# TEG Design for Waste Heat Recovery at an Aviation Jet Engine Nozzle

^{1}

^{2}

^{*}

## Abstract

**:**

^{−1}) can only be met for F ≤ 21%. When extrapolating TEG coverage to the full nozzle surface, the power output reaches 1.65 kW per engine. The assessment of further potential for power generation is demonstrated by a parametric study on F, convective HTC, and materials performance. This study confirms a feasible design range for TEG installation on the aircraft nozzle with a positive impact on the fuel consumption. This application translates into a reduction of operational costs, allowing for an economically efficient TEG-installation with respect to the cost-specific power output of modern thermoelectric materials.

## 1. Introduction

^{2}∙σ∙κ

^{−1}∙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].

_{eff}= 400 Wm

^{−1}K

^{−1}) and conservative TEG material efficiency (ZT

_{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.

_{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].

^{−1}(“APD” limit) if one considers only the positive effects that are related to the aircraft generator [28]. If the additional impact on the propulsive efficiency due to the heat transfer from the core to the bypass flow is taken into account, the requirement on the specific power density of the TEG reduces to 100 Wkg

^{−1}(“APD + CFD” limit).

^{−1}(“APD range-invariant” limit) is required according to the aircraft model.

## 2. Materials and Methods

^{TM}. The minimum element length was set to 65 µm. Depending on the length of thermoelectric legs, this resulted in a minimum element count of 813·10

^{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 A2 in the appendix, point to a deviation of all relevant operation parameters that are lower than 2% between FEM and CPM simulation.

^{2}∙σ) 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 HPVM 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

_{mean}= 1.14 for the uni-couple.

^{−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 µm 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. Metallic Cu bridges with a thickness of 200 µm form the electrical interconnects between the TE elements. Square-shaped cross section with a foot print of 1 × 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.

_{hg}= 623 K and T

_{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.

_{el}= V∙I. The resulting curve of P

_{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.

_{max}of 1.56 and 1.95 for the p- and n-type material, respectively, at the last step (case 2). This is clearly a free parameter variation without any specific optimization strategies for materials performance behind. Anyway, the best known laboratory values for advanced TE materials to date already exceed these assumed ZT values [40,41].

_{H}as compared to the outcome of the CFD simulations within every simulated parameter configuration of the model. The increase of α

_{H}reflects a hypothetic modification of the nozzle surface for an improved aerodynamic design, which was not optimized concerning its heat transfer in this study at all. However, room for further improvement on the heat exchange at the hot side is indicated by a certain insensitivity of the propulsive efficiency of the engine to the fluidic conditions at the core stream boundary layer [25]. The situation is significantly different at the cold bypass flow and it seems to give apparently much less space for heat exchange optimization. In order to maintain the detected positive effect on the propulsive efficiency from the acceleration of the bypass boundary layer, the HTC on the cold side is set to α

_{C}= 64 WK

^{−1}m

^{−2}for all discussed cases in this work. This value represents a flat surface design at the cold bypass flow, as it was assumed in the CFD calculations, which shall not impose a restriction for further optimization of heat exchange by e.g., vortex-generating or lamellar surface structures. Additional studies are needed to quantify the potential of an improved convective heat exchange at the bypass flow of the nozzle with minimal repercussions on the engine operation, but the conservation of positive effects on the propulsive efficiency due to the TEG. For the sake of completeness, further simulation results for a model with higher cold side HTC can be found in the supporting information in the appendix (Figure A2). Summarizing, Table 2 gives a survey on the cases and their respective parameter ranges, which will be discussed later on.

^{2}. With the given cross section of 1 mm

^{2}of each TE leg the footprint of one thermocouple equals A

_{TC}= 8 mm

^{2}(1 mm spacing between each leg), according to F = 25%. With this filling factor, 312 thermocouples can be connected within one TEM, yielding a total area covered by the TE legs of A

_{TE}= 624 mm

^{2}per TEM (Table 3).

