# TEG Design for Waste Heat Recovery at an Aviation Jet Engine Nozzle
## 1 Introduction  
Thermoelectric generators (TEG) convert heat into electrical energy [1] without the step of performing mechanical work in between, which makes them a favorable choice for energy harvesting applications in terms of robustness and reliability. The efficiency of thermoelectric (TE) conversion is determined on the material level by the figure of merit \(ZT\), which is formed by the Seebeck coefficient \(S\), and the electrical and thermal conductivity \(\sigma\) and \(\kappa\), respectively (\(ZT=S^{2}\cdot\sigma\cdot\kappa^{-1}\cdot T\)). The TE conversion of waste heat has been considered in the past for high power generation in many fields, such as to supply space probes [2; 3], or for automotive [4; 5; 6] and stationary applications [7; 8]. In contrast to this, TE energy harvesting for aviation was taken into account in the past with a focus on low power applications to supply sensor nodes. Many works have been conducted in the context of structural health monitoring [9; 10; 11], whereby a proof of principle could already been given during flight tests according to a few reported studies [12; 13]. The performance of today's aero-engines is already optimized to a high level. Further improvement by means of known concepts seems increasingly difficult and new technologies have to be considered in order to reduce the fuel consumption and environmental pollution of future aircrafts and to move closer to the specified goals by ACARE [14] and Flightpath 2050 [15]. This is linked to the fact that thethermal efficiency of gas turbines is mainly determined by the overall pressure ratio and the turbine entry temperature [16]. The increase of both parameters requires new material solutions that are investigated extensively. Another possibility for improvement is given by the management of heat flow, in order to decrease the amount of waste heat of engines that is lost to the environment. For this reason, focus is put on the recuperation of engine waste heat [16; 17]. Conducted works on TE high power applications in the hot gas environment have been restricted over the years to basic assessments from estimated temperature differentials and approximated heat flux conditions [18; 19; 20]. These studies led to restrained conclusions on the resulting performance and the assessment of a lacking technological and economic efficiency of TEG. Although admittedly lower in today's achievable efficiencies, TEG still avoids additional complex thermodynamic cycles, corresponding installations, and their handling for the jet engine system. This principally corresponds to an easy implementation and lower maintenance effort when compared to other emerging heat engine technologies (e.g., Organic Rankine Cycle). The occurrence of MW heat losses of turbofan engines [21], in contrast to the relatively low average electrical power requirements of today's mid-size aircrafts (180 PAX\(\sim\)45 kVA/engine) offers an attractive fuel saving potential from a direct conversion of engine heat into electrical energy by TEG. As shown in a previous work [22], the assumption of an efficient heat transfer by heat pipes (\(\kappa_{\text{eff}}\) = 400 Wm\({}^{-1}\)K\({}^{-1}\)) and conservative TEG material efficiency (\(ZT_{\text{mean}}\) = 0.8) yields a specific TEG power output between 1 kWm\({}^{-2}\) to 9 kWm\({}^{-2}\), which becomes attainable from of a first approximation of temperatures and heat fluxes on several sections of the reference engine: high- and low pressure turbine (HPT, LPT), interducts, and nozzle. The theoretically maximum available surface of the turbofan geometry would allow for an installation of approximately 15 kVA TEG power output per engine in total. However, due to the limited space, the installation of TEGs on high temperature sections of the engine (HPT, LPT) seems technically difficult, which favors an implementation at the nozzle. Thus, the effect of the TEG between the hot core stream and the cool bypass flow was investigated in detail for a location at the engine nozzle.