aerospace

Article Impact of Hybrid-Electric on Contrail Coverage

Feijia Yin 1,* , Volker Grewe 1,2 and Klaus Gierens 2

1 Faculty of Aerospace Engineering, Delft University of Technology, 2629HS Delft, The Netherlands; [email protected] 2 Deutsches Zentrum für Luft- und Raumfahrt, Institut für Physik der Atmosphäre, Oberpfaffenhofen, D-82234 Weßling, Germany; [email protected] * Correspondence: [email protected]

 Received: 31 July 2020; Accepted: 9 October 2020; Published: 12 October 2020 

Abstract: Aviation is responsible for approximately 5% of global warming and is expected to increase substantially in the future. Given the continuing expansion of air traffic, mitigation of aviation’s climate impact becomes challenging but imperative. Among various mitigation options, hybrid- (HEA) have drawn intensive attention due to their considerable potential in reducing greenhouse gas emissions (e.g., CO2). However, the non-CO2 effects (especially contrails) of HEA on climate change are more challenging to assess. As the first step to understanding the climate impact of HEA, this research investigates the effects on the formation of persistent contrails when flying with HEA. The simulation is performed using an Earth System Model (EMAC) coupled with a submodel (CONTRAIL), where the contrail formation criterion, the Schmidt–Appleman criterion (SAC), is adapted to globally estimate changes in the potential contrail coverage (PCC). We compared the HEA to conventional (reference) aircraft with the same characteristics, except for the propulsion system. The analysis showed that the temperature threshold of contrail formation for HEA is lower; therefore, conventional reference aircraft can form contrails at lower flight altitudes, whereas the HEA does not. For a given flight altitude, with a small fraction of electric power in use (less than 30%), the potential contrail coverage remained nearly unchanged. As the electric power fraction increased, the reduction in contrail formation was mainly observed in the mid-latitudes (30◦ N and 40◦ S) or tropical regions and was very much localized with a maximum value of about 40% locally. The analysis of seasonal effects showed that in non-summer, the reduction in contrail formation using electric power was more pronounced at lower flight altitudes, whereas in summer the changes in PCC were nearly constant with respect to altitude.

Keywords: hybrid-electric aircraft; potential contrail coverage; Schmidt–Appleman criterion; degrees of hybridization

1. Introduction Civil aviation satisfies modern society’s needs for mobility and is an essential economic driver. Air transportation demand increases at around 4.4% per annum and is forecast to maintain that growth rate for the next few decades [1]. Although the global COVID-19 pandemic has put a great challenge on the aviation industry, we expect that aviation will eventually recover, as aviation has become a fundamental part of the modern world, providing long-range mobility. Aviation is responsible for approximately 5% of the anthropogenic causes of global warming [2], and it is expected to increase substantially in the future. Given the continuing expansion of air traffic, mitigation of aviation’s climate impact becomes challenging but imperative.

Aerospace 2020, 7, 147; doi:10.3390/aerospace7100147 www.mdpi.com/journal/aerospace Aerospace 2020, 7, 147 2 of 18 Aerospace 2020, 7, x FOR PEER REVIEW 2 of 18

AnAn overviewoverview ofof the the climate climate impact impact of aviation of aviation associated associated with various with various species/ effspecies/effectsects is presented is presentedin Figure1 [in3 Figure]. Both 1 CO [3].2 andBoth non-CO CO2 and2 e non-COffects from2 effects NOx from (ozone NOx formation (ozone andformation methane and depletion), methane depletion),water vapor, water contrails, vapor, and contrails, direct aerosolsand direct are aerosols included. are Oneincluded. can see One that can CO see2 emissions that CO2 emissions share less sharethan halfless ofthan the half total of aviationthe total radiativeaviation radiative forcing (RF), forcing and (RF), the and rest the is from rest is non-CO from non-CO2 effects.2 effects. It is also It isnoticeable also noticeable that contrail that contrail cirrus is cirrus the largest is the contributor largest contributor to the total to aviation the total RF, aviation with some RF, uncertainties with some uncertaintiesin the current in level the ofcurrent understanding. level of understanding.

FigureFigure 1. 1. Aviation-inducedAviation-induced radiative radiative fo forcingrcing from from different different components for the year 2005 [3–10]. [3–10].

BecauseBecause of of its its long long lifetime, lifetime, aviation’s aviation’s climate climate impact impact from from CO CO2 is2 mainlyis mainly determined determined by the by amountthe amount of CO of2 CO emissions.2 emissions. The The induced induced perturbation perturbation ofof the the atmospheric atmospheric CO CO2 2 concentrationconcentration is is determineddetermined by by several several lifetimes lifetimes that that are are associated with individual processes, processes, such such as land-uptake (biosphere;(biosphere; 1–100 1–100 years) years) and and sediment sediment formation formation (1000 (1000 to to 10,000 10,000 years) years) [11]. [11]. Due Due to to the the long long lifetimes, lifetimes, thethe concentration concentration change change can can be be estima estimatedted to to first-order first-order by by accumulating accumulating CO CO2 emissionsemissions over over aviation aviation history.history. On On the the contrary, contrary, the short-lived non-CO 22 effectseffects depend depend not not only only on on the the emission emission quantity quantity butbut also also on the geographical location, altitude, time, and the local weather conditions. It It is is possible toto mitigate mitigate aviation’s aviation’s climate climate impact impact via via operat operationalional measures measures to to avoid climate-sensitive regions regions associatedassociated with with non-CO non-CO22 effects,effects, e.g., e.g., to to contrail contrail avoidance avoidance [12–17]. [12–17]. TheThe formation formation of of persistent persistent contrails contrails depends depends on on environmental environmental conditio conditionsns and and aircraft/engine aircraft/engine technologies.technologies. The The well-known well-known Schmidt–Appleman Schmidt–Appleman cr criterioniterion (SAC) (SAC) [18,19] [18,19] suggests suggests that that the the possible possible measuresmeasures to to reduce reduce aviation’s aviation’s contrail contrail formation are reducing the H 2OO emission emission index, index, increasing increasing the the fuelfuel lower lower heating heating value, value, or or decreasing decreasing the the overal overalll propulsion propulsion efficiency. efficiency. Va Variousrious options options can can affect affect thesethese three three measures, measures, e.g., e.g., new new aircraft aircraft design [20] [20] and alternative fuels [[21–24].21–24]. ElectricElectric aircraft aircraft is is one one of of the the possible possible options options as as well, well, since since using using a a battery battery will will eliminate eliminate exhaust exhaust emissions.emissions. Due Due to to technology technology limitations, limitations, a a purely purely electric electric aircraft aircraft would would not not be feasible. Instead, Instead, hybrid-electrichybrid-electric aircraft aircraft is is proposed proposed for for regional/narrow-body regional/narrow-body airliners [25,26]. [25,26]. For For long-range long-range flights, flights, thethe electric electric propulsion propulsion system’s system’s additional additional weight weight ma makeskes it it difficult difficult to to achieve achieve substantial substantial fuel fuel saving. saving. AA hybrid-electric hybrid-electric propulsion propulsion system consists of a a ga gass turbine turbine engine engine combined combined with with an an electric motor (EM)(EM) and and a a battery pack. There There are are several several possible possible ways ways to to connect connect these these components components in in a a power power train.train. The The most most frequently frequently proposed proposed configurations configurations are are the the series series and and parallel parallel type, type, as as demonstrated demonstrated inin Figure Figure 22.. InIn aa seriesseries configuration,configuration, thethe gasgas turbineturbine generatesgenerates electricityelectricity viavia aa generator.generator. EMEM thenthen usesuses the the electricity electricity to to drive drive a a fan/propeller. fan/propeller. Batteri Batterieses can can assist assist in in supplying supplying power power to to the the EM. EM. In In the the parallelparallel type,type, a gasa turbine and EMand drive EM thedrive fan /propellerthe fan/propeller simultaneously, simultaneously, with different with hybridization different hybridizationdegrees. In addition, degrees. the In operational addition, the flexibility operational of the flexibility parallel hybrid-electric of the parallel system hybrid-electric (HEPS) may system allow