_{noz}≅ 1.1 m

^{2}is available for the TEG installation at the nozzle, which gives space for 442 TEM of 50 × 50 mm

^{2}per engine. A possible implementation encompasses a TEM alignment within 13 rings around the nozzle body, each with 34 modules. Simulations of the thermal conditions at the nozzle revealed a radial symmetric temperature distribution. However, a minor axial temperature variation along the nozzle, which is confirmed to be <11 K for cruise conditions, was not considered for the simulations on the TEG design and the resulting power of the overall system at the nozzle.

## 3. Results

_{H}= 100 WK

^{−1}m

^{−2}/α

_{C}= 64 WK

^{−1}m

^{−2}), the optimal leg length for maximised power output equals l

_{opt}= 21.2 mm at F = 25% (Figure 6). Each thermocouple contributes 12.18 mW to the total power output of the TEM working at a temperature difference of 169 K across the TE legs. When considering the resulting heat flux, the efficiency equals η = 8.2%, which is a result of the optimized HPVM with its fitted temperature characteristic of transport properties with regard to the application temperature range. With the assumptions made on geometries and chosen material properties, the uni-couple exhibits the following operational characteristics at the nozzle (Figure 6). Resulting values of the mass, power output, and the power density of the TE module and the entire TEG are summarized in Table 4.

_{H}from 100 WK

^{−1}m

^{−2}to 500 WK

^{−1}m

^{−2}at the hot side yields a reduction of the optimal leg length for thermal resistance match, and in turn leads to an increase of the incident heat flux (Figure 7a). The lower mass translates into a higher gravimetric power density, which is likewise achievable by an assumed increase of the PF (Figure 7b).

_{G}of the TEG, the amount of SFC saving scales with the total electrical power output being delivered from thermoelectric recuperation. Due to the limited installation space, the power output is linked to the areal power density P

_{A}of the TEG (Figure 9).

## 4. Discussion

_{H}> 350 WK

^{−1}m

^{−2}is required to fulfil the “APD + CFD”-limit of 100 Wkg

^{−1}. The requirement of the “APD”-limit (173 Wkg

^{−1}) and the limit for a range invariant TEG installation (520 Wkg

^{−1}) are not achievable at all (Figure 7b). Neither, increasing the PF of the HPVM by 30% at α

_{H}= 100 WK

^{−1}m

^{−2}does fulfil the criteria for a beneficial TEG installation. Generally, the increase of α

_{H}reduces the thermal resistance within the heat transmission path, allowing for a reduced leg length and mass saving for the configuration. Varying α

_{H}from 100 WK

^{−1}m

^{−2}to 500 WK

^{−1}m

^{−2}yields a reduction of the optimal leg length by 30%, which translates into lowered thermocouple mass of 14.7%. Due to the matching of thermal resistances, the effective temperature difference at the TE legs remains almost constant, while the heat flux increases significantly for smaller leg lengths. This leads to an increase of gravimetric power density. Due to an unchanged α

_{C}, the mean temperature rises along the thermocouple with increasing α

_{H}. Since the material properties of the HPVM are fixed with regard to their initially set temperature characteristics, a higher mean temperature yields a continuously increasing bipolar contribution due to the approach to the intrinsic temperature domain of the supposed TE properties. In connection with non-vanishing temperature drops at the boundary, nozzle, and insulation layers, this results in a flattening of power density curves at higher α

_{H}, irrespective of the lower optimal leg lengths. Since the minimal gravimetric power requirement of the aircraft system of 100 Wkg

^{−1}is only satisfied at F = 25% by an improved convective heat exchange with a concurrent significant increase of materials performance, it is apparently not expedient to apply TE modules with higher filling factors for the application at the aircraft nozzle.

_{min}is limited for several reasons. First, the spreading resistance of components for heat conduction within the heat transmission path can lower the effective temperature difference at the TE materials, since heat has increasingly to be provided laterally through substrates or insulation layers to the thermocouple legs at low F. For instance, the United States National Aeronautics and Space Administration (NASA) demonstrated the feasibility of F = 3.4% within their GPHS-RTG [42] and even lower values for F

_{min}= 1% have been suggested as a practical limit, once materials with high thermal conductivity are used to connect the thermocouples to external heat exchangers [43].

