# TEG Design for Waste Heat Recovery at an Aviation Jet Engine Nozzle
## 4 Discussion
As a consequence, the heat flux density decreases for a particular set of HTC by approximately 10% when \(F\) is reduced from 25% to 3% (Figure A4). For the design points of the HTC (\(\alpha_{\rm H}\) = 100 WK\({}^{-1}\)m\({}^{-2}\), \(\alpha_{\rm H}\) = 64 WK\({}^{-1}\)m\({}^{-2}\)) and the set total surface (\(A_{\rm noz}\) = 1.1 m\({}^{2}\)), which is offered for TEG occupation, a total power output between 1.65 kW and 1.85 kW can be expected from the thermoelectric recuperation at the nozzle for \(F\) = 3% and \(F\) = 21%, respectively. This corresponds to 3.6% to 4.1% of the average electrical power output of the shaft-driven electric generator within each engine of the reference aircraft. The power output for \(F\) = 21% of 1.85 kW offers a total SFC improvement of 0.05% (Figure 11). A slightly lower SFC reduction of 0.045% is achieved at \(F\) = 5.5%, but with the advantage of a range invariant installation of the TEG, as the gravimetric power density exceeds 520 Wkg\({}^{-1}\). A possibility to improve the SFC saving is given by an increase of the installation space, which is calculated for an additional higher value of \(A_{\rm noz}\) = 1.5 m\({}^{2}\). Increasing simultaneously the performance of the convective heat transfer to \(\alpha_{\rm H}\) = 200 WK\({}^{-1}\)m\({}^{-2}\) the corresponding areal power density offered by the TEG could allow for a SFC improvement of 0.11% at \(F\) = 23.8%. Again, slightly lower SFC reduction of 0.096% is achieved at \(F\) = 6.3% for a range invariant installation of the TEG at the geometrically extended nozzle. A further but not yet investigated means to increase the power density is given by exchanging the TiAl by electrically insulating SiC. Due to higher thermal conductivity and simultaneously lower density, SiC could decrease the mass and the spreading resistance of the nozzle, while making the use of the AlN layer unnecessary, which would allow for an additional reduction of mass. Figure 11: Specific fuel consumption (SFC) improvement as a function of electrical power output of the TEG at the aircraft nozzle. The SFC is calculated on the base of data from [28]. Contributions from the bypass acceleration (CFD) and the reduced mechanical power of the generator (APD) add to the total SFC reduction. Ranges of SFC improvement are highlighted for two different occupation surfaces at the nozzle with varied HTC \(\alpha_{\rm H}\). The corresponding values of the electrical power output are calculated according to the respective areal power densities for the permitted ranges of \(F\), which fulfil the minimum gravimetric power density requirement. However, according to the simulation results a SFC saving between 0.05% and 0.1% seems plausible for the TE reuperation of waste heat at the engine nozzle. Though the nominal values might seem small, a considerable economic impact can be estimated from the beneficial impact on the operational costs. According to estimations from Boeing [18], a SFC improvement of 0.1% translates into a cost saving of 2.4 Mi0$/month for the entire US civil aviation sector. Our own estimations [46] on the base of a 0.1% SFC improvement yield a potential saving of 144 k$ per airplane over a typical life time of 28 years. Consequently, a return of investment during five years could be attainable for a 2 kW TEG system within the cost limit of <16 $/W. According to recent studies, the sum of material and heat exchanger costs for modern TE materials can be estimated below 10 $/W for \(F<10\%\) and at operating temperatures between \(T_{\mathrm{H}}=700\) K and Tc = 300 K [47], which might be relevant for a progressive approach of a high performant heat transport system at the nozzle with the use of heat pipes. When considering the total TE system costs (including manufacturing, heat exchanger, and material costs for thermoelectrics and ceramics) values < 20 $/W are offered by a certain number of today's TE materials at the temperature range between \(T_{\mathrm{H}}=523\) K and \(T_{\mathrm{C}}=293\) K [48].