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

applied sciences

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

Pawel Ziolkowski 1,* , Knud Zabrocki 1 and Eckhard Müller 1,2 1 German Aerospace Center—Institute of Materials Research, Linder Höhe, D-51147 Köln, Germany; [email protected] (K.Z.); [email protected] (E.M.) 2 Institute of Inorganic and Analytical Chemistry, Justus Liebig University Gießen, Heinrich-Buff-Ring 17, D-35392 Gießen, Germany * Correspondence: [email protected]; Tel.: +49-2203-601-3576

Received: 1 November 2018; Accepted: 13 December 2018; Published: 16 December 2018

Abstract: Finite element model (FEM)-based simulations are conducted for the application of a thermoelectric generator (TEG) between the hot core stream and the cool bypass flow at the nozzle of an aviation turbofan engine. This work reports the resulting requirements on the TEG design with respect to applied thermoelectric (TE) element lengths and filling factors (F) of the TE modules in order to achieve a positive effect on the specific fuel consumption. Assuming a virtual optimized TE material and varying the convective heat transfer coefficients (HTC) between the nozzle surfaces and the gas flows, this work reports the achievable power output. System-level requirement on the gravimetric power density (>100 Wkg−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.

Keywords: thermoelectric generator; energy conversion; energy harvesting; aviation; jet engine; speciﬁc fuel consumption; module design; ﬁlling factor; FEM; simulation

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 σ and κ, respectively (ZT = S2·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 [4–6] 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 [9–11], 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 the

Appl. Sci. 2018, 8, 2637; doi:10.3390/app8122637 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 2637 2 of 21 thermal 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 [18–20]. 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~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 −1 −1 (κeff = 400 Wm K ) and conservative TEG material efficiency (ZTmean = 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. 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 [26–28]. 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-driven Appl. Sci. 2018, 8, 2637 3 of 21

electric generator within the engine (1 kg/kWTEG). 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]. 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). Although the implementation of a TEG with the specified power density will improve fuel efficiency, it will reduce the maximum range of the aircraft due to the limitation on the maximum take-off weight (MTOW) of the aircraft. In order to reach a range invariant implementation of TEG, an increased electrical power density > 520 Wkg−1 (“APD range-invariant” limit) is required according to the aircraft model. Thermal boundary conditions from the CFD model have been transferred to a finite element model (FEM) of a thermoelectric uni-couple in this work. Operational characteristics of this uni-couple have been extrapolated to a full coverage of the nozzle surface with the specified geometry from GasTurb. Parametric studies on the TEG design have been conducted in order to verify the feasibility to satisfy the gravimetric power density requirements and to specify the requirements on TEG design and its resulting performance. The gravimetric power density is optimized by variation of the TE element lengths and the filling factor, which is a known concept for the matching of thermal resistance of a TEG module [30–33]. The filling factor is the ratio between the active surface of a TE module that is covered by the TE materials by the total surface of the module, which acts as the thermal coupling face to the heat source and sink, respectively.

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 µm. Depending on the length of thermoelectric legs, this resulted in a minimum element count of 813·103 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. 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 (Figure1). More details on the Appl. Sci. 2018, 8, 2637 4 of 21 individual TE transport properties can be found in the supporting information within the appendix of this publication (Figure A1). Appl. Sci. 2018, 8, x FOR PEER REVIEW 4 of 20

FigureFigure 1. FigureFigure of of merit meritZT ZTof aof virtual a virtual p-type p- (typea) and (a n-type) and ( nb-)type thermoelectric (b) thermoelectric material for material simulation. for simulation.The dashed The lines dashed represent lines ﬁts represent of measured fits of properties measured on properties Skutterudite on samples. Skutterudite Curves samples. shown Curves by light shownsolid lines by light show solid the temperature lines show curvethe temperature of ZT after thecurve shift of ofZT transport after the properties shift of transport into the temperature properties intorange the of temperature the nozzle application range of theis applied. nozzle Bold application solid lines is applied. show the BoldZT characteristic solid lines show of the the virtual ZT characteristicmaterial, which of the is considered virtual material, for the which simulation. is considered for the simulation.

First,First, the temperature temperature curves curves of ofthe the thermal thermal conductivity, conductivity, the Seebeck the Seebeck coefficient, coefficient, and the andelectrical the electricalconductivity conductivity of the Skutterudite of the Skutterudite materials materials are shifted are shiftedinto the into temperature the temperature range of range the ofnozzle the nozzleapplication application in order in to order represent to represent an optimized an optimized material. Asmaterial. an effect As of an the effect lower of mean the lower temperature mean temperaturethe resulting theZT resulvaluesting decrease. ZT values To decrease. consider To a reasonable consider a technologyreasonable leveltechnology of a future level TEof a material future TEduring material simulation, during simulation, the power the factor power (PF factor= S2· σ(PF) of = theS2∙σ p-) of and the n-typep- and n material-type material is increased is increased by an byimprovement an improvement of the of Seebeck the Seebeck coefficient coefficient and the and electrical the electrical conductivity conductivi by 40%ty forby 40%each for property, each property,whereas thewhereas thermal the conductivity thermal conductivity was kept was constant. kept constant. With that, With the HPVMthat, the with HPVM peak withZT valuespeak ZT of values1.2 (p-type) of 1.2 and(p-type) 1.5 (n-type) and 1.5 are (n- usedtype) asare input used for as theinput simulation. for the simulation. This corresponds This corresponds to ZTmean to= 1.14ZTmean for =the 1.14 uni-couple. for the uni-couple. TheThe operat operationalional characteristics characteristics of the TEG areare simulatedsimulated forfor aauni-couple uni-couple configuration configuration (Figure (Figure2) 2)under under consideration consideration of of all all relevant relevant effects, effects, likelike JouleJoule heatingheating and the Peltier, Peltier, Seebeck, Seebeck, and and Thomson Thomson effects.effects. The The nozzle nozzle of of the the aircraft aircraft is is modelled modelled by by a alayer layer on on one one outer outer side side of of the the 3D 3D configuration. configuration. DueDue to to weight weight minimization, minimization, the the nozzle nozzle is is supposed supposed to to be be made made from from TiAl TiAl with with a a temperature temperature dependentdependent thermal thermal conductivity conductivity between between 20 20–30–30 Wm Wm−1−K1−1K [34].−1 [34 The]. The thickness thickness of the of theTiAl TiAl is chosen is chosen to beto 2be mm 2 mm in inaccordance accordance to to the the original original design design of of the the nozzle nozzle body. body. Flat Flat surfaces surfaces are are assumed assumed for for externalexternal heat heat exchange exchange with with the the air air flows. flows. Due Due to to the the major major sensitivity sensitivity of of the the propulsive propulsive efficiency efficiency on on thethe flow flow condition condition at at the the cold cold bypass bypass boundary boundary layer layer [23], [23], the the modification modification of of the the hot hot nozzle nozzle surface surface onlyonly seems seems beneficial beneficial for for any any optimization optimization of ofthe the convective convective heat heat transport. transport. In order In order to minimize to minimize the temperaturethe temperature drop drop at the at the cold cold bypass bypass side, side, a direct a direct incident incident flow flow on on the the insulation insulation layer layer of of the the thermocouplethermocouple is is assumed assumed here. here. Thus, Thus, the the noz nozzlezle layer layer was was modelled modelled for the for hot the core hot corestream stream only. only.For reductionFor reduction of parasitic of parasitic temperature temperature drops drops a layer a layer of AlN of AlN with with a high a high thermal thermal conductivity conductivity of 170 of Wm170−1 WmK−1 −[35]1K −is1 introduced[35] is introduced to form toan form electrical an electrical insulation insulation between between the TE uni the-couple TE uni-couple and the metallic and the nozzle.metallic When nozzle. considering When considering the dielectric the strength dielectric of strengthAlN of 20 of kVmm AlN of−1 20[36], kVmm a minimum−1 [36], thickness a minimum of 325thickness µm is ofset 325 forµ thism is layer set for on this both layer sides on with both sidesregard with to weight regard tooptimization weight optimization and concurrent and concurrent electric insulationelectric insulation effect in effect the presence in the presence of high of DChigh voltages DC voltages generated generated by the by the entire entire TEG TEG at at the the nozzle. nozzle. MetallicMetallic Cu Cu bridges bridges with with a a thickness thickness of of 200 200 µmµm form form the the electrical electrical interconnects interconnects between between the the TE TE elements.elements. Square Square-shaped-shaped cross cross section section with with a foot a foot print print of 1 of × 11 ×mm1 mm2 for2 eachfor eachTE leg TE are leg assumed. are assumed. The spacingThe spacing between between the legs the is legs set to is set1 mm. to 1 The mm. filling The factor filling is factor varied is by varied the modification by the modification of the nozzle of the andnozzle insulation and insulation layer surface layer per surface TE thermocouple per TE thermocouple that exchanges that exchangesheat with the heat air withflows. the The air length flows. ofThe the length legs ofis theadjusted legs is to adjusted obtain to a match obtain aof match the thermal of the thermal resistance resistance of the of TE the thermocouple TE thermocouple to the to outsidethe outside resistances resistances within within the theheat heat transfer transfer path. path. An An aerogel aerogel filling filling in inthe the gaps gaps between between the the legs legs is is assumedassumed as as thermal thermal insulation insulation material material with with a a reasonable reasonable assumption assumption for for its its thermal thermal conductivity conductivity of of 0.030.03 Wm Wm−1−K1K−1 −[37,38],1 [37,38 in], inorder order to to minimize minimize parasitic parasitic heat heat bypass. bypass. Neither Neither radiative radiative nor nor convective convective heatheat transport transport within within the the aerogel aerogel-filling-filling was was considered. considered. Appl. Sci. 2018, 8, 2637 5 of 21 Appl. Sci. 2018,, 8,, xx FORFOR PEERPEER REVIEWREVIEW 5 of 20