Aerospace 2020, 7, x FOR PEER REVIEW 3 of 18 Aerospace 2020, 7, 147 3 of 18 (HEPS)Aerospace may2020, 7allow, x FOR forPEER full REVIEW electrical power through the climate-sensitive regions, such as contrail-3 of 18 vulnerable parts of a flight, hence eliminating contrail formation. for(HEPS) full electricalmay allow power for full through electrical the climate-sensitivepower through the regions, climate-sensitive such as contrail-vulnerable regions, such as parts contrail- of a flight,vulnerable hence parts eliminating of a flight, contrail hence formation. eliminating contrail formation.

(a) (b)

Figure 2. Schematic of (aa )hybrid-electric propulsion system: (a) series configuration,(b) (b) parallel configuration [27]. FigureFigure 2. Schematic 2. Schematic of a hybrid-electric of a hybrid-electric propulsion propulsion system: ( asystem:) series configuration,(a) series configuration, (b) parallel configuration(b) parallel [27]. Asconfiguration the first step[27]. towards understanding the climate impact of hybrid-electric aircraft, this As the first step towards understanding the climate impact of hybrid-electric aircraft, this research research investigates the effects on the formation of contrails when flying with hybrid-electric aircraft investigates the effects on the formation of contrails when flying with hybrid-electric aircraft (HEA). (HEA).As Athe parallel first stephybrid towards configuration, understanding as described the climate in Figure impact 2b, ofis considered.hybrid-electric In termsaircraft, of thisthe A parallel hybrid configuration, as described in Figure2b, is considered. In terms of the baseline aircraft, baselineresearch aircraft, investigates an earlier the effects study on suggested the formation a possible of contrails mission when range flying of 1000 with km hybrid-electric for a parallel hybrid- aircraft an earlier study suggested a possible mission range of 1000 km for a parallel hybrid-electric plane to electric(HEA). planeA parallel to allow hybrid reasonable configuration, benefits as of described fuel savings in Figure [26]. The 2b, A320is considered. type aircraft In terms is then of ourthe allow reasonable benefits of fuel savings [26]. The A320 type aircraft is then our potential baseline. potentialbaseline aircraft,baseline. an Figureearlier study3 shows suggested an example a possible of a mission power rangemanagement of 1000 kmstrategy for a parallel for a parallelhybrid- Figure3 shows an example of a power management strategy for a parallel configuration. The degrees configuration.electric plane toThe allow degrees reasonable of hybridization benefits of between fuel savings fuel and[26]. electricity The A320 can type be aircraft varied isto then achieve our of hybridization between fuel and electricity can be varied to achieve different mission performance. differentpotential mission baseline. performance. Figure 3 shows For contrail an example avoidance, of a it powerwould bemanagement better to have strategy a 100% forelectric a parallel flight For contrail avoidance, it would be better to have a 100% electric flight at the contrail-sensitive regions atconfiguration. the contrail-sensitive The degrees regions of hybridization of the cruise flightbetween only, fuel which and electricityis analyzed can in bedetail varied in the to currentachieve of the cruise flight only, which is analyzed in detail in the current paper. paper.different mission performance. For contrail avoidance, it would be better to have a 100% electric flight at the contrail-sensitive regions of the cruise flight only, which is analyzed in detail in the current paper.

Figure 3. An example power management strategy adapted from [26]. During taxi-out/taxi-in phases, Figure 3. An example power management strategy adapted from [26]. During taxi-out/ taxi-in phases, 100%100% electrical electrical power power is is used, whereas whereas during during take take-o-off,ff, climb, climb, and and cruise cruise conditions, battery battery and and Figure 3. An example power management strategy adapted from [26]. During taxi-out/taxi-in phases, turbofanturbofan engine engine are are used used in in parallel. parallel. The The arrow arrow on on the the mission mission profile profile indicates indicates different different flight flight stages. stages. 100% electrical power is used, whereas during take-off, climb, and cruise conditions, battery and TheTheturbofan paper paper engine is is organized organized are used inas as parallel.follows. follows. The In In Sectionarrow Section on 22, ,the the mission methods profile used indicates to predict different the potential flight stages. contrail coveragecoverage (PCC), defineddefined asas the the atmospheric atmospheric ability ability to to form form contrails contrails for for a given a given aircraft aircraft and and fuel fuel type type [28], [28],are elaborated. areThe elaborated. paper is The organized The conditions conditions as follows. of contrail of contrail In formationSection formation 2, the for methodsparallel for parallel hybrid-electric used hybrid-electric to predict configuration the configuration potential contrail are alsoare alsodiscussed.coverage discussed. (PCC), Section Sectiondefined3 analyses as3 theanalys the atmospheric eesffects the ofeffects the ability variation of to theform ofvariation contrails cruise altitude, forof acruise given degrees altitude,aircraft of hybridization, and degrees fuel type of hybridization,and[28], seasonsare elaborated. on and PCC seasons The changes. conditions on PCC Finally, changes.of contrail conclusions Finally, formation are conclusions drawn for parallel in Section are hybrid-electric drawn4. in Section configuration 4. are also discussed. Section 3 analyses the effects of the variation of cruise altitude, degrees of 2.2.hybridization, Methodology Methodology and seasons on PCC changes. Finally, conclusions are drawn in Section 4. We have envisaged a research roadmap (as presented in Figure4) to investigate the potential 2. MethodologyWe have envisaged a research roadmap (as presented in Figure 4) to investigate the potential of flyingof flying a hybrid-electric a hybrid-electric plane plane for for contrail contrail avoida avoidance.nce. The The complete complete research research chain chain contains contains the the relevantrelevantWe technicalhavetechnical envisaged aspects aspects a of researchof HEA HEA for roadmap contrailfor contrail formation(as present formation (theed greenin (the Figure box),green 4) the to box), investigate PCC calculationthe PCC the potentialcalculation procedure, of procedure,theflying operational a hybrid-electric the operational strategy ofplane HEAstrategy for to contrailavoidof HEA contrails, avoidato avoidnce. and contrails, The the actualcomplete and mitigation the research actual potential mitigation chain contains when potential flying the whenHEA.relevant Inflying thistechnical paper,HEA. aspects weIn this present ofpaper, HEA the firstwe for present steps contrail of theth formatione roadmapfirst steps (the (marked of greenthe inroadmap blue).box), the Subsequent (marked PCC calculation in research blue). Subsequentwillprocedure, cover the theresearch later operational steps will (marked cover strategy the in orange). laterof HEA steps Thisto (maravoid sectionked contrails, elaboratesin orange). and on Thisthe the actual detailssection mitigation of elaborates the methodology potential on the detailsofwhen the firstflyingof the steps methodologyHEA. (those In inthis blue). of paper, the first we steps present (those th ine blue).first steps of the roadmap (marked in blue). Subsequent research will cover the later steps (marked in orange). This section elaborates on the details of the methodology of the first steps (those in blue).

