THE EFFECT OF REFERENCE ENVIRONMENTS ON THE ACCURACY OF THE RESULTS OF AN EXERGY ANALYSIS OF AN AEROSPACE E N G N

Jason Etele

A thesis submitted in conformity with the requirements for the degree of Master of Applied Science (MASc.)

Graduate Department of the lnstitute for Aerospace Studies University of Toronto

0 Copyright by Jason Etele (2000)

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THE EFFECT OF REFERENCE ENWRONMENTS ON THE ACCURACY

OF THE RESULTS OF AN EXERGY ANALYSIS OF AN AEROSPACE ENGINE

Master of Appiied Science (MASc.)

Jason Etde

lnstitutc f a Aerospact Studies

University of Toronto

ABSTRACI'

An exergy anaiysis is appiied to a aabojet cirpinc for a range of altitudes h m O to 15,000 m (-50,000 A)

and for a 3,500 km flight to examint the effects of using d i n e m t =ferrire-vifonment modcls. Tbe d t s of

this anaiysis ushg a variable ricfaicncc environment (cqual to thc opcrating c n v h 1 1 1 ~ ~ ~ 1 t at ail timcs) are compared

to the results obtained using two constant r e f m cnWonmcnts (O and l5,OOO m). The rational cfficicncy of a

&jet was obscrved to daneax witfi inmas@ altitude, duc d y to an iachase in cxbaust cxcfgy emissions.

The accuracy of exergy d t s was found to be dependent on the choice of reference environment, wherc the use

of a constant refertncc enWoument can lcad to errocs as large as 52%. For most atmospberic applications, the use

of a variable refmact environment docs not add great compiexity to îhe exergy analysis while yiclâing the most

accurateriesults.

ACKNOWLEDCMENTS

nianLs must be extended to Profcssor Macc Rosen of Ryerson Polytechnic University, my CO-supervisor,

for d l his hard work and guidance with this thesis. From ori- the topic to encowagbg and ensiaùig

publication and dissemination of this work in the public forum, his continual help and support was an invaluable

resource. His many rhoughtful cornmats and discussions were pivotal in both the completion of this work and in

directing my academic career, and for this they arc tnily appreciated.

Thanks mus alsa bt given to Professot James Gdieb of the Univ6ty of Toronto lnstitutc for Aerospace

Studies, my cosupcrvisor, for his part in this woik His advice povided the motivation and M o n necessary to

complete this wodc in a timely d forthright fasbioa As =il, tbe knowlcdge a d savices extcnded both by him,

and through him by the institute sta& arc acLnowlcdged gratefiilly.

1 am pmud to bc tbe ht Mastet of Applied Scicnct student mdcr the joint supervision of both the

University of Tomnto and Rye~on Polytechnic University, and I sinccricly hope tbat 1 am tbt îjrst of many to enjoy

the benefits of îhk partaetship.

1 would also LiLe to thanL my fiimity and fieads, cqechiiy JacL, Ben, end Adam, whost continual prsa~e

was a blessing on m a ~ y a day.

F i support for this wrk was plmviddd h m tht NahPal Scieaces a d W h C o ~ c i l

of Canada, both through a studcnt scholarship and assistance with related rescarch expcnses, and is grtatly

V P ~ M

TABLE OF CONTENTS

. . II

iii iv vi vii viii

Abstnict Ac knowledgwats Table of Contents List of Tables List of Figues Nomenclature

1 .O introduction

2.1 Thermodynamic BacLgrounâ 2.2 Turbojet Pcrfontlllll~e 23 Excrgy 2-4 Turbojet Ex- Balance 2.5 Rational Efficiency 2.6 Loss Analysb 2.7 Opcrating and Refcrcnce Environmcnts

3.1 Fuel Exergy 3.1.1 Variable Rcf- Environment 3.1.2 Constant Rcf- Environment

3.2 Rationai Efficicncy 3.2.1 Variable Refericncc Environment 32.2 Constant Refericnce Enviromnent

3.3 Loss Analysis 3.3.1 Variable Ritferc~x Environment 3.32 Constant Rcf- EnWoamcnt

3.4 Exhaust Inss Analpis 3.4.1 Variable Rcfncnct Eovirolllll~~~t 3.42 Constant Rcfcrcncc Enwonment

4.0 Fligbt Profite Exergy Analysis

4.1 Flight Protile Description

4.2 Cumulative Rational Efficicncy

4.2.1 Variable Rcf- Environment 4.2.2 Consbnt Rtf- Environment

4.3 Cumulative bss Anaiysis

4 . 1 Variable Refcttacc Environment 4.3.2 Constant Ref- Environment

4.4 Cumulative Exhaust toss Anaiysis

4.4.1 Variable Referrncc Envirocment 4.4.2 Constant Reference Environment

5.1 Summary of F i g s 5.2 Conclusions 5.3 Recommendations

Appendix 1: Caiculation Parameters

Appendix II: Mathematical Description of Cumulative Efficicncy

LIST OF TABLES

Summary of Specined Tiabojct Opcrating Parameters.

Summary of Specined Tiirbojet Opcrating Parameters for a Cornpletc Flight.

Thennodynamic Quantitics at the Outlets of tbe Specified Engine Stations for Operathg and Reference

Environments of Sea Lcvcl.

Thmodynamic Quantitics at the Outlets of the Spccified Enginc Stations for Operathg and Reference

EnWonmcnts of 15,000 m.

Thennodymnïc Quantities at the Outicts of the Specincd Engïnc Stations at an Optratiag Environment

of Sea Levtl and a Rcfnencc Environment of 15,000 m-

Thermodyaamic Quantitics at the Outlets of the Spccificd En& Stations at an Operating Environment

of 15,000 m and a Rcferrnct Environment of Sea Lcvel.

Assumai Atmospberic Composition Used in Analysis.

Combustion Patametcrs.

Standad Themdymmic Ropcrties of CoMtitucats Involvd in Combustion.

LIST OF FIGURES

Turbojet e n g k sectional btealdown.

Variation of fwl (CH,) specüic exergy at various operating altinides using different ref-

environmentS.

Variation of nirbojet rationai cfficienq at various O& altitudes using differmt reference

environmentS.

Breakdown of overall cngiac losses into exttrnal and intcrnal components using a variable r e f m

environment at (a) sea icvel and (b) 15,000 m.

Bmkdown of overall engine losscs into extcrnal and int«aat compoacnts a! (a) sca level and @) 15,000

rn using a constant rcfennce cnviFonrncnt.

Breakdown of exhaust gas ernission into kinetic, physicai, and chernical componcnts using a variable

refeff~lce cnWo~llll~~lt at (a) sea level and (b) 15,000 m.

Breakdown of exhaust gris emission into kinctic, physical, d chcmicai componcnts at (a) sea level and

(b) 15,000 m uskg a constant rcfernrce environment.

Variation of turbojet c u r n ~ v c ratiord efficieacy ovcr a flight range of 3,500 km at a cruising altitude

of 15,000 m using various ~ C ~ C I ~ C L I C ~ environmcats.

Variation of-jet r a t i d diiçiency o n r a flight range of 3,500 km at a cniising altitude

of 1 5,OW m using various ~ ~ ~ C I ~ C L I C ~ envirol~l~llts.

Variation of turbojet cumulative exhaust cmission cxergy over a flight range of 3,500 km at a d s i n g

altitude of 15,000 m using various cefchact enviro~me~lts.

Variation of the physid exergy uxnpommî of tk cumulative exbaust loss o v e a flight muge of 3300 km

at a cniising altitude of 15,000 m using various r e f e r e n c e cnvironments.

Variation of tbc kinctic excrgy component of thc cumulative exhaust loss over a aght range of 3,500 km

at a cruising altitude of 15,000 m using various referacc mvironmmts.

Variation of the chernical cxcrgy componcnt of the cumulative exhaust loss over a flight range of 3,500

km at a cniising altitude of 15,000 m ushg vsxious tcfehl l~t environments.

Variation of atmosphcric temperature aad pnssirre h m sca level to 20,000 m.

vii

NOMENCLATURE

speed of sound

velocity relative to the fixed rcfercoce environment (c = L/ - V) specific kat at constant prwsure

specific kat at constant volume

total exergy

fiael to air ratio

specinc enthalpy

ratio of lost ex- to incoming ex-

mas

molar mass

P-

SM pwer

-PO-

heat transfer ratt

heating value

gas constant

specific cnttopy

time

tmperahire

local wldcity

flight vehicle vetocity

velocity relative to the propulsion unit

work pcr unit m a s

mole fiaction

fhw&mhb

t~ proportion by mass of constituent in refehcce environment

f l proportion by mass of constituent in h l

6 change in mas o f constituent ptr unit of h l burned

E specific exergy

Y net product of constituent by mass pcr unit o f h l bumed (y = 6 + p) or th ratio of sptcific heats

A proportion by mass of constituent in post-combustion mixture

rl turbojet composent efficiency

< specific exergy W o n

'4 rational efficieacy

- referencc environxncnt

C -mP"e='r

cum cumulative

i individual constituent

n nozzie

rel relative

srd standard

t turbine

lot total

vel velocity

2 .. station within propulsion unit

rate per unit t h e

O total or stagnation

- working fluid values (weighted average of COLlStitu~i1t values)

1 .O INTRODUCTION

Exergy, or availability, bas been used for several &cades for the analysis of ground-based power systms

and processes including gas and steam turôincs (Bisio, 1998; El-Masri, 1987; Facchini, 1999, Fiaschi, 1998; Gallo,

1997; Jin, 1997; Où, 1996; Tuma, 1999), diesel engines (Fijaikowski, 1997; R&opodos. 1997), solar power

systems florres-Reycs, 1998; Liu, 1993, beaî pumps and cxcbangers (Cotnelissan, 1 999; Roscn, 1 999), and tucls

and îüel proceshg (dcOLivcira, 1997; Stcpariov, 1995). As well as engineering pcesses, exergy has also bccn

applied to aaturally occ\Pring pheriommî (Zalda-Aguilar, 1998), specific physicai pbenomcaa (Sahin, 1998; Saidi,

lm), and entire corntries (Roscn, 1992). Howcvcr, givm ttie extensive trament of exagy in literaûxe (Ackcret,

1 962; Ahern, 1980; Barclay, 1995; BcQiagas, 1993; Cysz and Murthy, 1991; Dunbar, 1995; Jin, 1993; Kotas,

1995; Moran, 1994,1989; Stepanov, 1998) its application to the atrospact cngim bas becn limikd, with the first

such efforts king the works of Clarlre ancl Hotlock (1975) and Lewis (1976). h ie r works proviâe acamples of the

application of the excrgy concept to various types of acrospace engines (tuhojet, turboha, scramjct) (Brilliant,

1995a, 199Sb; Krcsia, 1992; Malinovskii, 1984; Mrirthy, 1994; Miarhy and Ravichadma, 1996) following the

approach of the eariier effhts. Hounva, in al1 these worLs the application of the exergy concept to tbe acrospact

engine diffm h m the traditiod appoech for aaalyzing tcmsaial systcms in two djstinct ways.

l k nrSt distindion is that the rwrospaa en* is typidy bascd on an o p (Brayton) cycle, wberc the

production of th- gaiaaliy involves tbt j d o n of exbaw gass at high tempaatures aad velocities. This mode

of operation leads to large atcrgy losses with the exbausî, which düfèr hm the exagy losses duc to irrevcrsibilities

within the system. M k g c exbaust loss, which is trpical of the arrospacc c n g k , lcads to low a r q y efficiencits

and has led to efforts (Ripninn. 1997, 1996a, 1996b, 19%~; Riggins and McCluitoa, 1995) to dcvelop a more

relevant second Iaw-based method for evaluaîing efficiencies based on an d a concept described by Curran

(1973). In these efforts the xcond law analysis appach is tailored for atrospacc engines, by comparing the

deswd output not to the o v d exergy input but to the output of the idealuied version of the cngine d e r

consideration. In this manner the acrospace cngine is wt unrcasonably "pcaalizadn for its large exhaust cxcrgy

content.

2

The second major distinction betwecn the applicdon of exergy maiysis to aerospace r a k than ground-

based systems relates to the s e l d o n of tbe rcfercncc envirocment, and this topic is tbe focus of the pesent thesis.

An exergy analysis rcquires the definition of a rcfctcnce envinniment. This r e f m environment is usually

modeled as the ambient environment, as tbis is thc actuai environment in which the sysîcm operates and with w&ich

al1 exchanges of matter and encrgy tak place. For ground-bascd systcms this environment normaliy remains

relatively anstant in practice. For aciospace engines howeva, the ambient operating conditions can vary

signincantly diiring a singie flight. la tbe prcvious works noted above, the exergy analyses were pcrformed using

a nxed environment, stlcctcd as a typical opcrating cnvhmmmt to which tbe perticular engine under consideratioa

might be exposed. This approach appeaft to follow that for ground-basai systmu, wkre it is sufncicnt in terms

of auaiysis accuracy and reaiism to establish a singie rcfmenct CLlYUO~lll~ll î . Howcva, the vanations in ambicnt

pressure and tcmperaturt ovcr the typicai op- range of any acmpcc cnginc (mm sca level to 15,000 m

(-50,000 ft)) arc significant and can sffèct tbe accumq of relevant exergy anaiyses if ignored

The traditional approach of a h e d rcfcrrncc environment is undstic for most acrospacc applications.

When one wishes to mode1 tbc rcferrncc environment as the ambicnt operating environment the rcfcrrncc

environment must be permitîui to vary as the opmitirig environment changes. A variable referma environment

needs to be able to accommoàatc conditions reriging h m those st sca lcvd to the ncar absolute zero tempctatrrre

and vacuian conditions of space (altbough tk degne to which spaec COLditions arc cxperienccd dcpads on the type

of aeroqmce engk k i n g consided). Thus the s e l d o n of a -Wonment mode1 involvcs a îrade+ff.

For examplc, the use of a iked reference environment, arbitrarily set at somc operating environment, bas (i) the

advantages of duccd calculation complexity and the abity to straightfonvdly asstss the cngine over flight

altitudes ranging h m g m d level to low Earth orbit and beyond, and (ii) the disadvantage of ha* a refctcace

environment difkrent h m the environment in which the systern opcratcs.