FigureFigure 2.2. SchemeScheme ofof thethe thermoelectricthermoelectric uni-coupleuni--couple conﬁgurationconfiguration composedcomposed ofof electricalelectrical insulationinsulation layerslayerslayers (IS),(IS),(IS), metallicmetallicmetallic bridgesbbridgesridges (MB),(MB),(MB), thethethe p-pp-- andand n-typen--typetype thermoelectricthermoelectricthermoelectric (TE)(TE)(TE) materialmaterialmaterial legs,legs,legs, andandand thethethe TiAlTiAlTiAl nozzlenozzle ((aa).).). SchematicSchematicSchematic ofofof thethe installationinstallation atat thethe aircraftaircraft nozzlenozzle andand illustrativeillustrative temperaturetemperature distributiondistributiondistribution alongalong thethe heatheat transmissiontransmission pathpath forfor FF = = 25% ((bb).).).

According to the CFD simulation, the gas temperatures of the core and the bypass flow are According to the CFD simulation, the gas temperatures of the core and the bypass flow are Thghg T = 623 K and T = 238 K, respectively, during cruise conditions. The simulations revealed =hg 623 K and Tcgcg = 238cg K, respectively, during cruise conditions. The simulations revealed considerably considerablylowlow heatheat transfertransfer low heat coefficientscoefficients transfer coefficients(HTC)(HTC) ofof thethe (HTC) convectiveconvective of the convective heatheat exchangeexchange heat exchangebetweenbetween the betweenthe airair flowsflows the air andand flows thethe andnozzle the and nozzle insulation and insulation surfaces surfaces (Figure (Figure3), respectively.3), respectively. Convective Convective heat transfer heat transfer is considered is considered at the atparticular the particular surfaces surfaces by the by appropriate the appropriate settings settings of theof the calculated calculated HTC HTC and and the the respective gas gas temperaturestemperaturestemperatures fromfromfrom CFD CFDCFD simulations simulationssimulations (derived (derived(derived from fromfrom [ [25])25[25])]) within withinwithin the thethe thermocouple thermocouplethermocouple model. model.model.

FigureFigure 3.3. TemperatureTemperature dependentdependent convectiveconvective heatheat transfertransfer coefficientscoefficients atat thethe hothot corecore streamstream ((aa))) andandand thethethe coolcoolcool bypass bypassbypass flow flowflow ( (b(b).).). The TheThe depicted depicteddepicted design designdesign points pointspoints indicate indicateindicate values valuesvalues for forfor a aa thermoelectric thermoelectricthermoelectric module modulemodule with withwith a fillinga filling factor factor of ofF F= = 25% 25% and and an an adjusted adjusted length length of of the the thermoelectric thermoelectric legs legs of of 21.2 21.2mm mm forfor thethe matchingmatching ofof thermalthermal resistance.resistance.

ForFor the determination determination of of the the electrical electrical power power output output one one terminal terminal is kept is keptat 0V atpotential, 0V potential, while whilean electrical an electrical DC current, DC current, II,, throughthroughI, through thethe couplecouple the isis couple variedvaried is fromfrom varied zerozero from upup toto zero thethe short upshort to circuitcircuit the short value.value. circuit TheThe value.according The terminal according vol terminaltage,tage, V,, isis voltage, usedused forforV ,thethe is used calculationcalculation for the ofof calculation thethe outputoutput of power,power, the output Pelel = V power,∙∙I.I. The Presultingel = V·I. Thecurve resulting of Pelel((II)) curve isis wellwell of approximatedapproximatedPel(I) is well approximated byby aa parabolicparabolic by fit,fit, a parabolic thethe maximummaximum fit, the ofof maximum whichwhich givesgives of which thethe maximummaximum gives the maximumelectrical power electrical output. power No contact output. resistances No contact have resistances been considered have been within considered the model. within The the efficiency model. Theof the efficiency uni--couple of the is calculated uni-couple from is calculated the ratio from of maximum the ratio ofpower maximum output power by the output incident by theheat incident flow at heatthethe givengiven flow atoperationoperation the given pointpoint operation ofof thethe pointelectricalelectrical of the current.current. electrical current. TheThe heat heat flow flow on on the thehot and hot cold and side cold of side the uni-couple of the uni configuration--couple configuration reveals a spatial reveals distribution a spatial duedistribution to different due thermal to different conductivities thermal conductivities of the p- and n-typeof the p material-- and n--type andtypethe materialmaterial heat spread andand thethe in heatheat the contact spreadspread bridgesinin thethe contactcontact and the bridgesbridges heat exchanger andand thethe heatheat plates exchangerexchanger (Figure platesplates4). Discrete (Figure(Figure data 4).4). DiscreteDiscrete on the heat datadata flux onon (normalthethe heatheat fluxflux component (normal(normal component of the heat flux vector) is takentaken atat everyevery nodenode ofof thethe surfacesurface forfor arealareal interpolationinterpolation andand Appl. Sci. 2018, 8, 2637 6 of 21

Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 20 of the heat flux vector) is taken at every node of the surface for areal interpolation and subsequent subsequentapproximation approximation by a continuous by areaa continuous function. Thearea incident function. heat The flow incident is finally heat determined flow is finallyby the determinedintegration ofby this the functionintegration over of thethis entire function top surfaceover the of entire the hot top side. surface of the hot side.