_{min}is limited due to the reduction of necessitated leg lengths for matching of thermal resistances. A decreasing leg length puts higher requirements on the electrical contact resistance between bridges and the TE legs in order to maintain a high power output of the TEM at low F. At typical values for the electrical conductivity of TE materials (~10

^{3}Scm

^{−1}), contact resistances between 10

^{−6}–10

^{−5}Ωcm

^{2}allow for a reduction of the leg length down to 0.1 mm, which was already successfully demonstrated in commercial TE devices for cooling [44] and generator applications [45].

_{H}= 100 WK

^{−1}m

^{−2}, α

_{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 α

_{H}= 200 WK

^{−1}m

^{−2}the power density requirements are fulfilled for slightly higher F. P

_{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 α

_{H}.

_{A}of the thermocouple. At α

_{H}= 100 WK

^{−1}m

^{−2}and α

_{C}= 64 WK

^{−1}m

^{−2}, P

_{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 α

_{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. As a consequence, the heat flux density decreases for a particular set of HTC by approximately 10% when F is reduced from 25% to 3% (Figure A4).

_{H}= 100 WK

^{−1}m

^{−2}, α

_{H}= 64 WK

^{−1}m

^{−2}) and the set total surface (A

_{noz}= 1.1 m

^{2}), which is offered for TEG occupation, a total power output between 1.65 kW and 1.85 kW can be expected from the thermoelectric recuperation at the nozzle for F = 3% and F = 21%, respectively. This corresponds to 3.6% to 4.1% of the average electrical power output of the shaft-driven electric generator within each engine of the reference aircraft.

^{−1}. A possibility to improve the SFC saving is given by an increase of the installation space, which is calculated for an additional higher value of A

_{noz}= 1.5 m

^{2}. Increasing simultaneously the performance of the convective heat transfer to α

_{H}= 200 WK

^{−1}m

^{−2}the corresponding areal power density offered by the TEG could allow for a SFC improvement of 0.11% at F = 23.8%. Again, slightly lower SFC reduction of 0.096% is achieved at F = 6.3% for a range invariant installation of the TEG at the geometrically extended nozzle. A further but not yet investigated means to increase the power density is given by exchanging the TiAl by electrically insulating SiC. Due to higher thermal conductivity and simultaneously lower density, SiC could decrease the mass and the spreading resistance of the nozzle, while making the use of the AlN layer unnecessary, which would allow for an additional reduction of mass.

_{H}= 700 K and Tc = 300 K [47], which might be relevant for a progressive approach of a high performant heat transport system at the nozzle with the use of heat pipes. When considering the total TE system costs (including manufacturing, heat exchanger, and material costs for thermoelectrics and ceramics) values < 20 $/W are offered by a certain number of today’s TE materials at the temperature range between T

_{H}= 523 K and T

_{C}= 293 K [48]. This opens a realistic window for an economically efficient installation of TEG in the future, especially under consideration of further optimization potential concerning particular assumptions that were made within this simulation study.

## 5. Conclusions

_{H}= 100 WK

^{−1}m

^{−2}) and the bypass (α

_{C}= 64 WK

^{−1}m

^{−2}) air flow, respectively, the performance of different thermocouple designs is simulated on the basis of a virtual material with a ZT

_{mean}= 1.1. Focus is placed on the identification of the appropriate filling factor F and TE element length in order to maintain a positive impact on the specific fuel consumption (SFC) of a reference aircraft [22]. The maximal gravimetric and areal power density of the TEG is simulated for 3% < F < 25%, with a concurrent determination of the optimal leg lengths for the matching of thermal resistances.