Tbc objective of this tbesis is to asscss the SCILSitivity of cxcrgy efficiencies of acrospace engines to the ust

of different refc~c~lccc~lvirunmait models, to assist those applyhg exergy d y s e s to such systems in majLltaining

reawnable accioacy, while not making tk adysis ovedy complu Such Irriowfadge sbould maLe ex- amiyscs

more widely uscd in acrospace design thaa is prcsentiy tbe case. Tbe thesis focuses on the signifiantiy varying

3

operating environment eacountered when applying exergy d y s i s to aerospace cngiws (as outlined in the work

of Clarke and Horlock, 1975) as opposed to ground-based systems. la addressing this issue, both continuaily

varying and constant r c f e h ~ ~ ~ ~ cnvironments are considencd As WU, the impact these choices of refcrrnce

environment bave on the accuracy of relevant excrgy quantitics is cxamineâ h m both an instantancous and

complete flight vicwpoint

2.0 THEORY

Ll

Ln order to examine the pcrfonnance of the various compoaents within a turbojet engine, it is convenient

to define a stagnation state. The stagnation state defined as the state reached by a fluid as it is decelerami to rest

adiabaticdy, reversibly, and without wd~ king atmcted can bt cxpressed using the foilowing fom of the energy

equation (Hill and Peterson, 1 Wî),

where h" is the stagnation (or total) eatbalpy of the fiuid

h is the local cntbalpy of the fluid

u is the local vclocity of the fluid

if the flow is frirther assumed to be caioricaiiy @kt (h = c a , Eq. (2) can be expressed as

wtiere P is the stagnation (or total) tcmperahrrt of the fluid

T is the local tempersturc of the fluid

c, is the specific h a î of tbc fluid at constant prtssurt

5

wth the additional assrimption thai the fîuid is themdly @kt (d = yRT), the Mach nrimber of the auid

can be expressed as

where a is the speed of sound

y is the ratio of spccifk heats of the fluid (c, / c, , noting thai c, is the specific heat at constant volume)

Substituting Eq. (4) into Eq. (3) yields the following expression for the relation bawecn the stagnation

temperature and the local tcmpcrasrvc in tenns of the tocai Mach number and the ratio of spccific heats (Hill a d

Peterson, 1992),

A simüar relation can bc dcrivad for the relation ktwccn stagnation pwsurr and local picssrrre, assuming

the flow to be isenmpic (Hill and Pacrson,1992):

F i 1 T h j e t engine broken dom into sections.

The performance d y s i s of a turbja engine is simplificd by ôd t i ng the cngine down into its various

components and examining each under cous d t i o a s . nùs process results in the scven stations show in Fig.

1. By s p e c m the fiow velocity through the eagine in terms of the Mach numbct, it is possible to tbeorctidy

detemine the cornpletc thennodynamic state of tûc flow withh the engk givcn certain assumed woormance

values for each en+ cornpuncnt. For the instantaneous exetgy analyses (cxcluding those in the flight profile

section) the Mormamx criteria whcrc takcn hm Cl& and Horiock (1 975) and am show in Table 1. In Table

1,

wbile f is the fuel to air ratio and Q, is the heating valut of the fivi (which in this study is methane, CHJ.

Table 1 Summary of Specincd Tiabojet Operathg Parameters (adapted h m C M e and Hodock, 1975).

section 1 Enpine Component I Performauce Criteria

3 to4 Combustor f , / f , = 0.95 0.30 f= 1/40

QR = 51445 kJkg

4 t o 5 Turbine a = 0.90 0.40

5to6 Jet Pipe p6/f13= 0.98 0.30

6t07 Noaile = 0.98 -

A more modern enginc is modeleci for the flight profile study, with an inmased comprcssor pressure ratio

and more reaiisiic cfficic~lcy values (sec Table 2). As wcü, two cngine operathg conditions, climb and cniisc, arc

modeled to accurately simulate tbe entUt flight pn le . Note tbat tbc aircraft uses a çnrising dcsccnt and hcnce docs

not change enginc opcrating conditions during this segment of the flight.

For the mst of the data nacded to calahte c n g h ~ petfôrmmœ (molecular composition of the ambient air,

atmospheric conditions at various altitudes, thermodynamic propcrties of the species involved in the combustion

process, etc.), see Appendix 1.

8

Table 2 Summary of Specined Trirbojet Operathg Parameters for a Complete Flight.

Section En* Compomt Performance Criteria Mach Number Climb [Cniist] (at exit plane) ~ ~ l i m b [~niise]

w F m s t m m - 0.80 [0.80]

EmxY

Exergy is defincd as the maximum work obtainable fian a systcm. To evaluatc the cxcrgy of a sûwn of

matter, it is convenienî to d e k the specific ex- M o n , C: This temi provides an expression for caicuiaiïng

the physical e x q of a sbeam of maücr, which can bc de- as the maximum work obtainable h m the strcam

of matter by bringing it h m an initial statc to the rcfcrcace star tfvough processes involving tbenaal interaction

only. For an intcmally rcversible heaî transfer process (hcncc the kat transfer occurs ovcr an idhitesimal

temperature gradient) the spbcific cnîmpy incrieasc can bc cqmscd as (Kotas, 1995)

3 to 4

4 t o S

S m 6

6to7

which cm be integrated to

Combustor

Turbine

kt Pipe

Nozzle

#',/fi = 0.90 10.951 f = 1/55 [1/50] QR = 51445 W b

a = 0.88 [O.=]

H6 / p",= 0.98 [0.98]

qm = 0.98 [0.98]

0.35 [0.30]

0.50 l0.401

0.40 [0.30]

-

where qmNe is the reversible heai transfer b e e n states 1 and O per unit mass

T is the temperature at which the heaî tramfer occurs

s, is the specific eatropy of the strcam of matter at the reference state O

s, is the specific entropy of the Stream of matter at the initial state 1

Neglecting any change in potcntial cricrgy, for steady flow through a wntrol volume whch the strcam of

matter is b m w h m its initial state to the ceference state, the ew%y equaîion @er unit mas) can be e x p d

as

wfiere w is the wu* per unit mats cxtr;ictsd hm tbe systcm bawetn statcs 1 and O (positive out of the system)

h," is the total spaSc entbalpy of the stream of matter at the rcfertncc statt O

h," is the total specific enthdpy of the stham of matter at the initial statc 1

Assuming the htat h a d e r to occur at the cefetcnce suite tnnpcratrrrc, the maximum wak obtahable k m

the system wouid occur wben t& kat transfkr ocum rcvasi'bly, hmce aüowing the substitution of Eq. (9) into Eq.

( 1 QI, yielding

where l i s the specific exergy function (ai a givcn state)

E , is the specinc exergy of the strearn of matter at state 1

Thus the exergy of the stream of matter c m be exprcssed as the difference between the specific exergy

functions at the initial and r e f m States. Furthcr, if the anam of matter is a s d to be an ideal gas (both

calorically and t k m d l y pcrfect) then tbe spbcific cxcrgy of a constitwnt of the stresm of matter can k cxprcssed

as (using state O as the rcfereace state 5).

wbere T, is the tempcniaire of îhe constituent

p, is the ~ U r c 0 f thc constituent

c,, is the specifk kat at constant pressure of the constituent

R, is the gas constant of the constituent

p, is tac refertnce environment prcssiirr

c, is the absolute velocity of the constituent with respect to a fixed rcference environment

29

For a generai control volume in motion one can writc an exergy balance as follows (Clarke and Horlock,

1975):

where P, is shaft power exaacted h m the wntrol volume

P, is thrusi powcr exttacted h m the ccjntrol volume

q, is the b a t transfér raie scross the control volume

T, is the temperaturt at the point of heat -fer

E, is the specilic exergy of constituent i in the mixture

m, is the mass flow rate of constinicnt i in the mixture

The di£Eêrence betwem the lefi and right band sides of Eq. (14) is equal to tbe irrwersiiility of the systcm.

The equality in Eq. (14) applies for ideai systems; for rd qskms thcre cxist irreversibilities.

The thrust powcr across slly componcnt witbin a turtmjct enginc, wherr the mass £ïow rate is constant

across the wmponent boundaries and the flight velocity of the ettgine is LI, can be written as foilows (Clarke and

Horlock, 1975):

where U is the flight velocity

V is the flow velocity, rcIative to the control volume boundaries, entehg and lcaving the wmpoacnt

(where the flow is parailcl to the flight direction)

For a ttabojct enginc, tbe incoming cxergy is provided by the fiiel a d as such most if not al1 of the excrgy

is chemical (a srnall amount of physical cxcrgy may exist due b tbc différence between the conditions of the fuel

storage and the referrnce cnviiionm«it). The spacific excrgy arphssion in Eq. (13) is insufEicient to d e k m k the

chemical exergy of the fiiel as it irnplicitly assumes tbat the substance ont is considering exists in the reference

environment. A diffêrcnt methoci is thrcfm uscd to d e t a n k tbc h l cxergy. Separating ihe specific fucl ex=

into diffèrent terms aliows a simpler calculation and bcttcr Lmderstanding of the total fkl exergy:

where e, is the exergy of the fuel at a standard rrfchncc tempaatwe and phssurie

e , is the ex- of the fiwl duc to the difkcnce between (a) tbc injection and rcf«encc envhnmcnt

12

temperature and p~essure and (b) thc standarû reference tempcratuff and pressure used to 6nd e, (this

value can be positive or negative)

E,, is the cxergy of the fucl duc to its Linetic cactgy, or velocity

Also, the temis in Eq. (16) can be cxpmscd foiiowing the apptoach of Clarke and Horlock (1975):

where is the number of mas units of constituent i in one mass unit of f k l

y, is the n u m k of mas uniîs of constitt~llt i pduced by the comptete combustion of one m a s Mi t of

fixe1

h, , and s, axe the cntbal~ and entropy of constituent i at specified conditions (see Appendix 1)

Note that y, can be positive or ncgative as it iephscnts the net products of combustion. Thus for 0, this

value is 4 when using CH, as f k l since there art no m a s imits of Q pffsent in tbc h l itselfl aad during complete

combustion 4 m a s units of O, arc coosumed with evcry one mass unit of CH,.

The panimetcrs in the relative hiel cxergy tcrm (Eq. (1 8)) can bc exprrssed using i d 4 gas laws (Clarke

and Horlock, 1975):

Ahi, = cJTi3 - TA Ah. = c,(Ti- - T A 1,

where T,, and p, are the tcmpcratirrr aad partiai phssure of constituent i as it enters the combustion proces (i.e.,

at station 3)

T, , and p, , are the ternpcrat\w ami partial pressure of constituent i in the rcference environment

T, and p, are the staadard tcmperatiar and phssiirc çorrcsponding to those uxd for the tabulated data

Since the speci.6~ excrgy expression in Eq. (13) does not include tcrtns for chernical excrgy, it is usefiil

d e n the chemical CoLIlpoSiticm of the substance uirk amsideration is the ssmt in both the opcrating and rcfèrcnce

environmentS. For the îub je t adysis this BsScrmpti01.1 is valid in al1 stations prior to the combustion chamber.

However, ôeyond this point an . . term must bc adkd to Eq. (13) to account f a the cbanicai excrgy crieated

by tbe change in working-fluîd chcmical composition during combustion (Le., the mole fiactions of cach coastiûmtt

in the working fluid aRa axnbrraiou düIèr ficm t h e of the same constituent in the d m envinwimcnt). Thus

after combustion a modified cxcrgy fimction is appiïed for the w o m fiuid (Clarke and Hodock, 1975):

wtiere the barred specific hcat and gas constant values arc those îhaî pcrtain to the worlring fluid as a whole

T and p arc the tcmpcraturc and picssinr of the working fluid

c is the absolute velocity of the worlcing fluid

A, is the mass W o n of constituent i per unit of postcombustion worlong fluid

x, is the mole fraction of cotlstitrient i in the worLing fluid

x, , is the mole M o n of coastihient i in the reference environment

14

Id

The rational cfficiency, Ir, is used here as a measme of &t for assessing and comparing systems and is

defined as the ratio of usefiil or desirad work obtaincd t'rom the systcm to the total quantity of incoming excrgy

(Murthy, 1994; Cysz and Murthy, 1991 ; Clarke anci Horlock, 1975). For a tubjet , dere the usefiil work is the

thrust,

where the incominp cxergy includes the exergy of both the fùel d the incoming air, Le.,

where the totai ex- loss in the numerator is the sum of the exergy losses for each cngine component. The

rightmost terrn in Eq. (25) is also refcmd to as the loss ratio, L.

To asscss an C@E ovcr an entire flight using thc rationai efficiency, a modification rnust be made to the

assessrnent variables. If considering only a bricf instant in time, tfK rational cfficiency as defincd by Eq. (23) is

suitable as it qmscnts the i n s t a n m values of thrust pounr and incomiq cxcrgy flow rate. Howcver ovcr an

entire flight, cumulative m e a m of these quantitics are ~equired Mo- tbe r a t i d efficicncy to account for

the cumulative effect of an entire fiight c m be done as foilows:

where $- is the cumulative rationai efficicncy

/ P,@d Ir the t h e w u s t h powcr srnnmed over the duration of the flight (which lasts h m

time=Otomnc naal timc=t)

/E-,,,,,&& is tbe instantaneous iacomiag cxergy flow rate s u , over tbc duration of the fiight

At the beginning of a flight, bot - the instaataneous (Eq. (23)) and cumulative (Eq. (26)) rational cfficiencies are

identicai. Ho-, at al1 times following, this is not necessarily tbe case (sec Appcndix il).

26

For design irnprovcrnent it is 0th insighdiit to divide the total exergy l o s into wastc exergy cmissions

(e.g., exergy discarcicd by the tiabojet with tbe cxhuist gascs) and the interna1 consumptions (or dcstmctions) of

exergy due to irreversibilitics accurring within the cnginc and its componcnts. Sincc the wastc excrgy cmissions

are of?.en the single largest l o s in a tubjet, it is helphil to fiirthcr subdividc this l o s into componcnts identifiing

loss characteristics. The thht main types of ex- in the wastc exbaust emissions are Irinetic, chernical, and

physicai cxergy. Tbese thme componcnts, prtstnt in Eq. (Z), can be c x p d inàividually as:

Lf the exhaust is assumed to wntain no uubumcd k l , the chernical uergy as e x p d by Eq. (28) is

sufncient to caicuiatc tbc cbanicai cxagy of tbt exhaust stream. With this asnmption, the chernid exergy is due

solely to the partial pressure M e t t ~ ~ c e ~ bctwecn the coirstituenis in fhe exhaust gas and the same constituents in

the re f-ce environment.

2 2

The analyses pitsented hn involve both ojmating and refeffncc environmcnts. The operating-

environment temperatme aad prcssuh arc thosc for tbt cmmt altitude, as the actual performance of the turbojet

is dependent on the incornhg flow conditions. The thrust produccd and the tkmodynamic propcrtics at points

within the cngiac a ~ e determiiled ushg opaating cnwonm«lt vducs. Howcva, the d t s of the ex- anaiysis

depend both on the performance of the enginc (and hcnce the operathg e n v i r o ~ ~ ~ ~ ~ ~ ~ t ) and on the referencc

environment conditions (iiiluding UK r c f n cnvironme~~t tmntcmpcraturt and pressure). Thus changes in the

reference environment ltave quantitics such as tbc t h un&" wbile causing efficimcics and losses calcu4ted

using the thrust to vacy, sometimes significantly.