Figure 4. Qualitative heat flowflow distributiondistribution onon the the hot hot side side of of the the thermocouple thermocouple for for an an exemplary exemplary set set of ofboundary boundary conditions conditions and and geometrical geometrical thermocouple thermocouple design design ( a(a),), areal arealinterpolation interpolation ofof discretediscrete node data on thethe normalnormal componentcomponent of of the the heat heat flux flux vector vector (b ),(b and), and continuous continuous area area function function of the of heatthe heat flux fluxon the onhot the sidehot side (c). (c).

With regard to the system level requirements on the gravimetric power density, further assumptions on the mass density of the different components are made (Table 1 1).). WhenWhen consideringconsidering lightlight-weight-weight silicide TE materials and contributions from the other components of the simulated configuration,conﬁguration, the mass of the thermocouple is calculated, which equals, for instance, 187 mg for the design case with F = 25% 25% at at its its optimal optimal TE TE leg leg length length of of 21.2 21.2 mm (T (Tableable1 1).). AdditionalAdditional weightweight wouldwould be introduced by mounting hardware, cabling, power processing units, and possibly batteries, which was not considered in this study.

Table 1. Material, geometry G, volume V,, density density ρ, and mass mm asas properties properties of of different different components components of the the thermoelectric thermoelectric uni-couple uni-couple conﬁguration. configuration. The The values values are representative are representative for a thermocouple for a thermocouple design withdesign a ﬁllingwith a factor filling of factorF = 25% of F and = 25% an adjusted and an adjusted length of length thermoelectric of thermoelectric legs of 21.2 legs mm of for21.2 matching mm for matchingof thermal of resistance. thermal resistance.

Part Material G [mm] V [mm3] ρ [gcmρ −3] m [mg] Part Material G [mm] V [mm³] m [mg] −3 Insulation AlN 2 × 4 × 0.325 2 × 2.6 = 5.2[gcm 3.2 [36] 16.6 TE Mg Si 1 × 12 ×× 421.2 × 2 × 21.2 = 42.4 2.3 97.52 Insulation 2 AlN 2 × 2.6 = 5.2 3.2 [36] 16.6 Bridge Cu 1 × 30.325× 0.2 2 × 0.6 = 1.2 8.92 [39] 10.7 Nozzle TiAl 2 × 4 × 2 16 3.9 [34] 62.4 TE Mg2Si 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 For everyNozzle studied parametricTiAl case,2 the× 4 × thermal 2 resistance16 of the3.9 thermocouple [34] 62.4 is matched with the sum of the effective heat resistances by convection plus the minor contributions of the TiAl and AlNFor layers every by variationstudied parametric of the TE legcase, length the thermal in the range resistance between of the 1 mm thermocouple and 25 mm. is Amatched matching with of thethermal sum resistancesof the effective is necessary heat resistances for the maximizationby convection ofplus electrical the minor power contributions output, since of the the TiAl product and AlNof the layers temperature by variation difference of the acrossTE leg thelength TE materialsin the range and bet incidentween 1 heatmm flowand 25 to themm. configuration A matching of is thermalmaximized resistances under these is necessary conditions for [the30]. maximization First, calculations of electrical are conducted power foroutput, a filling since factor the product of F = 25% of theusing temperature the HPVM difference(case 1 in Table across2). the The TE variation materials of the and power incident output heat with flow TE to material the configuration performance is maximizedis studied by under increasing these theconditions power factor[30]. First, of the calculations HPVM in three are conducted steps by 10%, for a each filling yielding factor aofZT F =max 25%of 1.56using and the 1.95 HPVM for the(case p- 1 and in Table n-type 2). material, The variation respectively, of the power at the output last step with (case TE 2). material This is performance clearly a free is studied by increasing the power factor of the HPVM in three steps by 10%, each yielding a ZTmax 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 Appl. Sci. 2018, 8, 2637 7 of 21 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]. In order to optimize the gravimetric power density apart from an increase of the materials performance, further simulations are carried out on the base of the HPVM but with smaller filling factors F (case 3), which yields a reduction of the thermal convective resistances on both sides of the thermocouple. Reduction of F is accomplished within the model by increasing the area of TiAl and AlN surfaces per uni-couple on both sides of the air flows. Additionally, the effect of a presumed improvement of the convective heat transfer on the hot side is studied by choosing a higher HTC αH as compared to the outcome of the CFD simulations within every simulated parameter configuration of the model. The increase of αH 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 −1 −2 on the cold side is set to αC = 64 WK m 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, Table2 gives a survey on the cases and their respective parameter ranges, which will be discussed later on.

Table 2. Simulation cases with their considered parameter ranges for different model properties: Hot

and cold side heat transfer coefficient αH and αC, filling factor F, leg length lTE and ∆PF as the change of the power factor as compared to the baseline material properties of the high performance virtual material (HPVM). ∆PF = 0 indicates the use of the HPVM, as defined in Figures1 and A1 in the supporting information, respectively.

−1 −2 −1 −2 Case αH [WK m ] αC [WK m ] F [%] lTE [mm] ∆PF [%] 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

For the determination of the TEG performance, the thermocouples are supposed to be connected to TE modules (TEM) with a footprint of 50 × 50 mm2. With the given cross section of 1 mm2 of 2 each TE leg the footprint of one thermocouple equals ATC = 8 mm (1 mm spacing between each leg), according to F = 25%. With this ﬁlling factor, 312 thermocouples can be connected within one TEM, 2 yielding a total area covered by the TE legs of ATE = 624 mm per TEM (Table3).

Table 3. Number of thermocouples, area per thermocouple ATC, and active area covered by 2 thermoelectric legs within a 50 × 50 mm thermoelectric module ATE, 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 2 ATC [mm ] 8 16 32 64 2 ATE [mm ] 624 312 156 78 Appl. Sci. 2018, 8, 2637 8 of 21 Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 20

TheThe coverage by by TEM TEM was was extrapolated extrapolated to to the the full full nozzle nozzle surface surface ( (FigureFigure 55)) byby aa linearlinear scalingscaling ofof extensive performance key key figures, figures, as calculated for the uni-coupleuni-couple configuration.configuration. The The relation betweenbetween operation operation parameters parameters of of a a single single leg, leg, a a uni uni-couple,-couple, TE TE module, module, and and TEG, TEG, respectively, respectively, is is ∼ 2 given in Table A1. According to the GasTurb engine design, a total surface Anoz = 1.1 m is available given in Table A1. According to the GasTurb engine design, a total surface Anoz ≅ 1.1 m2 is available × 2 forfor the the TEG TEG installation installation at at the the nozzle, nozzle, which which gives gives space space for for 442 442 TEM TEM of of 50 50 × 50 50mm mm2 perper engine. engine. A possibleA possible implementation implementation encompasses encompasses a TEM a TEM alignment alignment within within 13 13 rings rings around around the the nozzle nozzle body, body, eeachach with with 34 34 modules. modules. Simulations Simulations of the of thermal the thermal conditions conditions at the nozzle at the revealed nozzle arevealed radial symmetric a radial symmetrictemperature temperature distribution. distribution. However, However, a minor axial a minor temperature axial temperature variation variation along the along nozzle, the which nozzle, is whichconfirmed is confirmed to be <11 to K forbe <11 cruise K for conditions, cruise conditions, was not considered was not cons for theidered simulations for the simulations on the TEG on design the TEGand thedesign resulting and the power resulting of the power overall of system the overall at the system nozzle. at the nozzle.

