Analysis of Performance of Jet Engine from Characteristics of Components I : Aerodynamic and Matching Characteristics of Turbine Component Determined with Cold Air

NATIONAL ADVISORY COMMITTEE

FOR AERONAUTICS

./

RE7;; ~ ~

ANALYSIS OF PERFORMANCE OF JET ENGINE FROM

CHARACTERISTICS OF COMPONENTS

I-AERODYNAMIC AND MATCHING CHARACTERISTICS

OF TURBINE COMPONENT DETERMINED

WITH COLD AIR

By ARTHUR W. GOLDSTEIN ~ ' or s:&le by the Superintendent of Documents, U. S. Government Printing omce, Washington 26, D. C. ••• - Price 15 ceuts AERONAUTIC SYMBOLS I. FUNDAMENTAL AND DERIVED UNITS Metric English Symbol Abbrevia- Abbrevia- Unit Unit

-

tion tion <...

meter __________________ foot (or mile) _________ Length ______ l m ft (or mi) Tirne ________ second _________________ second (or hour) _______ t s sec (or hr) Force ________ weight of 1 kilogram _____ kg weight of 1 pound _____ F lb horsepower ___________ Power __ _____ P horsepower (metric) _____ hp ---------- miles per hour ________ {kilometers per hour ______ kph mph Speed _______ V meters per second _______ feet per second ________ mps fps 2. GENERAL SYMBOLS W Weight=mg v Kinematic viscosity Standard acceleration of gravity=9.80665 mLs p Density (mass per unit volume) - fJ 2 4 11 or 32.1740 ftLsec Standard density of dry air, 0.12497 kg-m- -s at 15° d W and 760 mmj or 0.002378 Ib-ft- sec2 1 m 8 Mass=-g Specific weight of "standard" air, 1.2255 kgZm or Moment of inertia=mkll. (Indicate axis of 0.07651 lb/.cu ft radius of gyration k by proper subscript.)

Coefficient of .. ~scosity 3. AERODYNAMIC SYMBOLS 8 Area Angle of setting of wings (relative to thrust line) i ..

8 Area of wing i, Angle of stabilizer· setting (relative to thrust m line) G Gap Resultant moment Span Q b n Resultant angular velocity Chord c b A Aspect ratio, S Reynolds number, p Vl where l is a linear dimen- R J.£ True air speed V sion (e.g., for an airfoil of 1.0 ft chord, 100 mph, standard pressure at 15° 0, the corresponding

q Dynamic pressure, !p Vll

Reynolds number is 935,400; or for an airfoil of 1.0 m chord, 100 mps, the corresponding

L Lift, absolute coefficient G = q~

L Reynolds number is 6,865,000) a Angle of attack

D Drag , absolute coefficient G = q~

v E Angle of downwash Angle of attack, infinite aspect ratio

Profile drag, absolute coefficient Gvo=~

Do Angle of attack, induced Angle of attack, absolute (measured from zero-

Indu ced drag, absolute coefficient C = ~

Vt lift position) Flight-path angle

Parasite drag, absolute coefficient C = ~s

Vll

a Cross-wind force, absolute coefficient C = q~

c

REPORT No. 878

ANALYSIS OF PERFORMANCE OF JET ENGINE FROM

CHARACTERISTICS OF COMPONENTS

I- AERODYNAMIC AND MATCHING CHARACTERISTICS

OF TURBINE COMPONENT DETERMINED

WITH COLD AIR

By AR TH UR W. GOLDS TEI N Flight Propulsion Re search Laboratory Cleveland , Ohio I ., ..

ational Ad isory Conlnlitt ee for e ronautlc s

H eadquaTters, 1724 F treet mv, Wa shington 25, D.

Created by aet of Congr approved M arch 3 19 15, f r th c upervision and direction of the cien t ifi c st u Iy of Lhe pr oblem of flight ( Code, titl 49, ec. 241 ) . It member hip wa i ncrea eel to 15 by act approved ~1 arch 2, 1929 . Th e members are appoint el by tb Pre iclent, and erve a u h without comp nation .

J KROME . H SA KER, . D., Cambridge, Ma s ., Chairman ALEXAND8R W ET M ORE, C. D., ecreta r .v, m i thson i an I nsLitut i on, Vice Chairman RON. JOHN R. ALI SO ', A i tant ec r etary of Corrunerce. EDWARD M . P OWER., 'l ajor Ge neral, nited States Air Force , VA NEVAR BUSH, Sc. D., hairman , Re earch and Del'elopment Deputy C hi ef of Staff, Mat~riel.

Board, Departm nt of Kational Defen e.

AU'l 'HUR K RAnIOKD, M . Vice PI' id ent, E ngin ee ring .

E DW ARD . CONDO, PH. D., Dir ecto r , National Bureau D ougla Aircraft o.

FUA)< CIS W. RmcHELD E RI 'ER, 'c. D., hief, United State St anda r d.