Aerospace 2020, 7, 147 4 of 18 Aerospace 2020, 7, x FOR PEER REVIEW 4 of 18

Hybrid electric aircraft (HEA): • Turbofan engine • Battery technology Change of propulsion efficiency • Power management strategy Derivation of Schmidt Appleman Criterion for HEA

Calculate the potential contrail coverage (PCC)

Calculate the changes of PCC w.r.t. various hybridizations

• A single day analysis to illustrate A given fleet size and routing the local changes of PCC network • Climatological analysis on the changes of contrail formation

The changes of PCC for a given fleet and network

The operational strategy for HEA to avoid contrail sensitive regionsn

Contrail avoidance by HEA + operations

FigureFigure 4. 4. A Aschematic schematic of a of research a research methodology methodology map to map investigate to investigate the potentials the potentials of flying of a flyinghybrid- a electrichybrid-electric aircraft (HEA) aircraft for (HEA) contrail for contrailavoidance. avoidance.

AnAn Earth Earth System System Model Model (EMAC) (EMAC) coupled coupled with with a a CONTRAIL CONTRAIL submodel submodel was was used used to to predict predict the the hybrid-electrichybrid-electric aircraft’s aircraft’s PCC. The The CONTRAIL CONTRAIL submod submodelel includes includes a a revision revision of of the the contrail contrail formation formation criterioncriterion for for HEA. HEA. Please Please note note that that in in this this analys analysis,is, we we focus focus on on the the contrails contrails formed formed at at the the engine engine exhaust,exhaust, whereas whereas aerodynamic aerodynamic contrails contrails are are not co considered.nsidered. The The formation formation of of aerodynamic aerodynamic contrails contrails mainlymainly depends depends on on the the aerodynamic aerodynamic design design of of aircraft, aircraft, especially especially the the airfoil airfoil [29], [29], which which is assumed toto be be unchanged unchanged in in this this analysis analysis and and of of minor minor importance concerning their climate impact [[30].30]. 2.1. The Base Model EMAC 2.1. The Base Model EMAC The ECHAM/MESSy Atmospheric Chemistry (EMAC) model is a numerical chemistry and The ECHAM/MESSy Atmospheric Chemistry (EMAC) model is a numerical chemistry and climate simulation system that includes submodels describing tropospheric and middle atmosphere climate simulation system that includes submodels describing tropospheric and middle atmosphere processes and their interaction with oceans, land, and human influences [31]. For the present study, processes and their interaction with oceans, land, and human influences [31]. For the present study, we applied EMAC (ECHAM5 version 5.3.02, MESSy version 2.52.0) in T42L31ECMWF-resolution, we applied EMAC (ECHAM5 version 5.3.02, MESSy version 2.52.0) in T42L31ECMWF-resolution, corresponding to a horizontal grid of about 310 km and a vertical resolution of roughly 1 km up to an corresponding to a horizontal grid of about 310 km and a vertical resolution of roughly 1 km up to altitude of approximately 30 km. The simulation time step is 12 min. Such a model resolution will an altitude of approximately 30 km. The simulation time step is 12 min. Such a model resolution will provide us with reasonable weather data to calculate the potential contrail coverage. provide us with reasonable weather data to calculate the potential contrail coverage. EMAC has been extensively validated with other models, for instance, ACCMIP presented EMAC has been extensively validated with other models, for instance, ACCMIP presented in in [32], concerning atmospheric dynamics, cloud occurrence, chemistry, etc. An overview is given [32], concerning atmospheric dynamics, cloud occurrence, chemistry, etc. An overview is given in in [33]. In this paper, we use the submodel CONTRAIL V1.0. Section 2.2 discusses details on the [33]. In this paper, we use the submodel CONTRAIL V1.0. Section 2.2 discusses details on the CONTRAIL submodel. CONTRAIL submodel. 2.2. The CONTRAIL Submodel 2.2. The CONTRAIL Submodel CONTRAIL is one of the submodels in EMAC, developed by Frömming et al. (supplement of [12]) CONTRAIL is one of the submodels in EMAC, developed by Frömming et al. (supplement of to calculate the potential coverage of persistent contrails instantaneously, with the EMAC resolution [12]) to calculate the potential coverage of persistent contrails instantaneously, with the EMAC specified in the previous section. The thermodynamic condition of contrail formation is given by the resolution specified in the previous section. The thermodynamic condition of contrail formation is given by the Schmidt–Appleman criterion [18,19], the derivation of which is presented in Section 2.3 of this paper. In the CONTRAIL submodel, the PCC is calculated as the difference between the

Aerospace 2020, 7, 147 5 of 18

Schmidt–Appleman criterion [18,19], the derivation of which is presented in Section 2.3 of this paper. In the CONTRAIL submodel, the PCC is calculated as the difference between the maximum possible coverage of both contrails and cirrus and the natural cirrus coverage alone. Supersaturation with respect to ice is used to determine if the contrails are persistent or not.

2.3. The HEA Extended Schmidt–Appleman Criterion Contrails form when the mixture of engine exhaust and ambient air reaches water saturation at a sufficiently low temperature, and they persist when the ambient air is ice-supersaturated. The mixing process is assumed to be isobaric; therefore, the mixing trajectory is represented as a straight line on the T-e diagram (see Figure1 of [ 34]; e is the partial pressure of water vapor in the mixture; T is the static temperature of the mixture). The slope of this straight line (G) determining the temperature threshold of contrail formation is given by the SAC and calculated using Equation (1).

p cp EIH2O G = · · (1) ε Q (1 ηK) · · − where p is the ambient pressure in Pa; ε is the ratio of the molar mass of water vapor and dry air (0.622 constant); cp is the isobaric heat capacity of air (1004 J/kg/K); Q is the lower heating value of fuel in MJ/kg; EIH2O is the water vapor emission index in kg/kg(fuel); and the notation (ηK) is the overall propulsion efficiency of the pure kerosene aircraft (reference), for which we assumed a value of 0.4 in the current study. This efficiency value was in line with the value computed using the aircraft/engine performance model presented in [27]. For HEA, the thrust power is provided by two energy sources, as defined by Equation (2).

