EQUILIBRIUM

REPORT 987

OPERATING PERFORMANCE OF AXIAL-FLOW TURBOJET ENGINESBY 31EANS OF IDEALIZED ANALYSIS

ByJOHN C.S.WDIHZSandEDWARD C.CHAPIS

SUNIMARY

A methodoj predicting equilibrium operating pe~wvnance offw-bujet engines has been deceloped, u’ifh the asaumpfion of.vimple model processes -for the components. Results of theanaly.sis are plotted in. terms of dimensionless parameterscomprim’n.gcritical engine dimensions and owr-all operatingrariab[es.

I’%isinvestigation.was madefor an engine in which the ra~io(.~fa~’al in[et-air relocity to compressor-tip relocity is con-.stant, which approximates turbojef engines U<ffl a.ria[-jiowcompressor.

Experimental correlation of the theory with datafrom sereralezisting axial-jfcwtype engines was good and showed closecorre[at[on beiween.calculated anc[ measuredperformance.

12JTRODUCTION

The equilibrium operating performance of a turbojet enginecan be predictedfrom a knowledge of the component. char-artwistics and ~the en=tie-design variables. A method ofobtaining equilibrium performance is presenteclin reference 1.Thii method consists in consicIering the engine b-y its com-ponents (compressor, burner, turbine, and exhaust nozzle)ancl computing over-all performance from the given charac-teristics of each component. Because component chara.c-tw+..tics are so complex ancI there are so many variables,computations based on available analyses are lengthy andare also limitecl to a single engine and operating point. forany one series of calcukt ions. A definite mwcl e.sists for amore general form of analysis that will permit an approximateeprediction of the performance of any engine configurationat any flight speed or altitude based on several criticaldimensions and operating variables.

The first step in such an analysis is that of describingmmplicat eclcomponent processes in some simplified manner.A method often successful& used is that. of approximatingactual processes by means of simple model processes with thefinal accuracy clependent on the degree of model refinement.Some work has already been done in apprcmimating turbojet-cornponent performance by means of ruode~ processes.Progress in the clescription of turbine performance by meansof modeI processes is reported in reference 2.

.Ananalysis in which the dimensions of the components arerelatecl to the performance of a turbojet engine was made atthe N’ACA Lewis laboratory during 1948 ancl is presentedherein. The results are presented in such a fashion that

tlwy are applicable topresentation requires a

any turbojet engine. This generalknowledge of the efficiencies of the

inditichud components, compressor and turbine, uncIertiarious operating conclitions. The performance of turbojehengines for constant efficiencies of compressor and turbinemay he read directly from the general presentation. Supw-imposition of compressor tmcl turbine characteristics uponthe general presentation permits accurate calculation of theperformance. Results of the analysis are compmed withexperimental data.

‘Ilk anaIysis is of interest for three reasons:(1) lt. is a step toward a rationaI ccdcuktion of turbojet-

engine “performance, the full realization of which will permitcalculation of performance from the clrawin=gof the engiq.e.

(2) The generakecl presentation shows how variations mimportant. design and operating parameters will influenceperformance.

(3] The analysis affords a method of accurately matchingcompressors and turbines for which the performance char-acteristics are known in detail.

SYMBOLS

The following symbols are used in this report:AA,a

cD

;hp1-.

31.

Mc,ll

.M~N

PPQRrT

—cross-sectionaI area, square feetturbine minimum-passage area, square feet-i-eIocity of souncl basecl on total temperature, feet

per secondconstant.compressor-rotor-blade-tip diameter, feetnet thrust, pounclsfuel-air ratio phls 1

-.

horsepowerratio of hdet-a.ir veIocity to compressor-blacle-tip

-relocitycompressor-bIade-tip Mach number based on inlet

temperaturecompressor-bIade-tip Mach number based on ambi-

ent tempei’atureflight Mach mlmlwr based on ambient temperatureengine speed, rpmtotaI pressure, pounds per square foot absolutestatic pressure, ponncls per square foot absoluteair flow, cubic feet per secondgas constant, foot-pounds per sIug ‘Rtotal-pressure ratiotottd temperature, ‘R

673 ‘“ ‘

https://ntrs.nasa.gov/search.jsp?R=19930092047 2018-05-16T14:31:32+00:00Z

674

vv.w‘r

6

?6

;

REPORT 987—NATIONAL ADVISORY CONkTTEE FOR-AERONAUTICS

velocity, feet per second ,compressor-blade-tip velocity, feet per secondmass flow, slugs pm secondratio of specific heat at constant pressure to specific

heat at constant volumeratio of compressor-inlet absoIute total pressure=to

NACA standard s=i-level absolute -pressureef%ciencyratio of compressor-inlet absolute total temperature

to NACA standard sea-level absolute temperaturemass density, slugs per cubic footpressure coefficient

Subscripts:b burnerc compressor

~ jetn nozzlor ramt turbineo ambient1 comprwor inlet~ compressor outlet3 turbine inlet4 turbine outlet5 nozzle outlet

ANALYSISDESCRIPTIONOF COMPONENT MODELS

In order to cstablisb theoretical equilibrium operating con-ditions, the performance of each engine component must bedescribed. ‘1’he descriptive equations for each componautand the development of the analysis are given in the appen-clix. The principal equations of the analysis are describedin the following paragraphs.