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

3.3. Results Results DueDue to thethe thermalthermal resistanceresistance of of the the convective convective boundary boundary layers layers at theat the core core and and bypass bypass flow, flow, only onlya fraction a fraction of the of gas the temperature gas temperature difference difference can be usedcan be at theused TE at material, the TE material, which limits which the maximumlimits the maximumpower output power and output efficiency and of efficiency the thermocouples. of the thermocouples. In presence of In external presence thermal of external resistances thermal the resistancestemperature the difference temperatur ate the difference TE material at the is TE a function material ofis thea function leg length. of the For leg small length. leg For lengths, small leg the lengths,reduced thermal the reduced resistance thermal of the resistance TE leg yields of the a high TE incident leg yields heat a flow high but incident low temperature heat flowdifference but low temperatureacross the legs. difference Consequently, across the power legs. Consequently, output and the the efficiency power output also become and the low. eff Thoughiciency high also becomeleg lengths low. provide Though an increase high leg of lengths the temperature provide difference, an increase the of increasing the temperature thermal resistance difference, of the the increasingthermocouple thermal lowers resistance the incident of the heat thermocouple flow, which yields lowers a the reduction incident of heat the power flow, which output yields above a a reductioncertain leg of length, the power likewise. output Hence, above as explained a certain above, leg length maximum, likewise. output Hence, power as is explained achieved above, for an maximumoptimal intermediate output power leg lengthis achieved based for on an matching optimal leg intermediate and parasitic leg thermal length resistancesbased on matching [30]. leg −1 −2 −1 −2 and parasiticFor the setthermal HTC atresistances both boundary [30]. layers (αH = 100 WK m /αC = 64 WK m ), the optimal leg lengthFor the for set maximised HTC at both power boundary output equals layersl opt(αH= = 21.2 100 mm WK at−1mF −2=/α 25%C = (Figure64 WK6−1).m Each−2), the thermocouple optimal leg lengthcontributes for maximised 12.18 mW power to the totaloutput power equals output lopt = of21.2 the mm TEM at F working = 25% (Figure at a temperature 6). Each thermocouple difference of contributes169 K across 12.18 the TE mW legs. toWhen the total considering power output the resulting of the TEM heat flux,working the efficiency at a temperature equals η =difference 8.2%, which of 169is a K result across of thethe optimizedTE legs. When HPVM considering with its fitted the result temperatureing heat characteristic flux, the efficiency of transport equals properties η = 8.2%, whichwith regard is a result to the of application the optimized temperature HPVM range. with its With fitted the temperature assumptions characteristic made on geometries of transport and propertieschosen material with properties, regard to the the uni-coupleapplication exhibits temperature the following range. With operational the assumptions characteristics made at the on geometries and chosen material properties, the uni-couple exhibits the following operational Appl. Sci. 2018, 8, 2637 9 of 21 Appl. Sci. 2018, 8, x FOR PEER REVIEW 9 of 20 nozzlecharacteristics (Figure6 ).at Resultingthe nozzle values (Figure of the6). mass,Resulting power values output, of the and mass, the power power density output, of theand TE the module power anddensity the entireof the TEGTE module are summarized and the entire in Table TEG4. are summarized in Table 4.

FigureFigure 6. 6.Simulation Simulation results results of a of thermocouple a thermocouple with F with= 25% F and= 25% for convective and for convective heat transfer heat coefficients transfer of α = 100 WK−1m−2/α = 64 WK−1m−2. 3rd order polynomial fits of power output (a), temperature coefficientsH of αH = 100 C WK−1m−2/αC = 64 WK−1m−2. 3rd order polynomial fits of power output (a), differencetemperature (b), difference efficiency ( (bc),), andefficiency hot side (c), heat and flux hot (sided) as heat functions flux (d of) as the functions leg length. of the Red leg lines length. indicate Red thelines leg indicate length forthe maximumleg length powerfor maximum output. power output.

Table 4. Mass m, maximum power output Pmax, gravimetric power density PG, and power densities Table 4. Mass m, maximum power output Pmax, gravimetric −power1 −2 density PG, and −power1 −2 densities per area for a HPVM-based TEM with F = 25% at αH = 100 WK m and αC = 64 WK m . PA_TEM per area for a HPVM-based TEM with F = 25% at αH = 100 WK−1m−2 and αC = 64 WK−1m−2. PA_TEM relates relates the areal power output to the total footprint of the TEM, while PA_TE is the ratio between power outputthe areal and power the active output surface to the oftotal the footprint TEM occupied of the TEM, by TE while legs only. PA_TE Values is the ratio for mass between and powerpower outputoutput areand scaled the active up for surface the entire of the thermoelectric TEM occupied generators by TE legs (TEG) only. at Values the nozzle, for mass which and consists power of output 442 TEM. are scaled up for the entire thermoelectric generators (TEG) at the nozzle, which consists of 442 TEM. −1 −2 −2 F = 25% m [g] Pmax [W] PG [Wkg ] PA_TEM [Wcm ] PA_TE [Wcm ] PA_TEM PA_TE TEMF = 25% 58.4m [g] Pmax 3.8 [W] PG [Wkg−1] 65.06 0.152−2 −2 0.61 TEG 25812.8 1679.67 [Wcm ] [Wcm ] TEM 58.4 3.8 65.06 0.152 0.61 TEG 25812.8 −1679.671 −2 −1 −2 Increasing αH from 100 WK m to 500 WK m 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 Increasing αH from 100 WK−1m−2 to 500 WK−1m−2 at the hot side yields a reduction of the optimal ﬂux (Figure7a). The lower mass translates into a higher gravimetric power density, which is likewise leg length for thermal resistance match, and in turn leads to an increase of the incident heat flux achievable by an assumed increase of the PF (Figure7b). (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). Appl. Sci. 2018, 8, 2637 10 of 21 Appl.Appl. Sci.Sci. 20182018,, 88,, xx FORFOR PEERPEER REVIEWREVIEW 1010 ofof 2020

FigureFigure 7. 7. OptimalOptimal legleg lengthlength andand heatheat fluxflux ﬂux (( aa),), gravimetric gravimetric powerpower densitydensity (( bb)) asas a a function function ofof thethe hothot sideside heat heat transfertransfer coefﬁcientcoefficientcoefficient (HTC) (HTC)(HTC)α αHαHH... The TheThe gravimetric gravimetricgravimetric power powerpower density densitydensity is is shownis shownshown for forfor the thethe HPVM HPVMHPVM and andand for forforan increasedanan increasedincreased power powerpower factor factorfactorPF ofPFPFthe ofof thethe HPVM HPVMHPVM by threebyby threethree steps stepssteps of 10%, ofof 10%,10%, each. each.each.

IncreasingIncreasing the the the surface surface surface for for for the the the convective convective convective heat exchange heat heat exchange exchange per thermocouple per per thermocouple thermocouple on both sides on on both both effectively sides sides effectivelydecreaseseffectively the decreasesdecreases thermal thethe resistance thermalthermal of resres theistanceistance convective ofof thethe boundary convectiveconvective layers. boundaryboundary The lower layers.layers.F TheTheyields lowerlower the reductionFF yieldsyields thethe of reductionthereduction optimal ofof leg thethe length optimaloptimal for legleg the lengthlength matching forfor ofthethe thermal matchingmatching resistances ofof thermalthermal (Figure resistancesresistances8a), which (Figure(Figure allows 8a),8a), for whichwhich a signiﬁcant allowsallows formassfor aa significantsignificant reduction (Figuremassmass reductionreduction A3). (Figure(Figure A3).A3).

FigureFigure 8.8. OptimalOptimal legleg lengthlength lloptopt ((a(aa)) ) anan anddd gravimetricgravimetric gravimetric powerpower power densitydensity density PGPG (((bb))) asas as aa a functionfunction function ofof thethe the hothot sideside heatheat transfer transfer coefficient coefﬁcientcoefficient ααHH forforfor differentdifferent different fillingfilling ﬁlling factors factors FF ofof the the thermocouple. thermocouple.

