle
## 5 Conclusions  
The application of thermoelectric generators (TEG) on the nozzle of an aviation jet engine was studied by finite element modelling. Temperatures of the core stream and the bypass flow are derived from CFD results [25] and are applied as boundary conditions to the FEM simulation of various thermocouple configurations. In conjunction with effective heat transfer coefficients (HTC) between the flat surfaces of the nozzle and the core (\(\alpha_{\mathrm{H}}=100\) WK\({}^{-1}\)m\({}^{-2}\)) and the bypass (\(\alpha_{\mathrm{C}}=64\) WK\({}^{-1}\)m\({}^{-2}\)) air flow, respectively, the performance of different thermocouple designs is simulated on the basis of a virtual material with a \(ZT_{\mathrm{mean}}=1.1\). Focus is placed on the identification of the appropriate filling factor \(F\) and TE element length in order to maintain a positive impact on the specific fuel consumption (SFC) of a reference aircraft [22]. The maximal gravimetric and areal power density of the TEG is simulated for 3% < \(F<25\%\), with a concurrent determination of the optimal leg lengths for the matching of thermal resistances. The requirement on the gravimetric power density, which was determined from of a parametric aircraft model [28], cannot be fulfilled for a thermocouple design with \(F=25\%\), neither by an increase of the HTC nor by a reasonable improvement of materials performance. The minimum break-even point of gravimetric power density (100 Wkg\({}^{-1}\)) for TEG implementation with a positive impact on the SFC but with the drawback of a reduced flight range of the aircraft is attainable for \(F<21\%\). The low HTC (\(\alpha_{\mathrm{H}}=100\) WK\({}^{-1}\)m\({}^{-2}\), \(\alpha_{\mathrm{C}}=64\) WK\({}^{-1}\)m\({}^{-2}\)) of the convection heat exchange at the flat nozzle surface turned out to be the bottleneck for the maximization of the TEG performance. Consequently, the requirement for a range-invariant installation (520 Wkg\({}^{-1}\)) only becomes attainable for \(F<5.5\%\). For \(A_{\mathrm{noz}}=1.1\) m\({}^{2}\) of occupation surface at the nozzle a power output between 1.65 kW and 1.85 kW is expectable from the TEG per engine within the design domain with a positive SFC impact. Under reasonable assumptions of an increased occupation surface (\(A_{\mathrm{noz}}=1.5\) m\({}^{2}\)) and improved heat exchange by convection (\(\alpha_{\mathrm{H}}=200\) WK\({}^{-1}\)m\({}^{-2}\), \(\alpha_{\mathrm{C}}=64\) WK\({}^{-1}\)m\({}^{-2}\)), the power output of the TEG increases to 2.72 kW to 3.07 kW within the design range (\(F<23.8\%\)), which shows sufficiently high gravimetric power density in order to maintain a positive SFC impact. The resulting savings on the SFC is in the range between 0.05% and 0.1%, which translates into a considerable reduction of operation cost for the aircraft. This cost reduction opens a window for an economically efficient TEG installation. A return of invest during approximately five years is estimated, if the total costs of the thermoelectric reuperation system stay below 16 $/W, which is a reasonable value for high performance TE materials from today's point of view. Further improvement of the power output and the resulting SFC saving seems realistic by the increase of the nozzle surface, exchange of particular materials for more performant heat transfer, and by optimization of the convective heat exchange by the modification of surface structures. Though, the installation of TEG in engine sections with higher temperature levels was not investigated in detail yet, it offers a significantly higher power output and SFC improvement capability when compared to the nozzle installation [22]. Further studies have to verify the entire optimization potential and to clarify the possibilities for more progressive integration concepts for TEG in aviation engines.