. FV = ηK m Q + ηE PE (2) · f · · . where F is the thrust requirement in N, V is the flight speed in m/s, m f is the fuel flow rate of kerosene in kg/s, ηE is the overall efficiency of the aircraft when electric power is working alone, the notation (PE) is the electric power in watts. Accordingly, the original SAC was adapted using the assumption that kerosene plus electric power are combined to the necessary power FV results (details are discussed in AppendixA). The revised calculation procedure for slope G leads to Equation (3), which considers the effects of various degrees of hybridization. cp pa R EIH2O G = · (3) · 0 ε R(1 ηK)Q + (1 R)(1 ηE)Q − − − E . . . where Rm f /m fmax . For the same thrust power, the maximum fuel flow rate (m fmax ) corresponds to the fuel consumption of the reference aircraft, where only kerosene is used. Hence, at pure liquid-fuel = = 0 operation, R 1, and pure electric operation, R 0. The notation (QE) is a quasi-electric energy content, defined in Equation (4): 0 Q := Q (ηK/ηE) (4) E · Note that the SAC derivation in this paper only applies to the situation where batteries provide electric power. A battery has no water vapor emission. Suppose the electric power is provided by a or another gas turbine via a generator. In that case, water vapor is emitted by these components. A different form of the Schmidt–Appleman criterion must be derived to consider the effects of water vapor emitted by, e.g., the fuel cell. Aerospace 2020, 7, 147 6 of 18

3. Results

3.1. The Threshold of Contrail Formation Calculated by SAC On the basis of the SAC derivation in Section 2.3, we studied the threshold of contrail formation for HEA. Figure5 shows how the contrail factor G varies with the share of electric propulsion. It is zero forAerospace pure 2020 electric, 7, x FOR propulsion PEER REVIEW (R = 0) and increases non-linearly with the fraction of liquid-fuel6 of 18 propulsionAerospace until 2020, 7 it, x reachesFOR PEER its REVIEW maximum at full liquid-fuel propulsion. The shape of the curve6 of depends 18 depends on the efficiency 𝜂 of the electric powertrain. The higher is 𝜂, the flatter the relation close on the efficiency ηE of the electric powertrain. The higher is ηE, the flatter the relation close to R = 1. dependsto 𝑅=1 .on the efficiency 𝜂 of the electric powertrain. The higher is 𝜂, the flatter the relation close to 𝑅=1.

FigureFigure 5. Dependence 5. Dependence of of the the contrail contrail factor factor GG on the ra ratiotio R R for for parallel-hybrid-electric parallel-hybrid-electric propulsion. propulsion. Figure𝑅=1 5. Dependence of the contrail𝑅=0 factor G on the ratio R for parallel-hybrid-electric propulsion. R = 1 is full is fuel full propulsion,fuel propulsion,R = 0 is full is full electric electric propulsion. propulsion. Parameters Parameters for for the the calculation calculation havehave been 𝑅=1 𝜂is =0.4full fuel propulsion, 𝑅=0𝑝 = 250 is full electric𝑄 propulsion. =(𝜂 ⁄𝜂 )𝑄 Parameters for the calculation have =been , Q=43.2 MJ/kg,= hPa, 0and= ( ) . ηK 0.4, Q = 43.2 MJ/kg, pa 250 hPa, and QE ηK/ηE Q. been 𝜂 =0.4, Q=43.2 MJ/kg, 𝑝 = 250 hPa, and 𝑄 =(𝜂⁄𝜂)𝑄. For the maximum temperature ( 𝑇 ,) ([35], Equation (5)), at which contrail formation is For the maximum temperature (Tmax,) ([35], Equation (5)), at which contrail formation is possible, possible,For thewe studiedmaximum the effectstemperature of various ( 𝑇 𝜂,) with([35], respect Equation to the (5)), fraction at which of electric contrail power formation (see Figure is we studied the effects of various ηE with respect to the fraction of electric power (see Figure6). For a possible,6). For a wemore studied efficient the electriceffects of system various with 𝜂 a with high respect 𝜂, it needsto the fractiona relatively of electric high electric power (seeshare Figure (R is more efficient electric system with a high ηE, it needs a relatively high electric share (R is very small) to 6).very For small) a more to achieveefficient a electric substantial system lowering with a of high 𝑇 𝜂. In, it ourneeds example, a relatively the maximum high electric temperature share (R atis achieveverywhich a small) substantial contrails to achieve can lowering be aformed substantial of whenTmax lowering. only In our liquid example,of 𝑇fuel .is In used the our maximum (example,𝑅=1) is the−40 temperature maximum°C. To reduce temperature at whichthis by contrails5 K,at can bewhichto formedachieve contrails a when maximum can only be formed temperature liquid when fuel ofonly is − used45 liquid °C, ( Rit fuelneeds= 1 is) isusedroughly40 (𝑅=1◦ C.𝑅=0.3 To) is reduce−40, or °C. 70% To this of reduce the by 5thrust this K, toby power achieve 5 K, a − maximumtoneeds achieve to temperature be a providedmaximum of by temperature the45 electricC, itneeds of motor −45 roughly°C, when it needs itsR efficiency =roughly0.3, or is𝑅=0.3 70%0.8. For of, or thethe 70% thrustsmaller of the power efficiency, thrust needspower the to be − ◦ providedneedsreduction byto be the in provided 𝑇 electric is larger.by motor the Thiselectric when may motor its sound effi whenciency paradoxical, its isefficiency 0.8. but For isit the 0.8.is the smallerFor consequence the smaller efficiency, efficiency,of the the simple reduction the reduction in 𝑇 is larger. This may sound paradoxical, but it is the consequence of the simple in Tmaxphysicalis larger. fact Thisthat contrail may sound formation paradoxical, is easier butwhen it the is the exhaust consequence gas is colder, of the for simple what is physical higher fact that contrailphysicalcombined formationfact overall that propulsioncontrail is easier formation efficiencies. when theis easier exhaust when gas the is colder,exhaust forgas what is colder, is higher for what combined is higher overall combined overall propulsion efficiencies. propulsion efficiencies.

Figure 6. Dependence of the maximum temperature at which contrails are possible, 𝑇, on the ratio 𝑇 FigureFigureR for 6. Dependenceparallel-hybrid-electric 6. Dependence of of the the maximum maximum propulsion temperaturetemperatur. Parameterse at atare which which as in contrails Figure contrails 4. are arepossible, possible, T, maxon the, on ratio the ratio R forR parallel-hybrid-electric for parallel-hybrid-electric propulsion. propulsion.Parameters Parameters are are as as in in Figure Figure 4.4 . This paper considered the technology level of 2030 for electric motor, inverter, and battery, as summarizedThis paper in [27,36].considered Furthermore, the technology a typical level valu of 2030e of 0.9for forelectric fan efficiency motor, inverter, was used. and Eventually, battery, as

summarizedthe value of 𝜂in [27,36]. was about Furthermore, 0.8. This value a typical was then valu usede of 0.9 in thefor furtherfan efficiency analysis was of PCC.used. Eventually, the value of 𝜂 was about 0.8. This value was then used in the further analysis of PCC.