TheThe incident incident heatheat perper thermocouplethermocouplethermocouple grows growsgrows as asas a aa consequence consequenceconsequence of ofof the thethe reduced reducedreduced thermal thermalthermal resistance resistanceresistance of oftheof the the convective convective convective boundary boundaryboundary layers layers layers and TE and and legs TE TE (Figure legs legs (Figure (FigureA4). The A4). A4). reduction The The reduction reduction of F increases of of FF the increasesincreases gravimetric the the gravimetricpowergravimetric density powerpower signiﬁcantly densitydensity significantlysignificantly (Figure8b). While ((FigureFigure the 8b8b minimum).). WhileWhile thethe requirement minimumminimum requirement forrequirement a positive forfor effect aa positivepositive on the effectSFCeffect is onon determined thethe SFCSFC isis determineddetermined by the resulting byby thethe gravimetric resultingresulting gravimetricgravimetric power density powerpowerP densityGdensityof the PP TEG,GG ofof thth theee TEG,TEG, amount thethe amountamount of SFC ofsavingof SFC SFC scales saving saving with scales scales the withtotal with electrical the the total total power electrical electrical output power power being output output delivered being being from delivered delivered thermoelectric from from thermoelectric thermoelectric recuperation. recuperation.Duerecuperation. to the limited DueDue installationtoto thethe limitedlimited space, installationinstallation the power space,space, output thethe is powerpower linked outputoutput to the areal isis linkedlinked power toto densitythethe arealarealPA powerpowerof the densityTEGdensity (Figure PPAA ofof9 the).the TEGTEG ((FigureFigure 99).). Appl. Sci. 2018, 8, 2637 11 of 21

Appl. Sci. 2018, 8, x FOR PEER REVIEW 11 of 20

FigureFigure 9. 9.Areal Areal power power density densityPA asPA a as function a function of the of ﬁlling the factorfilling F factorfor different F for different HTC αH ( HTCa). Converted αH (a). dataConverted of PA in data dependence of PA in dependence on αH for different on αH forF different(b). F (b).

4.4. Discussion Discussion −1 −2 F −1 −2 UsingUsing the the HPVM HPVM with with F == 25% 25% and and optimized optimized leg length, a a minimum minimum ααHH >> 350 350 WK WKm m is −1 isrequired required to to fulfil fulfil the the “APD “APD + +CFD” CFD”-limit-limit of of100 100 Wkg Wkg−1. The. requirement The requirement of the of “APD” the “APD”-limit-limit (173 −1 −1 (173Wkg Wkg−1) and) the and limit the for limit a range for ainvariant range invariant TEG installation TEG installation (520 Wkg−1 (520) are not Wkg achievable) are not at all achievable (Figure −1 −2 at7b). all Neither, (Figure7 increasingb). Neither, the increasingPF of the HPVM the PF byof 30% the at HPVM αH = 100 by WK 30%−1m at−2 doesαH = fulfil 100 the WK criteriam fordoes a fulfilbeneficial the criteria TEG installation. for a beneficial Generally, TEG installation. the increase Generally, of αH reduces the increase the thermal of α Hresistancereduces thewithin thermal the resistanceheat transmission within the path, heat transmissionallowing for path,a reduced allowing leg length for a reduced and mass leg lengthsaving andfor themass configuration. saving for the −1 −2 −1 −2 configuration.Varying αH from Varying 100 WKαH from−1m−2 100to 500 WK WKm−1m−2 toyields 500 WKa reductionm yields of the a optimal reduction leg of length the optimal by 30%, leg lengthwhich by translates 30%, which into translates lowered into thermocouple lowered thermocouple mass of 14.7%. mass Due of 14.7%. to the Due matching to the ofmatching thermal of thermalresistances, resistances, the effective the effective temperature temperature difference difference at the TE at legs the remains TE legs almost remains constant, almost constant,while the whileheat theflux heat increases flux increases significantly significantly for smaller for smallerleg lengths. leg lengths.This leads This to leadsan increase to an increaseof gravimetric of gravimetric power powerdensity. density. Due to Due an unchanged to an unchanged αC, the meanαC, the temperature mean temperature rises along rises the thermocouple along the thermocouple with increasing with increasingαH. Since theαH .material Since the properties material of propertiesthe HPVM ofare the fixed HPVM with regard are fixed to their with initially regard set to temperature their initially setcharacteristics, temperature characteristics,a higher mean temperature a higher mean yields temperature a continuously yields increasing a continuously bipolar increasingcontribution bipolar due contributionto the approach due toto thethe approachintrinsic temperature to the intrinsic domain temperature of the supposed domain ofTE the properties. supposed In TE connection properties. Inwith connection non-vanishing with non-vanishing temperature drops temperature at the boundary, drops at thenozzle, boundary, and insulation nozzle, layers, and insulation this results layers, in a flattening of power density curves at higher αH, irrespective of the lower optimal leg lengths. Since this results in a flattening of power density curves at higher αH, irrespective of the lower optimal leg lengths.the mini Sincemal gravimetric the minimal power gravimetric requirement power of requirement the aircraft ofsystem the aircraft of 100 systemWkg−1 is of only 100 Wkgsatisfied−1 is at only F satisfied= 25% by at Fan= improved 25% by an convective improved heat convective exchange heat with exchange a concurrent with a significant concurrent increase significant of materials increase of materialsperformance, performance, it is apparently it is apparently not expedient not expedient to apply toTE apply modules TE moduleswith higher with filling higher factors filling for factors the forapplication the application at the ataircraft the aircraft nozzle. nozzle. ThisThis might might take take into into accountaccount thatthat progressprogress towardstowards maximal ZT--values~2values~2 would would represent represent a a significant improvement for future TE materials with technological relevance and high stability from significant improvement for future TE materials with technological relevance and high stability from today’s point of view. Against this background and in conjunction with reasonable assumptions on today’s point of view. Against this background and in conjunction with reasonable assumptions on the the performance for the convective heat exchange at the nozzle, a beneficial TEG application is performance for the convective heat exchange at the nozzle, a beneficial TEG application is attainable attainable only for smaller filling factors. However, the minimum applicable filling factor Fmin is only for smaller filling factors. However, the minimum applicable filling factor F is limited for limited for several reasons. First, the spreading resistance of components for heat conductionmin within several reasons. First, the spreading resistance of components for heat conduction within the heat the heat transmission path can lower the effective temperature difference at the TE materials, since transmission path can lower the effective temperature difference at the TE materials, since heat has heat has increasingly to be provided laterally through substrates or insulation layers to the increasingly to be provided laterally through substrates or insulation layers to the thermocouple legs thermocouple legs at low F. For instance, the United States National Aeronautics and Space atAdministration low F. For instance, (NASA) the demonstrated United States the National feasibility Aeronautics of F = 3.4% and within Space their Administration GPHS-RTG [42] (NASA) and demonstrated the feasibility of F = 3.4% within their GPHS-RTG [42] and even lower values for even lower values for Fmin = 1% have been suggested as a practical limit, once materials with high Fminthermal= 1% conductivityhave been suggested are used to as connect a practical the limit,thermocouples once materials to external with highheat thermalexchangers conductivity [43]. are used toSecondly, connect theFmin thermocouplesis limited due to to the external reduction heat of exchangers necessitated [43 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 Appl. Sci. 2018, 8, 2637 12 of 21

