A Mission Assessment of Aero Engine...

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A MISSION ASSESSMENT OF AERO ENGINE LOSSES

Oskar Thulin Jean-Michel RogeroChalmers University of Technology Airbus Operations S.A.S.

SE-412 96 Goteborg, Sweden 31060 Toulouse Cedex 09, [email protected]

Tomas GronstedtChalmers University of Technology

SE-412 96 Goteborg, Sweden

Abstract

A detailed and systematic lossbreakdown of a direct drive two-spoolturbofan aero engine integratedto an aircraft corresponding toa technology level of year 2020is produced from engine missionpoint performance simulations. Theanalysis includes the fundamentalmission points throughout a commercialaircraft mission. The breakdown alsoincorporates the inherent effectsof the propulsion system such asengine weight and nacelle drag. A newterm, installed rational efficiency,is proposed to fully assess theperformance of the propulsionsubsystem. Combining the detailedcomponent loss analysis with theassessment of the installation effectsprovides a systematic as well aseffective way of analyzing the fullimpact of an aircraft component, likethe engine subsystem, on the aircraft.This can be used to truly assess theperformance of one propulsion unitcompared to another.

Nomenclature

A AreaC Absolute velocityF ThrustL/D Lift over drag coefficientI Irreversibility rateI? Normalized irreversibility rateMa Mach numberP PowerQ Heat transferR Gas constant

T TemperatureU Flight velocityV Relative velocitya Accelerationcx Thrust coefficientg Gravitational constanth Specific enthalpym Mass flowp Pressures Specific entropyx Mole fractionsΨ Rational efficiencyα Angle of attackβ Mass proportion of constituent

in fuelδ Deviation angle between aircraft

direction and engine directionε Specific exergyγ Path angleλ Mass fraction of constituent per

unit of post combustion fluidη Polytropic efficiency

Subscripts

Booster Intermediate pressure compressorBrn BurnerD DragDBP Bypass DuctFanBP Fan Bypass sectionHPC High pressure compressorHPT High pressure turbineICD Inter Compressor ductIntake Engine intakeITD Inter turbine ductJetP Core nozzle duct

(incl. Turbine Rear Structure)L LiftLPT Low pressure turbineRBP Reintroduction of

surge avoidance bleed in Bypass duct

Copyright c©2015 by Oskar Thulin.

Published by the International Society of Airbreathing Engines (ISABE), with permission.

mailto:[email protected]

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S ShaftT ThrustW Weightbld Bleedcabin Cabineng Enginef Fuel, Formationi Iteration variablein Into control volumeout Out of control volumesf Standard formulass Standard statesyst System level∞ Ambient condition30 High pressure compressor

exit (total)40 High pressure turbine

entry (total)

Introduction

Reducing engine losses is ofparamount importance in theaerospace industry. Using theconventional method to estimateirreversibility, different lossesare typically accounted for usingturbomachinery efficiencies, pressureloss coefficients, mechanicalefficiencies and mixing losses. Tofully comprehend how the differentengine parameters may affect theoverall performance requires extensiveexperience and trade-offs are madeusing parameters of different impact,e.g. compressor efficiency, nacelledrag and engine weight. Propulsionconcept development, selection andintegration is truly one of the mostcomplex challenges in an aircraft, itconstitutes a highly multidimensionaland tightly coupled system.

Today, parametric studies on abaseline model are typically used toestimate the effect of incrementalimprovements to the engine. Thismethod does not allow for a way tomake the losses comprehensible, onlyto study the effect of a change.Methods exist, based on exergyanalysis, that are able to assessthe component contribution to theoverall losses and relate the lossesto each other in a unified framework.

Surprisingly, exergy based methodsstill seem to be in limited usefor analysis of aero gas-turbineengines. Having said this, itshould be noted that monitoringand analysing entropy productionis a common method for aero engineturbomachinery component analysis.The entropy production term, isdirectly related to the exergydestruction through the multiplicationwith a reference temperature. Theuse of entropy production in analysisof turbomachinery can hence be seenas nothing but an implicit use of theexergy methodology. However, for aeroengine systems the situation stillseems to be that exergy analysis is inlimited use.

Using the exergy methodology allowsanalysis of the engine performancein one common currency, that fullytakes advantage of the possibilitiesin the first and second law ofthermodynamics. Exergy calculationsrelate the thermodynamical propertiesof a fluid stream to an equilibriumstate to determine the work potentialat each station in the engine. Thefurther away the thermodynamicalproperties are from the equilibriumstate, the larger the work potentialis. Tracking the loss of workpotential in each component throughoutthe cycle clearly indicates where theirreversibilities occur.

Horlock and Clark pioneered thefield of exergy analysis by applyingit to a turbojet as early as 1975 [1].Their original work was derived fromextending the work of Evans [2]. In1995, Brilliant extended the analysisfor a turbofan engine [3] which wasstudied at the cruise point. Rothand Mavris wrote a series of paperson the subject, especially interestingfor the scope of this work is a fullmission study of a military fighteraircraft from 2000 [4]. Gronstedtet al. used exergy analysis in thecruise point to evaluate differentfuture commercial engine concepts



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including a turbofan 2050 reference,a pulse detonation combustion engineand an open rotor engine [5]. Zhaoet al. continued the explorationof exergy analysis by applying itto better understand the benefitsof intercooling in turbofan aeroengines [6].