Aerospace 2020, 7, 147 7 of 18

Aerospace 2020, 7, x FOR PEER REVIEW 7 of 18 This paper considered the technology level of 2030 for electric motor, inverter, and battery, as summarizedA further example in [27,36 of]. Furthermore,the parameters a typicalfor SAC value on di offferent 0.9 for aircraft fan effi ciencyis pres wasented used. in Table Eventually, 1. The numbersthe value were of ηE calculatedwas about for 0.8. an This altitude value of was 11 thenkm. Fi usedgure in 7 the shows further three analysis critical of mixing PCC. lines: one for conventionalA further aircraft example with of an the overall parameters efficiency for of SAC 0.4, one on for diff HEAerent with aircraft 40% is electric presented power, in and Table one1. Thefor HEA numbers with were 80%calculated electric power. for an These altitude three of 11 mixi km.ng Figure lines7 ranshows from three the critical engine mixing exhaust lines: conditions one for andconventional were tangential aircraft to with the water an overall saturation efficiency pressure of 0.4, line. one At for the HEA same with flight 40% altitude, electric the power, temperature and one thresholdfor HEA with and 80%the slope electric G decreased power. These with threethe increase mixing of lines electric ran frompower the in engineuse. Therefore, exhaust conditionsthe chance forand HEA were to tangential form contrails to the reduced water saturation as the electric pressure power line. fraction At the sameincreased. flight altitude, the temperature threshold and the slope G decreased with the increase of electric power in use. Therefore, the chance for HEATable to form 1. Calculated contrails parameters reduced as for the the electric Schmidt–Appleman power fraction criterion increased. on hybrid-electric aircraft.

Table 1. Calculated parameters for the Schmidt–ApplemanHybrid- criterion on hybrid-electricConven aircraft. Parameters Descriptions Electric tional Units Conventional Parameters Descriptions Hybrid-ElectricAircraft Aircraft Aircraft Units Electric power Aircraft Electric power 40% 80% 0 [−] fraction 40% 80% 0 [ ] EIH2Ofraction Water emission index 1.25 kg/kg(fuel)− EIH2O Water emission index 1.25 kg/kg(fuel) ηη OverallOverall efficiency efficiency 0.8 0.8 0.4 0.4 [−]] − TheThe lower lower heating heating value value of the QQ 43.243.2 MJ/kg MJ/kg of the fuelfuel GG SlopeSlope at 11 km at altitude11 km altitude 1.6 1.6 1.1 1.1 1.8 1.8 Pa/K Pa/K

Figure 7. Mixing line for threshold conditions. Water Water va vaporpor pressure vs. temperature phase diagram representing thermodynamicsthermodynamics of of contrail contrail formation format forion a conventionalfor a conventional aircraft withaircraft overall with propulsion overall propulsionefficiency of efficiency 0.4 (blue line)of 0.4 and (blu HEAe line) with and two HEA diff erentwith degreestwo different of hybridization: degrees of hybridization: 40% electric power 40% (redelectric line) power and 80%(red electricline) and power 80% (greenelectric line). power The (g tworeen blackline). curvesThe two are black the saturation curves are vapor the saturation pressure vaporcurves pressure for water curves (solid) for and water with (s respectolid) and to with ice (dashed). respect to Theice (das verticalhed). dashed The vertical lines representdashed lines the representtemperature the threshold temperature for the threshold conventional for the aircraft convention (blue),al HEAaircraft with (blue), 40% HEA electric with power 40% (red), electric and power HEA with(red), 80% and electricHEA with power 80% (green). electric power (green). 3.2. Changes in Potential Contrail Coverage 3.2. Changes in Potential Contrail Coverage We studied the variations of potential contrail coverage caused by different effects, for instance, We studied the variations of potential contrail coverage caused by different effects, for instance, altitude, degree of hybridization, and seasons. In this section, we present the results. The data are altitude, degree of hybridization, and seasons. In this section, we present the results. The data are based on a one-year simulation with EMAC, including the updated CONTRAIL submodel (see above). based on a one-year simulation with EMAC, including the updated CONTRAIL submodel (see For illustration purposes, we first present results for an arbitrary day in winter to give an impression above). For illustration purposes, we first present results for an arbitrary day in winter to give an of an actual weather situation and then present climatological values. All the results were obtained impression of an actual weather situation and then present climatological values. All the results were with 0.8 electric power efficiency and 0.4 kerosene system efficiency. obtained with 0.8 electric power efficiency and 0.4 kerosene system efficiency.

Aerospace 2020, 7, 147 8 of 18 Aerospace 2020, 7, x FOR PEER REVIEW 8 of 18

3.2.1. One-Day One-Day Case Case Study Study Figure8 8aa showsshows thethe PCCPCC ofof conventional aircraftaircraft atat 300300 hPahPa (FL300) on a specificspecific day. In contrast, the changes in PCC caused by 50% electric hybridization of HEA (i.e., R = 0.5 in Equation (3)) at the same altitude isis givengiven inin Figure Figure8 b.8b. For For the the pure pure kerosene kerosene case, case, the the contrails contrails were were mainly mainly formed formed at the at themid-latitudes mid-latitudes and and polar polar regions, regions, where where the local the temperature local temperature was su ffiwasciently sufficiently low to form low contrails.to form contrails.With 50% With thrust 50% power thrust supplied power by supplied the battery, by the the battery, reduction the in reduction contrail formation in contrail was formation observed was at observedabout 30◦ atN about and 40 30°◦ S, N where and the40° tropopauseS, where the climbed tropop toause the climbed higher altitudes. to the higher The localaltitudes. temperature The local in temperaturethis region was in this close region to the was temperature close to thresholdthe temper forature the threshold pure kerosene for the aircraft. pure kerosene A transition aircraft. to HEA A transitionlowered the to HEA temperature lowered threshold the temperature by a few threshold degrees Celsius.by a few Itdegrees was also Celsius. noticeable It was that also the noticeable contrail thatformation’s the contrail reduction formation’s was very reduction much localizedwas very with much a maximumlocalized with value a ofmaximum around 0.4,value which of around might 0.4,have which been might related have to the been local related temperature to the local and humidity.temperature and humidity.

2 2 Figure 8. TheThe potential potential contrail contrail coverage coverage (PCC) (PCC) (contour) (contour) and and geopotential geopotential (black (black contour; contour; m m2 s−2s)− at) 300at 300 hPa hPa (FL300) (FL300) on a on specific a specific day: day: (a) conventional (a) conventional aircraft; aircraft; (b) absolute (b) absolute changes changes caused caused by HEA by HEAwith 50%with electric 50% electric power. power.

When increasingincreasing the the flight flight altitude altitude from from 300 hPa300 tohPa 250 to hPa 250 (FL340), hPa (FL340), for the conventionalfor the conventional reference referenceaircraft, we aircraft, found we the found areas ofthe potential areas of contrail potential coverage contrail in coverage the tropical in the regions tropical as wellregions (Figure as well9a). (FigureFor HEA, 9a). with For 50%HEA, of with electric 50% hybridization, of electric hybridiz the reductionation, the of reduction contrail formation of contrail was formation more pronounced was more pronouncedin the tropical in regions,the tropical as seen regi inons, Figure as seen9b. in Figure 9b.

Aerospace 2020, 7, 147 9 of 18 Aerospace 2020, 7, x FOR PEER REVIEW 9 of 18

2 2 Figure 9. The PCC (contour) and geopotential (black(black contour;contour; mm2 ss−−2)) at at 250 250 hPa hPa (FL340) (FL340) on on a a specific specific day: ( a)) conventional conventional aircraft; aircraft; ( b) absolute changes caused by HEA with 50% electric power.power.