Secondly, Fmin is limited due to the reduction of necessitated leg lengths for matching of thermal resistances.Appl. Sci. 2018, 8 A, x decreasingFOR PEER REVIEW leg length puts higher requirements on the electrical contact resistance12 of 20 between bridges and the TE legs in order to maintain a high power output of the TEM at low F. Attypical typical value valuess for the for electrical the electrical conductivity conductivity of TE materials of TE materials (~103 Scm (~10−1),3 contactScm−1 ),resistances contact resistances between between10−6–10−5 10Ωcm−6–102 allow−5 Ω forcm a2 reductionallow for of a reductionthe leg length of the down leg lengthto 0.1 mm, down which to 0.1 was mm, already which successfully was already successfullydemonstrated demonstrated in commercial in TE commercial devices for TE cooling devices [44] for and cooling generator [44] and applications generator [45]. applications [45]. Finally,Finally, thethe concurrentconcurrent reduction of F andand lower lower leg leg lengths lengths promote promote a aparallel parallel heat heat flow flow through through thethe gapsgaps ofof thethe thermocouplethermocouple configuration, configuration, which which can can lead lead potentially potentially to to a asignificant significant reduction reduction of of thethe efficiencyefficiency inin casecase ofof convectionconvection or heat transport transport by by radiation. radiation. For For open open or or evacuated evacuated TEG, TEG, the the applicationapplication of of low-emissivity low-emissivity metallization metallization layers layers has has turned turned out out to be to an be appropriate an appropriate means means to reduce to radiativereduce radiative heat exchange heat exchange within TEMs. within Using TEMs. solid Using filling solid of gaps filling by aerogelof gaps material, by aerogel as considered material, as by considered by the simulation model of this work, effectively prevents parasitic thermal crosstalk the simulation model of this work, effectively prevents parasitic thermal crosstalk between the hot between the hot and cold side of the thermocouple by convection. Selective simulations on the impact and cold side of the thermocouple by convection. Selective simulations on the impact of the parasitic of the parasitic heat conduction through the aerogel revealed a maximum decrease of power output heat conduction through the aerogel revealed a maximum decrease of power output of 0.67%, which is of 0.67%, which is supposed to be a tolerable value. supposed to be a tolerable value. Lowering the filling factor F yields high mass savings due to significantly lowered thermal Lowering the filling factor F yields high mass savings due to significantly lowered thermal resistance of the convective boundary layers and reduced optimal leg lengths of the thermocouple. resistance of the convective boundary layers and reduced optimal leg lengths of the thermocouple. Reducing F from 25% to 3% reduces the thermocouple mass by 43% (Figure A3). At the design point Reducing F from 25% to 3% reduces the thermocouple mass by 43% (Figure A3). At the design point of of the convection HTC parameters at the nozzle (αH = 100 WK−1m−2, αC = 64 WK−1m−2), the minimal the convection HTC parameters at the nozzle (α = 100 WK−1m−2, α = 64 WK−1m−2), the minimal gravimetric power density requirement (“APD +H CFD”-limit) is fulfilledC for the HPVM for F < 21% 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 (Figure 10). When considering only the positive impact on the reduced mass and mechanical power of of the engine generator (“APD”-limits), a beneficial installation of TEG becomes attainable for F < the engine generator (“APD”-limits), a beneficial installation of TEG becomes attainable for F < 12.4%, 12.4%, while access to a range-invariant TEG implementation is given for F < 5.5%, respectively. while access to a range-invariant TEG implementation is given for F < 5.5%, respectively. Improving Improving the hot side convective HTC to αH = 200 WK−1m−2 the power density requirements are the hot side convective HTC to α = 200 WK−1m−2 the power density requirements are fulfilled for fulfilled for slightly higher F. PG H= 100 Wkg−1 is attainable for F < 23.8%, while the range-invariant −1 slightlyinstallation higher requiresF. PG =F 100< 6.3%.Wkg Accordingis attainable to for theF simulation< 23.8%, while results, the range-invariant the range for maximum installation requiresgravimetricF < power 6.3%. Accordingdensity at F to = the3% simulationis given between results, 800 the Wkg range−1 and for 1200 maximum Wkg−1 in gravimetric dependence power on density at F = 3% is given between 800 Wkg−1 and 1200 Wkg−1 in dependence on α . αH. H

FigureFigure 10.10. GravimetricGravimetric powerpower densitydensityP PGG ofof aa HPVM-basedHPVM-based TEMTEM asas a a function function of of the the ﬁlling filling factor factorF Ffor

differentfor different HTC HTCαH. αPHG. PisG displayedis displayed together together with with the the required required levels levels from from the the aircraft aircraft model. model.

TheThe decrease of of mechanical mechanical power power taken taken from from the the turbine turbine shaft shaft by the by generator the generator scales scales with the with theelectrical electrical power power output output of the of the TEG, TEG, while while the the positive positive impact impact on on the the propulsive propulsive efficiency efficiency by by accelerationacceleration of the bypass flow flow is is linked linked to to the the heat heat flow flow dissipated dissipated by by the the TEG, TEG, which which is is likewise likewise connectedconnected over the thermocouple efficiency efficiency to to the the power power output output of of the the TEG. TEG. Thus, Thus, the the quantitative quantitative determinationdetermination of the SFC saving requires requires the the determination determination of of the the amount amount of of electrical electrical power power providedprovided byby thermoelectricthermoelectric recuperation. When When considering considering the the limitation limitation on on the the installation installation space, space, the power output is determined by the achievable areal power density PA of the thermocouple. At αH = 100 WK−1m−2 and αC = 64 WK−1m−2, PA 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 αH (Figure 9b). This is connected to the finite thermal conductivity Appl. Sci. 2018, 8, 2637 13 of 21

the power output is determined by the achievable areal power density PA of the thermocouple. −1 −2 −1 −2 −2 At αH = 100 WK m and αC = 64 WK m , PA stays below 1680 Wm , independently from the filling factor applied. Reducing the filling factor from 25% to 3% yields a reduction of the areal power Appl. Sci. 2018, 8, x FOR PEER REVIEW 13 of 20 density in the range of 10% for a particular αH (Figure9b). This is connected to the finite thermal conductivityof the components of the within components the heat within transmission the heat path transmission and the corresponding path and the corresponding spreading resistances spreading on resistancesboth sides of on the both thermocouple sides of the thermocoupleconfiguration. configuration.Due to the low Duethicknesses to the low of the thicknesses nozzle and of theinsulation nozzle andlayers, insulation which layers, are minimized which are inminimized order to in receive order to a receive maximized a maximized gravime gravimetrictric power power density, density, the thecomponents components set seta considerably a considerably thermal thermal resistance resistance for for the the lateral lateral heat heat transport, transport, which which lowers lowers the effective temperature differencedifference atat thethe TE materials. As a consequence, the heat flux flux density density decreases decreases for a particular set of HTC by approximately 10%10% whenwhen FF isis reducedreduced fromfrom 25%25% toto 3%3% (Figure(Figure A4A4).). −1 −2 −1 −2 For the design points points of of the the HTC HTC (α (αHH = =100 100 WK WK−1m−2m, αH ,=α 64H =WK 64−1 WKm−2) andm the) and set total the set surface total 2 surface(Anoz = 1.1 (A nozm2),= which 1.1 m is), whichoffered is for offered TEG occupation, for TEG occupation, a total power a total output power between output between1.65 kW and 1.65 1 kW.85 andkW 1.85can kWbe expected can be expected from the from thermoelectric the thermoelectric recuperation recuperation at the at the nozzle nozzle for forF =F = 3% 3% and and FF == 21%,21%, respectively. ThisThis corresponds corresponds to to 3.6% 3.6% to 4.1%to 4.1% of theof the average average electrical electrical power power output output of the of shaft-driven the shaft- electricdriven electric generator generator within eachwithin engine each ofengine the reference of the referen aircraft.ce aircraft. The power output for F = 21% of 1.85 kW offers a total SFC improvement of of 0.05% 0.05% (Figure (Figure 11).11). A slightly lower SFC reduction of 0.045% is achieved at FF == 5.5%, but with the advantage of a range −1 invariant installation ofof thethe TEG,TEG, asas thethe gravimetricgravimetric powerpower densitydensity exceeds exceeds 520 520 Wkg Wkg−1. A A possibility to improve the SFC saving is given by an increase of the installation space, which is calculated for an 2 additional higherhigher valuevalue ofof AAnoznoz == 1.5 1.5 m m2. .Increasing Increasing simultaneously simultaneously the the performance performance of of the the convectiv convectivee −1 −2 heat transfer toto ααHH == 200 WKWK−1mm−2 thethe corresponding corresponding areal areal power power density density offered offered by by the the TEG TEG could allow for a SFC improvement of 0.11% at FF == 23.8%. Again, slightly lower SFC reduction of 0.096% is achieved at F = 6.3% 6.3% for for a a range range invariant invariant installation installation o off the the TEG TEG at at the the geometrically geometrically extended extended nozzle. nozzle. A furtherfurther butbut notnot yet yet investigated investigated means means to to increase increase the the power power density density is given is given by exchanging by exchanging the TiAl the byTiAl electrically by electrically insulating insulating SiC. Due SiC. to Due higher to higher thermal thermal conductivity conductivity and simultaneously and simultaneously lower density, lower SiCdensity, could SiC decrease could decrease the mass the and mass the spreading and the spreading resistance resistance of the nozzle, of the while nozzle, making while the making use of the AlNuse of layer the AlN unnecessary, layer unnecessary, which would which allow would for an allow additional for an additional reduction ofreduction mass. of mass.