Compressor,—The development of the analysis rcquircethat a simple expression for comprmsor mnss flow be lmoum.The ratio of inlet-air velocity to compressor-hludc-tip veloc-ity Kc for a..xia]-flow compressors has been found to beapproximately constrmt, part.icuhwlyat or nmr design speed.Hence, with the use of this rclation, the foliowing expressionfor compressor air flow TY.can bc dweloprd:

(1)

The power to drive the compressor may be expressed m

w. -f.()llP’=550 ‘qC ~c—1—. R.TO(r,)‘=’[(F’-J(2)

Turbine,—In order to obtain a simplified expression forthe gas flow through the turbine l~t, the turbiuc and theturbine nozzle were considcrecl similar to a.simple channcl ofvmying cross section. The expression for Wt is then writ[cn

(3)The turbine power may be expressed as

-E ( 7’-)4’-LFI“).hp, —550 v~ ~t—l

(Herein-A, is the turbine milli~rlllln-il~s~ngcarcn.)Exhaust nozzle,—The exhaust nozzle is described in U1O

same manner as the turbinti and the cqunt.ion for UN Iiow. through the exhaust nozzle. l.womcs

mm= 4 27,P, -4+(3’)’1(9’’-(3 “](-Yu––I)R

(r,)27,

EQUILIBRIUMPERFORMANCE

The assumptions are now staled and all descriptive equa-tions are combined to define equilibrium operating perform-ance of the complete engine.

Assumptions,—Equation (3) is used as an approximationfor M’, in order to. avoicl complications in the equilibriumanalysis. For Iow-reaction turbines and turbines operatingat or near choking conclitions, the approximation is of sufE-cient accuracy. A further assumption made using equation(3) is that the turbine pressure ratio used in calculatingequilibrium performance is considered to be the total-pressureratio from the inlet to the outlet of thu turbine. Theturbine pressure ratio in equation (3) should be the totaLto-stutic pressure ratio across the turbine; however, the errorin this assumption is small. Figure 1 shows the magnitude

(5)

of error in using r~as the tottil-to-tohd prwsuro rntio in thoexpression

[(’f-(’)%]

rather thtm the total-to-static pressure. TIM error r[’aclwsa maximum of about 5 percent at low values of r’. If amore accurate solution is required, a factor C can lx! includedti equation (3), as shown, to correct the error.

The burner pressure ratio r, appearing in equations (3)and (5) represents a mewurc of the pressure drop in theburner. In order to make the equations as simple as pos-sible, this pressure ratio -was included rather than a morecomplicated equation for the 10ss.

EQUILIBRIUM OPERATING PERFOR3L41WE OF .4.SL4L-FLOWTURBOJET EXGIKES BY MEANS OF IDEALIZED ANALYSIS 675

~GCEE l.—ReIation between turbiitotal-prfsaure-mtfo parameter and total-ta+tatic-Dreesnre-rarioperarrreter. Turbojet engine A.

The areasA, and An in equations (3) and (5), respectively,are effective flow- areas rather than actual passage areas.These areas -werec.alculatedusing equations (3) and (5) and

obserred engine data. Experimental variation from averagevalues of A=/As for two engines is plotted against enginespeed A’ in figure 2.

In the development of equation (5), the turbine-outlettemperature T1 -was determined assuming the turbinetemperature drop to be isentropic. Thus, the turbine-out.lettemperature used in the theoretical mdcula.tionsis somewhatIower than the actual temperature. The error involved inmaking this assumption, however, is small and can beneglected. (See reference 3.)

Equilibrium.-In order to estabIish equilibrium operationof a turbojet enginel two general conditions must be satisfied.The compressor air flow plus fuel f70w must equal the gasflow through the turbine and the exhaust nozzle, and the ~1.power deIivered by the turbine must equal the power neces-sary to drive the compressor. In this anaIysis, no air isassumed to leave the system and no mechanical Iosses areassumed to be incurred. From these relations and the fiveequations developed from the component-ruodeI a.naI@s,equationa may be demdoped that define equilibrium perform-ance of the complete turbojet engine.