From a purcly physical vicwpoint, tbc most 8ccuratt choicc of rtf- cavironmcnt is one that models

the instantaneous environment in which the systcm operatts. For a tuhojet engiae, the use of a reference

environment other tban the opaating cnviroruncnt can neate the illusion of the Mgested air containing exergy, and

hence the possibility of produchg useful wo& or thnist, without the nœd for tbe exergy containcd in the h l .

3.0 INSTANTANEOUS EXERCY ANALYSIS

3+1 E u m s z g Y

An understaading of how the exergy of the fivl is affccted by a changïng xef- environment is

important as h l is the primary source of cxergy entering the turbojet and because most exergy-based efficiency

measUres involve fiK1 ex-. The acciiracy of exergy analyses and cngine cornparisons is improved wiîb such an

understanding. The cbcmical cxcrgy of tbc h l entering the turbojet for three cases of reference environmcnts is

illustrated in Fig. 2. The fuel is taken to be methane (CH,). In two cases, thc r r f m environment corresponds

to a fixed altitude (sea lcvcl or 15,000 m). In the third case, a refettnce cnWoment wbich varies with altitudt is

considered.

3.1.1 Variable Rdercna Environment

As seen in Fig. 2, tbt diff'~'~ between tbc fiwl exetgy at sca h l and 15,000 m (-50,000 ft) is kss than

0.6%. As discusd later, however, the overd cnginc efficiency varies by approximntrly 2% (sec Fig. 3) whcn

using a variable r e f m c n v i F o m Tbt variation in fivl exergy causes part of the cagine efficiency variation

and is discussed bere. Note thet in most discussions aAer this d o n , the fiwl exergy is tteated as neatly constant

in relation to other f8ctors. Tbe fucl cxagy can be broken down into main componcats (Eq. (1 6)): standard,

relative, and velociîy. The standad mm u t ü k s strrndard thamodynamic data in ddamining enthalpy and cntropy,

while the relative tcrm modifies tfKst standard values to îhc appropriate environmental conditions. Since the

standard exergy of the f k l (Eq. (17)) is calculaicd on tét basis of tabulatcd enhipies and entropies takai at a

specified constant tempcraatre and pressure which do not vary with the rcfe- envimameni, a change in the

reference pressure has no effect on any of the stanchd b l enthalpies or enîmpics. Howcver, since al1 cntropy

values used in the calculstions are multiplieci by th ~ C L C L ~ C ~ tcmperahrrr to c h c m k excrgy, the lowering of the

reference temperature as th altitude is incread has îhe cat~ct of iM=teasuig the overaiI value of the standard fuel

exergy term. Once the tropopaux is ~cachcd (- 1 1,000 m) and the rcfcrcncc ternp«aturt becornes constant the

standard fiiel exergy tenn remains uncbangd

The velocity contribution to the incoming fut1 exergy is rcIativcly s u d cornparcd to the relative and

standard terms, which are approximatcly two a d threc orders of magoitudc larger than the velocity term,

respectively. Ho-, tbc velocity term is also sigdicantly affèctcd by the incoming h l conditions aad as such

can be more dominant depcnding on the injection state of the h l . Tbc M o u r of the velocity term parallels tbat

o f the standard h l cxcrgy term in tbat it rcmains constant once the tropopause is reached. This bchaviour is due

to the fact that a constant Mach nianber flight proflie was considercd for this analysis. S ine the fuel cxergy due

to velocity is equal to the M c «mgy of the incornhg h l (Eq. (19)) which is in turn qua1 to the kinetic tne%y

of the flight vehicle in this case (as the incornhg h l injection velocity was specifïed as zero), the velocity

component of the fbel ex- decreascs with decreasing flight velocity. wth a constant Mach number tlight profile,

as the altitude increaçcs and the opcrating tcmpaaturc decr#ises, îhe fligùt velocity decteases, thereby dccrcasing

the fbel exergy dut to velocity. Howcver, oncc the tropopause is rrached and tbe opcrating tempcratiirt remaias

constant, the flight velocity and the velocity component of the h l ex= also rrmain fixed.

19

In assessing the behaviour of the relative fuel exergy camponent (Eq. (1 8)), it is convenient to suwividc

it into enthalpy and entropy portions for cach of the constituents involved in the combustion pocess. Since both

the specified IiK1 injection temperature and pressure, as weil as the tempemhm and pessurt for the tabulateci data,

are constant (at 320 K, 1 MPa d 298 K, O. 1 MPa respectively), the comspnding property M~~CILC~S and ratios

are also constant- For the h l , which in this case is CH,, Eqs. (20) and (21) show îhat ttie relative enthalpy and

entropy are constant and thus indtpendcnt of îhe rcfcrenct en*-t. Combined with the assunption of cornpletc

combustion (hence y = O in Eq. (18)) al1 the constituent variables in Eq. (18) are constant for CH, (bowever,

although the entropy tenn is constant, the e x q y cvaluatcd using this entropy is not, as it is dependent on the

reference environment temperaturt).

Thereforc, when asscssing the behaviour of the relative cntbalpy a d entropy terms, one only needs to

consider the bchaviour of the othct spies involved in îbc combustion proctss. Taking aü tbc othcr s~acies (O,,

H,O, and CO3 combined, several tcnas in Eq. (1 8) can bc climirintrri diie to thc fact that = O. Sincc the N, present

in the operating cnviromncnt is &dard inert, ail the excrgy values sssociatod witb this species cancel out of the

overall cxergy balance and as such accd not bc considcd

The~tbed in~bctuncnthcre facnctcnWMunent and the staadatdtccnpcratinrs, the larga is

the combine- enthalpy tenn for the consti~cnts O,, H,O, and CO, (Eq. (20)). This observation is duc to the fact

that although the enthaipy tcmi for the q is negativc, the cnîhaipy terms f a both the Y0 and the CQ are positive

and greater in magnitude than the ncgative O, tenn. Thus thc lowcr the ref- environment ttmpcratum, the

greater the total relative entbalpy portion of the relative fiKl ex- tena

Considering the relative entropy terms, t k exists an opposition betwan the temperature and pressure

temis. For the H,O and Cq icnns, a lowcr rcf- temperature rcsults in a more positive mtropy value whereas

a lower reference pressure lwults in a more negative catropy value. The oppsi te bebaviour is truc of the entmpy

terms associated with the 0, Furtber, the multiplying of the relative entropy tcrms for d l the m e s by the

reference environment tempctaturt ais0 affects tbe o v d relative f k l cxcrgy term.

Howcver, since it bas bacn establisbod that the standard h l cxcrgy tcrm incrcases as the altitude is

increased (due to tbe âaxcase in r e f m -) d and the effact of the velocity tcmi is ntgligible with

20

respect to the other two terms, it can be coacluded that since the overall f k l exergy decreases the net effeçt of the

relative exergy terrn (the combination of the enthalpy and entropy krms of aU the species) is to decrease as the

altitude is increased- Thus aithough the dative enthalpy tenns act to inmase the dative firel exergy mm, the net

effect of the relative atropy tcnns is to dcaease its value, and this decmse is gream in magnitude than the incmase

due to the enthalpy tcrms ( ' y appioximately two orders of magnitude).

From a more physicai vicwpobt, one wouid cxpcct that the demashg ieference environment piesme with

increasing altitude would lead to an incrcast in fiwl ex- if the f k l injection pressure is higher than the referrcnce

environment jxessmc. Howcver, it is also expected that any sort of incfcasing temperaturP differençe wodd also

increase the excrgy of tbc h l , which is not tnre in this case. This couter-intuitive result arîses h m the mamer

in which the overall fkI ex- is calcuiateû. For any single substance within a mixaat, chcmid excrgy is neascd

by the difference in tbc partial pricssiat of the substance within the mixture and within the refercnce environment

However, since most firels do not cxist in a ûaditiod rtfcriençc enviromnent (usuaiiy taken as ambicnt ait) it is

impossiile to determine a parcial presswc of the f k l in the referencc environment. Thus a morc M e d method

is required for calculaihg tbc fiici ex- taking into m u n t its absence h m the r c f m c e environment. For this

purpose the process of combustion is useci, as for xnost cases (as in this case) the products of combustion are found

in the reference environment and hcact t&ir chernid ex= can bc dcuiaîcd in tbc staadard nrqnner. The overail

exergy of combustion (and hcnce the h l ) is relatai to the diffetcbce bctwecn the excrgy of the reactants and the

products.

The kt that each element involvat in the combustion pmcess (rcactmts and products) reacts diffkrentiy

to the changing referrncc environment when calculatirig their relative entropy contribution (Eq. (2 1 )) to the relative

fuel exergy gives rise to the coun1c~-intuitive d t s obscrved Since the effm of the decffasing referma pressure

is dependent on the partial pressure and hcncc mole M o n of cach substance involved in combustion, it is more

dominant in the 0, relative entropy tenns as the mole fiaction of this constituent is at least one order of magnitude

larger than any other (neglecting &). Henœ the demashg mfenace pmsm aéds mom exergy to the reactant side

of the combustion proccss than it does to tbc product side. Howcver, the effcct of the decreasing reference

temperature is motie dominant in thc &O a d CQ reIative entropy terms as these are proportional to the values of

21

the specific heats, which are larger for tbese substams than for q . Ihe expected increase in cxergy due to a mer temperature diffémcc is present, only this incffast is larger in tùe prûducts of combustion îhan ihe reactants. By

adding more exergy to the producîs of combustioa, tbe difièrence beîween ceactants and poducts is r e d d tbereby

reducing the exergy available h m the combustion pmccss and hemx the h l . Overaii, th efféct on the relative

entropy term of the d e - i n g refehnce temperature is largcr in magnitude than the effect of the decreasing

reference pressure and hence the relative fuel entropy tenn decmscs with incteasing altitude as d e d d d e r .

Furthermore, since the decmue in tbc relative fiwl cntropy tcrrn is d u to the e f f a of the decrcasing tcmpcrancrt,

once the tropopause is rcached tbc d e c t of the only muah@ chaaging rtfercnce panuneter, the decrcasing

pressure, is to incrase the relative fbcl catropy tcrm thcreby increasing the relative h l excrgy tcrm as wciî.

Tbe befiano~r of the relative entropy tam dominates the bchaviour of the relative f ie l excrgy tcrm, sincc

it is appmximatcly 25 times largcr than the relative cnthalpy tena aAct being multiplied by the refercncc

environmtnt tempcratrrrc. Oncc in tbe tropopause both the standetd and relative hicl cxcrgy tefms act to inntaSe

the o v d fbel aergy with fiatha iacrcascs in altitude as b w n in Fig. 2 (sec the variable r c f w environment

curve).

3.12 Constant Rcfercnce Environment

In the cases in Fig. 2 where tbc referiemx envitonment rrmaias coasrant with pammeter values set to those

for a specific altitude, the incomi.ng iùel ex- rcinains almost uncbaaged as altitude cbangcs. As was earlier

esiablished, tbe s î a n k d h l exergy terms arc depcndcnt solely on the rcfehnce envitournent temperature and so

remain fixed wbm the referencc environment is fixai. Tbt relative fiicl exergy tenn rcmains constant

as it is dependent on both the refcrcnce cnvironrnent tcmperaîwc and pressure &ch arc both constant when a

constant referenœ environment is uscd. It is also noted that the relative fkl cxcrgy tcrm is dependent on the mole

h t i o n of the products of combustion in the refctebct environmat. But in this study the chernical composition

of the referme environment rtmaibs constant with dtitudc (Le., air is treated on a molar basis as 79.67% Na

1 8.77% O,, 1.53 % H20, and 0.03% CO2 ).

22

The velocity term of the kl exergy is responsible for the very d decrease with attitude exhibited by

the two constant refeffnce environment c w e s in Fig. 2, bclow the tropopause. The small magnitude of this

decrease confvms out earlia observation of tbe minor effect of this term on the overall lùel exergy. This d l

decrease is due to the fact tbat the kinctic energy of the Oight vehicle (which is the same for any ref-

environmeat consiclecui), and hence the h i , is calculatcd using the cumnt operating environment. Since kinctic

energy is directly qual to excrgy, as tbe altiadt b x a s s , the opcrating tcmperaarrie dccteascs CU the velocity

tenn in the fwI cxergy as discussad earlicr, which accounts for the small de- shown in the curvcs. Once the

tropopause is hachad, however, the operathg temp«aturie and hcacc the veiocity term in the h l exergy become

constant. Above 11,000 m al1 the tcmis comprishg the fiwl exergy are constant and heuce the constant r c f e t ~ ~ ~ ~ e

environment cwes in Fig. 2 are constant in the tropopause.

23

32

Exergy aaalysis helps develop a good understanding of how cfficientiy a system is operating relative to

ideaiity and of the sources (iocations d causes) of the major inefficieacies. The raiionai efficiency defmed by Eq.

(23) is used here to assess systern performance.

3 . Variable Refercna EmvVonment

For the case of the variable dchncc envimurneut, the rationai efficicncy of the turbojet is seen in Fig. 3

to decrease as altitude incrcascs, firom a maximum value of approximaicly 16.9% at sca lcvel (SI") to 15.4% at

15,000 m. Since the rational efficiency depends both on tht incoming h l ex- aad the tbnrst producd by the

engine (the usefiil work extracted) it is usefui to examine the bcbaviour of tbe thnist as the altitude is incrcased.

The decffasing efficicncy bclow 1 1,000 m might suggcst tbat the th& poduœd by the enginc damases sincc tbc

analysis of the incornhg fiKl exergy showcd tbat î k change in this valut over tbe givcn altitude range is less than

0.6% (heM.R nearly constant). Howieva, the thrust bcbally irin#ises with altitude, going h m a value of 797 N at

sea level to 833 N at 15,000 m (using an incoming air mass flow rate of 1 Ws). This increase in t h is due to

the manner in *ch the thermodynamic d y s i s is pdonned.

Since the engine is specined as always expaadiag the exhaust gascs to amiosphcric pressure (which in

practice means baving a variable geumetry nozzlc). the ejectal relative velocity of these gaises rcmains f d y

constant with altitude (sec Tables 3 and 4). Howcvcr, the incoming velocity chmues duc to the demeshg

operadng temperatuh and constant flight Mach numbcr. 'Thus tbe inucme in velocity ricross the turbojet is greatcr

at higher aititude, translating into a iarger thrust.