Rosen previously took a smallstep in the direction of providinga commercial engine mission studybut the analysis failed to provideunderstanding of the loss sourcesthroughout a commercial aircraftmission [7]. Rosen assumed engineperformance data and flight conditionswhich are far from typical airlineoperation. This paper provides abreakdown of the irreversibilitiesduring the different main pointsthat constitute a full mission of acommercial aircraft engine. A moderndirect-drive two-spool turbofan enginewas chosen as the engine architecturein this study, due to its dominatingmarket share.

This paper will not only provide adetailed study of a multi-operatingpoint turbofan but also aims atextending the concept of exergy fromthe analysis of pure thermodynamiceffects to include the consequences ofthe implementation on the aircraftto the overall mission energyrequirements and hence be able tofully compare different implementationintegrated at vehicle level. Paulusand Gaggioli wrote a simple butinspiring contribution presenting theexergy associated with lift [8]. Theanalysis in this paper includes weightfrom the engine and the pylon, as wellas drag caused by the nacelle. Theanalysis also includes engine bleedand power extraction. Includingthe installation effects will givea direct comparison between theengine aerodynamic properties and massassociated with the engine. A newterm, installed rational efficiencyis proposed, making it possible tocompare the complete impact on the

aircraft for one propulsion unit withanother.

Aero Engine Exergy Theory

The most significant energy fluxesin an aero component are thrust,mechanical work, kinetic energy,thermomechanical energy and chemicalenergy. These fluxes are thereforeincluded in the aero engine exergyanalysis presented here. Theformulation is based on the work ofHorlock and Clark [1]. Horlock andClark provided the analysis for theassumption of perfect gas. However,in this paper the treatment has beenadopted to real gases to be used instate of the art engine performancecodes.

The maximum work that can beobtained for an aero engine systemis given by

∑i

miεi

in

≥ PS + PT −∑i

∫ T−T∞T

dQi

+

(∑imiεi

)out

(1)

and is illustrated in Fig.1. Themaximum work is obtained in reversiblelimit at which equality holds [9].The equation corresponds to the exergybalance of the incoming and outgoingexergy fluxes and is a measure of theirreversibility of the system.

Figure 1: Second law ofthermodynamics applied to thereference frame of the engine



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The irreversibility rate, alsocalled the exergy destruction I,is formed as a difference whenbookkeeping the exergy crossing theboundaries of a control volume:

I =

(∑imiεi

)in

−(∑imiεi

)out

−PS − PT +∑i

∫ T−T∞T

dQi. (2)

When the reference environment isset to the ambient conditions, thetotal magnitude of exergy that entersinto the system is equal to the exergyof the fuel. Relating the componentirreversibilities to the total exergygives the ratio of irreversibility foreach component, then

I?

=I

mfεf. (3)

Adding up all the irreversibilitycontributions give a ratio of thetotal irreversibility

I?syst =

∑i Ii

mfεf. (4)

The rational efficiency expressesthe useful work of a control volume inrelation to the incoming exergy flux.The useful power generated by the aeroengine is the thrust it provides tothe aircraft as well as the bleed andpower it potentially supplies to thecabin. Cabin bleed and power are notcommonly included in the rationalefficiency term. However, it isuseful work delivered to the aircraftand hence it ought to contribute tothe useful work term. Thus we define

Ψsyst =

∑i PT,i +

[(mε)bld + Ps

]cabin

mfεf. (5)

The different terms in Eq.1 aredescribed in more depth inthe Appendix.

Installed rational efficiency

The net thrust generated by theengine is propelling the aircraft. Apart of this thrust is compensatingfor the fact that the engine subsystem adds weight and engine external

drag to the aircraft. This paperpresents a method to account forthese losses of useful power, totruly assess the full impact ofthe engine subsystem towards theaircraft. The principle of accountingfor engine components as the weightand potential drag that need to becompensated for can be extended toinclude every aircraft componentin order to truly assess the fullperformance of the aircraft in asystematic way. The authors havechosen to apply the method to theengine and its installation to givethe engine community a way to assessthe full engine performance.