Equating the two expressions for mass flow (equations (1)and (3)) and the power expressions (equations (2) and (4))pro-i-idestwo separate expressionsfor the compressor pressureratio re. The equation for equilibrium operation can bedetermined by setting the t.-woequations for r. equal to eachother:

With the assumption of constant values for -YC,~~, and rb,and with rr held constant for any one series of calculat.ions,

()equation (6) e----ressesthe speed parameter~jKJfc “~ ;

1! o

as a function of the temperature parameter j(T3/?’o) ~~~.and r~.

The turbine pressure ratio r, can be combined with rc andthe quantity rJr~ plotted against functions of engine speedand temperature to indicate the pumping capacity of anycompressor-turbine configuration.

In this anal-ysis,however, it.is of more interest to develop

a correlation of nozzIe-to-turbine minimum-passage-arearatio AJA ~as a function of engine speed and temperature.

, I —

Hence, by combination of equations (3) and (5), the foIlowingexpression for An/At can be developed in terms of rt :

‘[($,($+] (,).A= (r,} ‘i’

‘=[(3%%9%1After the equilibrium operating conditions have been =_.

established, the ana.lysiacan be expanded to provide specificperformance figures. As an example, an expression for enginenet. thrust per unit turbine area F/P&c is developed in theappendix. The find expression for this quantity is given inthe following equation:

(8)

GENERALIZEDEQUILIBRIUMCH_4RTS

EquilibriumoperatingIines.-The generalsolutionof the I ture parameter j ~ q.q ~for three values of AJA~ and twoTO

eq~brium equ~tions is-shommin figure 3 in which the speed I -raIuesof r,.E!merimental data indicated that the Dressureloss in the

f $.() burn~r had to be accounted for in establ%ng correct equi-parameter $ KJL ~ M plotted against the t.e.mpera-

Iibrium performance. The average value of pressure ratio

676 REPORT 987—NATIONAL ADVISOR1” COM!WTTEE FOR AERONAUTICS

2.2’

kS+l* Tur&jetm enginetu ) o Ai? o Bo — A (average~ 2.0 =-----0 (average 1-2

0 MI

~ * Q

k ~ ! (>+ g

f

N E: .5 /.&a ~ i2------- .. ----- ------- ------- ------ ------ ,------- ----- ------- ------- ------- ------ ------ ------ ------- ------ ------- ------

f

$

1.60,000 ~ooo 8,000 9,000 10,,000 11,000 12,000 19,000 14,000 /q

i%g,ne speed, A?,rpm

I+YGUREZ-Experimcntaf varfotion of ratio of nozzle area to turbine minimum-passageareswith crrginhsfwed for two turbojet cnginm.

$oeedparamefer, ~ . c ~“KM[ ~ )x

FIGUREs.—aeneral solution of equilibrium eqrmtions for several ratias of nozzle area toturbine mfnimum-poeewe area and two ram pressureratios with the assumption of noburnerpressureloss.

~ Loa4 0 0 $.

.:-<I 1,,

Turbojet—~Lo6 ~

❑

enghe <t

t’ A b 1_o

20

6-) A :

? /.04ct

b 0

Q ~b“L - b!’k L(32Q 2,000 ~000 6,000b8,000 l~ooo 12,000 14,000IQOOO

Eqine “speed, N, rpm

FIGUIUI4.–ExIxvimcntrd variation of burner pressureratio with engtne spw?dfor threeturbojet engines.

across the burner was used (fig. 4) rather than a more com-plicatccl factor for this 10ss.

A comparison of experimental dat~”from.”& a.sia.l-flow-t..ypeengine with @e theoretical curves calculated fo~ nopressure loss in the burner (r~ of 1.00) and for an assumedconstant rbof 1.05 is shown in figure 5. Similar correlationwas macle with data from other engines, indicating that in-

Ioo

3.2

sI I 1

Burner pressure. _ . . ,IS ratro r

,’gl@3

J ~cufcj~tedj “ ‘“.—...=..— J.— .—,

<,,

--.-- f.05— ‘ ....., ....—..– -“,.—— ..—L- /)

.‘ o Turbo].e+ engine 8

; 2.4.’-— ..- .,.#- —-

.-.”

[—

-. /Q ~o — — — — — — +------

..- ..- =--:---

$..”.

..-+ “

0 -, --g ~aj. ~ / ‘

/.“ .- ..-=

s / ‘~

-—.

/24 I J.6’ .8 1.0 /!2 /.4 “—-i6 1.8

.$peea’pcz-crmei’er, * K,M[+)X

FIGURE5.—ComparLwnof experimrnhd dsta and ealculatodequililwium opwathrt! lines furtwo assumed burner preesuroratke. Ratto of nozzlo area to turl)Inc minlmumwrssc~area, 1.93;ram pressureratio, 1.04.

clusionof thisconstantfactorof 1.05made Ihe thwrclidcurves sut%cient~yaccura.tc for most purposes.