The decreasc in rational cfficiency with increasing altitude, cven though more ttvust is pdiaced, can be

explained by noting tbat the grcatcr thnist is being produccd at tbe cxpcnst of higher losses. Tbc iargest conûibution

to the losses in the turbojet arc xen in Tables 3 and 4 to be associated with the cxhaust, which riçcounts for more

than haif of the total cngine loss (the other major contributor king the cornbustoc). CIearly, the incffase in the

exhaust loss h m approxhately 34% at se9 level to 5% at 15,000 m is the priaciple teason for the decrcad

efficiency of the overail enginc with incre9s'ing altitude. Alîhough Tables 3 and 4 indicate tbat al1 stations except

24

for the nozzle actuaîiy incur 10- losses at higher altitudes (no& ihat eacb station in the tables is taken at the exit

plane of the speçified component), these i n d e5ciencies are more than offset by the 5% incr~ase in the

exhaust loss.

The in- in exhaust l o s with baeasing altitude is caused by tbe changing r e f m environment.

The decrieasing refercncc envitorment temperature and pessure witb iacreasing altitude increase the exergy of the

exhaust jgases. As am be seen f b m Eq. (22), a largcr temperaturc gradient anâ a mort negative pnssure d i f f i

(final r e f m environment pnsstar - initial exbaust pressure) h x a u e thc excrgy of a given flow. In the particular

case considered here, since the exhaust and ccferc~lce environment prrssurrs are always cqual (as the gascs arc

al- expanded to the opcrating environment picssrnric), the prwsuh tmns in the exergy expression arc zero. As

envirument t e m m demases with k m s h g altitude the exbaust exergy increaxs, i-e., in going f h n sea lcvel

to 15,000 rn the actual exhaust ex= flow nite increascs by approximaîcly 8.5% h m 697 to 757 kW (in each of

theTables3tbrougb7,tbc~Exe%yRate~~"iSnotthcsameastbtspacifctotalcxe%y(~)

due to the fact that at the cxhaust plant (station 7) the mass flow rate is no longer quai to the incoming air mass

flow rate of 1 kg/% but ratber tht incoming air m a s flow rate plus î k incoming fuel mas flow rate).

Figure 3 Variation of turbojet rational cfficiency at various operating altitudes using différent refcrcnce environmentS.

25

Although the exergy of the exhaust is incrieased, this incrcased wok potential is emittd as a waste since

the turbojet bas no means of amacting it. It is due to the i n d exhaust exergy loss tbat the overall engine

efficiency decreases with increasing altitude despite producing more thnist and incurring reduced losses in most

engine components. Above the troposph wbere the rcference tempetanirc becornes constant, the decrease in

rational efficiency with firrthcr increascs in altitude bacomes much less pmnounceâ (îess tban 0.1% bctwcca 1 1,000

and 15,000 m). For a constant refchncc avironment tcmpcniture, the exhaust cxergy iwnains constant, In the

tropopause, the thmst rpmaias constant as it varies only with inict tcmptrature for the thcrmodynamic calculation

methcd employed here for engine performance. The vcy slight de- in rational efficiency in the tropopause

is caused by the small increase in iacoming f ù l e x q y (approwimAtcly 0.1% as setn in Fig. 2).

3.2.2 Cowtrat Meiena 5vVonment

Fixing the rcfehnce envimnmcnt at the environment conespondhg to 15,000 m d t s in a demase in

efficiency at se. level of 1.6% over the case whcn the sctual altitude is used as the rrfêrmx environment.

Although the thnist produced is iadepcndeat of the cb iœ of rcferiehce environment, tbt cngiat efficiency damases

due to the behaviour of the incorning air. In most cxcrgy analyses, the surrouadings arc a source of z«o cxergy.

However, when the rcfertncc environment is ditfkent than the opcrating environment h m which the turbojet

ingests air (as is the case wbcn a t 5,000 m ref- enWo-t is U . a! sca Ievcl), the incoming air poseses

physical exergy. Sincc in this case the incornhg air is at a bigher prcswc ami temperatirrc îban the r e f m

environment, the cngine appears to bc receiving extrgy h m the icicombg air fiow as wcll as h m the firtl. Tbe

exergy of the air is physical in nature, as tbc chernical composition of the atmospheile is not varied with altitudt ( a h

note that the incornhg air poseses no kinctic excrgy as the refaicrict environme~lt is always assumeû to be at rcst).

This increasc in incornhg exergy is rcspoasible fot the dcamsed engk efficiency, as the cnginc appcars

to be receiving edditiod exergy whiie stiii poducing the same amount of thnist. At sea Icvcl, Ihe cboice o f a

lS,OOO m ref- environment cmatcs the "illusionn of an extra 142 k W (sec Table 5) of incoming exergy while

the thrust produced is still797 N (the samc value as found in the variable rcfercncc environment case), thertby

reducing the r a t i d cfficieacy (Eq. (23)). As the opcrasing aititude incrieases, the diffkmnœ bawecn tht opcratiag

26

and reference environments decreases, reducing the fidtious exergy in the incornkg flow. At 15,000 m, the

efficiencies for the! variable d 15,000 rn cefetience cnWonmcats are eclual, as tbe incoming air flow exergy is zerr,

in both cases.

A similar phenornenon occurs when the ref«ence avironment is fixed at sea level conditions, o d y the

effects are opposite. in this case the cfficiencics for the variable and constant reference environments are equal at

sea level and diverge as the altitude increases. Since the operathg ternpcrahat a d pressure decrease fiom the sea

level values as the altitude is increased, a fictitious negative exergy is attributed to the incoming air flow. This

negative exergy indicates that the operating environment is no longer a source of zero exergy (or cven positive

exergy as in the prwious case) but rathtr ihat wo* must bc dom on the air flow takm h m the opcmîing

environment to bring it to ~fcritncc environment conditions. Thus it appcars as though ihe cxergy entering the

engine in the fuel must first ovcn=ome the incoming ncgative exergy beforc it can produce th- But, sincc the

thrut produced rrmains unchangui by the Fcfercncc envirwmcnt (833 N at 15,000 m), the efficicacy of th turbojet

inmeases. At an altiadt of 15,000 m tk use of a sea kvel rcfetrcncc cnvironmait causes the cxergy of the incoming

air to be -1 65 kW (sa Table 6), and the cfficiency to hcrcase by approxbately 22%.

The behaviour of the constant dèrcncc environment ciavcs in Fig. 3 exbibit a distinct change at tbe 1 1,000

rn isothenn, For the sea lcvcl curvc this efféct occurs because, although the use of a constant sea levcl refermx

environment increasts efficiency with increasing altitude, the actual engine efficiency demases with altitude up

to the tropopause by a similar amount such that the two effccts approximately cancel out. However, in the

tropopause the actual mgine efficiency remaias ncariy constant and thus therc is no tradc off k t w c a opposing

tendencies, allowiag the efficiency to incrcast due to the negative cxetgy of the incoming air. The change in the

15,000 m reference mWonmcnt cuve in Fig. 3 at the tropopaust is caused by the same efféct. In this caçc the effect

of using a constant r t f c r e~y environment causes the cngine eflticieacy to daxease as altinde dmeases h m 15,000

m to the troposphere (- 1 1,000 m). Howcver, in the tmposphere the actual cngine cfficicncy increases as altitude

decreases, thereby canceiing the tEndency for the incoming-aîr positive exergy to de- the engine efficieacy.

3 3

Exergy adys i s provides a tool for cvaluating not ody efficiency, but also the causes and Iocations of

losses. A proper identification o f system inefficiencies aids in performance improvement efforts.

33.1 Variabk Refercncc Envllonment

As pointed out in the pricvious section, the exbaust l o s is tbe nisjor contributor to the incfficicncy of the

&jet. Most efforts b the thnist of a turbojet aiso uicreasc the exbaust loss (e-g., incrcasing the exhaust

gas t e m m and/or vetocity to produce more thnist). However, this emission loss is difTerent ihaa losses due

to intenial irreversibilitics (e.g., fiction, pressuh loss, e) which cxist in any real system. The extenial loss

incurred through the ejection of tbe cxbaust gases is somewhat rrtnevable.

Thediv is ionbetwlccnintaaalandextcmal l~wt ientbe~aiv iro~~e~l tkuscdastbt~f«ence

environment is shown in Fig. 4 at bot& sca kvcl and 15,000 m. At sea l e n l tk r a t i d efficiency is appmramatciy

t7%andhencetbeexe%ylossis83%. Ofthisloss,65%isexttnialintbatexcrgyisejectedwitbthtexhaust~.

The remainïng 35% is intenial losses duc to irrevctsible pmceses (mixing, combustion, fiction, etc.).

Brerkdown of Tot81 L o i s 8 t SIL (SIC Reference Envl ronment)

Figure 4

6reakdown of Total Lo8s 8tlSaJl m (1SQlb m Reference Envlronment)

BmkQwu of o v d cngine ex- losses into extemal a d intcmal componeats using a variable ref- cavllonment at (a) sta level anci (b) 15,000 m.

30

At 15,000 m it can bc seen in Fig. 4 that the intemal losses decrease h m 35% to 30% while the external

losses increase fmm 65% to 7û% as altitude is incmsed. Thus the engine reduces the percentage of the total l o s

due to irreversibilitics despitc âccmsiuig overail efficiency with incr#ising altituâe. This oôsendon supports the

trend seen in Tables 3 and 4, where al1 the engine components except the mzzle and the exhaust have lower

individual losses at higher altitudes. The incrtase in the exteml los petceatage is due to the f ~ t that as the

operaîing environment hmascs altitude, tbe tempemure and prcssiire both deaxase. Sincc in this case the

reference environmeut is ttie same as the opcrating envllonment, the lower ref-ce environment temperature

createsmoreex~inthcxbaustgascmiSSio11~(tbcprcssuretenninEq-(22)iszeroastheexhaustgaspressure

is equal to the refetence environment phssure). Note that a! 15,000 m the total extrgy los krcascs to

approximateiy 85% of the total incoaüng cxetgy (as the rational efficiency demases to approximatcly 15%).

From a practical viwpoint these d t s aic impocîant as tbcy provide a cleam rnrderstanding of the

behaviour of the cngine. The ratiod efficiency indicates tbat the cnginc becornes l e s efEcient with increasing

altitude. Furtber, tbese d t s show that intcrnal losses, or irrcversibilities, are reduced at highcr altitudes. The

extemal 105s due to tbe txhaust loss &on is riesponsible for the decreased en* efficiency at h x a s e d

altitudes, not an incmsc in the irrcvmible Ioss rneciukms (fiction, mW,g, etc.) traditionally associated with

decreased efficiencies.

3 3 3 Constant Rctennce Environment

Foiiowing Fig. 4, a loss bmMown is shom in Figs. Sa and Sb, but with the rcfcrc~lct environment held

constant at 15,000 m and sca leve1 respectivcly. It is evident tbat at sea lcvcl the use of a 15,000 m rcference

environment leads to a fhke increase ( h m 65% to 78%) of the cxbaust eniission losses for the turbojet as a fiaction

of the total loss. Tùis is duc to the firct that ushg a higher altitude rcference ~~~viroamcnt than the opcrating

environmcnt incnascs the mbaust gâs cxagy dut to the rcfehnçe cnviro~ll~le~~t teiûperanrrie abd piicssurr

(see Eq. (22)). The increased ex- of the cxhaust gascs increascs the extenial pncentage of the total l o s and thus

decreases the intenial pcrcentagc.

Braakdown of Total Loss at S/L (15,OQ) m Reference Envlronment)

Internat 1

Brcakdown of Total Loss r t 15,QX) m ( S I L Reference Envlronment)

External 52%

Figure 5 Bmakdown of overd engioe exergy losses into emexd and intenial wmponents at (a) sea level and (b) 15,000 m using constant rcfemice envllonments.

This innwseinthtexternal losspcrcentagektobcexpsctcdgivcn~fictiti~~~~exc%ycntcringthe

turbojet (àescxibeù in the rational cfficicncy section, 3.2). Since this exces ex- does not r d i y cxist, it cannot

be wnverted into thrust and hencc must be considered a los. Howevcr, this los is idqxdtznt of any of the

ifieversible processes present within the cngine, as its magihde is estabLished before the iacoming fiow enters the

engine. Thus the fictitious exergy must bc ejectcd as an extcmal loss b b y increasing the cxtcxnai -rage of

the total los.

The oppositc tFcnd is evident when a constant sca levcl reference environment is used at an operating

environment of 15,000 m. By compariDg Figs. 4b and Sb it can be seai that in this case the extemal losses daxease

h m 70% to 52% of the total los. The mec- rrspomible for this shiA am sirnilar to those for the constant

15,000 m refmce environment case oniy opposite in effect. The increased phssurit and tcmpetature of the sea

b e l refeffnce environment over the 15,000 m operating environment reduce the ex- of the exhaust gascs and

hence deçrease the -rage of extemal cxcrgy loss as a h t ion of the total loss.

In this case, the incoming air contains negative cxergy (which indicates that work must be done on the

operating environment air to bring it to riefcrrncc environment conditions) but the propertiw of this exetgy rrmaio

the same. It is stiJl a fictitious quantity and thus must still m t as a loss (as it criimot be cowcitad into thnrst), and

as before, this loss is iadependent of any intenial Vrevcrsibilitics within the engine. Howcver, the &vc valut

of this quatltity duccs the magnitude of the extenial loss and heM.R givts rise to a demeasc in the external 105s

32

portion of the total loss, as opposed to the increase s x n d e n using a constant 15,000 m reference environment-

Aithough the choice of reference environment has only a minor effect on the exergy based rational

efficiency (les thiin 2.5%), the total loss bndid~wn reveals fiPther informaîiom One of the main practical benefits

of exergy anaipis is îhat it pnnits losses to be betier &fined and characterized, thefeby aiiowing designers to better

direct efforts to hxease efficiency to the areas tbaî have tbe most potential for, or nad of, improveme~lt. Ha, the

impact of the cboiœ of reference environments is significant, as variations of appmxbately 18% are seen in some

important parameters. Such discrepancies not ody affect the accuracy of analysis calcuiations but aiso obscure

general trends. In going 6um sea level to 15,000 m, for example, the internai losscs dcaase by approyimntply 5%

(see Fig. 4) but wIien using a constant refeipnce envhnment the opposite îmd appesrs (as secn in Figs. 4a and 5b

or Figs. 5a and 4b).