The external drag is easilycompensated for by multiplying theobject’s velocity with the thrust thatis required to balance the drag force,namely

PT,drag = UFdrag

cos(α− δ). (6)

Compensating for weight is slightlymore complicated. Using a knownlift over drag ratio provides a wayto accomplish this. Combining theforce balances of an aircraft inthe directions of parallel to aswell as perpendicular to the flighttrajectory, gives the equation thatis necessary to evaluate how muchthrust is required to carry a certainweight. This equation, as opposedto the drag, can be divided intotwo parts: 1) a dissipating and a2) non-dissipating and hence exergyaccumulating part. The steady statecontribution of the non-dissipativepart is accumulated as potential powerin climb and can later on be harvestedin descent. The acceleration termswill add to the momentum and are bydefinition non-dissipative. The termcorresponding to the misalignment ofthrust to the aircraft trajectory,cos(α − δ), contributes to the dissipativepart when different from one. Theproduct when multiplying the thrustequation with the object’s velocityis equivalent to the magnitude of



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the useful power that is consumedin order to carry a certain weight.The equation with the different partsdenoted explicitly becomes:

PT,weight =

Umeng

cos(α− δ)

aD +1

L/DaL︸︷︷︸

Acceleration

+ g sin(γ)︸︷︷︸Potential

+1

L/Dg cos(γ)︸︷︷︸

Dissipative

.(7)

Using the drag- and theweight-thrust equation, i.e. Eq.6and Eq.7 respectively, along withthe ordinary engine component lossbreakdown makes it possible toassess the impact of all differentengine related subsystems towards theaircraft.

Here a new term called installedrational efficiency is introduced, totake the deduction of power neededto compensate for the weight anddrag associated with the enginesubsystem. In descent, the harvestedpotential exergy adds, along withthe fuel exergy, to the incomingexergy flux. In climb, the storedpotential exergy is seen as storedwithin the control volume and therebynot yet consumed. Including storedand harvested potential exergy inthe numerator is also valid for theirreversibility equations in Eq.2and Eq.3. For reasons previouslyoutlined the bleed and power suppliedto the airframe need to be included innumerator. The full equation becomes

Ψsyst,inst =

∑i PT,i−(

PT,eng-W + PT,eng-D

) +

[(mε)bld + Ps

]cabin mfεf − PT,eng-W-stored potential

+PT,eng-W-harvested potential

.

(8)It shall be noted that engine weight

is not only a burden for the systemsince it also contributes to wingload alleviation. This is howevera secondary effect which is complex toassess. Its influence has thereforebeen neglected in this paper.

Engine architecture and mission point specification

As an example to carry the analysisa generic aircraft equipped bytwo-spool generic engines wasdefined by Chalmers based on publicinformation. The engine setup wasdesigned in a multi point designprocess in PROOSIS R© [10] to reflect atypical modern engine of a technologylevel corresponding to year 2020.Some important information about thePROOSIS R© setup regarding exergy canbe found in the Appendix. The engineperformance can be seen in Tab.1.

The mission-point specificationfrom an external aircraft model canbe seen in Tab.2, where mid climb,top of climb, begin of cruise, end ofcruise and descent are all included.A lift-over-drag coefficient as wellas an angle that describes how theengine is lined up compared to theaircraft are both required for theinstalled exergy calculations. Theyare assumed to be 23 and 2.5 degrees,respectively. The lift-over-dragcoefficient will in reality differslightly over the different points.For simplicity reasons it has beenchosen to be constant in frame of theanalysis in this paper.

Engine performance modeling doesnot typically require design ofengine internal component areas.However, knowledge about the componentvelocities is necessary when usingthe exergy methodology. Engine areaswere designed to be corresponding totypical engine component Mach numbersin cruise. These Mach numbers, thatcan be found in Tab.3, were selectedbased on the work by Grieb [11], andextrapolated to year 2020 performancelevel.

To compensate for the engine subsystem weight and drag additionalmodeling was required. Nacelledrag was assessed for the differentmissions points by using a Chalmersin-house code based on the report



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Table 1: Engine specifications for different mission points

Mid Climb Top of Climb Begin of Cruise End of Cruise Decent

ηFAN-BP 0.93090 0.92900 0.93073 0.93078 0.48999ηFAN-CORE&BOOSTER 0.90472 0.89483 0.90417 0.90561 0.87688ηHPC 0.90406 0.89397 0.90616 0.90856 0.86553ηHPT 0.91116 0.91100 0.90897 0.90849 0.85016ηLPT 0.91309 0.91068 0.90947 0.90933 0.88538T30 (K) 838.99955 800.82353 774.07702 768.23483 553.35047T41 (K) 1733.01201 1682.95751 1604.90967 1589.00544 1154.98451OPR 41.65294 45.39788 41.68407 40.97466 9.27412BPR 12.62240 12.34636 12.66769 12.73707 22.57642FPR 1.47680 1.53658 1.48324 1.47292 1.03847πFAN-CORE&BOOSTER 2.26981 2.37901 2.28933 2.27048 1.28911W1 (kg/s) 311.16049 184.42970 181.68668 180.54454 180.40627SFC (mg/Ns) 13.41601 14.45390 14.69187 14.71214 -167.61114

Table 2: Mission point Specification


alt (ft) 20000 37000 37000 37000 20000M 0.589 0.77 0.79 0.79 0.589α (deg) 2.78 3.29 2.97 2.84 2.63γ (deg) 2.79 0.54 0.00 0.00 -3.15FN(N) 37500 20500 18000 17500 -500time after take-off (min) 8 25 25 95 105

Table 3: Engine component Machnumbers

MaIntake,out 0.603MaBooster,out 0.422MaICD,out 0.482MaHPC,out 0.263MaBrn,out 0.150MaHPT,out 0.420MaITD,out 0.368MaLPT,out 0.322MaJetP,out 0.322MaFanBP out 0.452MaDBP,out 0.452MaRBP,out 0.452

ESDU 81024 [12]. Engine sub systemweight was modeled in an in-housedeveloped conceptual design toolcalled WEICO [13]. The engineweight was estimated to 3280kg.The conceptual design of the engineincluded 3 booster stages, 10 HPCstages, 2 HPT stages and 7 LPT stages.Weight for pylon was also includedin the analysis since it is a directeffect of having an engine mountedon the wing and ultimately attachedto the aircraft. It was estimated to492kg.