The efTectof burner pressure loss, indicated by the burnerpressure ratio r~, on the theoretical equilibrium opwatinglines for. values Qf xam pressure ratio of 1.00 and 2.(.)0 isshown in figure & This loss in tho burner has the grcnlcst

( .)‘C KJf, .!- ieffect at low values of the speed parameter —Al Tsv t

and rLtlow ram pressure ratios. “At lugh ram pressure rat10s,the burner pressure10SShas a very smn.11efTccton cquilibriu[~~operation. Hence, for curren~ engine designs am] probablefuture clcsigns, the assumption of a c.onst?mtrb is of rcason-rtble accilracy. For engines opemt ing at low speeds andtemperature ratios, the wwmpt ion becomes less accumt w

Equilibrium for r, values of 1.00 and 2.00 and for scvcrttldifferent w&w of AJA, for a burnw prcssuro ratio of 1.05 isshown in figure 7.. Ml subsequent cxporhnent.alvcrifh}atk)nsare based on this chart,. If all the paramckw were known,this type of chart.would pwmit x gmval cxploration of tlweffects of component dimensions and oporating vmialdcs ohthe equilibrium operating pcrformwmc of any WbojcLengine.,

EQUILIBRIUM OPERATING PERFORMANCE OF AXIAL-FLOW TURBOJET E3’GINES BY -MEANS OF IDEALIZED AiWALYSIS 677 __ .

I I ,----=- -,> 3.6 I ~~— 1 t I I 1 I 1 I I

f I ,, ‘.b ,

2.a : .: L5 “2% .’ 3.0: I ;/ ..’

,: .’2.4

,, .’; .? ,

i : ,’1: -~}

I

20 I‘/

t

1.6 /

o .4 .8 1.2 [6 .20 2.4 28

Speed pamme fer, f!4+ =fc(m )

1 1 1 1 1! 1 1 ! I 1

12 m

ISt Rom pressnreratio, 1.03.(b] Rsnt pressureratio, 2AM.

FrGLTtE&-Etfect of burner prezznre rstio on genersl equilibrium cperating lime for sem?mfrazioscf nozzk srea to turbine minirnrrm-pnrsweares and tm rem pres-mreratios.

Net thrust.—.$fter the equilibrium analysis is made, it. ispossible to use the resultant kno-dedge of component per-formance in calcukt ing the o-rer-dl performance factors,such as net thrust. Figure S shows theoreticrd curves of

1

F/Pw4,plotted against the speed parameter *4 ()~KC.Mc “~ ‘.

t qc?lt

These curres include the constant burner-pressure-dropfactor. In order to cletermine F/P~, from this analysis,the efficiency produc~ ~c~’ must be assumed constant whenpoints are desired at flight speecls other than zero. Theaccuracy of this mmimption is subsequently disc=ed.

40v

Rafio of nozzk ureu I I I

fo turbineminimum-Ram pressure“1ratio–—

possage area ,& 2-0: _

r.G 36!

A, — “l+ ,G , ---.- M

,’1-q;

:% g~

: :. ,.

I,-?30

& :, Is : ,’

Q ; .20 ,’E :y .28

, ,’

V ~r’ #’t ,

Q 30/

/:,

Q : ,’:/ ,’>24 ,

Q : .’kQ / / ,’

E 2.0 / ,’~

/ ‘/

1.60.4 .8 /2 1.6 .?0 24 28

Hf%

Speed paramef er, ~ K.ht ~

FIGCEE?.—Equilibrium operating Iines for turbojet engfne wfth .wersf ratios of nozzIe sreato turbtne mir.dmnm-pasmgesrm and tw rem presmre ratioz. Burner pressureratio,L05. -.

AAc +-’

I I I I I I I I I I IRatio of nozzk oreo Ram~r;~suce Turbojet

— fo +urbi= minimup- enginepassage area r.

— +&

L065;Og

! (&kykfed) I I

-----4.8

2.00

,Rafioof nozzk area

,

do *O furtine minimum- q’A

pussage area & ,~~

: :,

/.5i d;20 : !

k&2 : !& : /:

jj,

: , I, %

$ : ,, :ay Z4

: ; “, {

/

rY

: ;t ,‘hm : ,’> :~ 1.8 r~ ❑ l’/~ 40

i[5 ‘L /

A.8

// yc

n 9

Lo .4 .8 L2 i-o .?0 24 ““

.-

()fxSpeed parameter, ‘##K,M. —V*Z’C

F~GtXUZ8.-EEect of sy?ed parameter on turhjet+ngfne thrnzt for seversl rotim of norzlearea to turbine minfmurn-p~.ssge eres srd two rnm prersrrre ratios. Burner prersuremtio, 1.0s.