When we increased the flight altitude further to 200 hPa (FL390), HEA with 50% of electric When we increased the flight altitude further to 200 hPa (FL390), HEA with 50% of electric hybridization had no significant change in contrail formation. At this level, the ambient temperature hybridization had no significant change in contrail formation. At this level, the ambient temperature was far below the threshold for contrail formation for conventional aircraft. HEA did not lead to was far below the threshold for contrail formation for conventional aircraft. HEA did not lead to a a sufficient lowering of that temperature threshold with 50% electric power. However, increasing sufficient lowering of that temperature threshold with 50% electric power. However, increasing the the hybridization to 90% allowed for a further reduction of the temperature threshold for contrail hybridization to 90% allowed for a further reduction of the temperature threshold for contrail formation. Accordingly, a reduction in contrails was observed in several locations of the tropical region, formation. Accordingly, a reduction in contrails was observed in several locations of the tropical as shown in Figure 10b. region, as shown in Figure 10b. 3.2.2. Effect of Degree of Hybridization In Figure 11, we present a statistical analysis of the local reduction of contrail coverage when different hybridization degrees were considered. The annual mean PCC was used. We observed that the contrail coverage remained nearly unchanged with a smaller fraction of electric power in use (less than 30%). As the hybridization rate increased from 10–90%, an exponential reduction trend was found, which was already indicated by the theoretical analysis in Figures5 and6.

Aerospace 2020, 7, 147 10 of 18 Aerospace 2020, 7, x FOR PEER REVIEW 10 of 18

22 −22 Figure 10. TheThe PCC PCC (contour) (contour) and geopotential (black contour;contour; mm s− )) at at 200 200 hPa hPa (FL390) (FL390) on on a a specific specific Aerospaceday: 2020( (aa)) conventional conventional, 7, x FOR PEER aircraft; aircraft; REVIEW ( (b )) absolute absolute changes changes caused by HEA with 90% electric power. 11 of 18

3.2.2. Effect of Degree of Hybridization In Figure 11, we present a statistical analysis of the local reduction of contrail coverage when different hybridization degrees were considered. The annual mean PCC was used. We observed that the contrail coverage remained nearly unchanged with a smaller fraction of electric power in use (less than 30%). As the hybridization rate increased from 10–90%, an exponential reduction trend was found, which was already indicated by the theoretical analysis in Figures 5 and 6.

FigureFigure 11. 11.Distribution Distribution of theof reductionthe reduction in PCC in with PCC respect with to direspectfferent to degrees different of electric degrees hybridization. of electric hybridization.

3.2.3. Climatology of Contrail Formation The zonal annual mean values of PCC for the reference aircraft and various hybridization degrees are presented in Figure 12. Figure 12a shows the potential contrail coverage for the conventional aircraft, which was also used as a baseline to evaluate different degrees of hybridization effects. From Figure 12b–d, the degree of hybridization increased from 30% to 50% and up to 90%. Again, corresponding to the SAC theory, HEA did not form contrails at the higher temperature and could not form contrails in the lower region of the potential contrail coverage of conventional contrails. Therefore, the reduction of HEA in contrail formation occurred mostly at the lower flight altitudes. However, as the hybridization increased, the altitude range, where contrail formation was reduced, grew.

Aerospace 2020, 7, 147 11 of 18

3.2.3. Climatology of Contrail Formation The zonal annual mean values of PCC for the reference aircraft and various hybridization degrees are presented in Figure 12. Figure 12a shows the potential contrail coverage for the conventional aircraft, which was also used as a baseline to evaluate different degrees of hybridization effects. From Figure 12b–d, the degree of hybridization increased from 30% to 50% and up to 90%. Again, corresponding to the SAC theory, HEA did not form contrails at the higher temperature and could not form contrails in the lower region of the potential contrail coverage of conventional contrails. Therefore, the reduction of HEA in contrail formation occurred mostly at the lower flight altitudes. However, Aerospaceas the 2020 hybridization, 7, x FOR PEER increased, REVIEW the altitude range, where contrail formation was reduced, grew. 12 of 18

FigureFigure 12. Annual 12. Annual zonal zonal mean mean potential potential contrail contrail coverage coverage andand changeschanges due due to to electric electric hybridization: hybridization: (a) conventional(a) conventional aircraft; aircraft; (b) 30% (b) 30%electric electric hybridization; hybridization; (c) 50% (c) 50%electric electric hybridization; hybridization; (d) 90% (d) 90% electric electric hybridization. hybridization.

3.2.4.3.2.4. Seasonal Seasonal Effects Effects

On theOn basis the basis of the of the annual annual simulation simulation results,results, we we studied studied the the seasonal seasonal effects. effect Figures. Figure 13 presents 13 presents the the variationsvariations inin PCC PCC for for 90% 90% of hybridization.of hybridization. The results The results were grouped were grouped into four seasonsinto four at four seasons pressure at four pressurealtitudes. altitudes. Generally, Generally, we expected we expected the largest the eff largesect (i.e.,t effect the greatest (i.e., the reduction greatest in PCC)reduction on the in lowest PCC) on the lowestpressure pressure level, since level, the since temperatures the temperatures on that level on werethat closestlevel were to the closest SAC-temperature to the SAC-temperature threshold. threshold. Similarly, we expected the PCC reduction to become smaller towards higher pressure altitudes with their lower temperatures. This pattern was evident in the figure, except for summer. There were more substantial reductions on 150 hPa (FL450) and 200 hPa (FL390) levels in summer than in the other seasons. This behavior was partly due to higher temperatures, closer to the SAC- threshold, but lower relative humidity than those in different seasons may contribute to PCC reduction. The reduction was found to be more or less constant in summer at all flight levels (differences were insignificant), although the difference between the actual and the SAC-threshold temperature increased with flight level. It is likely that a decreasing frequency of high humidity (including ice-supersaturation) cases balanced the temperature effect such that the PCC reduction in summer depended little on the flight altitude.

Aerospace 2020, 7, 147 12 of 18

Similarly, we expected the PCC reduction to become smaller towards higher pressure altitudes with their lower temperatures. This pattern was evident in the figure, except for summer. There were more substantial reductions on 150 hPa (FL450) and 200 hPa (FL390) levels in summer than in the other seasons. This behavior was partly due to higher temperatures, closer to the SAC-threshold, but lower relative humidity than those in different seasons may contribute to PCC reduction. The reduction was found to be more or less constant in summer at all flight levels (differences were insignificant), although the difference between the actual and the SAC-threshold temperature increased with flight level. It is Aerospacelikely 2020 that, 7, ax decreasingFOR PEER REVIEW frequency of high humidity (including ice-supersaturation) cases balanced the13 of 18 temperature effect such that the PCC reduction in summer depended little on the flight altitude.