3 3

3.4

The loss analysis in section 3.3 identifid exhaust emission as the singie Iargest contributor to the overall

exergy loss of the enginc. As such, thïs arcs pritscnts thc grratest possibility for inmead efficiency. Howcver, in

order to consider proper recovexy of the excrgy h m the exhaust, it is neccssary to aaalyze the exergy of the flow

to detemine both the potmtial size of any gains and the nature of the exergy to be recovercd. By doing this, the

areas of greatest potential loss duct ion can be d y identifid

3.4.1 V d a b k Rclcreacc Environment

Since the cxcrgy of the fuel is pucely chernical in na- (the vclocity cxcrgy component being negligiblt

due to the speciEied input COLditions), t h ex- in the cxhaust might be expected to contain much chernical exergy.

However tbk is not thc case as sccn in Fig, 6. At both sca level and 1 5 . 0 m the chunical excrgy in the uthaust

stream is only 4% and 3% zcspectively, of the total exbaust exergy. This s d contribution ariscs h m the fact

that the exhaust stream is non-combusti'ble Cm this d y s i s cornpletc combustion is assurnad). Thus the only

chernical ex= present in the cxhaust is duc: to the diflrèrcncc in mole M o n s of tbe exhaust gases Icaving the

turbojet and the same COIIStitucnts pwscnt in the nfaierice mviro-t. Tbc smaü de- o b c d in cbanical

exergy as the altitude inchascs is due to the fkt that the tmpmtwe demases with altitude and the spacific

chemicai exergy cxphssion Eq. (28) is depeadcat on the rcfchacc environment tempcntturr.

Physical ex= d e s up most of tbe exhaust cxcrgy (52% at sca lcvel and 53% at 15,000 m). Physical

exergy is treated hcrc as the cxergy obtained by hvcrsibly bringing a flow to thcrmai and mechanical equilibrium

with the referwce environment. In this case, the physical excrgy is strictly thermal since the cxhaust gascs are

expanded to the operating cnviro~ment prssrnic. Ho-, had the aaalysis bacn pcrfotmcd wiîh a h e d gcometry

nozzle (heace a constant exhaust phssurt), a portion of tbc physical cxergy containcd in the cxhaust would ùc due

to the exiting pressure k ing differrnt h m the rcfercnec cnWoxunent prtssure (Eq. (27)). The second kgest

component of the exhaust exergy is the kinaic cxergy of the expeiied gasts (44% of the total exhaust loss at boîb

altitudes). Thus the two factors (i-c., t k high tanpaaartr and vclaity of tht arpciied gascs) tbaî cause the abausi

to contribute greatly to overall eagine loss are the same Eaciors th@ allow the cngine to producc thnist. Fig. 6 also

34

indicates tbat although the total exbaust loss varies with altitude, h m 697 kW at sea level to 757 kW at 15,000 m

(see the Exhausî Exeigy Rate Exithg E@nc in Tables 3 and 4)- the composition of this loss i.emains fibly constaut

with altitude.

Breakdown of Exhaust Loss 8t S/L ( S I L Usference Envlronment)

Breakdown of Exhrust Loss 8ti5.000 m (15.m m Reference Envlronment)

Figrire 6 BLCZLLdOwn of exhaust gas cxagy anision into kinetic, physicai, and chernical compoaents using a variable rcfcrcnçc envimmcnt at (a) sea level d (b) 15,000 m.

3.4.2 Constant Merencc Environmeat

The errors introduccd by using a constant refcrence cnnrOnmeat arc more pronouacd when evaluaîing

the exharist loss breEikdown than wbtn evaluafing the rational &cicncy (as is the case for th bFeaLQwn of tbt total

ïoss as weii). Considering the case wticre tbc rcfcienoe cnviro~~m~llt is held constant at 15,000 m whilc operating

at sea level (Fig. 7a), 65% of tbe cxbaust loss is physid in nature. This value is 13% gmatcr than when the

operating environment is used as the rcfehncc environment (Fig. 6a). 'The kacase is due to two fwtors: the

increase in the thermal portion of tht physical cxergy as wcU as an additional prcsme rclated component. Since

the reference enviro~l~ l~~l t temperrrtiae is 10- in this casc thsii tbe opcrating environment tcmperaturr, thcre exists

a mer temperature diffkrenœ betwœn the exhaust tempcniatrr (which is the samc for both Figs. 6a and 7a as the

operating enviromnent is the same in both cascs) and the rcfercncc envitoment temperaturc. In addition tberit is

a différence bmmcn th exhaust piicsslrrt and the nfaa~x enviroiunait pmswe as the d y s i s specifies acpension

35

to the opemting environment pessure, which in this case is at sea ievel conditions. Since the pmsure at sea lwel

is higher than that at 1 5 . 0 m, a fictitious positive physical exergy component is intrioduced in the exhaust.

Since the kinetic ex- component of tbe cxhaust is solely dcpcndent on the velocity of tbe outgoing gases

(which is dependent on the operating environment), the cboice of refcrence environment bas no effect on the

magnitude of this componcnt of the exergy loss. HOWCYQ~ as scai in Figs. 7a and 6a it appears as though the kinctic

contribution to the o v d cxbaust l o s bas been r c d d to 33% h m 44%. This decrcase is attributable to the

increase in the total amount of excrgy bcing ejected k m the engine duc to the inchasc in physical exergy* h m

697 kW to 937 k W (xe Tables 3 and S), while the kinetic exergy of the gases Fcmains f i x d

This cEect is also parrially rcspoilsible for tbe decreast in the pcrccntage of chcmicd exergy in thc exbausî.

However, in this case the a d magnitude of the chernicd ex- also decrtaxs due to the lower refehnce

eavironmenttcmpratilrt. Itsbouldbcnoted,ho~,tbatinboththevariableaid~1tfaaiccenwO~13etlt

cases the peFccatage of exbaust loss duc to côemical excrgy is relaiively small (approximately 4%).

Breakdown of Exhaust Loss at SIL (15mi m Reference Envlronment)

Breakdown of Exhaust Loss a t l q 0 m (SIL Reference Envlronrnent )

Figure 7 B d d o w n of cxhaust gas exergy emission into kinetic, physical, and chemiçal components (a) sea levcl and (b) 15,000 m using constant ncfchace envhnments.

hthccasewtrerietbtncfcrriicccnvirOnmentisheld~atsea~evel whileopcratingat 15,000 rn, the

physical exergy componeat of the exbaust dccmscs to 25% h m 53% (Figs, db and 7b). This dinehll~e is duc to

36

the same two mechanisns as in the constant 15,000 m ceference environment case, only the e f f w are m d .

The increased r e f m enviroament temperatiire decreescs the tcmperaane gradient betwem the exbaust gares and

the reference environment, tbertby decricashg the thermal component of the physical exergy. Also, a negative

physical ex- exists due to the fact that the exhaust pressure is lower than the reference environment pressure.

That is, since the exbaust gascs are cxpanded to the opcrating environment pressure (which is at 15,000 m in this

case), work must bc done on the gases to bxing tbem to the nfcrence environment pressure. As seen in the loss

analysis (section 3.3). this negative exergy is fictitious and duc solely to the fact tbat the reference environment is

not identical to the opcratiag cnvironmcnt. H o w u , siacc the tbamal component of the physical cxergy is larger

than this fictitious nqative component, the o v d physicai cxcrgy compoacnt rcmains positive (although this does

not have to be the case as illustratal in the cumulative cxbaust loss analysis (section 4.4)).

This drastic reductim in physical cxergy rrducts the total amount of cxcrgy cxiting the engine, h m 757

k W to 478 kW (set Tables 4 and 6), a d b c ~ x the percentage of the toial cxbaust l o s due to WC excrgy

increases to 69% h m 44%. This inneasc is again duc solely to the fàct that the overall cxbaust cxcrgy changes

due to tbe physical exergy compoacat's 4epeadcnce on the c b i a of rcf«eace cavironrncnt, as the magnitude of

the kinetic cornpriait is depcndcst oa tk Opcrating anhxmmt only. T h chcmical exergy kmses slightly h m

the variable referrricc environment case duc to the increast in r t f m environment tcmpatue. This effect,

combiaed with the o v d decrieasc in exbaiist cxagy, gives rise to the bxeaw in the Qcrrxntage of cbcmicai cxergy

to 6% as shown in Fig. 7b.

In both cases considcrtd, it is important to note that not only does the choice of a constant reference

environment skew the accuracy of tbc aualysis by as much as 28% but it also indicates fiilse g e n 4 trends. In

either case a constant rtfèrcncc aiviroament indicaies tbat tbe composition o f tbe cxhaust loss varies with altitude,

thus suggesting the possibiity of mhh izbg a givcn type of l o s rhrough a carefiilly c b n cniising altitude. In

going k m Fig. 6a to 7b, the use of a constant sut lm1 refcrract environment indicatcs tbat the physicai exergy

component of the exbaust l o s k x a ~ ~ ~ with incrtasing altitude while the kinctic componeat increases (the same

trend is predicted using a constant 15,000 m rcfercnce environmtllt, set Figs. 6a and 7b). But in actuality the

exhaust exergy composition is approximatcly constant with altitude despite the actUat magnitude of the mbElust loss

vasriog-

To examine the effects of differmt r e f m environment models on the accuracy of an cxergy analysis

applied to an e a t k flight pronle, the characteristics of the flight must first be establisbai. For the prcscbt analysis,

a cruising altinide of 15,000 m (-50,000 A) is used over a g r o d distance of approwjmntely 3,500 km

(approximately the disiaucc bctwœn Tor- and Vanamver) with both the departuh and destination aerodromes

assumed to be at sea level. To mach tbc cniising altitude tbe allcratt uses a constant rate of climb of 3,OOO mimin

(- 10,000 Wmb) which results in a tirne of 5 min to mach cruise altitude. The descent portion of tbe £iight is

accomplished usiag a constant desccnt angle of 10 degrecs undcr c r u k powcr conditions. Tbe engine opcrating

parameters in climb arc d i n i t fÏom thosc in cniisc (sce Table 2 fot Gtails) but because a auising desant is usai,

the engine operating pamdms in both cnllsc and desant arc identicai. The total fiight tirne is approximately 4

hrs.

As a meas- of merit for tfn o v d efaciency of the cnginc during the flighf the cumulative rational

efficiency as defincd by Eq. (26) is usui.

43.1 Variable Rderena Eivironmeat

The variable rcfkmz en- CIPve in Fig. 8 shows the c u m U v e miional cfficicncy of tbt turba,jet

decreasing rapidly at the beginning of the flight and tkn lcveling off asymptotically. At a distance of O km (and

h m at an altitude of ses Itvel) the cumulative raiional cfficicncy is 2227% which is idcnticai to the urstantancous

rational efficiency (Eq. (23)) valut at this point (see Fig. 9). However, as the allcratt climbs and thcn establishes

itself'at the cniise altitude, the cumulstivc r a t i d cfficieacy daxeass to a value of 20.04% a! a distancc of 3,445

km. This yields a maximum variation of 223% o v a îhc entire flight. The instantanaous rational cfficicncy valucs

also Vary by apprioximately the saine amounf with tbc d u c damashg h m that at sea level to 20.57% at the nid

of the climb segment (a distaact of 73 bn) and dropping fiPrher to a value of 20.02% as the cngine operathg

38

parameters are modiaed for the adse coadition, thus yielding a maximum variation of 2.25%.

The fact that the cumulative tlrtional efficiency at 3,445 km (20.04%) is almost identical to the

instantaneous rational cfficiency during cniise (20.02%) is to & expected given the length of the flight. Sincc the

a i d spends the majolity of its operathg îime imdcr cniisiag coaditions which are constant, any variations caused

by the climbing and descending portious of thc flight arc ovenrvhclmed by the significantly larger cruise segment-

This f k t is evident h m the sbapc of the cumulative rational dficicacy c\avc. At tk btginning of the ûight where

the ai& has spent no timc cniisin& the climb coaditioos dominatc the kbaviour of the cumulative curve. Thus

the rapidly decrtasiug instaataneous r a i i d cfficieacy d u h g the c h b portion of the flight (Fig. 9, for pd

distances h m O to 73 km) dominates tk khaviour of the cumulative m e in tbis region (Fig. 8, for pund

dhances h m O to 73 km). At the end of thc tlight tk r a t i d & c i c ~ ~ c y inrreases due to tbe descent

in the same manner tha! it deaieassd during tbc climb segment Howcvcr ewn givcn this rapid increase, the effect

of the instantar~~us rational efficicncy is much less pnounced on thc cumulative curve as only a very d

increase in the cumulative rationai cfficiary is secn in Fig. 8 star&ng a! 3,445 Inn.

O 500 1000 1500 2000 2500 3000 3500 Grourid Distsnce (km]

Figure 8 Variation of trirbojct cumulative rational cfficieacy over a flight range of 3,500 km at a cniising altitu& of 15,000 m using various ref- environmentS.

39

Thus the more tirne is spent rinder cniising conditions, the more the cumulative efficiency d t s tend to

reflect the instantaneous results during cniist (which are constant).

The s t a b i i and averaging n a m of cumulative rcsuits causcs the sudden variations in UIstaataneous

efficiencies to be mucb less visible in the cumulative d t s . Specifically, the cumulative efficiencies somewhat

mask (i) the sharp dechase in instantaneous cfficiency during the climb segment of the flight, and (i) the srnall

instantaneousefficicncy plateau scen as the e n g k catcrs tbc tmpoparise Mder climb conditions (pst tbis plattau,

the engine switchcs operating parameters from ciimb to cruise scttings, thus creathg the discontinuous (vertical)

change in the -US raîional eff iciaq). This s t a b u and avcr8ging effect is even more noticeabte during

the descent portion of the fi@, as phviousiy mentioned, as ody a d incrase in the cumulative ratiod

efficiency is observed despite the relatively large incrrast in the instantancous cfficicncies.

Note that alîhough tbc aircraA starts to dcsccnd at a distamx of 3,425 ha. the instantaaeous rationai

efficiency changes very littk at this point It is mt untü the tropospbcre is reachcd at a distance of 3,445 km that

the instantancous efficiency stare to incriCaSc rapidly.

- Figure 9 Variation of tiaboja iiutrntrneous r a î i o d efficiency over a fight range of 3,500

ian a! a cniising dtitudc of 15,000 m ushg various referena envimnmcnts.

O 500 1 O00 1500 2000 2500 3000 3500 Ground Distance [km]

40

in Fig. 9, the 15,000 m and variable =ference cnviromnent curves arc idcatical during c h , but the

15,000 m re fmce envitonment curve starts to dccrease a! the stmt of tbe descent whereas the variable r c f m

environment cuve docs aot krcasc dramatidy until a small distance later wbnc the aircraft cc-cnttrs the

troposphere. This delay in inatas'i instantawous efficiency on the variable ccf- environment cuwe is due

to the fact thaî in tht tropopause the uistantaneous efficiehcy is nearly constant (sec Fig. 3) and as such no change

is visible.

