# TEG Design for Waste Heat Recovery at an Aviation Jet Engine Nozzle
## 1 Introduction
While this site is certainly subjected to fewer design constrains, it poses the drawback of potentially lower temperature difference at the TEG in comparison with a location at other engine sections with higher temperatures and heat flux. In order to quantify the reduction of the fuel consumption, combined numerical methods have been applied to forward simulation data to a parametric model of the aircraft using the Pacelab Aircraft Preliminary Design (APD) software environment [23]. As the reference engine, a second generation geared turbofan engine with an unmixed nozzle and design-freeze in 2030 was chosen, together with an appropriate mission profile [22]. The most influential parameters of today's civil turbofan engines (bypass ratio, overall pressure ratio, turbine entry temperature, etc.) have been extrapolated to meet the prospective technology level in 2030 [22]. For definition of the geometry and the engine thrust requirements, the engine was designed with GasTurb [24] for top of climb as the design point (DP). By this, the resulting geometrical flow paths have been sized, allowing for the study of operational behavior of the engine by variation of engine power settings. As described in a previous work [25], the heat transfer calculation at the nozzle was accomplished by solving the three-dimensional (3D) Reynolds-averaged Navier-Stokes (RANS) equations using the computational fluid dynamics (CFD) solver TRACE [26; 27; 28]. The results of the CFD calculation were forwarded to a one-dimensional (1D) MODELICA model including the TEGs for computation of the heat flow from the core to the bypass. Here, the equivalence of the fluidic and thermal boundary layer thickness was assumed for the calculation of the heat transfer coefficients of the boundary layers, corresponding to a Prandtl number = 1. This process was repeated iteratively for the precise calculation of the heat transfer at the nozzle. Based on the results on the heat flux a sensitivity analysis on the thermoelectric figure of merit \(ZT\) was accomplished for the evaluation of the fuel saving potential by means of a mission-based performance modelling of the aircraft using the Pacelab APD environment [29]. According to the aforementioned works the fuel saving potential of a TEG is based on two effects. First, the generation of electrical energy by the TEG allows a slight mass reduction of the shaft-drivenelectric generator within the engine (1 kg/kW\({}_{\text{TEG}}\)). The lowered mechanical power, which is taken by the generator from the driving shaft, translates into an efficiency improvement, and this in turn leads to a reduction of the specific fuel consumption (SFC). According to the APD model of the reference aircraft the maximum saving on SFC equals 1% for a vanishing mechanical power usage by the conventional generator (total replacement by TEG) [22]. In this case, the TEG must provide the entire average power output of the generator, which equals 45 kVA per engine according to the APD model. Secondly, due to the heat transfer from the hot core stream to the cool bypass flow the bypass boundary layer is accelerated, whereas the core boundary layer is decelerated. For top-of-climb and at cruise conditions, the effect on the bypass flow shows an outweighing impact on the propulsive efficiency of the aircraft with maximum improvement in SFC of approximately 0.1% [2]. The SFC improvement yields a saving of fuel mass, which can be traded with the additional mass introduced by the TEG. The break-even is reached on the aircraft level if the fuel efficiency improvement outweighs the weight impact of the TEG. According to the mission-based APD evaluation, a fuel efficiency improvement is already given for a gravimetric electrical power density of the TEG \(>\) 173 Wkg\({}^{-1}\) (\"APD\" limit) if one considers only the positive effects that are related to the aircraft generator [28].