Exergy breakdown of the engine thermodynamic cycle

A breakdown of the total exergyis performed at each mission pointto indicate what is useful, asseen from the control volume of thepropulsion system. Aggregating themission points that are presented inthis paper as well as one take-offpoint into a total mission breakdownenables the possibility of showingthe full mission engine performance.A mission total breakdown of whatis useful for the engine can befound in Fig.2(a). The total wascalculated by summing the productsof the exergy flow per time unit withthe time spent on each point during aregional aircraft mission. The fuelburn before take-off is neglectedin this analysis. The aircraftwas considered to land at the samealtitude as it took off from. Thethermodynamical reference used in theexergy calculations was changed alongwith the changing ambient conditionat different altitudes since the



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Propulsive Power : 31.85%Cabin Supplied Bleed and Power : 1.61%

Irreversibility : 66.54%

(a) Total exergy

Fan incl. Booster : 3.69%

HP Compressor : 2.17%

Burner : 18.04%

HP Turbine : 1.35%LP Turbine : 1.51%

Core Exhaust Thermal : 19.78%

Core Exhaust Kinetic : 1.69% Core Exhaust Chemical : 3.84%

Mechnical : 1.13%Bypass Duct : 3.03%

Bypass Nozzle : 0.90%BP Exhaust Thermal : 2.09%

BP Exhaust Kinetic : 6.22%

Other : 1.10%

(b) Irreversibility

Figure 2: Mission Total - Breakdown.

Table 4: Results of the Total Breakdown of all mission points normalized withfuel exergy


Propulsive Power 0.31433 0.35670 0.36009 0.35961 -0.02235Cabin Supplied Bleed and Power 0.01250 0.01636 0.01795 0.01832 0.04513Irreversibility 0.67317 0.62694 0.62196 0.62206 0.97722Rational Efficiency 0.32683 0.37306 0.37804 0.37794 0.02278



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Mid

Clim

b

Top

of

Clim

b

Beg

in o

f C

ruis

e

En

d o

f C

ruis

e

Decen

t−10

0

10

20

30

40

50

60

70

80

90

100

110

[%]

Propulsive Power (negative thrust)

Propulsive Power

Cabin Supplied Bleed and Power

Irreversibility

(a) Normalized with fuel exergy

Mid

Clim

b

Top

of

Clim

b

Beg

in o

f C

ruis

e

En

d o

f C

ruis

e

Decen

t

−100

102030405060708090

100110120130140150160170180190200

[%]

Propulsive Power (negative thrust)

Propulsive Power


Irreversibility

(b) Normalized with total missionaverage consumed exergy

Figure 3: Mission point comparison - Exergy breakdown.

instantaneous ambient conditions issetting the instantaneous limit ofthe maximum work possible of a systemduring a process that brings thesystem to complete equilibrium itsthe surroundings.

Almost two thirds of the enteredfuel exergy is corresponding toengine internal irreversibilities.The additional part is constitutingthe rational efficiency where thepropulsive power is about twenty timesas large as the cabin supplied bleedand power.

The simulated mission points thatconstituted the mission are presentedindependently in both Fig.3(a) andTab.4. It can be noted that thehigher loaded mid climb point whichis further from design conditionshave a lower rational efficiency thanthe lower loaded top of climb andcruise points. The descent point issimulated having a negative thrust,this causes the irreversibilitiesto be larger than the entered fuelexergy. Each point is normed with thefuel exergy that is consumed duringthe corresponding point. This showshow well the engine performs at a

specific point but does not providea way to compare the losses betweenthe points to each other.

In order to give the perspective ofhow the points compare to each otheran additional stacked bar chart wascreated, as seen in Fig.3(b). Thischart was not normed with the fuelexergy consumed at the point butinstead the mission total average fuelexergy. The more highly loaded midclimb point consumed significantlymore fuel which make the magnitudesignificantly larger than for theother points. The cruise pointsconsume about 90% of the total missionaverage fuel exergy. The lattercruise point slightly less due tothe lower lift requirement causedby the lower fuel weight. The largerelative engine irreversibility in thedescent point can be seen to be smallin absolute numbers in comparison tothe other points.

Irreversibility breakdown of the engine propulsion cycle

The analysis is also accompanied bya breakdown of all irreversibilitieson component level. When summing up



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the irreversibility percentages in theirreversibility breakdown, it equalsthe magnitude of the irreversibilityin the total exergy breakdown.