Figure 11. SpeciﬁcSpecific fuel consumption (SFC) improvement as a function of electricalelectrical power output of the TEG TEG at at the the aircraft aircraft nozzle. nozzle. The The SFC SFC is calculated is calculated on the on thebase base of data of data from from [28]. [Contributions28]. Contributions from fromthe bypass the bypass acceleration acceleration (CFD) (CFD) and the and reduced the reduced mechanical mechanical power power of the ofgenerator the generator (APD) (APD) add to add the tototal the SFC total reduction. SFC reduction. Ranges Ranges of SFC of SFC improvement improvement are are highlighted highlighted for for two two different different occupation surfaces at the nozzlenozzle with variedvaried HTCHTC ααHH. The corresponding values of the electrical power outputoutput are calculated according to the respective areal power densities for the permitted ranges of F, whichwhich fulﬁlfulfil the minimumminimum gravimetricgravimetric powerpower densitydensity requirement.requirement.

However, according to the simulation results a SFC saving between 0.05% and 0.1% seems plausible for the TE recuperation of waste heat at the engine nozzle. Though the nominal values might seem small, a considerable economic impact can be estimated from the beneficial impact on the operational costs. According to estimations from Boeing [18], a SFC improvement of 0.1% translates into a cost saving of 2.4 Mio$/month for the entire US civil aviation sector. Our own estimations [46] on the base of a 0.1% SFC improvement yield a potential saving of 144 k$ per airplane over a typical life time of 28 years. Consequently, a return of investment during five years could be attainable for a 2 kW TEG system within the cost limit of <16 $/W. According to recent studies, the sum of material and heat exchanger costs for modern TE materials can be estimated below 10 $/W for F < 10% and at operating temperatures between TH = 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 TH = 523 K and TC = 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 The application of thermoelectric generators (TEG) on the nozzle of an aviation jet engine was studied by finite element modelling. Temperatures of the core stream and the bypass flow are derived from CFD results [25] and are applied as boundary conditions to the FEM simulation of various thermocouple configurations. In conjunction with effective heat transfer coefficients (HTC) between −1 −2 −1 −2 the flat surfaces of the nozzle and the core (αH = 100 WK m ) and the bypass (αC = 64 WK m ) air flow, respectively, the performance of different thermocouple designs is simulated on the basis of a virtual material with a ZTmean = 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. The requirement on the gravimetric power density, which was determined from of a parametric aircraft model [28], cannot be fulfilled for a thermocouple design with F = 25%, neither by an increase of the HTC nor by a reasonable improvement of materials performance. The minimum break-even point of gravimetric power density (100 Wkg−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 −1 −2 −1 −2 HTC (αH = 100 WK m , αC = 64 WK m ) 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%. 2 For Anoz = 1.1 m 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. 2 Under reasonable assumptions of an increased occupation surface (Anoz = 1.5 m ) and improved −1 −2 −1 −2 heat exchange by convection (αH = 200 WK m , αC = 64 WK m ), 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. The resulting savings on the SFC is in the range between 0.05% and 0.1%, which translates into a considerable reduction of operation cost for the aircraft. This cost reduction opens a window for an economically efficient TEG installation. A return of invest during approximately five years is estimated, if the total costs of the thermoelectric recuperation system stay below 16 $/W, which is a reasonable value for high performance TE materials from today’s point of view. Appl. Sci. 2018, 8, 2637 15 of 21

Further improvement of the power output and the resulting SFC saving seems realistic by the increase of the nozzle surface, exchange of particular materials for more performant heat transfer, and by optimization of the convective heat exchange by the modification of surface structures. Though, the installation of TEG in engine sections with higher temperature levels was not investigated in detail yet, it offers a significantly higher power output and SFC improvement capability when compared to the nozzle installation [22]. Further studies have to verify the entire optimization potential and to clarify the possibilities for more progressive integration concepts for TEG in aviation engines. Although the limitation on the convective heat transport clearly represents the major bottleneck for a performant application at the aviation nozzle, future materials must still offer an attractively high ZTmean 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: Conceptualization, writing—original draft preparation, project administration, and funding acquisition, P.Z.; Formal analysis, investigation, data curation, and visualization P.Z. and K.Z.; Writing—review and editing, and resources P.Z. and K.Z. and E.M.; Supervision, E.M. Funding: This research was funded by the German Federal Ministry of Economic Affairs and Energy in the framework of Germany’s Fifth Aeronautical Research Program (LUFO-V), grant number 20E1303. The authors likewise thank Dr. Sieber from the MTU Aero Engines AG for the financial support. Acknowledgments: This research was funded by the German Federal Ministry of Economic Affairs and Energy in the framework of Germany’s Fifth Aeronautical Research Program (LUFO-V), grant number 20E1303. The authors likewise thank Dr. Sieber from the MTU Aero Engines AG for the financial support. Fruitful discussions with Ragnar Somdalen and Fabian Ahrendts from the Institute of Thermodynamics of the Technical University of Braunschweig, Christoph Bode from the Institute of Jet Propulsion and Turbomachinery of the Technical University of Braunschweig, Dragan Kožulovićfrom the Hamburg University of Applied Science, and Kai-Daniel Büchter from Bauhaus Luftfahrt e.V. are gratefully acknowledged. Conflicts of Interest: The authors declare no conflict of interest.