678 REPORT 987—NATIONAL ADVISORY

EXPERIMENTALVERIFICATIONOF THEORETICALCURVES

With the theoreticalequilibriumperformance nowestab-

lished,the theoreticalequilibriumoperatinglinesmay be

compared..withexperimentaldata.

COIvlMIti”EE FOR AERONAUTICS

Experiinental clata from severrd turbojet engines havingdifferent area ratios are shown in figure 9 comparci{ with thetheoretical equilibrium operating lines. Tho thcmvticrtl

curveswere made assuming constant ratios of specific hints

3.2 - . . . . . ...—. ..- ., .—)I

,’,’

,

t 2.8 -,

r

b

&m.

h;’* )

‘%/

/ i’

l.-/

/

{ 2.4 , Io

Eo

;o

i

? 2?7 ,0

~ I t)

~u

o0

00° ❑

$f 1.6, 0 n

(c) (d) (e)

L2.8 1.2 ““ L6 20 .4 .8 L2 1.6 .4 .8 L2 L6

()Speed.pwamefer, ~ K=M= & %

(a) Turbojet engine A; ratio of nozzle area to turbtne miniium-passage m’ea,2.W, rampressureratio, 1.00.

(b) Turbojet engine B; ratioof nozzle mea to turbine minfimrm-paesrwearea, LW mmprewrro ratio, 1.04.

(c) TurboJet engfne C; ratio of nozzle srea to turbffe mfnfmuru-pazsw area, I.W, rampressureratio, 1.20.

(d) Turbojet engine A; ratio of nozzle area to turbine ruinimum-passsgeare% 1.7* rampressureratio,I.CO.

.

(e) Turbojet engine B; r%tioof nozzle erea to turbine mfnimum-psssagearea, 1.96;ramPressure ratios, 1.04and 2.07.

FIGURE9.—Comperisorrof calculatedequilibrium operatingHuesand =wrimentd data for.seveti turbojet eM@. Brrrner pressureretlo~lSM.

EQUILIBRIUM 0PEXL4TING PERFORMANCE OF AXIAL-FLOW TURBOJET ENGINES BY MEANS OF IDE.4LIZ.EDAN-411YSIS 679

of 1.40 and 1.32 in the compressor and turbine, respecti~-ely.A constant buiner pressure ratio of 1.05 was used and theareas were assumed to be effective flow areas.

The experimental data points -mere calculated usingaverage values of effective areas and observed values of K.at each data point.. E.xperimentalcmre~ationis good enoughto make the assumptions used in the analysis appear to bewithin reasonable accuracy. Hence, the equilibrium operat-ing Iines can be considered as accurate as the parameteraand applicable to any turbine-type engine.

Further use can be made of the equilibrium charts if Kcand ~c~~are constant for a partictiar engine or if a means isawdable for determining the values of these quantities atany desired operating point-.

Assumption of constant KC.—Many compressors ha~-e aconstant ratio of axial inlet-air velocity to compressor-tipvelocity KC in at. least- some part, of the operating range.Figure 10 is a replot of figure 9(e) except that in this figure

I IIu o 1.04❑ 207

7Ratio OF in!et-a;r

velacify ?0cam~essor- tip

velaci?yKc

0.500

I (Cohgfed) ~ .3.2 ——..--- i.oo ,

I,’b’ /

< II I I I ,!U II

I I r I I P/ 1“,, I t I

~ I /r! It? Y n

o$ L6&

0 Q

/.2o .4 -8 L2 1.6 2.0

FIGCRE 10.—EMectof aewming constant ra:io of axial frdet-air wlocity to compresaar-tipvelocity on correlation between cakrsk!tedequfiikrm operatff lime and experimentaldata. Turbojet engine B; ratio of nrmde area to tnrbine mfnfmom-pwage area, 1.96.

the K“cused in calculating the experimental speed parameterwas an average value. Experimental correlation is still goodwhen the engine is operating at. high flight speed but ispoorer as flight speed is reduced. This effect can be partlycsplained by figure 11, -which shows how the equilibriumoperating line shifts on the compressor-performance mapwhen the ram pressure is changed. .kt high r. values, theoperating line moves lower on the constant engine-speedlines into the more vertical portion of the cumes -wheretheassumption of constant Kc becomes more accurate.

Assumption of constant w ~.—Whenthe equilibrium cur~esare used to determine dimensional effects upon temperatureratio and engine speed, a kno-dedge of the variation in the

3.6

23.2.o-42c1= 2.8Elk2~ 2.4xL2~ 2.0

&

‘3f.6’

L2.80 .85 .30 .95 Loo f.05 Lio lf5 L2Q... - —

Mass -flow parameter, ~~

F~G~E Il.—Effect of ram pressureratio on position of equfhbriom opcratffg tine on cam-prerswr-performancemap. Trrrlmjet engine E; ratio of noszIe area to turtime minfnrum-

wawe area, 1.90.

efficiency product qe~tis necessary. In many instantes thisproduct may be known at all points of operation. When anassumption of this product muck be made, constant ~.q~maybe of sufficient accuracy. Figure 12 shows the variation ofVNtwith ATfor an engine having two different exhaust-nozzleareas and inclicates thatt assumption of constant. ~C~tforthese engines is within reasonable accuracy.