A total mission irreversibilitybreakdown is presented inFig.2(b). Looking at the differentirreversibilities, some are moreaccessible to decrease than others.Work has previously been done onexcluding the irreversibilities fromthe analysis that are considered to beimpossible to lower. To assess whattechnology that cannot be inventedwould be highly unproductive in termsof looking for future engine concepts.As well as it would make comparisonbetween different concepts problematicand understanding of how the lossestruly distribute hard.

The total turbomachinery lossescorresponds to 8.72 fuel exergypercentage units of which 40%originates from the turbomachinerylocated on the high pressureshaft. The turbomachinery lossesare equivalent of a little bitmore than 13% of the total engineirreversibility. Even though theturbomachinery related losses aresmall in comparison to the otherirreversibilities, as being one ofthe major weight drivers in the engineit is important that high efficiencyis achieved at lower component weight.

The burner contributes as one ofthe two major sources to the totalirreversibility. This is despite thatcombustion efficiency is almost atone. The combustion irreversibilitiesis an inherent effect of constantpressure combustion used in turbofans.The large irreversibilities comesfrom the massive entropy productionin combustion. In order to limitthe entropy production, it would bebeneficial to combust at a steepercurve in a temperature-entropy (TS)diagram. Constant volume combustionis a way to accomplish this sinceisochores on a TS diagram are steeper

than isobars.

The ducts have a very smallcontribution to the engine propulsionsystem irreversibilities, needlessto say that well-designed ducts arehowever important for the performanceof the other component as well asit is important for limited engineweight. The only exception to thestatement about low irreversibilitiesin the ducts is the bypass duct whichhas a much larger contribution to theirreversibilities due to the largemagnitude of mass flow that is passedthrough the duct. The bypass nozzlecompared with the core nozzle showa similar effect that is also mainlycaused by the large mass flow.

The mechanical efficiency is set to99.8% for both shafts. A resultingirreversibility of 1.13% makes itclear that the large amount of powerthat is transferred via the shaftsleads to much higher losses on asystem level than what is indicatedby the efficiency number by itself.

Unused exergy in the flow leavingthe engine is included in the exhaustcomponent. Note that all exhaustirreversibilities are broken down intothe different exergy fluxes. The termcorresponding to "thermomechanical"exergy is here named "thermal" sinceit better describes the specificexergy flow. The reasoning is thatthe pressure difference to ambientconditions will only contribute in thenozzle thrust term and not show up asan irreversibility.

Thermal exhaust irreversibilitiesis a result of that the flow isenergized in the engine cycle and thennot brought to thermal equilibriumwith the ambient conditions. Thethermal exhaust irreversibilityis the largest contribution to thetotal irreversibilities, it causesnearly 30% of the engine cycleirreversibility. The exhaust flow forthe core is in excess of 450 degrees



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Table 5: Results of the Irreversibility Breakdown of all mission pointsnormalized with fuel exergy


Inlet 0.00501 0.00440 0.00486 0.00496 0.01744Fan incl. Booster 0.03314 0.03337 0.03259 0.03258 0.13138Intercompressor Duct 0.00147 0.00132 0.00143 0.00145 0.00267Core leakage 0.00046 0.00051 0.00054 0.00054 0.00035HP Compressor 0.02220 0.02251 0.02083 0.02049 0.03819Burner Inlet Duct 0.00120 0.00107 0.00115 0.00117 0.00200Burner 0.18433 0.15986 0.16776 0.16949 0.28672HP Turbine 0.01302 0.01092 0.01219 0.01248 0.03579Interturbine Duct 0.00072 0.00064 0.00069 0.00070 0.00119LP Turbine 0.01484 0.01412 0.01524 0.01545 0.01672Jet Pipe Duct 0.00073 0.00065 0.00070 0.00071 0.00120Core Nozzle 0.00070 0.00102 0.00104 0.00103 0.00030Core Exhaust Thermal 0.20108 0.19523 0.19110 0.19051 0.27044Core Exhaust Kinetic 0.01726 0.02159 0.01540 0.01429 0.00661Core Exhaust Chemical 0.03716 0.04036 0.03988 0.03978 0.03348Mechnical 0.01141 0.01142 0.01153 0.01155 0.00803Bypass Duct 0.02821 0.02475 0.02737 0.02794 0.10147Booster Bleed into BP 0.00000 0.00000 0.00000 0.00000 0.00374Bypass Nozzle 0.00738 0.00904 0.01023 0.01043 0.01652BP Exhaust Thermal 0.00056 0.03525 0.03163 0.03026 0.00280BP Exhaust Kinetic 0.09229 0.03890 0.03583 0.03625 0.00021BP Exhaust Chemical 0.00000 0.00000 0.00000 0.00000 0.00000

kelvin warmer for the simulated enginethan the ambient conditions in cruise.This temperature difference does notin itself contribute to the thrustat all and hence can be seen as amajor term. The bypass thermalirreversibility is much lower sincethe only increase of enthalpy takesplace in the bypass section of thefan.