90th percentile

75th percentile: Q3

1

Q

- 3

Q Median

= IQR 25th percentile: Q1

th 10 percentile

(a) (b)

FigureFigure 13. Seasonal 13. Seasonal effects effects on on the the changes changes of of potential potential contrailcontrail coverage coverage at at various various pressure pressure altitudes altitudes for 90%for 90%electric electric hybridization hybridization (a) (anda) and the the explanation explanation of ofthe the boxplot boxplot (b (b).). DJF: DJF: December, December, January, January, and February;and February; MAM: March, MAM: March,April, April,and May; and May;JJA: June, JJA: June, July, July, and and August; August; SON: SON: September, September, October, October, and November.and November. For the For boxplot: the boxplot: the 10th the 10thand and 90th 90th percentiles percentiles of of the the data are are plotted. plotted. Triangle Triangle indicates indicates the mean value. As the altitude increases, e.g., at 150 hPa (FL450), the values at 90th percentile and the mean value. As the altitude increases, e.g., at 150 hPa (FL450), the values at 90th percentile and 75th percentile are equal to the minimum of the datasets as zero, therefore not visible in Figure (a). 75th percentile are equal to the minimum of the datasets as zero, therefore not visible in Figure (a).

4. Discussion4. Discussion ThisThis study study demonstrated demonstrated the the effects effects of hybrid of hybrid-electric-electric aircraft aircraft on on potential potential contrail contrail coverage. coverage. The actualThe contrail actual contrail properties properties—the—the number number of soot of soot particles particles related related to usingusing a a hybrid-electric hybrid-electric propulsion propulsion system,system, the thelifetime lifetime of ofcontrails, contrails, etc. etc.—were—were notnot considered. considered. Earlier Earlier research research shows shows that the that number the number of soot particles produced by a turbofan engine is strongly dependent on the thrust setting [37]. A higher of soot particles produced by a turbofan engine is strongly dependent on the thrust setting [37]. A thrust setting would lead to an increase in the combustion temperature, hence, increasing the rate of higher thrust setting would lead to an increase in the combustion temperature, hence, increasing the soot formation, and vice versa. As different degrees of electric hybridization were considered, the gas rate turbineof soot engine’sformation, thrust and setting vice versa. and the As number different of soot degrees particles of variedelectric accordingly. hybridization The changewere considered, in soot the gasparticles turbine will a engine’sffect the contrails’ thrust setting actual optical and the properties, number thus of thesoot resulting particles contrail varied radiative accordingly. forcing. The change inFurthermore, soot particles the will Schmidt–Appleman affect the contrails’ criterion’s actual derivationoptical properties, in this paper thus isthe applicable resulting for contrail a radiativehybrid-electric forcing. propulsion system, for which the electric power is generated by battery. If the choice goesFurthermore, for a fuel cell the hybrid-electric Schmidt–Appleman propulsion criterion’s system, one derivation would require in this a dipaperfferent is consideration. applicable for a hybridThe-electric SAC for propulsion the fuel cell typesystem of hybrid, for which system the depends electric on power how the is fuelgenerated cell’s exhaust by battery. is handled. If the If choice a goesheat for exchangera fuel cell is hybrid used to-electric collect the propulsion fuel cell’s exhaustsystem, heat, one thewould water require vapor ata thedifferent fuel cell’s consideration. exhaust The SACis then for condensed the fuel cell into type a liquid. of hybrid In this system case, contrails depends are on only how formed the fuel from cell’s the gas exhaust turbine is exhaust. handled. If a heatThe exchanger SAC derivation is used in to the collect current the paper fuel cell’s can still exhaust be valid. heat, However, the water if vapor no condensation at the fuel processcell’s exhaust is is then condensed into a liquid. In this case, contrails are only formed from the gas turbine exhaust. The SAC derivation in the current paper can still be valid. However, if no condensation process is involved, the fuel cell then also produces water vapor in the exhaust, which must be considered to derivate an alternative SAC. As observed from our analysis, the reduction in contrail coverage by hybrid-electric aircraft is mostly localized. The consequences are twofold. In a case where the flight route does not cross a region of reduction (that is, the temperature is significantly lower than the contrail formation threshold even for a high portion of electric power), flying with a hybrid-electric aircraft does not affect the contrail formation. Still, the contrail properties (lifetime, optical thickness, and eventually individual radiative forcing) may change with the degree of hybridization. In another case where the contrail reduction is possible along the flight route (that is, the temperature is close to the contrail formation threshold), using a large fraction of electric power at that specific location would effectively reduce contrail formation. For the second case, a specific power management strategy can be developed to design the hybrid-electric system. Eventually, we expect the actual effect to be a

Aerospace 2020, 7, 147 13 of 18 involved, the fuel cell then also produces water vapor in the exhaust, which must be considered to derivate an alternative SAC. As observed from our analysis, the reduction in contrail coverage by hybrid-electric aircraft is mostly localized. The consequences are twofold. In a case where the flight route does not cross a region of reduction (that is, the temperature is significantly lower than the contrail formation threshold even for a high portion of electric power), flying with a hybrid-electric aircraft does not affect the contrail formation. Still, the contrail properties (lifetime, optical thickness, and eventually individual radiative forcing) may change with the degree of hybridization. In another case where the contrail reduction is possible along the flight route (that is, the temperature is close to the contrail formation threshold), using a large fraction of electric power at that specific location would effectively reduce contrail formation. For the second case, a specific power management strategy can be developed to design the hybrid-electric system. Eventually, we expect the actual effect to be a convolution of the existing air traffic patterns with the PCC-reduction patterns. In further analysis, we will investigate the effectiveness of contrail avoidance by hybrid-electric aircraft, considering the routing effects. In addition, in our analysis, we used a typical value of 0.4 as the overall propulsion efficiency, and we left it constant regardless of the amount of electrical power used. As more electrical energy is used, the gas turbine engine’s thrust setting is reduced; correspondingly, the propulsion efficiency would decrease slightly. If we consider such efficiency deterioration, the temperature threshold of contrail formation for the hybrid-electric system is reduced further (see, e.g., Equation (1) and Figure6 of this paper). The lower temperature threshold implies that contrail formation is more likely to decrease, but it requires a thorough analysis in future research.

5. Conclusions

This paper presents the changes in potential contrail coverage when flying with hybrid-electric aircraft. On the basis of the analysis, we have drawn the following conclusions:

The atmospheric areas of contrail formation of hybrid-electric aircraft are smaller than those of • conventional aircraft and require lower atmospheric temperatures. The reduction in contrail formation by hybrid-electric aircraft is more pronounced in a tropical • region where the temperatures are higher. With a small degree of hybridization (below 30% in the current study), the contrail coverage • remains nearly unchanged. A maximum reduction of about 40% in contrail coverage was observed locally, with 90% electric power in use. In non-summer, the reduction in potential contrail coverage by hybrid-electric aircraft was more • noticeable at lower flight altitudes. In contrast, the changes in potential contrail coverage were nearly constant (about 20%) for all flight altitudes studied in summer.