^{−1}) for TEG implementation with a positive impact on the SFC but with the drawback of a reduced flight range of the aircraft is attainable for F < 21%. The low HTC (α

_{H}= 100 WK

^{−1}m

^{−2}, α

_{C}= 64 WK

^{−1}m

^{−2}) of the convection heat exchange at the flat nozzle surface turned out to be the bottleneck for the maximization of the TEG performance. Consequently, the requirement for a range-invariant installation (520 Wkg

^{−1}) only becomes attainable for F < 5.5%.

_{noz}= 1.1 m

^{2}of occupation surface at the nozzle a power output between 1.65 kW and 1.85 kW is expectable from the TEG per engine within the design domain with a positive SFC impact. Under reasonable assumptions of an increased occupation surface (A

_{noz}= 1.5 m

^{2}) and improved heat exchange by convection (α

_{H}= 200 WK

^{−1}m

^{−2}, α

_{C}= 64 WK

^{−1}m

^{−2}), the power output of the TEG increases to 2.72 kW to 3.07 kW within the design range (F < 23.8%), which shows sufficiently high gravimetric power density in order to maintain a positive SFC impact.

_{mean}with regard to the application temperature range, in order to maximize the absolute power output and SFC saving. However, the thermoelectric recuperation of waste heat of aviation jet engines provides beneficial effects to the aircraft system, due to a lowered mechanical power by the engine generator and the acceleration of the bypass flow. Consequently, robust and performant TEGs could contribute to improve the fuel consumption of future aircrafts, which makes them a favorable choice, particularly with regard to other unexplored installation locations or additional positive side-effects on the system level (e.g., de-icing of engine components).

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Material properties for the FEM simulation: Thermal conductivity (

**a**), electrical conductivity (

**b**) and Seebeck coefficient (

**c**) of p-type (left) and n-type (right) thermoelectric legs. The dashed lines represent fits of measured properties on Skutterudite samples. Curves shown by light solid lines show the temperature courses after the shift of transport properties into the temperature range of the nozzle application has been applied. Bold solid lines show the property characteristics for the virtual material, which has been considered for the simulation. The broken dashed lines show the temperature mean values of the bold solid lines.

**Figure A2.**Gravimetric power density P

_{G}of TEG design with a filling factor F = 25% in dependence of the convective hot side heat transfer coefficient (HTC) α

_{H}for different cold side HTC α

_{C}: 100 WK

^{−1}m

^{−2}(

**a**), 125 WK

^{−1}m

^{−2}(

**b**), 150 WK

^{−1}m

^{−2}(

**c**), 175 WK

^{−1}m

^{−2}(

**d**). The curves are shown for application of the high performance virtual material (HPVM) and for an increased power factor PF of the HPVM by three steps of 10%.

**Figure A3.**Thermocouple mass m

_{TC}at the respective optimal leg length as a function of the hot side heat transfer coefficient α

_{H}for different filling factors F of the thermocouple.

**Figure A4.**Incident heat flow Q

_{TC}(

**a**) and hot side heat flux density (

**b**) Q

_{A}at the respective optimal leg lengths as a function of the hot side heat transfer coefficient α

_{H}for different filling factors F of the thermocouple.

**Table A1.**Relation between operation parameters obtained for a uni-couple configuration and corresponding values for a TE module (TEM) and a TEG. N denotes the number of uni-couples in a series connection within a TEM, whereas M denotes the number of TEM in a series connection within a TEG.

Property | Single Leg | Uni-Couple | TE-Module | TEG |
---|---|---|---|---|

Seebeck coefficient | S_{n}, S_{p} | S = S_{p} + |S_{n}| | N∙S | N∙M∙S |

Electric Resistance | R_{n}, R_{p} | R = R_{p} + R_{n} | N∙R | N∙M∙R |

Thermal Conductance | K_{n}, K_{p} | K = K_{p} + K_{n} | N∙K | N∙M∙K |

Voltage | V_{n}, V_{p} | V = V_{p} + V_{n} | N∙V | N∙M∙V |

Electric Current | I_{n}, I_{p} | I_{np} | I_{np} | I_{np} |

Electrical Power | P_{n}, P_{p} | P = P_{p} + P_{n} | N∙P | N∙M∙P |

Heat Flow | Q_{n}, Q_{p} | Q = Q_{p} + Q_{n} | N∙Q | N∙M∙Q |

Efficiency | η_{n}, η_{p} | η_{pn} = P/Q | η_{pn} | η_{pn} |

**Table A2.**Validation of the FEM-based simulation by comparison to analytical results obtained from a constant property model. The validation was accomplished without consideration of convective heat transfer coefficients.