The exhaust gases are more rich onH2O and CO2 than the gas compositionfound in the ambient air, thesecompositions have different exergylevels due to the different set ofpartial pressures. For the exhaustgas the exergy is higher. It couldbe theoretically possible to obtainwork from gases with various partialpressures, but would be highlyimpractical in reality. One couldsee this loss as a direct result ofthat fuel is burned.

The last but not least term isthe kinetic irreversibilities inthe exhaust flows. All kineticenergy in the exhaust flow does notcontribute to the thrust, the kinetic

irreversibility is corresponding tothe portion of the kinetic energy thatdoes not propel the aircraft. Thisterm is hence directly related to thepropulsive efficiency.

The outcome of the irreversibilitydistribution of the different missionpoints can be seen in Tab.5.

Radar charts were produced toillustrate how the irreversibilitieschanges comparing the differentmission points. The largest losssources can be found in Fig.4(a)and the corresponding sources normedwith the mission total average fuelexergy is illustrated in Fig.4(b).The mid climb point does not chokein the bypass nozzle which explainsthe much lower thermal exhaustirreversibility, but on the other handsignificantly higher kinetic exhaustirreversibility, compared to the topof climb and the cruise points. Theother components irreversibilitiesperform quite similar normed with thespecific mission point fuel exergyconsumption but when compared whennormed with the mission total average



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(a) Large (b) Large normalized with total mission averagefuel exergy

(c) Mission Points - Mid Size (d) Mid Size normalized with total mission averagefuel exergy

Figure 4: Mission Points - Irreversibilities (All charts scaled after largestincluded loss).

Table 6: Results of the Total Breakdown of all mission points normalized withconsumed exergy


Propulsive Power to Aircraft 0.28249 0.31137 0.31185 0.31003 -0.13966Cabin Supplied Bleed and Power 0.01269 0.01646 0.01795 0.01832 0.04094Engine System Weight - Potential (stored internal) 0.01533 0.00611 0.00000 0.00000 0.00000Engine System Weight - Potential (harvested) 0.00000 0.00000 0.00000 0.00000 0.09285Engine System Weight - Dissipative 0.01368 0.02818 0.03219 0.03307 0.07335Nacelle drag 0.00764 0.01322 0.01605 0.01652 0.04603Engine Irreversibility 0.68350 0.63076 0.62196 0.62206 0.88649Installed Rational Efficiency 0.29518 0.32783 0.32979 0.32835 -0.00586



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fuel exergy the points scale with thethrust requirement.

Losses smaller than for theconsidered large losses, but stillsignificant, are included in themid size irreversibilities chartsin Fig.4(c) and Fig.4(d). Theperformance of the turbomachinerycomponets in relative terms can beseen to stay relatively constant forthe climb and cruise points.

Installed exergy breakdown

Analysis including the installationeffect of engine weight and dragbrings the control volume from lookingat the engine propulsion cycle to thefull engine sub system. An exergybreakdown focusing on the engine subsystem has been made for the differentmission points. The mission total canbe seen in Fig.5.

The fuel exergy that goes towardsthe potential exergy in climb can beseen to be balanced with the harvestedpotential exergy in descent. Thisorigins from that take off and landingis taking place at the same altitudeand that the control volume mass iskept constant throughout the mission.

The simulated mission points arepresented in Tab.6 and Fig.6. Thecruise points perform at about aninstalled rational efficiency of about32.9%, this can be compared to therational efficiency at 37.8% of thepropulsion cycle. The total installedrational efficiency is 29.41% and theengine cycle rational efficiency is33.46%.

Regarding the descent point,seen from the engine sub system,the negative contribution to theairframe is in terms of the magnitudeeven larger than for the enginepropulsion cycle. The engine subsystem also needs to compensate forthe dissipative term of the weightequation as well as the nacelle drag.

Discussion and Conclusions

An installed exergy analysis hasbeen applied to a turbofan of atechnology level corresponding to year2020 simulated for the main missionpoints that constitute a full flightmission. The analysis extends onprevious work both by including theeffects of weight and drag directlyassociated with having a propulsionsystem connected to the aircraft, aswell as by featuring detailed studiesfor the different mission points.The simulation of various missionpoints help understand the propulsionsystem performance under the differentoperating conditions. The developedmethodology for the installationeffects can also be used to assessthe effect of any aircraft componentin one common unit. The propulsionsystem installation effects accountsfor about 4% of total work potentialin the fuel seen over a full flightmission. Comparing it to the thrustpower delivered to the aircraft theratio becomes one to seven.

A new figure of merit to capturethe true performance of a propulsionsystem has been proposed, namely theinstalled rational efficiency. Themeasure utilizes the advantages ofexergy analysis when relating thepropulsion unit supplied useful powerto the work potential found in thefuel. The useful power is the powerthrust delivered to the aircraft frameas well as the bleed and shaft powersupplied to the cabin. The powerthrust delivered to the aircraftframe is the thrust supplied by theengine cycle when compensating for theeffects of the thrust misalignment,the weight and the drag associatedwith the propulsion system. Theinstalled rational efficiency for thesimulated turbofan of a technologylevel to correspond to year 2020 is29.41%.