Do ALD B. Du CAN, Vice Admiral, D eputy hief of Xa\"al W eat her Bur au.

Operation (A ir ) . CARL P. UTZ, General, Chief of taff, United Lates Air Force.

R. M . H AZE , B ... , Chief Engineer, Alli son Divi ion, General OUVILLE \Y RIC';HT, C. D., Dayton, Ohio.

M oto r Co r p. THEODORE P . W uwwr, Sc. D ., Administrat I' of C ivil A ero - WILLIAM L IT'I 'LEWOO D. M. E ., Vi e Pre iel nt, I ~ n in eering, naut ic , Department of Commerce.

American A irlin e y tem .

THEODORE C. Lo NQUE T, Rear Admiral , A ssistant hief fo r Research and Development, Bu r eau of Aeronautics, Xal 'Y Department.

H UG H L. DRYDE)< , PH. D., Di rector of . leronautical Research JOHN F. VICTORY, LL:\I. , Rxecliti ve ecretary J OliN W. CUOWI ,E Y, J R., B . ., ,· Issociale Dir eclor of Ae"onallticai HeSNtrch E. 1I . IIA~IBlmI.1N, R.recltlit ·e O.fficer HENRY J . E . R I, II ), . C. D. , Dir ect r, L angle.v ;\[ emo rial Ae r onautical Labo ralor.v, L angley Field, Va.

MITT! J . DI .; l"l lJ IN CE, B. S" D i r eclo r Amc Aeronautical Labo r ator. I·, Mofr ctt Field, Calif .

EO\\'ARD R. lIARP, LL. B., .cirector, Plight Propul s ion R esea r ch L abo r atory, Cleveland A ir po r t, Clc1'eland, Ohio TECHNICAL COMMITTEE AEROOYNAMICS OPERATING PROBLE!

SELF-PROP I ~ I , [ ,E O GUIDED :\ 11 lLE POW8R P LANTS ~ 'O R AIR RAFT AIRCUAFT CON 'I'll CT IO/\ I NDUST RY CONSUI,TING Coordination of R esearch Need of Militm'y and Civil Avia l ion Pr epm'ation of Research Prograllls Allocation of P"oblems Pr evention of DupHcation Considemtion of I nllenl':o ns AMES AEUONA '!'ICAL L ABO R A'l'O RY, LA NGLE Y MEMOR I Al, AERONAUT I CA I ~ L ABORATORY, M off tt Ficld , Calif.

La ng l e~ ' Fi c ld, Va .

FLIGHT PROI'U LSION R E EA RCH LABORA ' rORY , C l eveland Airport, C l eveland, Ohio Condnet, under unified conl1'ol, for all agencies, of scientific research on the fundam. ental problems of flight OFn E OF AERONAUTl AL I " I'E Lr,IGENCE, W aS hin gton, D.

Col/eclion, classific ation, com.pilation, and di semination of scientific and t ec hni cal il~rormalion on aeronautics II

REPORT No. 878

ANA LY SIS OF PERFORMANCE OF JET ENGINE FROM CHAR AC TERISTI CS OF COMPONENT I -A ERODYNAMIC A ND MATCHING C HARA CTERISTI CS OF TURBINE COMPONENT DETERMINED WITH C OLD AIR By ARTHUH W. GOLDSTEIN SUMMA R Y the jet engine, the assumed eompres or pre sure ratio \Va 3.36; th e compl'e or inl et -a il' temperature, 440 ° R; and the The peljormance of the tur-b ine component oj an NA 'A compre~ or inlet-air pre nrc , 7:39 pounds p er s quar e foot.

re ·earch jet engine was inve ligat ed with cold air. Th e inter- Flight speed was 470 miles per hOLD ' and altitude, 33, 000 feet.

action and the matching Qf the turbine with the NACA eight- The turbine work output wa so divided betw een the st ag e compte 01' weTe computed with the combination considel'ed stages th at the ratio of the temp erature drop to average as a jd eng ine . Th e oveT-all perjoTmance oj the engine was then temperaL ure for each tage was th e arne for both tage detennined. Th e in t emal aeTodynamics wer studied to the in order to maintain Mach nUlnber approximately the extent of in ve ligat in g the pelj01·mance oj the fir st statoT ring same for th e two stage. Th e velocit ie between blade and its inf lu ence on the tUTbine pel:foTmance. FOT this ring, nng arc hownin th e followi.ng tab l e: the stream-jilament method for computing velocity distribution permitt ed efficient sections to be de igned, but the design concli- Tangential 'I'angential tion of jree- v01·tex flow with unijoTm axial ve locities was not Axial velocity ve locity Station v~locity at Lip at root obtain ed. Th e actual air flow was 0.96J,. of the design value at ([t/sec) ([t/s ec ) ([t / ec ) design pTes ure ratio and speed and was 0.98 at de ign speed Entrance stator L ___ • ______ _ 209 o o and enthalpy drop. Rotative peed jor optimv.m efficiency Exit s tawr L _______________ _ 2? 600 Entranc rotor L ___________ _ 422 -195 (0 .875) wa 180 revolution l)er second a compaT d with the Exit'·otorL ________________ _ -828 -999 2!l9 Emrance stator If _____ . ____ : -3 17 -204 design sp ed oj 1 3J,. Tevolution pel' econd (e fficiency, 0.823).