Author Contributions: Conceptualization of this study, V.G. and F.Y.; derivation of the Schmidt–Appleman criterion for hybrid-electric aircraft, V.G. and K.G.; formal analysis and writing the original draft, F.Y.; writing—review, V.G. and K.G.; funding acquisition, V.G. and F.Y. All authors have read and agreed to the published version of the manuscript. Funding: Initial work received funding from the SESAR Joint Undertaking under grant agreement no. 699395 under the European Union’s Horizon 2020 research and innovation program within the Exploratory Research project ATM4E. The individual author of this work receives funding from the Dutch Research Council (NWO) under the talent scheme VENI and in-kind contribution from DLR-Oberpfaffenhofen. The project number is 17367. Conflicts of Interest: The authors declare no conflict of interest. Aerospace 2020, 7, 147 14 of 18

Nomenclature

Abbreviations DJF December, January, and February EIH2O Water vapor emission index kg/kg(fuel) EM Electric motor HEA Hybrid-electric aircraft JJA June, July, and August MAM March, April, and May PCC Potential contrail coverage PDF Probability density function RF Radiative forcing SAC Schmidt–Appleman criterion SON September, October, and November Symbols cp Isobaric heat capacity of the air J/kg/K F Thrust N G The slope of the mixing line pa/K . m f Fuel mass flow rate kg/s p Ambient pressure pa PE Electric power W Q The lower heating value of fuel MJ/kg R Degrees of hybridization [ ] − The maximum temperature at which Tmax C contrail formation is possible ◦ V Velocity m/s The ratio of the molar mass of water ε [ ] vapor and dry air − The overall efficiency of the electric η [ ] E powertrain − The overall efficiency of the pure η [ ] K kerosene aircraft −

Appendix A. Derivation of Schmidt–Appleman Criterion for Hybrid-Electric Aircraft The thermodynamic theory of contrail formation was developed for traditional jet engines many years ago [18,19]. A modern derivation is provided by [35] using the conservation principles of mass, momentum and energy. The traditional engine type has only one source of energy, namely, the fuel with its specific energy content Q. For each kilogram of fuel burnt, a mass of EIH2O kilogram water vapor is produced and emitted. For a . . fuel flow rate of m f uel, the rate of water vapor emission is m f uelEIH2O. The condition for contrail formation is the Schmidt–Appleman criterion (SAC). The most important factor in the theory is the so-called contrail factor G = dep/dTp, that is, the change of partial pressure of water vapor in the exhaust plume, ep, with plume temperature, Tp. This change occurs when the plume is expanding and mixing with ambient air. This mixing is isobaric at ambient pressure, pa, and the mixing trajectory of the exhaust gases in a thermodynamic, e T, diagram is thus a straight line with slope G. The endpoint of that trajectory at infinite mixing − is represented by the ambient conditions: water vapor partial pressure, ea, and temperature, Ta. Thus we find

ep ea G = − (A1) Tp Ta −

It is practical to use mass mixing ratios qx = εex/pa, where ε = 0.622 is the ratio of molar masses of H2O and air. The partial pressure of water vapor at the engine exit is

. . pa ma qa + m f EIH2O ep = · . ·. (A2) ε · ma + m f

. where the notation (ma) is the mass flow rate of air through the engine. In this derivation, we do not consider the separation of the core flow and bypass flow, as the two air streams mix anyway at the engine exit within a few milliseconds. Such a consideration will avoid an unnecessary complication of the equations. The equation states Aerospace 2020, 7, 147 15 of 18 that the vapor partial pressure at the engine exit is composed of that carried by the air needed to burn the fuel plus the contribution from the fuel itself. Since an electric motor does not emit water vapor, there is hence no contribution. Thus, the numerator in the formula for G is

. . pa m f (EIH2O qa) pa m f EIH2O ep ea = · . . − . · . (A3) − ε · ma + m f ≈ ε · ma + m f where the approximation is possible since EIH2O qa. The aircraft needs a thrust F to overcome drag and friction. When it flies with a velocity V, the engines must produce a power . FV = η m Q + η P (A4) K· f · E· E That is, two sources of energy, from the liquid fuel and the electric motor, add their powers with their respective thermodynamic efficiencies, ηx. The notation (PE) is the (variable) power of the electric engine. PE varies . in response to variable fuel flow, such that the above sum equals FV. Thus, PE is a function of m f .

. P = P0 a m with P0 = FV/η and a = Q (η /η ) (A5) E E − · f E E · K E

0 Here, P is the electric power when it is driving the aircraft alone. The higher the fuel flow, the lower PE is. E . The maximum fuel flow to achieve a thrust power of FV is m fmax = FV/ηKQ. It turns out to be useful also to define a quasi-electric energy content, namely,

. 0 = 0 = = ( ) QE : PE/m fmax a Q ηK/ηE (A6)

As the efficiencies are never 1.0, the remaining part of the produced power is wasted for heating and expelling the exhaust gases (from the burnt fuel and the air flowing through the engine). These are thermal and kinetic energies. For the present derivation, we neglected the kinetic energy since it is much smaller than the thermal energy. Thus, we have . h .   . i (1 η )m Q + (1 η )P = cp ma Tp Ta + m Tp (A7) − K f − E E − f That is, the engine air is heated from its ambient temperature to the plume temperature, and the gas added by burning the liquid fuel is heated to Tp as well. (A few other energy sources and sinks are neglected here: the enthalpy of the liquid fuel, the heating of the engine parts, for instance). The symbol (cp) is the heat capacity (at constant pressure) of air. After a few steps, we find

. . . (1 ηK)m f Q + (1 ηE)PE cpm f Ta (1 ηK)m f Q + (1 ηE)PE Tp Ta = −  −  − −  − (A8) − . . ≈ . . cp ma + m f cp ma + m f

This approximation is possible since the enthalpy of the ambient air is much smaller than the energy content of the fuel or the energy produced by the electric motor. Dividing Equation (A3) by Equation (A8) gives an expression for the contrail factor

. c p m EIH2O p a f · G = .  .  (A9) ε · (1 η )m Q + (1 η )P m − K f − E E f where the dependence of PE on the fuel flow is made explicit for clarity. Now it appears convenient to normalize the fuel flow rate by its maximum,

. . R := m f /m fmax (A10)

At pure liquid-fuel operation, R = 1, and at pure electric operation, R = 0. Having this and the other definitions from above, we arrive after a few steps at a favorable expression for G:

cp pa EIH2O G = · R (A11) ε R(1 η )Q + (1 R)(1 η )Q0 − K − − E E Equation (A11) is the desired expression. It has the correct limiting properties. For R = 1 we retain the form of the traditional SAC, but for pure electric propulsion, R = 0, hence, G = 0, which implies that contrail formation is impossible. Aerospace 2020, 7, 147 16 of 18

From here, it is relatively straightforward to formulate a generalization to more than two energy sources. Let

. X FV = ηKm f Q + ηiPi (A12) i where apart from the liquid fuel, we have a number of energy sources (index i) that do not produce water in the exhaust. Then we introduce in analogy to the derivation above:

. 0 = 0 = 0 = ( ) Pi : FV/ηi, Qi : Pi /m fmax ηK/ηi Q (A13)

0 Furthermore, we define weights wi Pi/Pi . It can then be shown that X w = 1 R (A14) i − i

With these prerequisites, we finally arrive at a straightforward generalization of Equation (A11):

cppa EIH2O G = R (A15) P 0 ε R(1 ηK)Q + wi(1 ηi)Q − i − i

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