The installed rational efficiencyterm offers a way of assessing the



13

ISABE-2015-20121

Engine System Weight - Potential (stored internal) : 0.35%Engine System Weight - Dissipative : 2.68%

Nacelle drag : 1.37%Engine System Weight - Potential (harvested) : 0.35%

Propulsive Power to Aircraft : 27.45%Cabin Supplied Bleed and Power : 1.61%

Engine Irreversibility : 66.54%

Figure 5: Mission Total - Total installed exergy breakdown

Mid

Clim

b

Top

of

Clim

b

Beg

in o

f C

ruis

e

En

d o

f C

ruis

e

Decen

t

−20

−10

0

10

20

30

40

50

60

70

80

90

100

110

120

[%]

Propulsive Power to Aircraft (negative thrust)

Propulsive Power to Aircraft


Engine System Weight - Potential (stored internal)

Engine System Weight - Potential (harvested)

Engine System Weight - Dissipative

Nacelle drag

Engine Irreversibility

Figure 6: Mission point comparison - Installed exergy breakdown normalizedwith consumed exergy



14

ISABE-2015-20121

propulsion system performance inflight decoupled from the aircraftmodel. Using an aircraft angle ofattack, an aircraft path angle and anaircraft lift over drag coefficient,which are all predefined from anaircraft model, makes this possible.One could use these parameters asapplied in this paper to evaluateother engines that are designed for asimilar mission type in order to get acomparative measure between differentengine configurations.

Acknowledgments

The authors want express theirgratitude to Airbus S.A.S. fortheir support and funding of thiswork. The authors also want to thankJonas Lafrenz Schwanemann who duringhis internship made a significantcontribution on the subject ofextending the Exergy analysis to takethe full effects at aircraft level.

Disclamer

The data published in this paper weregenerated solely to be a supportto the analysis exercise and arenot related to any Airbus productcharacteristics.

References

[1] Clarke, J. M., and Horlock,J. H., 1975., ‘‘Availabilityand propulsion’’, Journal ofMechanical Engineering Science,17, p. 223.

[2] Evans, R. B., 1969., ‘‘Aproof that essergy is the onlyconsistent measure of potentialwork’’. PhD thesis, DartmouthCollege.

[3] Brilliant, H. M., 1995. ‘‘Secondlaw analysis of present andfuture turbine engines’’. InJoint Propulsion Conference. AIAA95-3030.

[4] Roth, B., McDonald, R., andMavris, D., 2000. ‘‘A methodfor thermodynamic work potentialanalysis of aircraft engines’’.In Joint Propulsion Conference,Vol. 38. AIAA2002-3768.

[5] Gronstedt, T., Irannezhad,M., Xu, L., Thulin, O., andLundbladh, A., 2014., ‘‘Firstand second law analysis of futureaircraft engines’’, Journal ofEngineering For Gas Turbines andPower, 136.

[6] Zhao, X., Thulin, O., andGronstedt, T., 2015. ‘‘Firstand second law analysis ofintercooled turbofan engine’’.In ASME Turbo Expo. GT2015-43187.

[7] Rosen, M. A., 2009., ‘‘Exergylosses for aerospace engines:effect of reference environmenton assessment accuracy’’, Exergy,an International Journal, 6.

[8] Paulus, D. M. J., and Gaggioli,R. A., 2003., ‘‘The exergyof lift and aircraft exergyflow diagrams’’, InternationalJournal of Thermodynamics, 6,pp. 149--156.

[9] Kotas, T. J., 1985. The ExergyMethod of Thermal Plant Analysis.Butterworths.

[10] Empresarios AgrupadosInternacional. Proosis -Propulsion Object OrientedSImulation Software. The VIVACEEuropean Cycle Program.

[11] Grieb, H., 2004. ProjektierungVon Turboflugtriebwerken.Birkhauser.

[12] ESDU International plc, 1981.Drag of axisymmetric cowls atzero incidence for subsonic Machnumbers.

[13] Grronstedt, T., Au, D.,Kyprianidis, K., and Ogaji,S., 2009. ‘‘Low pressuresystem component advancements



15

and its influence on futureturbofan engine emissions’’. InProceedings of ASME Turbo Expo2009: Power for Land, Sea andAir, GT2009.

[14] McBride, B. J., and Gordon,S., 1994. Computer Program forCalculation of Complex ChemicalEquilibrium Compositions andApplications. NASA RP-1311.

16

Appendix

Exergy Analysis Theory

Without detailed knowledge ofthe heat transfer process the termneeds to be simplified in orderto be implemented. In case of theassumption of a perfect gas, the heattransfer integral can be rewrittenaccording to

−∑i

∫ Qi0

T − T∞T

dQi =−∑i

dQi

dT

∫ Ti,endTi,start

T − T∞T

dT

=−∑i

Qi

1− T∞ln[Ti,end/Ti,start

][Ti,end − Ti,start

].

(9)

If the temperature is, or can beapproximated as constant during theheat transfer, the heat transferintegral in Eq.1 simplifies accordingto

−∑i

∫T − T∞

TdQi = −

∑i

QiTi − T∞

Ti. (10)

This is also consistent when takingthe limit of Eq.9.