Property | CPM | ANSYS | Deviation |
---|---|---|---|

Electrical resistance R [mΩ] | 182.389 | 185.386 | 1.64% |

Thermal conductance [10^{−3} W/K] | 0.835 | 0.83 | 0.59% |

Effective Seebeck coefficient [µV/K] | 401.1 | 402.325 | 0.30% |

Optimum current η_{max} [A] | 0.39 | 0.385 | 1.28% |

Optimum current P_{max} [A] | 0.439 | 0.434 | 1.13% |

Maximum power P_{max} [10^{−3} W] | 35.283 | 34.925 | 1.01% |

Incident heat flow Q_{in} [10^{−3} W] | 442.142 | 438.756 | 0.76% |

Maximum efficiency η_{max} [%] | 7.98 | 7.96 | 0.25% |

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**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.

**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**).

**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 4.**Qualitative heat flow distribution on the hot side of the thermocouple for an exemplary set of boundary conditions and geometrical thermocouple design (

**a**), areal interpolation of discrete node data on the normal component of the heat flux vector (

**b**), and continuous area function of the heat flux on the hot side (

**c**).

**Figure 5.**Example for an occupation of the nozzle surface by TE modules (TEM) (Courtesy of Fabian Ahrendts, TU Braunschweig). The shown design implies the application of vertical bars for improved heat exchange at the bypass flow, which is not considered in the simulation. Inset: Overall vision of TEM alignment on an aviation nozzle.

**Figure 6.**Simulation results of a thermocouple with F = 25% and for convective heat transfer coefficients of α

_{H}= 100 WK

^{−1}m

^{−2}/α

_{C}= 64 WK

^{−1}m

^{−2}. 3rd order polynomial fits of power output (

**a**), temperature difference (

**b**), efficiency (

**c**), and hot side heat flux (

**d**) as functions of the leg length. Red lines indicate the leg length for maximum power output.

**Figure 7.**Optimal leg length and heat flux (

**a**), gravimetric power density (

**b**) as a function of the hot side heat transfer coefficient (HTC) α

_{H}. The gravimetric power density is shown for the HPVM and for an increased power factor PF of the HPVM by three steps of 10%, each.

**Figure 8.**Optimal leg length l

_{opt}(

**a**) and gravimetric power density PG (

**b**) as a function of the hot side heat transfer coefficient α

_{H}for different filling factors F of the thermocouple.

**Figure 9.**Areal power density P

_{A}as a function of the filling factor F for different HTC α

_{H}(

**a**). Converted data of P

_{A}in dependence on α

_{H}for different F (

**b**).

**Figure 10.**Gravimetric power density P

_{G}of a HPVM-based TEM as a function of the filling factor F for different HTC α

_{H}. P

_{G}is displayed together with the required levels from the aircraft model.

**Figure 11.**Specific fuel consumption (SFC) improvement as a function of electrical power output of the TEG at the aircraft nozzle. The SFC is calculated on the base of data from [28]. Contributions from the bypass acceleration (CFD) and the reduced mechanical power of the generator (APD) add to the total SFC reduction. Ranges of SFC improvement are highlighted for two different occupation surfaces at the nozzle with varied HTC α

_{H}. The corresponding values of the electrical power output are calculated according to the respective areal power densities for the permitted ranges of F, which fulfil the minimum gravimetric power density requirement.

**Table 1.**Material, geometry G, volume V, density ρ, and mass m as properties of different components of the thermoelectric uni-couple configuration. The values are representative for a thermocouple design with a filling factor of F = 25% and an adjusted length of thermoelectric legs of 21.2 mm for matching of thermal resistance.

