# TEG Design for Waste Heat Recovery at an Aviation Jet Engine Nozzle
## 2 Materials and Methods
Metallic Cu bridges with a thickness of 200 \(\upmu\)m form the electrical interconnects between the TE elements. Square-shaped cross section with a foot print of 1 \(\times\) 1 mm\({}^{2}\) for each TE leg are assumed. The spacing between the legs is set to 1 mm. The filling factor is varied by the modification of the nozzle and insulation layer surface per TE thermocouple that exchanges heat with the air flows. The length of the legs is adjusted to obtain a match of the thermal resistance of the TE thermocouple to the outside resistances within the heat transfer path. An aerogel filling in the gaps between the legs is assumed as thermal insulation material with a reasonable assumption for its thermal conductivity of 0.03 Wm\({}^{-1}\)K\({}^{-1}\)[37; 38], in order to minimize parasitic heat bypass. Neither radiative nor convective heat transport within the aerogel-filling was considered. Figure 1: Figure of merit \(ZT\) of a virtual p-type (**a**) and n-type (**b**) thermoelectric material for simulation. The dashed lines represent fits of measured properties on Skutterudite samples. Curves shown by light solid lines show the temperature curve of \(ZT\) after the shift of transport properties into the temperature range of the nozzle application is applied. Bold solid lines show the \(ZT\) characteristic of the virtual material, which is considered for the simulation. According to the CFD simulation, the gas temperatures of the core and the bypass flow are \(T_{\rm{hg}}=623\) K and \(T_{\rm{cg}}=238\) K, respectively, during cruise conditions. The simulations revealed considerably low heat transfer coefficients (HTC) of the convective heat exchange between the air flows and the nozzle and insulation surfaces (Figure 3), respectively. Convective heat transfer is considered at the particular surfaces by the appropriate settings of the calculated HTC and the respective gas temperatures from CFD simulations (derived from [25]) within the thermocouple model. For the determination of the electrical power output one terminal is kept at 0V potential, while an electrical DC current, \(I\), through the couple is varied from zero up to the short circuit value. The according terminal voltage, \(V\), is used for the calculation of the output power, \(P_{\rm{el}}=V\cdot L\). The resulting curve of \(P_{\rm{el}}(I)\) is well approximated by a parabolic fit, the maximum of which gives the maximum electrical power output. No contact resistances have been considered within the model. The efficiency of the uni-couple is calculated from the ratio of maximum power output by the incident heat flow at the given operation point of the electrical current. The heat flow on the hot and cold side of the uni-couple configuration reveals a spatial distribution due to different thermal conductivities of the p- and n-type material and the heat spread in the contact bridges and the heat exchanger plates (Figure 4). Discrete data on the heat flux (normal component  
Figure 3: Temperature dependent convective heat transfer coefficients at the hot core stream (**a**) and the cool bypass flow (**b**). The depicted design points indicate values for a thermoelectric module with a filling factor of \(F=25\%\) and an adjusted length of the thermoelectric legs of 21.2 mm for the matching of thermal resistance. Figure 2: Scheme of the thermoelectric uni-couple configuration composed of electrical insulation layers (IS), metallic bridges (MB), the p- and n-type thermoelectric (TE) material legs, and the TiAl nozzle (**a**). Schematic of the installation at the aircraft nozzle and illustrative temperature distribution along the heat transmission path for \(F=25\%\) (**b**). of the heat flux vector) is taken at every node of the surface for areal interpolation and subsequent approximation by a continuous area function. The incident heat flow is finally determined by the integration of this function over the entire top surface of the hot side.