# TEG Design for Waste Heat Recovery at an Aviation Jet Engine Nozzle
## 2 Materials and Methods  
The modelling is done for a thermoelectric uni-couple by a 3D steady state temperature dependent FEM simulation using built-in thermoelectric tetrahedral elements (Type: 226) of ANSYS WorkbenchTM. The minimum element length was set to 65 \(\upmu\)m. Depending on the length of thermoelectric legs, this resulted in a minimum element count of 813\(\cdot\)10\({}^{3}\) for the uni-couple model. The FEM simulation was validated by a comparison to an analytical 1D constant properties model (CPM) of the TE elements stacked with contact and heat exchanger layers. Details on the CPM and governing equations for thermoelectric power generation can be found in [32]. The results of this comparison, which are summarized in Table 1 in the appendix, point to a deviation of all relevant operation parameters that are lower than 2% between FEM and CPM simulation. Though simulation was conducted for all flight phases of the chosen mission profile, the geometry optimization and detailed performance calculations have been performed for the cruise phase, which has the highest temporal share (87%) of the total mission time (395 min) for the set flight distance of 2850 nautical miles (NM). Based on material properties, measured on n- and p-type Skutterudite samples, high performance virtual thermoelectric materials (HPVM) are defined by the modification of the temperature characteristics of the real TE transport properties (Figure 1). More details on the individual TE transport properties can be found in the supporting information within the appendix of this publication (Figure 1). First, the temperature curves of the thermal conductivity, the Seebeck coefficient, and the electrical conductivity of the Skutterudite materials are shifted into the temperature range of the nozzle application in order to represent an optimized material. As an effect of the lower mean temperature the resulting \(ZT\) values decrease. To consider a reasonable technology level of a future TE material during simulation, the power factor (\(PF=S^{2}.\sigma\)) of the p- and n-type material is increased by an improvement of the Seebeck coefficient and the electrical conductivity by 40% for each property, whereas the thermal conductivity was kept constant. With that, the HPVVM with peak \(ZT\) values of 1.2 (p-type) and 1.5 (n-type) are used as input for the simulation. This corresponds to \(ZT_{\text{mean}}=1.14\) for the uni-couple. The operational characteristics of the TEG are simulated for a uni-couple configuration (Figure 2) under consideration of all relevant effects, like Joule heating and the [PERSON], Seebeck, and Thomson effects. The nozzle of the aircraft is modelled by a layer on one outer side of the 3D configuration. Due to weight minimization, the nozzle is supposed to be made from TiAl with a temperature dependent thermal conductivity between 20-30 Wm\({}^{-1}\)K\({}^{-1}\)[34]. The thickness of the TiAl is chosen to be 2 mm in accordance to the original design of the nozzle body. Flat surfaces are assumed for external heat exchange with the air flows. Due to the major sensitivity of the propulsive efficiency on the flow condition at the cold bypass boundary layer [23], the modification of the hot nozzle surface only seems beneficial for any optimization of the convective heat transport. In order to minimize the temperature drop at the cold bypass side, a direct incident flow on the insulation layer of the thermocouple is assumed here. Thus, the nozzle layer was modelled for the hot core stream only. For reduction of parasitic temperature drops a layer of AlN with a high thermal conductivity of 170 Wm\({}^{-1}\)K\({}^{-1}\)[35] is introduced to form an electrical insulation between the TE uni-couple and the metallic nozzle. When considering the dielectric strength of AlN of 20 kVmm\({}^{-1}\)[36], a minimum thickness of 325 \(\upmu\)m is set for this layer on both sides with regard to weight optimization and concurrent electric insulation effect in the presence of high DC voltages generated by the entire TEG at the nozzle.