# TEG Design for Waste Heat Recovery at an Aviation Jet Engine Nozzle
## 4 Discussion
Finally, the concurrent reduction of \(F\) and lower leg lengths promote a parallel heat flow through the gaps of the thermocouple configuration, which can lead potentially to a significant reduction of the efficiency in case of convection or heat transport by radiation. For open or evacuated TEG, the application of low-emissivity metallization layers has turned out to be an appropriate means to reduce radiative heat exchange within TEMs. Using solid filling of gaps by aerogel material, as considered by the simulation model of this work, effectively prevents parasitic thermal crosstalk between the hot and cold side of the thermocouple by convection. Selective simulations on the impact of the parasitic heat conduction through the aerogel revealed a maximum decrease of power output of 0.67%, which is supposed to be a tolerable value. Lowering the filling factor \(F\) yields high mass savings due to significantly lowered thermal resistance of the convective boundary layers and reduced optimal leg lengths of the thermocouple. Reducing \(F\) from 25% to 3% reduces the thermocouple mass by 43% (Figure 10). At the design point of the convection HTC parameters at the nozzle (\(\alpha_{\rm H}\) = 100 WK\({}^{-1}\)m\({}^{-2}\), \(\alpha_{\rm C}\) = 64 WK\({}^{-1}\)m\({}^{-2}\)), the minimal gravimetric power density requirement (\"APD + CFD\"-limit) is fulfilled for the HPVM for \(F\) < 21% (Figure 10). When considering only the positive impact on the reduced mass and mechanical power of the engine generator (\"APD\"-limits), a beneficial installation of TEG becomes attainable for \(F\) < 12.4%, while access to a range-invariant TEG implementation is given for \(F\) < 5.5%, respectively. Improving the hot side convective HTC to \(\alpha_{\rm H}\) = 200 WK\({}^{-1}\)m\({}^{-2}\) the power density requirements are fulfilled for slightly higher \(F\). \(P_{\rm G}\) = 100 Wkg\({}^{-1}\) is attainable for \(F\) < 23.8%, while the range-invariant installation requires \(F\) < 6.3%. According to the simulation results, the range for maximum gravimetric power density at \(F\) = 3% is given between 800 Wkg\({}^{-1}\) and 1200 Wkg\({}^{-1}\) in dependence on \(\alpha_{\rm H}\). The decrease of mechanical power taken from the turbine shaft by the generator scales with the electrical power output of the TEG, while the positive impact on the propulsive efficiency by acceleration of the bypass flow is linked to the heat flow dissipated by the TEG, which is likewise connected over the thermocouple efficiency to the power output of the TEG. Thus, the quantitative determination of the SFC saving requires the determination of the amount of electrical power provided by thermoelectric recuperation. When considering the limitation on the installation space,  
Figure 10: Gravimetric power density \(P_{\rm G}\) of a HPVM-based TEM as a function of the filling factor \(F\) for different HTC \(\alpha_{\rm H}\). \(P_{\rm G}\) is displayed together with the required levels from the aircraft model. the power output is determined by the achievable areal power density \(P_{\rm A}\) of the thermocouple. At \(\alpha_{\rm H}\) = 100 WK\({}^{-1}\)m\({}^{-2}\) and \(\alpha_{\rm C}\) = 64 WK\({}^{-1}\)m\({}^{-2}\), \(P_{\rm A}\) stays below 1680 Wm\({}^{-2}\), independently from the filling factor applied. Reducing the filling factor from 25% to 3% yields a reduction of the areal power density in the range of 10% for a particular \(\alpha_{\rm H}\) (Figure 9b). This is connected to the finite thermal conductivity of the components within the heat transmission path and the corresponding spreading resistances on both sides of the thermocouple configuration. Due to the low thicknesses of the nozzle and insulation layers, which are minimized in order to receive a maximized gravimetric power density, the components set a considerably thermal resistance for the lateral heat transport, which lowers the effective temperature difference at the TE materials.