Rafio of nozzle areufo +urbine min;mum+

passo~e area~

0 1.+5g.7 n 225s

%-0 I

:n

n ❑

5.6 9

~c

0

.5 a-$

t .58,0C0 !0,000 !2,#o

Engine spee~4N~prnI O/DO [8,(XW

1 IGCRE 12–Esp+rimental mristion of efficiency product with engine speed. Turhjetengbw A; ram pressureratio. 1.00.

If values of K. and q.~, are known at each operating point,the theoretical curves agree fai.dy w-eIIwith the mperimentaldata. h assumption of constant, K. for a.n a..-tiaflowotfieieengine is reasonably accurate for engines operating at highflight. speed, especially near the design engine speed..

DISCUSSION

With the general results of the analysis completed, manymore result-scan be developed from the main calctiations.Three of these developments are discussed.

Analysis for engine speed limited by stress.-In aII the1

()~Kckfe ~ ‘curves presented so far, the speed parameter ~L Vcqt

680 REPORT 987—NATIONAL ADVISORI” COMMITTEE FOR AERONAUTICS

has includedthe lfach number of the compressor-bladetipMCbasec?on the compressor=inlet total temperature. Hence,vertical lines drawn from the abscissa of the equilibriumcharts r-irelines.of constant compressor-tip Mach number pro-vided that the other factors in the speed parameter remainconstant. This form of presentation is most practical whenthe compressor-tip Mach number is considered to limitengine speed. If stresses limit the rotational speed, a.speedparameter containing engine speed would be more desirable.Figures 13 and 14 show equilibrium lines and thrust lines,respectively, using a speed parameter with M, replaced by aMach number M,, Obased on ambient temperature. Verticallines using this new speed parameter represent lines ofconstant N if the other factors in the parameter remainconstant.

Variation of exhaust-nozzle axea.—If an engine has avariable-area exhaust nozzle, the equilibrium curves offigures 7 and 13 would be useful in determining the correctexhaust-nozzle area An for diflerent altitudes and ram pres-sures. The correct nozzle area can be determined, dependingon the particular region of operation on the charts, the rampressure, the altitude, and the engine-speed limiting factors.For example, assume that it is required to determine the A.necessary to maintain either constant N or constant MCwhen r, is increased from 1..0!3to 2.00. When the engine isassumed to be operated initially with an r, of 1.00, an An/Alof

Tz2.0, and aj TOV,vt of 2.1, the two speed parameters pre-

viously mentioned are equal and have a value of approxi-mately 1.2. (See “figs.7 and 13.) If an r, of 2.00 is applied to”the engine, A. cloes not “have to be changed to operate atconstant M. (fig. 7). If 1? is to be maintained constant,however, it can be seen from figure 13 that An must be de-

1—Rafio of r’IQzz fe are=”

?0 furbineminimum: I Ram”

4.0 posso~n area ‘- pr~~,~re- “

~ -..

I ,/.5 , 2.0 —/?0

.—---- .200

F 11!1/11”1/ “;l I$3.6 i I 1,: I I

.4 .8 1.6 20 2a- = 32.SW pcrk<er based cm ornbien?4tiwr-a+w-e

~lGUl[.E13.—Vm’iafionof equiIibrimu operafitig linrs with speedpammeter beeed on ambienttemperature for several ratios of nozzIe area to turbffe minimum:pn~age area”snd tworam pressureratios. Burner pressureratio, 1.05.

6.4I

I Ram — -upr~’tuJe 2.(7

5.6rr ‘

—. : 34 _------- i% #“-I

r4.8 : :

,: ,

1% -~{ I?afioof nozzfe urea ; .— ..-—..—

h furbineminimtim- :fl

4.0~ passage orea.j + ~._ /

g -~ ;’5 1!

h: : P.u

Qi’

/i. :~ 2.4 /

&.,I

!.5/1.6 t

/ft

:t/

.8 //

//

/

o.8 i2 1.6 2.0 2.4 21@

$eed parame%r based on ambIJnf fcm.oernfwe

*K’M”.e (&)

FIOUBE14.–VmIarion of thrust parameterwtth 9p?edpmametcr Wed on e.rnbhmttempma.ture for severalraticc of nozzle area to turbfne mlnlmum-pfissfrgoarm and two ram pressureratios, Burner pressureratio, 1.05.

creased to maintain the same paramctws at tin rr of 2.oo.The same type of analysis of proper nozzle area can bcrarried out on figure 14 to determine t.ho 1hrust paramch~r.Because the equilibrium lines for the two ram prwww ratioscross, depending on the operating rang(!! Am might bc i.u-weased or decreased for correct opwat ion when r~is changmi.The correct exhaus%nozzle area can be determined for each~ltitudeby a similar type of analysis using thmc charts.