Part | Material | G [mm] | V [mm³] | ρ [gcm^{−3}] | m [mg] |
---|---|---|---|---|---|

Insulation | AlN | 2 × 4 × 0.325 | 2 × 2.6 = 5.2 | 3.2 [36] | 16.6 |

TE | Mg_{2}Si | 1 × 1 × 21.2 | 2 × 21.2 = 42.4 | 2.3 | 97.52 |

Bridge | Cu | 1 × 3 × 0.2 | 2 × 0.6 = 1.2 | 8.92 [39] | 10.7 |

Nozzle | TiAl | 2 × 4 × 2 | 16 | 3.9 [34] | 62.4 |

**Table 2.**Simulation cases with their considered parameter ranges for different model properties: Hot and cold side heat transfer coefficient α

_{H}and α

_{C}, filling factor F, leg length l

_{TE}and ΔPF as the change of the power factor as compared to the baseline material properties of the high performance virtual material (HPVM). ΔPF = 0 indicates the use of the HPVM, as defined in Figure 1 and Figure A1 in the supporting information, respectively.

Case | α_{H} [WK^{−1}m^{−2}] | α_{C} [WK^{−1}m^{−2}] | F [%] | l_{TE} [mm] | ΔPF [%] |
---|---|---|---|---|---|

1 | 100–500 | 64 | 25 | 1–25 | 0 |

2 | 100–500 | 64 | 25 | 1–25 | +10/20/30 |

3 | 100–500 | 64 | 3–25 | 1–25 | 0 |

**Table 3.**Number of thermocouples, area per thermocouple A

_{TC}, and active area covered by thermoelectric legs within a 50 × 50 mm

^{2}thermoelectric module A

_{TE}, each classified according the filling factor F.

Property | F = 25% | F = 12.5% | F = 6.25% | F = 3.125% |
---|---|---|---|---|

TC Number [–] | 312 | 156 | 78 | 39 |

A_{TC} [mm^{2}] | 8 | 16 | 32 | 64 |

A_{TE} [mm^{2}] | 624 | 312 | 156 | 78 |

**Table 4.**Mass m, maximum power output P

_{max}, gravimetric power density P

_{G}, and power densities per area for a HPVM-based TEM with F = 25% at α

_{H}= 100 WK

^{−1}m

^{−2}and α

_{C}= 64 WK

^{−1}m

^{−2}. P

_{A_TEM}relates the areal power output to the total footprint of the TEM, while P

_{A_TE}is the ratio between power output and the active surface of the TEM occupied by TE legs only. Values for mass and power output are scaled up for the entire thermoelectric generators (TEG) at the nozzle, which consists of 442 TEM.

F = 25% | m [g] | P_{max} [W] | P_{G} [Wkg^{−1}] | P_{A_TEM} [Wcm^{−2}] | P_{A_TE} [Wcm^{−2}] |
---|---|---|---|---|---|

TEM | 58.4 | 3.8 | 65.06 | 0.152 | 0.61 |

TEG | 25812.8 | 1679.67 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Ziolkowski, P.; Zabrocki, K.; Müller, E. TEG Design for Waste Heat Recovery at an Aviation Jet Engine Nozzle. *Appl. Sci.* **2018**, *8*, 2637.
https://doi.org/10.3390/app8122637

**AMA Style**

Ziolkowski P, Zabrocki K, Müller E. TEG Design for Waste Heat Recovery at an Aviation Jet Engine Nozzle. *Applied Sciences*. 2018; 8(12):2637.
https://doi.org/10.3390/app8122637

**Chicago/Turabian Style**

Ziolkowski, Pawel, Knud Zabrocki, and Eckhard Müller. 2018. "TEG Design for Waste Heat Recovery at an Aviation Jet Engine Nozzle" *Applied Sciences* 8, no. 12: 2637.
https://doi.org/10.3390/app8122637