42.2 Constant Refereoce Eaviroment

The use of a constrint sca lcvcl rcf- environme~lt to cvaluatc the cumulative rational cfficiency

p d u œ s enors in both numaical and predicted trends. At an opcrating altiadt of sea levtl (for a dista#x

traveled of O km), th variable and sta kvcl cttnrcs in Fig, 8 are ideatical at a value of 2227h. HOWCVQ, wbcrras

the variable rcfcrcba enviromnent c\nw idcates that tbc mgk efncicncy decrcases as the flight ptogrrssff tbe

sea level r e f m environment curie shows the oppsite trend, with the cume ceaching a maximum value of

23.71 % at a ground distance of 3,425 km, a variation of 1.44%. Tht cumulative sca lcvel ciavc starts to daxmsc

at the start of tbe descent dut to the markai change in iosîantaneous rational efficiency shown in Fig. 9 at the start

of the descent. This khaviour is in contrast to that for the variable cumulative rational efficiency curvc which

reaches a minimum at the point the aVcraft descends iuto tbe troposphert, at a g n , d distanct of 3,445 hm.

The cumulative sca h l r c f a m e t envirionmait ciavt tads asymptotidy towards tht instantaneous sar

level refetcnce environment value during cruise (23.72./0) and, as show by the valut of the cumulative rational

efficiency at 3,425 km, this value is ncariy nached. The maximum m o r (the maximum dif5èrcacc bctwccn thc

variable and sea kvel refehacc environment cumulative rational cficiencics) occurs at the start of the desccnt

portion of the flight and is cqual to 3.6%. This d t is diffèrent h m the instantancous r d t s , whcrt tbe

maximum error occurs aî the end of the climb segment (73 km) while the engine is still opctating under climb

conditions. in this case, the use of a sca level refchncc environment predicts an instaotaiicous rational efficieacy

of which, w k n oompiiribd to the valuc pedicted for tbc variable hfercnce environment m e of 20.SW3

yields a maximum enw of 4.1 8%. Howcva compnring the instantaneous d t s during cniise, the enor betwaai

4 1

using a variable and sea level refereace enviro-t is 3.70"/0. This is the asyxnptotic limit, i.c., the maximum value

which is approached but never reacbed of the ermr between the cumulative m e s as the flight distance is iacreased,

The tessons for the kmsing cumulative rational efficiency when using a constant sea level rieferc~lce

environment while cniising at an altitude of 15,000 m arc the same as those outlied in the insiantawuus rational

efficiency discussion ( d o n 32). The use of this rieference cnvironmet~t ctcates tme "iilusionW of negative exetgy

eut- the engine with the airflow at ail altitudes above sea level. As the aght time incItascs (whicb r c q h the

aircraft to increase alt ide to the cruising height), the qusntity of this ncgative ex- iricresses, causing the

cumulative rational efficiency to hxcase- Since the entire flight is spent at altitudes above sea 1-1, the engine

continues to 'ïugcst" ncgative exergy, d t i ng in a total accumulation of appmximateiy -2.40 GJ. This fictitious

exergy is signifïcant in quantity, mpmcnting approximatcly 15.7î% of the total exergy input through the fiwl of

15.27 GJ. (Note: thc ex- inpd with tbt f k l cvaluated using a variable rcfrrence environment is appoximntciy

15- 19 GJ.)

The use of a umstant 15,000 m ~ ~ ~ C L ~ C I I C ~ enMronwnt proûuccs a cumulative tatioaal efaciebcy c\ave with

a similar shape as the amstaat sea kvel hfaracc enviroament mt, but displad negatively on tbc efiiciency axis.

This d t is to be expcctcd, as the use of a 15,000 m r e f m cnvironmcnt at an opcrating altitude of sea level

creates the Wusion" of positive cxergy in the incoming airflow. This adclcd C X ~ &xascs the doaa l &cicacy

compared to the case for a variable =ference environment, yielding a value of 19.42% a! sea lcvcl (for both the

instantaneous and cumulative values). Howevcr, as th flight time increascs during climb, the reference and

operathg environm~~lîs approach aad ev~~~tuaiiy mctt rrt thc cnrisiag aitiade. thus e- tb fictitious positive

ex= in the incoming airflow. in this case, the total accumulation of fictitious exergy is approximaiely 0.05 GJ

compared to the c u m w v e c x q input tbrough the h l of approximately 15.19 GJ (a diffkracc of t h ordm

of magnitude). Thus the fictitious exergy represcnts a rnuch d e r percentagc of the total actuai exergy input,

appmximately 0.32%.

The largest difference bctwœn tbt 15,000 m and variable rcfmce environment cumulative rational

efficiencies (Fig. 8) occiirs a! sca level a d is quai to 2.85% (siace this is at the beginning of the fight, it is also

the largest diffac~lct in tk valuts). Tbt cumulative 15,000 m nferenoe cnWonment m e incileascs

with altitude (again predicîhg tb oppositc û e d hm tbt variable rtfacnct e n v i r o ~ ~ u ~ ~ ~ t case) to a valuc of 20.01%

42

at 3,425 km which is very near the asymptotic value of 20.02% (the instantaneous cruise value using a 15,000 m

reference environment). Thus the predicted variation in the cumulative rationai efficicncy over the entire fZight is

0.59%

The results indicate two main advantagcs in using the cuxnulative, rather thau the instantaneous, rational

efficiency to evaluate engine performance over an entire flight:

1. Tbe nrst is that the sharp changes and irregularities secn in the instantaneous efficiencies (Fig. 9) are put

into better perspective in temrs of th& i m w on enginc efficiency over an entire flight. For example, the

peak instantancous rational efnciency of 24.75% at 73 km under climb conditions when using a constant

sea level rcfcrrncc cnviFonment is mt observed in ihe cumulative d t s becausc it occurs for such a short

duration.

The second advantage is tbat the cumulative d t s chonstrate more c l d y the advantage of using a

constant r t f t m ~ x envirocunent cquivalent to the cruis i i altitude conditions. Fmm tbe i r i s t a n ~ u s

viewpoint alone, both the sea level and 15,000 m zefercnce eavironmeats produce somewhat sirnilar

maximum enws (approximatcly 4% a d 3% hspectiwiy). F ~ o m thesc ricsults donc, one might expect that

e i k chice of castant rcfaa~x cnvironmcnt d d producc s i m . enors. Howcver, since th

of tbe flight is conductd at a cniisc altitude of 15.000 m, the sea levcl rcfcrrnçc environment mriiatains

its error as dis&ncc traveled haeass, while the 15,000 m refehnce environment reduces it. This error

reduction is cleariy shown on the cumulative d t s (Fig. 8) as the 15,000 m and variable r e f m

environment CUNCS converge and almost intcrsect Thus for the 15,000 rn case the m r is reduced by

orders of mapitdc as diSElPYX traveld incrrsscs wbaFas for tfic sea levei case, the curve diverges h m

the variable curve and aqmptoticaUy approaches a 3.70./0 m r . Furthexmore, the dcQendance of the

amount of arior ieduction or m o n on distance is also shown in the cumulative resuits. At a distame

of apptoximrdcly 1,000 km, the cumulative efficiency for the 15,000 rn refcrieacc envimnment no longer

exhibits most of tbc FM produad ditring thc tiginnurg portion of the aight through the use of this choie

of ref- environment, while at tk same distance tbe sca lcvcl refcrence environment c w e has attairvA

most of its maximum enw. Tbe instaut8ncous d t s show w correlation behwen accumuintrY1 error and

distance flown.

43

4a

This section examines the contribution of the exhaust gas crnission to the cumulative exergy los, ia a

similar manncr as donc for the total los brcakdown in section 3.3. In this case however, the percentagc of exergy

contained and accumuiated in tbe exhaust over an entire flight is expresd as a percentage of the total cumulative

incoming exergy, as opposui to a pcrcentage of the total cxergy loss (which is used in section 3.3). Since the

exhaust has aiready becn idcntitied as tbc major contributor to cngine losses, it is belicvat tbat it is more informative

to know the exbaust crnission cxcrgy as a perccntage of the cumulative mergy input as opposd to the cumulative

total l o s (whicb is itsclf a pcrcentage of the cumuiaîive exergy input).

43.1 Variabk Rdertnce Enviroameat

Tbe variable hfericncc cnvironrricnt anve in Fig. 10 sbows that the cumulative exhaust cxergy pcnmitage

inciieases at the bcginning of the flight, and then levels off asymptotidy to a constant value. The rapid increase

in exhaust cxcrgy percenage bctwccn distanoes of O and 73 km is due to the iacrwsing aitindt during this phase

of flight, when the r e f e h ~ ~ environment jmamc and temperature dccrease and the cxc%y of the txbaust gasts

coniespoadlligly increasc. At sca levcl (a distance of O km) 5029% of the cumulative cxergy input is lost tbrough

the exhaust while at 3,445 km this value iacraises to 56.41%, a varïaîion of 6.1%. As with tbe cumulative rational

efficiency results, the cumulative exhaust loss c r ~ v c asymptotidy qprcmhes tbe iastantawous exhaust 105s value

during cniise of 56.4% as the flight distciacc is iaa#iscd Therit is a 'tmriil k a w s e b e y d a distance of 3,445 km

in the insîantaneous pcnrmtage of the input ex- contained in the exhausi, because tbc descent occurs. But due

to the much pester time spcnt at cruising conditions, tbe short duration of this phase of flight bas little impact on

the cumulative resuits.

43.2 Constant Refercace Environment

With a constant sts levcl ceference environment, the cumulative exhaust cxergy percentage dccreases as

the flight progreses, going h m a value of S O B ! ! ! at a grouad distance of O hn (sea levcl) to a valut of 37.8%

at 3,425 km, a variation of 12.42% (as expaclad, the latter pmcentage is near tbe insbntaneous cxbaust cxergy

44

percentage during cniise of 37.76%). This trend is opposite to that exhibite. by the variable refeiwice environment

curve in Fig. 10 where exhaust cmissioas contain increasing exergy as the fligôt progresses.

Since~dacrraseincxhaustac%ybecomcsgreatcrasthtdiff~~i~~~~~thcoperatiagdricfctcnce

environment pressmes incrtgses (due io the fsaft tbat the exhaust gases are expanded to operaiing environment

pressure), the constant sca level curve in Fig. 10 dccregses as the aircraff climbs (bctwacn O and 73 km). Aiso,

although the exhaust gascs ah at a higba temperature than tbe reference aivitonment temperatirrc at sea Ievel, the

thermal portion of the cxbausl excrgy is still becr#iscd when cornpared to the variable r e f m environment case.

This decrease occras becausc the sca h l - is kgber tban the ttmpcraturc at 15,000 m, tbus dccreasibg

the apparent thermal dfl-.

O 500 1000 1500 2000 2500 3000 3500 Ground Distance [km]

Fin 10 Variation of *jet cumulative cxhaust cmission cxcrgy over a flight range of 3,500 km at a cnrising altitude of 15,000 m using various ref- cnvhnmcnts.

At the start of the flight the values of tbe exhaust excrgy as a pcrccntage of incominp exergy for both the

sea levei and variable rcf- a~virommts are the samt. Howevcr, es tbe flight proghsscs, the sea lcvcl curve

diverges h m the variable ciave and iesches a mwimurn m r at 3,425 km of 18.54%. This is in contrast to the

45

maximum error of 3.67% obscrvcd in the cumulative rational efficiency values using a constant sea level refcrcnce

environment (which also occurs at the same point in the flight). Although both the cumulative rational efficiency

and exhaust exergy behave qualitatively in the samc manner when a constant sea levcl rrfcrcnce environment is

use& the cumulative exhaust exergy exhibits both a larger variation in vaiues during a single Qight and a iarger ermr

when wmpared to the values obtained using a variable rcf- avironment,

For the constant 15,000 m rcfncnce environment in Fig. 10, the cumulative cxhaust exergy pcrccntage

decreaçes fiom 63.85% at tbe beginning of the flight (a distance traveled of O hn) to a value of 56.54% (whkb is

s i m h to the instantancous cxhaust cxergy pcrccntage in cruise of 56.47%) at a distame of 3,425 km, a variation

of 73 1%. As with tfie use of a consCant ses kvei dcrrnce enwonment, this choie of rcfércme environment leads

to the cumulative cxhaust excrgy decrcasing wiîh iacrieasing flight distame, a trnid oppositc to that observed for

the vanable rcfmnic enWonmcnt curvc. in this case, ho-, the referenct tcmpaahrn and ptsz~crt

are Iower tban the opaatiag environment valua. So that is a ncgaîive pwsine dincrence at sea kvcl which taxis

to increase the vatue of the exbaust excrgy. This &kt is rcsponsiblc for tbc crppahnt inchased exbaust excrgy

petcentage seen at sea level fa the 15,000 m rcfehncc enwonment came. As tbc flight distance increascs, the

differencebetweentheopcratingardriefermccenwoamentsdscnascs(atradoppositctothatforthew~sca

level case), reducing the &kt of thc fictitious presmrc diff- d bencc causing the exbaust cxergy penxnEBge

to decrease and to approach tbe variable rcfmacc envitonment values. Note also thaî the innease in the

ternperatute différence betwcn exhaust tempeniaac d r c f m environment tcmperaapt crcatcd by the use of

a 15,000 rn reference environment at sea lcvei as compared to t& ternpcranirr diffêrence present wbea ushg a

variable xeference environment is duced with hcmuïng altitude and flight distance. Thus the maximum crror

between the 15,000 m aad wuiable ~efcrence environmcnt d u c s of cxbausî atcrgy perccntage is 1 3.56% and occurs

at the beginning of the flight, as opposcd to the constant sca level cuve which bas a maximum e m r at the end of

the cniise segment of the flight.

The cumulative exbaust cxergy pttcentage CUNCS in Fig. 10 show more clauiy the errors in trmds tban

the instantancous d t s (as in Figs. 4a a d Sb or Figs. Sa and 4b). Noting that the ijrst 73 km of the flight

represeats the c h b segment, Fig.10 clearly shows tbat the use of a constant refericncc cnWonment leads to tbe

46

emneous finding tbat exbaust exergy witb increasing altitude. While tbis result is disceniable fiom the

instantaneous results, it is mt as obvious. F w t k , as with the cumulative ratiod efficicncy d t s , tbe cumulative

exhaust exergy rcsults sbow the advantagc of using a constant rcfcrcnœ environment with conditions equal to those

at the cmising altitude, as this se ldm resuJts in a cnor, as op- to an iacreasing enot for a constant

sea level reference environmcnt, as ground di- is hmased. Although botb chices of refcrc~lce tnvk~cuneat

can lead to maximum enors of simiiar maguitude (14-194, the choice of CO-t refc~cllce environmeut

significantly affects the enors in tbe cumulative d t s as the flight ptogrcsses. Both the cumulative rationai

efficieacy and cumulative arhaust exergy pcrcentage indicatc thrtf with a sufliciently large CWSing distaace* the

results for a constant 15,000 rn refchllce environment are h s t identical to tbosc for tbe variable tcfehacc

environment.