Incorporation of observed component characteristics,. -.J7hechart of figure 7 describes the equilibrium opcrot ingperform~nce of any turbojet engine. By further cxpnnsicmof the analysis, however, this chart may be modified tcrallow superimposition of specific compressor nnd turl.k

maps gn the generalized equilibrium porformancc chart.,The rtddition of. values of r. on the chart. permits mor~accurat~ and complete performance pwdictions for 4tspecificcompressor-turbine combination. IJines of constant. com-pressor pressure ratio rs and constant turbine ml io arcshown in figure 15.

With the addition of lines of conshmt r, and r, on [he .

equilibrium performance chart., it. is now possihlc LOsuper-impose gn the chart comprwaor and turbine pcrformftncwchara.eteristicswith the assumption of Uspecified lr-unprra-tum ratio at the design point. Bmrmse an original assLlmp-tion of qt must be made to inilid.e th cah:ulations.,swcrdrepeated calrda tions are necessary to match the compressorand the” turbine accurately on the equilibrium pwformanrechart. The compressor efficiency ~c, velocity ratio indicnicdby CK,, and the surge Iinc obtained from cxperimcnlal dainon a compressor are shown in iigurc 16. Similarly, figure 17

.

EQUILIBRIUM OPERATING PERFOR&m’cE oF ~=AL-FLo~ Tmo=T ENGLNES By ~IE-~s oF ~EALrzED ‘N=YSIS 6s1 ..—

I—.— Cofnpre!sor preissu-e rob, r.---—---- 7iibinepressure rofio;rt I I I

Rafio of mzzle ores #o fwbi~ rninim-possuge oreu,.A.lAt4.5 I\ \ \ \ , \ ---;0“

; iy i, ~, - ,/ /.-<-\.ti..-’””‘\

I I ‘-1. >.,>.-1 \ X’ /, ..55 40,

‘-““)? “’‘., “y

30 \ ..’””-” Y ‘, ‘\ ./ “<\t II

\ ‘ ‘\ > f \\.

1, .,’ ‘\,

2.5.

/“<co

\r

Y.

\ ‘y ‘“ ‘., ‘“A , ‘N-, *4d.2.0

.

1

.

\ ..

,,‘i.

K \/.5

foff~t

(a)/.0

4.5

\1

\

4,0

3.5 \

i / \ .\\, ‘\, \

3.0 \

i\ .

\

‘\, ● i.,

‘>.

2.5\.

\. \

\\ \ , ‘\ .

\%.’ .

\, \ \. ?, \.

“a .’ ‘\.d. I

\ : \ ,’ \

/5 (b) / J !/ ‘k’, (;.. ‘k ‘“ I.o ‘y ‘>-, ‘ ‘;&.. ‘;;>

u .4 .8 !.2 1.6 2.0 .24 2.8 3-2 3.6 4.0 4.4 4.8~.2 ~

@eed parcnneie~~KJ%()

f v,

V. m

IaI Rsm pressureratio, I.WI. (b) Ram preesm’eratio, 2(XL

l%rwi I?i.-(+eneral equilibrium cumes showing Ifnes of e.mstmt compressorpressureratio and tnrbffe presmre ratio for sew?rol ratios of nozzIe area to turbine minimum-PSSX areaand two rom pressureratios. Burner pmrure ratio, 1.05.

shows the efficiency contours for a selectecl turbine. Figures16 ancl 17 thus contain sufEciently complete information oncomponent characteristics to permit. accurate cleterminationof equilibrium pertorma.nce but still retain the more generalequilibrium performance.

WMM~RIZIXG REM~RES

It. has been shown that.it is possible to determine equilib-rium performance of a turbojet engine by means of simple

model processes developed for each of the components.

The results are presented in a series of graphs with equilib-rium engine performance plotted in terms of temperatureratio, engine speed, flight. Mach number, and componentdimensions, such as ratio of compressor-inlet.area to turbineminimum-passage area ancl ratio of turbine minimum-passage area to e-xlmust-nozzdearea.

The analysis is e-xpa.ndedfurther to permit calculation of

682

FIGUBE 16.-

REPsSRT 987—NATIONAL ADVISORY’:(%MmTEE FOR AERONAUTICS

.L.u *

‘ h.).

’86 \‘ ‘ / ‘8,b- . Is I I

;

\~~ ,’/ j

‘. Compres90~ preawre‘8, ‘.