Appendix A In order to get a more comprehensive overview on simulations and to allow readers to establish correlations between simulation results and different application boundary conditions and thermocouple designs further information is given within this supplementary information. This comprises the temperature dependent courses of transport properties (thermal conductivity, electrical conductivity and Seebeck-coefficient) considered for the p- and n-type thermoelectric materials within the simulation. The gravimetric power density in dependence of the cold side heat transfer coefficient is shown additionally, which is not discussed in the publication due to the difficulty to improve the cold side convective heat exchange without losing the positive effect on the fuel consumption by acceleration of the bypass flow. Although the potential for further improvement on the convective heat transfer at the cold bypass flow and possibly connected repercussions on the engine operation still have to be investigated in detail, these results confirm a significant positive impact on the gravimetric power density of the TEG, and might be helpful for prospective considerations. Additionally simulations results on the evolution of the thermocouple mass and the hot side heat flow and heat flux density, respectively, are shown as the function of the hot side heat transfer coefficient for different filling factors. Though, these results are not discussed extensively throughout the publication, they reflect central key figures of the particular TEG designs, and shall therefore be displayed within the supporting information for the sake of completeness. Since operation parameters are obtained for a uni-couple configuration, but scaled to an TE module and finally projected to a TEG at the engine nozzle, governing relations are given within this appendix in order to support the understanding Appl. Sci. 2018, 8, 2637 16 of 21

(see Table A1). In order to increase the conﬁdence level of the FEM-based numerical simulations, a validation of the operation parameter has been conducted by means of a comparison to an analytical constant property model (CPM). Results are displayed in Table A2 and conﬁrm a maximum deviation of all relevant operation parameters to be less than 2%. Appl. Sci. 2018, 8, x FOR PEER REVIEW 16 of 20

Figure A1. A1.Material Material properties properties for the for FEM the simulation: FEM simulation: Thermal Thermalconductivity conductivity (a), electrical (a conductivity), electrical conductivity(b) and Seebeck (b) coefﬁcientand Seebeck (c )coefficient of p-type (left)(c) of andp-type n-type (left) (right) and n thermoelectric-type (right) thermoelectric legs. The dashed legs.lines The dashedrepresent lines ﬁts represent of measured fits properties of measured on Skutteruditeproperties on samples. Skutterudite Curves samples. shown byCurves light solidshown lines by showlight solidthe temperature lines show coursesthe temperature after the shiftcourses of transport after the propertiesshift of transport into the pro temperatureperties into range the oftemperature the nozzle rangeapplication of the has nozzle been application applied. Bold has solid been lines applied. show Bold the property solid lines characteristics show the property for the virtual characteristics material, forwhich the hasvirtual been material, considered which for has the been simulation. considered The for broken the simulation. dashed lines The show broken the dashed temperature lines show mean thevalues temperature of the bold mean solid valu lines.es of the bold solid lines.

Figure A2. Gravimetric power density PG of TEG design with a filling factor F = 25% in dependence of the convective hot side heat transfer coefficient (HTC) αH for different cold side HTC αC: 100 WK−1m−2 (a), 125 WK−1m−2 (b), 150 WK−1m−2 (c), 175 WK−1m−2 (d). The curves are shown for application Appl. Sci. 2018, 8, x FOR PEER REVIEW 16 of 20

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 Appl. Sci.for 2018the virtual, 8, 2637 material, which has been considered for the simulation. The broken dashed lines show17 of 21 the temperature mean values of the bold solid lines.

Figure A2. Gravimetric powerpower densitydensityP PGof of TEGTEG design design with with a a ﬁlling filling factor factorF =F 25%= 25% in in dependence dependence of Appl. Sci. 2018, 8, x FOR PEER REVIEW G 17 of 20 of the convective hot side heat transfer coefficient (HTC) αH for different cold side HTC α−C1: 100−2 the convective hot side heat transfer coefﬁcient (HTC) αH for different cold side HTC αC: 100 WK m (WKa), 125−1m−2 WK (a),− 1125m− WK2 (b−1),m 150−2 (b WK), 150−1m WK−2 −1(cm),−2 175 (c), WK 175− WK1m−−12m(d−2). (d The). The curves curves are are shown shown for for application application of of the high performance virtual material (HPVM) and for an increased power factor PF of the HPVM the high performance virtual material (HPVM) and for an increased power factor PF of the HPVM by by three steps of 10%. three steps of 10%.

FigureFigure A3. A3. ThermocoupleThermocouple mass mass mmTCTC atat the the respective respective optimal optimal leg leg length length as as a afunction function of of the the hot hot side side heatheat transfer transfer coefficient coefﬁcient ααHH forfor different different filling ﬁlling factors factors FF ofof the the thermocouple. thermocouple.

Figure A4. Incident heat flow QTC (a) and hot side heat flux density (b) QA at the respective optimal

leg lengths as a function of the hot side heat transfer coefficient αH 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.

Uni- Property Single Leg TE-Module TEG Couple Seebeck coefficient Sn, Sp S = Sp + |Sn| N∙S N∙M∙S Electric Resistance Rn, Rp R = Rp + Rn N∙R N∙M∙R Thermal Conductance Kn, Kp K = Kp + Kn N∙K N∙M∙K Voltage Vn, Vp V = Vp + Vn N∙V N∙M∙V Electric Current In, Ip Inp Inp Inp Electrical Power Pn, Pp P = Pp + Pn N∙P N∙M∙P Heat Flow Qn, Qp Q = Qp + Qn N∙Q N∙M∙Q Efficiency ηn, ηp ηpn = P/Q ηpn ηpn Appl. Sci. 2018, 8, x FOR PEER REVIEW 17 of 20

of the high performance virtual material (HPVM) and for an increased power factor PF of the HPVM by three steps of 10%.

Appl. Sci.Figure2018, 8A3., 2637 Thermocouple mass mTC at the respective optimal leg length as a function of the hot side18 of 21 heat transfer coefficient αH for different filling factors F of the thermocouple.

TC A FigureFigure A4. A4.Incident Incident heat heat flow flowQ QTC ( a(a)) and and hot hot side side heat heat flux flux density density ( b(b) )Q QA at at the the respective respective optimal optimal legleg lengths lengths asas aa functionfunction of the hot hot side side heat heat transfer transfer coefficient coefficient ααH Hforfor different different filling filling factors factors F ofF theof thethermocouple. thermocouple.

TableTable A1. A1. RelationRelation between between operation operation parameters parameters obtained obtained for for a a uni-couple uni-couple conﬁguration configuration and and correspondingcorresponding valuesvalues forfor a TE module module (TEM) (TEM) and and a aTEG. TEG. NN denotesdenotes the the number number of uni of uni-couples-couples in a inseries a series connection connection within within a TEM, a TEM, whereas whereas M denotesM denotes the number the number of TEM of TEMin a series in a seriesconnection connection within withina TEG. a TEG.

Property Single Leg Uni-CoupleUni- TE-Module TEG Property Single Leg TE-Module TEG Seebeck coefficient Sn, Sp S = SCouplep + |Sn| N·SN·M·S Electric Resistance R , R R = R + R N·RN·M·R Seebeck coefficient n pSn, Sp S = Spp + |nSn| N∙S N∙M∙S Thermal Conductance Kn, Kp K = Kp + Kn N·KN·M·K Electric Resistance Rn, Rp R = Rp + Rn N∙R N∙M∙R Voltage Vn, Vp V = Vp + Vn N·VN·M·V ElectricThermal Current Conductance In, IpKn, Kp K =Inp Kp + Kn NInp∙K N∙M∙KInp Electrical PowerVoltage Pn, PVp n, Vp P V= P=p V+p P+n Vn N·∙PNV N∙M∙·VM ·P · · · HeatElectric Flow Current Qn, QpIn, Ip Q = QpI+np Qn NInpQN Inp M Q Efficiency ηn, ηp ηpn = P/Q ηpn ηpn Electrical Power Pn, Pp P = Pp + Pn N∙P N∙M∙P Heat Flow Qn, Qp Q = Qp + Qn N∙Q N∙M∙Q Table A2. Validation of the FEM-based simulation by comparison to analytical results obtained from a Efficiency ηn, ηp ηpn = P/Q ηpn ηpn 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 ηmax [A] 0.39 0.385 1.28% Optimum current Pmax [A] 0.439 0.434 1.13% −3 Maximum power Pmax [10 W] 35.283 34.925 1.01% −3 Incident heat flow Qin [10 W] 442.142 438.756 0.76% Maximum efficiency ηmax [%] 7.98 7.96 0.25% Appl. Sci. 2018, 8, 2637 19 of 21

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