One significant diffiamcc Wwum the cumuiative exbarist arngy pmxntage and the cumulative rational

efficiency d t s involves thc magnitudes of the potential errors caused by ttie use of a constant rcfcrcncc

environment. As fouad for tbe instrmtaasr,,us d t s , the c h i a of xef- envirionment bas a impact (one

order of magnitude) on tbt numericd accuracy of the cumulative exhaust emission ex- percentage than the

cumulative rationai cfficiency- As WU, tbc pndided trcads ushg a constant refercllcc environment are erroneous,

being approximately oppsite in form to tht trends for the variable rcfaicace cnviFonment case, with the magniîude

o f the predicted variation in m r by as much as 6.30% for the cumulative exbaiust ex- pcrccatagc.

49

It is usefiil to know how the b d d o w n of the exhaust l o s changes over an entire flight to ensure that

efforts to recover any losses arc effeçtive and W O R h M t over the entire flight, not j~ over a single fligbt sqgmeW

Here, variations of each of the three major components of the cumulative exhaust loss (physical, kinetic, and

chernical) are ilI& s q m k l y for VIYious rcferience cnvironments over the 3,500 km flight used in the previous

sections.

4.4.1 Variabk Rcirnace Emvironment

For a variable rcfere#x environmeni, each of tfit compoaeats of the exbaust loss CS only slightly over

the flight, as illustrated by the beariy constant variable tcfcrcncc environment curves in cach of Figs. 1 1, 12, and

13 (noting that the cumulative chcmical c x q m e appears to exhibit a lacger variation dut to the enlaqged

vertical d e ) . In aii cases tbc cumulative exhaust exergy breaLdown mxmins ncariy constant ovcr the flight,

comprised approwinintcly of 34% physical, 63% WC, and 3% chernical exagy.

Grourd Distance (km]

Figure 11 Variation of the physicai ex- cornponeat of the cumulative c x h u î loss ovcr a flight range of 3,500 km a! a altitude of 15,000 m ushg various fcficnce cllvironmcnts.

Chemical Exergy Component [% of Cumulathre Exhauat Exetgy)

O h ) W * c n a , ~

Kinetic Exergy Cornponent [% of Cumulath Exhaust Exergy)

4 4 h) L 0) Q,

O O O O O O O O h,

Figure 1 1 shows ibe physicalcxergy pcnxntage contribution to the cumulative exhaust loss, which

decreases slightly h m a valw of 35.86% at sea lcvel to a value of 34.16% at a grouad distance of 3,500 Irm; a

variation of 1.70%. The kïnetic exeqy componcnt of the crnnulative cxhaust loss bebavcs in the opposite fashion

of the physicai exergy component with a value of 6O3!E! at the start of the fligùt which inmwws slightiy to a valw

of 63.21% at a g r o d distance of 3,500 km, a variation of 2.82% (Fig. 12). In both of t k v, the effact of

changing altitude is d c i e n t l y srnail (as evidmd by the beginning portions of the cuves wâich reprc~eflt the

ciimb segment of the flight) tbat tbe final cnllsc desent has no perceptible i d - on tbe behaviour of the ciavcs.

nius the final values cited in this discussion iirt those occurxing at the «id of the flight, at a groumi distsnce of

approximately 3,500 km.

Figurc 13 shows tbc cumulative chernical exergy éencasing b m 3.75% of the cumulative exhaust loss

at a distance of O km to 2.63% et a distance of a9pn,ximntr!ly 3,500 km. Due to tbc d magnitude of the cbcmical

ex- with any choiœ of derence cnvironmart, the variation of 1.12% sbomi in Fig. 13 ap~cars much greata than

the variations CXpcneMxd by the other mbeust components, ewn thougb it cxpcriences the d c s t change of tbt

exhaust components over the fiight.

4.4.2 Constant Referrau Environmcit

The use of a constant sea lcvel rcfcrcace environment bas an impact on the acciiracy of the cumdative

exhaustexergybrealrdownwhich is large,cvcngmucrin k t than its impact on thecumulative total l o s bFtaLdown

(which involved arors as kgc as 1%)). At At bcghing of the flight, for both tbe variable a d constant sea level

refmce environmcnts, the physical m%y compoacat valut is 35.86% (sec Fig. 11). Howicvcr iastead of

temaining nearfy constant with distanoc, tbe sea levcl rcfercnce environment curve daxemes sharply to a value of

- 17.53% at a grouad distance of 3,425 km (the start of the desccnt). This is a variation of 53.39%, compared to the

variation of 1.70% for the variable ricferrnce environment curvt. Also, as mted in previous sections, the cumulative

curve approaches the instantaneous cniist value, which in this case is -1825%.

Thus the cumulative physicai cxagy componcnt of thc exhaust is su under-prcdïcted for the sea lcvel

re fa~nce environment tbat the exhaust conûb not only no physicaî exergy, but instead a pbysicd exergy dcncit.

This ncgative numerid d u c is duc to t& positive plcssiirt ~~ nitased when using the sca level rcfehaa

50

environment pressure where the opcrating envu0-t pressure is equal to that for the cruising altitude of 15,000

m. This fictitious pressue diffkmœ cieates tbe illusion of negaiive -cal excrgy existhg in the exhaust during

al1 phases of the flight, given that ody at two iustants durhg taiceoff and landing is the a i r d at an operating

environment of sea b e l . Thus although the tcmpnuure diffetc~ce crcates positive physical exergy, the much

greater difference betwecn the exhaust gas plrssuh aad the rcfixmx environment pressure during cruise

overwhelms this positive cxergy and thus crcates the illusion that the cxhaust contains q a t i v e physical exergy.

At altitudes betow approximately 11,000 m, the exhaust still contains positive exergy h m an instantaneous

viewpoint, as the positive themial portion of the cxcrgy is gmater tban the ncgativc p~cssurr portion. Howevcr, the

positive physical cxetgy accumulated during the climb segment of the fiight under 1 1,000 m is quickly diminished

by the negative phfical ex- accumuiatcd diaing flight h v e 1 1,000 m (i-e. cruisc).

Alîhough ovcraü î k cxharist still has positive cxagy, this wvc physical compoacnt creatcs tk illusion

that l e s exergy is cxiting the engine tùrough the exhaust. This d t is consisicnt with d t s for the cumulative

loss analysis (section 4.3, Fig. IO) in that the use of a constant sca lcvel rcfcrcncc environment decreascs the

percentage of the ~ll l~ulative eyhnirpt loss. Over the entire flight, in fact, for a constant sea l m 1 refercncc

environment, appolcimatcly 4900 MJ of ex- is jected with the arhaust over the fiight range of 3,500 km. This

value is approxjmatcly 43% lcss than the actuai value of approximaItly 8565 MJ for a variable t c f m

environment. This decreasc in cumuiatiw exbaust ex- is duc eatirely to the ncgative physical cxcrgy showun in

Fig. 1 1 for the sea level rcfcrrnce ~vVonment.

This negstivt physical cxergy kads to marlrcd incr#iscs in the M c compormt of tbt cumulative exhaust

exergy for a constant sca l m 1 ~~ cnvironmcnî. Since, as d i s c d in prcvious d o n s , the kinetic exergy

of the exhaut is indepeadent of tbc cboicc of rcfererwx e n v i r o ~ ~ ~ ~ ~ ~ l f the h ames in Fig. 12 might bc expectcd

to be identical. Howcvcr, men though the total lcinetic cxergy cjectcd with the exhaust over the flight distance of

3,500 km is constant at approximaîcly 5400 MJ, this quantity tcpresents a largcr pctcentage of the cumulative

exhaust exergy givcn the bchaviour of the physical ex= camponent. At tbe beghmbg of the flight, the values

for the sea levet and variable mfncncc environment curves art identical at 60.3996, but the former incr#iscs with

distance to a maximum valu of 1 1 1 39% a 3,425 lm. This variation of 48.1% is much gnater than the maximum

5 1

variation exhibited by the variable ref- caviroameut curve of 2.82%. In fact over the cnajority of the flight,

the sea Ievel reference environment c u m in Fig. 12 indicates that the kinetic component of the cumulative exhaust

exergy is greater than (Le., over 1 Wh) the cumulative exhaust cxcrgy itsclf. This nnding can also be scen by

cornparhg the cumulative exhaust mergy jected over the entire flight of 4900 MJ (wbea using a constant sea level

referma environment) to the cumulative kinetic ex- cjccted through tbe exhaust of 5414 UI (when using any

choice of refmnce environment).

Chernical ex= comprises a siuill pcmntsge of the cumulative exbaust exergy, varying h m 3.75% at

sea level to a value of 6.15% at the stact of the descent (3,425 km) when using a constant sea level reference

environment. This incmase is duc to the decrrase in overall cumulative cxhaust exergy for a sea lcvcl referrnce

environment (as is tbt casc for tk Linctic cxagy componcnt), altbough in this case the magnitude of the chernical

exergy component is also inmead slightly comparcû to the variable rcferc~x environment case due to its

dependance on thc xcfrrcnct cnvitoamcat tempcmüm (Eq. (28)) which rtmains at the sea level value.

When using a constant sea lcvel rcfercnce environmat, the maximum «lor in the chernical txtrgy

component of 3.52% (evalmd ris the greatcst d i £ f e h ~ ~ in values bawecn the variable and sca level rcfercnce

environment m e s in Fig. 13) occias at tht start of the dcsccnt, at a dkianœ of 3,425 km. This d t is consistent

with those for the other flight-profile hsults. For the physical exergy component the maximum emr is

approximately 5 1.69?/0 whertas for tbc WC ex- camponent it is 48.1 8% (sec Figs. 1 1 and 12 rcspectively).

These values are similar to thc maximum variations expmiciictd ovcr the flight, maiiil.y becaust with the variable

reference environment a nearly constant acbaust exergy breaLdown is observed at al1 altitudes (and hence distances).

The use of a constant 15,000 m refcrcnce enviromctlt le& to enoaeous trends similar ta those for the

constant sea level refmencc «iWoment. The major diffkrencc is tbat instcad of starting at values qua1 to those

obtained using a variable rcfehace cnwOnmcnt, the cuves for the 15,000 m rcfemwx environment start at the

maximum error and baçome mort accurate as the flight pmpscq epproaching ihe variable rcferience enviro~lll~nt

curves asymptotically. Thus in Fig. 1 1 the valut of the physical component of the cumulative exhaust exergy is

initidly 56.58% at sca level and âaxeasa to a minimum of 34.41% at a distance of 3,425 km, a variation of

22.17%. At sca Icvei, the maximm ernn is 20.72'?'/i but by a dizrtrincc of appoximatcly 200 km this emia bas b c a

52

rcduced by one order of magnitude and over the flight distance of spproximately 3,500 km the error is almost

cornpletely eliminated. This decrrase in the physical component of the cumulative exhaust exergy is due to the

reduction of the errer ihduced thrwgh tbe usc of a hi* altitude rcfehnce cnvùlonment than operating environment

at the start of the flight. Since tbc errot is at a maximum when the aucraft is at sea Icvel, the fictitious positive

pressure-related physid cxcrgy is the largest at this point. At al1 timcs during the clmb segment, h o m e r , this

fictitious exergy is continually reducad, becoming zm, as the cniisc altitude is reached, Thus, this cboice of

referençe environment produccs crror only during tbe climb aad dtscait segments of tbe flight Givm tk sbort span

of tirne spent uadcr tbese conditions relative to the en& fiight tirne, the cumulative results for the 15,000 m

reference environment exhibit much less crror than the d t s using a constant sea lcvel rcfcrence enviFonmcnt

The cumulative exhaust ex= cjacted over the fligb; üsing a constant 15,000 m ttfcrc~lcc enviro-t

is approximately 8633 MJ, which is only 0.8(r? greatcr tban the value for a variable r e f w cnviro-t

(approximaîely 8565 hU). This d différence is attributable to tbc minimni impact tbat the climb and descent

segments have on tht cumulative d t s . The rmPamimi enws obtai#d whca using a amstant 15,000 m derence

enWoument are large because this enot occm at tht btginning of the Qight, thus the heaviiy weighted effect of

the mise segment is abscat.

Comsponding to tiie inaieasod pbysical compobcnt of the cxagy of îhc exhausi at sea levcl is a d w e a d

kinetic campomat (sec the 15,000 ref- ~~~viroamcnt curvc in Fig. 12). As mcntioned carlier, the magnitude

of the kiwtic componuû of the cumiiiativt cxhaust cxcrgy is indepcndtnt of the cboice of reference environment.

However, the increase in tbc physical camponent iiicreasts the ov& cumulative exergy, with the cfllect of

decreasing the pmmitage of the cxhaust cxctgy in kinetic form. Thus tbe 15,000 m refercnce environment c m

has a value of 41.48% at a distancc of O km (sea level) a d krcases to a maximum of 62.9% at a distancc of 3,425

km, a variation of 2 1.49%. The maximum crror of 18.91% occurs at sca levei and is contindy reduced with

inmaskg ground distancc until the descent segment of the Qight is reached (at which point tbcre is a vezy small

inctease in errer). Tbe chcmical compoaeat of the cumulative cxhaust exergy bas an initial value of 1.93% which

iacteases to 2.61% cd 3,425 km, a variation of 0.68%. This imx#isc is agair~ niiiinly duc to the fàct that the fictitious

presmre-relatai physicai componcnt of the exhairrt accrgy is duccd as the a ciimbs (d in small part is diit

53

to the dependence of the chemical exergy component on the refcrtnçe enenment temperatme). The maximum

error in the chemical exergy component occurs at sca lcvel a- the start of the fiight and is equal to 1.82%.