‘1* ‘s 00 +io; ./ # 1: : ‘. .

,

‘ ‘8$ q’ ‘j j

‘. r=

/,, ‘., ‘.

2 : ,

MJ. /‘.‘.

‘\#

L6 — I4

I 5 hConrp,ress 0P I

e fflclenoyS?e S2.. “

_.=

L.?.4 .8 /.2 M

A.KM ;%H

.Z4 28Speed pa~ameter —

* At e c T=qt

-Comprcsor-component chsroeteristiosfrom compressordata with”equilibrium oporstii tiis. Rsm pressurerstio, 1,60;burner pressureretfo, 1.06.C, proportion

---

()Speed parameter, ~ . . ~7,‘KM : ~

FIGURE 17.—Tnrbine efficiencies from experimental data superimposed on equilibriumoperattnglhres, Ram pressurersitioj“1.w burner pressureratio, 1.05.

lal[ty efmstallt.

engine fit. thrust and component chmwctcristits, such Mcompressm-pmsstireratio tlIKl compressor pressurecocffkicnt.

Expe.r&ntal correhttion of the theory with dtxta fromseveral esisting axial-flow-type engines was good rtndshowedclose correlation between calculated and measured per-formance.

Although the theoretical results arc chiefly upplicable toengines Laving a constant ratio of axial inlet-air velocity tocompressor-tip velocity, these results can be used for anytype of turbojet engine if the value of this ratio is known.

. .— . . . ..

LEWIS l?LIGHT PROPULSION LABORATORY,

NTATIONAL ADVISORY COMMITTEE FOR AERONAUTICS,

CLEVELAND, OHIO, February M, 1940.

APPENDIX

DER1~~TI03J

Diagram of turbojet engine.-The foIIowing diagram showsthe location of stations in the engine:

o+ --lcom-

ressor Burner2 3 4

-

Compressor air flow,-If the ratio of compressor-inlet-airvelocity to compressor-blade-tip velocity is considered con-stant., the equation for compressor air flow can be developedas follom”s:

0. . .w. =lic

T1VD*4

Q/&= T’,

?rLIN= Vc

K.= 1“,/1’.

?.—1

T,= Z’l)(rr) ‘c

OF EQUATIOM

Therefore,

Turbine air fiow.-l?rom reference 4,

(1)

~,– 1 n-,’2 A.$2a32p32=[($(5+1

Then

(3}

Nozzle airflow,— The nozzle-air-flow equation is cleter-mined in the same manner as equation (3):

(5)

Compressor power.—The compressor power can be ex- 1 Power baIanoe.—Because hpc=hp, and l~,=jli’c, the fol-mwssedas lowing expression em be developed from equations (2)

Tc—l

I and (4) for r.:7=—1

- “(’c-l)(~)-[’--]”l)(r.] 7’ = 1+-f ~c(-y,—1) To

T,= T,(r,) “= Compressor-turbine air-flow balance.-Siiarly, from

Then equations (1) and (3), a second expression can be de-doped:

T=—I

‘[-1

7=—17c+L

n“. -y.

()

~KcA.Jr,) ~G r, IFM,

‘P’=550 q. ye—lRTO(rJ 7’ (rJ 7’ – 1 (2)

rc=— —

Turbine power.—The turbine power is l=”~~(i)’’r[(:~-(:~%] ‘M)1 -r’-l

‘f (+T3[+yq (4,

Final equilibrium.-Clombination of the power-balance and

hpt=~m ~,_lffov+balance equations (.-1) and (.%2),respecti~ely, to elWl-nate rCgives

(6)

6.S3

684 REPORT .987—NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

Ratio of nozzle area to turbine minimum-passage area,—

~ombination of the nozzle and turbine mass flows yields

U’n= w,

d 27’ An

= (’Y,– I)h’ -d%(%)’(r,) 27;

Then

(7)

Net thrust,—..i convenient expression for ncl thrust. canbe developed as follows:

REFERENCES

1. Goldstein, Arthur W.: Analysis of Performance of Jet Engine fromCharacteristics of Components. .I-Aerodynamic and MatchingCharacteriatiw of Turbine Component Determined -with Cold.4ir. NACA Rep. 878, 1947. ” (Formerly NACA TN 1459.)

2. Kochendorfer, Fred D., and Nettles, J. Cary: An AnalyticalMethod of Estimating Turbine Performance. NACA Rep. 930,1949. (Formerly NACA RM E8116.)

,3. Palmer, Cd B.: Performance of Cw~prcwm-Turbine JcL-Propulsion Systems. NACA ACR L5E17, 19-!5,

4. Taylor, G. I., and llaccoll, J. W.: Aerodynamic Theory, W. F’.Durand, cd.. vol. III, div. H, p. 224. Reprinted, C. L T., 19.13.