Regarding the steady flow energyequation, the only difference whenmoving from the relative to theabsolute frame of reference is thechange in velocities and the additionof the thrust power term. Therefore,by subtracting the equation from onereference frame to the other, thethrust power can be written as

PT =

∑i

mi

C2i

2−V 2i

2

in

−

∑i

mi

C2i

2−V 2i

2

out

.

(11)Using the velocity definition

(C = U − V), the expression can besimplified to

PT =U

2

∑i

mi(U − 2Vi

)in

−

∑i

mi(U − 2Vi

)out

.(12)

Under the assumption of one inflowand one outflow, the equation can bereduced to

PT = mU(Vout − Vin). (13)

If the exhaust nozzle of theengine is choked, then the pressuredifference will also contribute to thethrust power. Also, the coefficientof thrust will affect the momentum.The following equations are valid forthe nozzle:

PTin→nozzle =U

∑i

micxVi

nozzle

−

∑i

miVi

in

and

PTnozzle→∞ =∑i

UAnozzle,i

(pnozzle,i − p∞

).

(14)

The specific exergy is calculatedby Eq.15. It includes the differentforms of exergy that are applicableto an aero engine flying at a constantaltitude, i.e. a thermomechanicalpart (also commonly known as thephysical exergy), a kinetic part and achemical part, i.e.

ε = h− h∞ − T∞(ssf − ssf,∞)︸︷︷︸Thermomechanical

+C2

2︸︷︷︸Kinetic

+T∞(∑i

λiRi lnx

xi,∞

)︸︷︷︸

Chemical

.

(15)Fuel exergy is defined as the

maximum work obtainable comparing thestate of resting unburned fuel to whenthe chemical potential of the fueland the reference environment are incomplete equilibrium with each other.Since the chemical part in Eq.16 isderived assuming that the speciesconsidered are present in both thesystem and the reference environment,a different approach must be used. Amethod for evaluating the exergy of afuel or for a mixture of species thatdo not solely consist of species inthe reference environment is describedin detail by Kotas [9]. One shallnote that this is not equal to theLHV value even though it will be quitesimilar in magnitude. In conformitywith the LHV and the HHV calculations,the main contributing energy term inthe fuel exergy calculation is basedon heat of formation. The entropyfor the products after a combustionis much larger than the for thereactants, i.e. heat is captured bythe products. The entropy difference

17

when comparing the products andreactants is included in the chemicalfuel exergy term. The difference inenthalpy and entropy comparing thethermomechanical state of the fuelto the ambient conditions is includedin the thermomechanical term. Theequation is

εf = εf,phys + εf,kin + εf,chem, (16)

where the subcomponents are calculatedby the following formulas

εf,ther.mech =

∑i

βi

[hi − hss,i

]−∑i

λi

[h∞,i − hss,i

]− T∞

∑i

βi

[si − sss,i

]−∑i

λi

[s∞,i − sss,i

],εf,kin =

∑i

βiC2i

2and

εf,chem =∑i

(βi − λi

)∗(∆h◦f,i − T∞∆s

◦f,i

).

Simulation setup

Fuel exergy is different from theLHV value since it in addition tothe difference in chemical enthalpyalso includes the change of entropycomparing pre and post combustionas well as the thermomechanicaldifference between the two states.A way to calculate fuel exergy canbe found in Eq.16. This methodrequires full knowledge of the fuelcomposition. Jet A is a mixture ofvarious hydrocarbons which thereforebecomes less straight forward tomodel. The engine performance codethat was used in this project includesboth values of LHV as well as tablesto assess the enthalpy differencebetween two different temperatures.Using both the LHV value and theenthalpy table can account for mostof the enthalpy contribution inthe fuel exergy equation. The LHVvalue for the chemical enthalpycontribution and the enthalpy tablefor the thermomechanical enthalpycontribution of the unburned fuel.Since performance simulations areusually performed at low relativehumidities the vapor will not

condense when taking the exhausts tothermodynamical equilibrium with itssurroundings. This implies that theLHV shall be used rather than the HHVvalue in the fuel exergy equation toassess the maximum available work.

Furthermore, combustion of C12H23 wasassumed to be representative of Jet Ain similarity with the NASA developedcombustion code Chemical Equilibriumwith Applications [14]. This wasused to assess the post combustionthermodynamical enthalpy contributionas well as all entropy terms includedin the fuel exergy equation. Sincethe fuel exergy term is larger thanthe LHV term, using this will leadto that the calculated loss of thecombustion chamber is larger thanif comparing with the fuel enthalpydifference. The kinetic exergy forthe injected fuel was assumed to bezero since it would only have a minorcontribution compared to the otherterms.

The exergy equations described inEq.15 cannot handle constituents thatsolely exist in either the referenceor the actual state. Water is aproduct of the combustion process,an implication of this is that thewater content needs to be largerthan zero in the reference state. Inorder to minimize the effect of thenon-zero water content but still allowfor proper calculations, the ambientrelative humidity is set to 1%.

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