The choice of rrfetcllcc environment clcarfy bas the grtatest impact on the results prcsentbd in this section,

The use of a constant se- level referrnce enviroment leads to maximum emrs (defined as the largest diff-ce

between constant a d variable rcfercnce environment m e s ) as large as 52%, 2.5 times as large as the maximum

error pduced in the cumulative total l o s analysis (19%) and 13 thes as iarge as the maximum enor produceci in

the curnuiative rational efficiency anaiysis (4%). As with the cumulative total loss aaalysis, the choice of any

constant r e f m enWonmeat kads to thc pradiction of fàisc W. h the case COLlSidered hem, the actual exhaust

loss breakdown is approxuilatr-ly coascimt during tk aght (which is show much more clearly in Figs. 1 l,l2, and

13 than in Figs. da and 7b or Figs. 7a and 6b), with vMations limitai to appmximately 1-3% for the three exbaust

components oves dhmcs of O to 3,500 km. The use of a constant sea levcl refnence envimament, howcvcr,

predicts variations as k g c as 53% bawdcn componcnt pcrcaitagc values at O and 3,500 km- Tbc use of a consrant

reference environment quai to tbe cniising aititudc can d u c c the cnurs by approximatcly balf, with maximum

errors of approxhaîcly 21% (as opposcd to 52%) anâ vaciaiions over the flight of approximatcly 22% (as opposcd

to 53%). As urcli, the use of this cboice of refchnct cnviFonmeat tuxîs to rnitigate the errw poduccd, with the crror

decreasing as the length ofthe cniising segment of the flight is inmead in duration.

5.0 CONCLUDMG REMARKS

LI

The results of the ex- anaiysis p r f d h m on a turbojet engine indicate that the exhaust emissions

contain the majority of the ex- loss. ï h i s result is consistent with the results reported in previous worlcs

(Brilliant, 1995; Clarke and Horlock, 1975; Kresta, 1992; LRwis, 1976; Malinovskü, 1984). The ove& rational

efficiency of the engine is shown to decrcase by apptoximately 2% fiom sea b e l to the tropopause (- 1 1,000 m),

mainly due to the iacrraçc in the acrgy los asociatd with the cxhaust etnissions. For a typicai modern cngine

the overall rational efficiency is approximatcly 20%, wtuch is bctter than the older engine used in Clarke and

Horlock (1 975) which has a raiioaal dcicacy of appn,ximately 16%. Above the tropopeuse the rational efficieacy

remains neariy constant, &'bithg only a sligbt dcctieast with altitude (les thaa 0.1%). Wbcn a coastant refkmœ

environment is uscd, the rational efficiency remains ncarly constant as altitude increases up to the tropopause and

increases with altitude above the tropopeusc. Tbe maximum enors produccd through tht uçc of a constant rrfcrrmx

environment on the accuracy of the rational efficiency of tbc engine (both iristantaneous and cumulative) are

approxhately 2-3%

For both a constant and variable refcrcact environment, the fùel exergy reniains nearly constant at all

altitudes up to 15,000 m, with the variable r e f m environment case showing the largcst variation (less than

0.6%).

The intenial cxergy losses (those aüributable to irrcversible processes within the cngine) decrease with

increasing altitude. At sca level the in- cxergy losses comprise 8pproximatcly 35% of the total cxergy los,

and this value decrtases to 30% at 15,000 rn using the older engine operating parameters found in Clarke and

Horlock (1975) (beace the exhaust cxergy los increases h m 65% to 70%). Over an enîire flight, the cxhaust

exergy loss comprises bctwaca 50-55% of the cumulative bcoming ex- when using typical modem cngine

operatuig parameters, this value inrreasing with brea&ug altitude (i.e., 50% at çea level, 55% at 15,000 m, a trend

*ch is consistent with the instantaneous rcsults). The use of a constant rcference environment predicts an opposite

trend with the exhsust excrgy loss dccreasing with incrcasiag altitude and bcnce the interaal excrgy losses

increasing, Ieaâhg ta enws as large as 1% ovcr a flight distance of a p p r o ~ l y 3,500 km. The use of a &cd

55

reference environment with parametcrs cofiesponding to low-altitude conditions (sea level) leads to an d e r

prediction of the exhaust exergy loss at al1 aititudes except the reference environment altitude, this value

is over-predicted if the referace environment panmetcm ah h e d at conditions for a higher altitude (1 5,000 m).

Although the magaitude of the ew)inirft l o s varies with altinide, rhe composition of this ioss nmains

neariy constant when a variable rtfereaa environment is used However, the use of a constant refcrenct

environment causcs the bdcdown of the cxhmd loss to be dcpendent on altitude. A refercnce environment

diffant than the opcrating environment (whetha it takes on pmmmetcr values for higher or lowcr altitudes) causes

the physical componcnt of ttat exhausî loss to dccmasc with inmasing altiîudc and the kinetic contribution to

increase (tbe chanid componcnt king negligii at aopoximately 2 4 % ia al1 cascs amsidemi). Tbe dinaicnces

between the indicated anâ auuai (as found using the operating environment as tbe refehnœ environment, i.r., the

variable r e f m environment case) wm-t contributions ~ 8 0 be as large as 28% for the olda engine

considerd anâ 52?A for a more typical modem ~I@E w&ri using a constant rcf- envirioment. This cmr is

also depeadent on tht cboia of orwistant hfcraiec cnviromncnt. The use of a constant ricfncncc avironment with

conditions equivaieat to those for the Cnrising altitude am reduee this maximum cnor by mort than half and produce

cumulative d t s nearly identical to the varidle r c f m environment values ovcr a su8oiciently large flight

d i m .

52

The choiœ of =ferracc cnvllonmen! was sbown to have a negligible impact on the analysis of the incoming

fiiel exergy, which is signifiant as the fkl rcprsents the oniy source of cxergy input into the cugine. Howcver,

it was also noted that dcptnding on the fùel storage conditions, this conclusion could chauge.

Overalt, the use of a constant refnence cnvironmcnt yields rationai cfficicncies tbat art reasonably accurate

wmpared to those f o d ushg the actual operating enviroumeat as the rcf- environment. HOWWQ, the

behaviour of the rational efficiaicy as altitude is variai is depadent on t& rieference cavito~lll~~lt, with a constant

reference environment prcdicîing fiaise bmds. Although the acc\cracy in the magnitude of the rationai efficiency

is still probably witbin acaptable engineering l imits dcpending on the application, given the disctcpancy in

56

predicted trends, the potential for larga mors exists as the difference between the operating and reference

environments increases.

The choice of ricfcrrnce arvirollll~~lt bas a grtgter impact on the accuracy of d t s relating to the locations

and causes of exergy losses. In the analyses performed herein, the maximum errors obtained in the exhaust loss

evaluation (as a perccntage of the total mcrgy input) through the use of a constant reference environment c m be in

excess of 4.5 times largm tban tbt maximum crrws produced in the rationai efficiency redts. Thus tbe prediclcd

breakdown of the total loss into intenial and exttrnal components can bc signitlcantly affected by the rcferrnce

environment. Since this type of loss an- is signifiiamt in detcnniniag . - whcrc the key inefficiençies arc locatad,

errors on the oder of 1% can grcatly d u c e the bcncfits of tùis type of anaiysis. A 13,000 m (-50,000 fi)

difference in altitude bttween thc operating and derence environment can lead to the erroneous conclusion that

the exhaust emission asergy loss is not the major contributor to the ovcrall inefficicacy of the tiaboja engine,

indicaîing instead tbat the irircvasi'blc losses ah cquivaicat in maguitude. As weil, the use of a constant xefcreace

environment is unsuitable for predicting tbe behaviour o f the exhaust loss dur* a cornpletc flight, as this choice

of reference environment indicatcs that the exhaust loss dccrcascs, instead of &masiq, with incrcasing altitude.

The choiœ of rcfacncc aivirwmcnt bas tht impect on the brealrdow of the cxhaust exmgy 105s.

Here, errors approximately 13 times greater than tbose for the rationai efficicncy d t s art observed when using

a constant refercnce environment. With maximum errors of approximately 52% (using typical modem cagine

operating parameters), tâe use of a constaut hfe~eacc chvùorimcnt is Likely hckpaîc f a my desigrt..impmvemeat

efforts. Aithough in aU cases tk chemical cxergy component of the exhaust l o s was propcrly identifid as king

relatively small, both the physid and kinetic componcnts weh found to be sensitive to the choiœ of c e f ~ t ~ t l ~ e

environment, which is aot actuaily the case. As shown using a variable refmcnce cnvirom~~~t , the composition of

the exbaust los is idepdamt of altitude, with both tbe physid end WC cxcrgy components cuntributing nearly

equally (dependhg on the enginc operathg parameters) to the o v d cxbaust cxetgy los.

From an instantancous vicwpoinî, tbe crrors prduced thn>ugh the use of a constant reference envhnmcnt

are approximately equal, wtietber the refmmce environment conditions correspond to high- or low-altitude

conditions. Howcver, ovcr an entire flight, thc cboice o f a wnstaat ritf«ri3cc environment corrtsponding to the

57

cniising altitude can s i g a i n d y d u c e the maximum cumulative enors produced, and mitigate the impact of any

errors accumulated during tbe climbing and descending segments of the flight. The greater the fligbt distance, the

more a constant r c f m envllonmcat comspom to the cruising altitude will producc d t s appoaching thosc

obtained using a variable reference environment This emr-reduction eff'ect is tbe most proaouoccd in the exhaust

loss analysis, for which the cmws art tbt largest wben using a constant ~ feh l l çc environment. Houmer, the error-

reduction e f f i is depedmt on the lcngth of the cniisc segment of the flight and would be lcss noticcable for

shorter flights, whch the climb and descent segments rrprcscnt a siflcant portion of the ovedi flight.

For aaalysis and dcsign wuxk the use of a constant t c f i esyùonmeat appcars to bc unsuitable in mli~ly

instançes for aaxatcly guiding impovumnt effoits, as the locations of the greatest losses and the causes of thtsc

losses are not pmpdy charactcrized-

sa - Carie shouid be cxeLMScd whcn using a amtant ~ ~ ~ C ~ C I L C C cnvllonment fa bdh instaatancous asmmmts

of engine performance auci cumulative enginc -ts ovcr entire flighs, given th innrrirrne;cs tbrd can ensue.

However, the use of a constant r e f m environment may pmve suitable uadcr conditions wheh thc operating

environment is ciifficuit to define as a rtf- environment. For example, for space applications the lack of

atmosphcrie remdes the merbod used behin to eyaluate the h l ex- void, as tk products of combustion arc not

present in a vacuum. In cases like this a m t derence environment comsponding to high altitude conditions

may prove more suitable tban a variable refehncc enviro~~ent.

For most aîmospheric a i d applications, the use of a variable rcferrnce environment (equal to the

operating environment at al1 timcs) does m t add great complexity to the ex- calculations and yields accurate

results that c m be used to evaluate cngïne perfomiance under my combination of operaîing conditions. The

universality of the exergy cfficiency pamnder allows the cornparison of various engbe types (turboprop, hirbofan,

turbojet, scramjet) using a single term. It also allows compoatnts witbin an eagiae to be compared using a single

term without resort to differcllt efficicncy parametm for diffcrent componcnts (Le., cornpressor efficicncy,

combustor efficieacy, etc.). Givcn the clarity and consistcncy with which an cxctgy d y s i s has ôcen show11 to

58

describe the operation of a turbojet engine, it is hoped that its use will be hther employed in the aerospace

propulsion commuaity to engines under current development.

Several reammendations for future work are also meritcd. F i as the present work is ümited to altiades

bdow 15,000 rn (-50,000 A), the nsearcb in tbis area should be extended for higher altitudes (low Earth orbit and

beyond) where even more sevcre changes arc observai in the opcrating environment. Space as a rcftrence

environment provida a unique cballcnge in applying an cxergy anaiysis, but one that h u i d be ovcrwmc if exergy

analyses are to aid in the dcvclopmcnt of fiiturr propulsive devices. As well, given the large amount of cxergy

containeci in the exhaust cmissions of thc turbojet, rcscarch into methods of utilizing this excrgy should be

underiakm as such efforts could yicld improvcments in engine cfficiencies.

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APPENDIX 1: Calcuhtion Parrrmeters

The variation in both atmospbenc tearpaature and pressure as altitude is Urcreased h m sea level to 15,000

m and beyond is shown in Fig. 14 (with ovcrlaying data points h m McCormick, 1995). The sharp change in the

variation in the temperaaite curve occurs at tbe sîart of the tropopause at approximately 1 1,000 m, above which the

temperature remains constant until the stratosphere is reached (not shown on the figure). The two altinides used

most o h in this report ah sea level and 15,000 m which have ternpcratirres of 288 K and 2 17 K and pressures of

10 1 kPa and 12 kPa, respectively.

Pressure [kPa)

O 50 100 1 50 200 250 300

Figure 14 Variation of ahnosphenc tcmpcmturc and pressure h m sea level to 20,000 m

The chernical composition of the reference environment, Le. tbe proportion by mass or mole of each

constituent in the atmospheic, is show in Table 7. Table 8 shows the values of the various parameters used to

evaluate the chemicai exergy of both the fuel and the postcombustion mixture. Note that since the h l is mcthane,

complete combustion occurs according to the formula

CH, +20,-CO2+2H,O

Tabk 7 Assumed Atmosphcric Composition Used in Analysis.'

Table 8 Combustion Panimaers.'

Constituent

w

N2

O2

CO*

H20

'adapted k m Clarke and Horlock (1975)

The last set of data required to calculate the chernid exergy of the tirel ah the standard thermodynamic

quantities in Eqs. (1 7), (20), and (21) for each constituent involved in the combustion process. These values are

shown in Table 9 (bmed on data in Clarke and Horlock, 1975) and rcpresent the values at a temperature of 298 K

and a pressure of 100 kPa

'adapted h m Clark and Horiock (1 975)

M

Fp;/irmol]

28

32

44

18

a

IkaSgJ 0.78000

021000

0*00035

0.00965

x

~ m o V m o i ~ I

0.7%74

O. 18769

0.00023

0.01533

Table 9 Standard Thcmiodynamic Roperties of Constitumts involved in Combustion.'

'adapted h m Clark and Horiock (1975)

The fonn of the cumulative rational efficiency curve can bc detamkd by considering the following

discussion. Taking the instantaneous thst power and instantaner>us incoming exergy flow rate to vary linearly with

timc, t, one can represent these curves with the fallowing equations:

PT = A t +b

which when integrated over time yields

whete a = An, g = G/2. and c a d ciadtue ammnts depeading on the Limits of intcgration (which ricprcscnt the le@

of the flight in the appropriate imits of time).

The analysis so fiit includcs aii tbc possible sœmuios encomtericd durhg a flight, as ihe thrust power can

increase (climb), d- (descat), or stay constant (cniisc) using Eq. (32). Thus to calculate the cumulative

d o n a i efficiency at any point dong tbc fi@ pronle rrqiims cvaiuahg thc ntio of !PT (t) dt to fi + (t) dt (see

Eq. (26)) which yields tbe following expiession:

67

Thus as t increascs (which in nnn means the flight distance increases for a givea cruising speed) the higher

order terms becorne les significant. In the ümit as t (or &se distance) approaches idhity,