Exit stator ll _______________ _ 290 898 Entrallce rotor 1L ___ • ______ _ 290 387 -2 17 Exit rotor 1L _______________ _ 346 -816 -991 Entrance stator IIL ________ _ 346 -305 -196 INT ROD UCTION The ::; AOA two- tage tLu·b in e wa ' designed and bu il t Th e e ve lo ci ti.es were compu ted on th e a umption of radial under the direction of Eastman N. Jacobs by th e AOA equilib ri um, con tant gas ener gy and en tropy, and free- Olevel and laboratory sta ff as a co mpon ent of a jet engine, vortex flow from roo t to t ip. Th ese ass ump tion result in 'which ervcd as a tool for t he t udy of the behavior of this a con tant axial velo city over th e blade span, which may be I' ngine type. Til compr or c omponent of th e e ngin e wa demonstrat ec l by c on ideration of the c ondition for ra lial to be th e NACA ei ght - tage co mpr e s'or eli u sed in refer- equilibrium of pr es ure with no r ad ial flow: en ces 1 to 3. A tu rbin e in vest i gat ion wa made at the C level and l aboratory dur ing 1945 wi th an inl et -air tempera- ( l) tu r e of 190 F a nd a range of eq uival ent turbine peeds from 102 to 1 2 revolutions per eco nd and pre m e ratio from wher e l.16 to 2.60. Thi s in ve ti gation was co nduct ed to eva lua te p pre sure, (lb/ q ft) t he blade-de i gn proced ure by detrrmining Lhe performance p den it y, (s lug/cu ft) of tl JC first stator riilg and it influence on over-all tmb in e c" whirl-ve lo c it y co mpon en t, (ft/s c) pe rformance, to determine the p e rform ance of the turbine r eli tanc e from axis of an nu l ar ch anne l, (It) withou t the co n st raint impo ed by operating the com- For conven ience, all sy mbo l used in this r e por t arc defined pr essor and th e t mb ine togeth er, and to u e these data to in appendix A.

investi gn te the m atc hin g of the t mbin e and the compr essor.

Th e eq ua tio n rel at ing ent h alpy c han ge to ent ropy ch ange i D ESC RI PTION OF T H E TU RBI NE dp dH = Td S+ p Design eonditions .- Th e turbine wa designed for the where fo llowing opf'rating con dit i on : inl et pres ur e, 2400 pounds H e nth alpy, (It-Ib/ iu er) per sq uar e foot; inl et -ga te mp e rature , 1400° R ; ga flow, T ga te mp erature, (0 R ) 4 .1 pounds per second; power output to th e sha ft, 296.5 S gas e ntrop y , (ft-lb/ ( lug )(O R )) horsepower ; and rotor p Cf'd, 13,010 rpm. For operation in REPORT KO. 7 -NATIONAL ADVI ORY COMMITTEE FOR AERONAUTIC Therefore, In the design proced ur e, the a swnption was made that dp c 2 all th e losses took place in the rotor and th e stage efficiency - = dH - Td = ~ dr p r wa 0.90 based on tota l pr es ures and temperature.

The flow channels betwe n the blade weI' de igned to The energy equation i provide guidance a - the xit by making both walls nearly parallel to the de ired flow " a ngle for a distane app roximately equal to the exit-channel \\"idth. From the channel exit toward the entrance, along the suction (co nvex ) side of tbe blade , the r adius of curv atme was dec rca cd as the channel where C is th e velocity in feet per second and the ub cript width increa cd toward the region ncar the leading edge.

T indicates stagnation tate. Insertion into the equilibrium The amber line was pointed in the li["ection of the incoming equation give flow. Blade trailing edge were 0.03 incb thi ck, except for th e econd row of tator blades, wbich ,, -e re co, tings with (2) trai li ng-edge thicknes e vary ing from 0.020 to 0.015 inch.

The leading-edge radius of cW' vature was taken as 15 per- If the flow i isentropic and the ga of uniform energy leve l, cent of the maxim um t hi ckness.

When a blacl section h ad tbus been roughly de igne cl, the and velocity distribution on the suction ide of the bladc wa computed by mean of the stream -fil ament theory de cribed (3) in reference 4. Thi method was modified to account for the varying ma flow pc]" unit blade h ei ght in the channel where C is the axial-velocity component in f et pe l' e ond.

a du e to r adia l How by as uming for eacb section a linear Other u eful form of equat ion (3) are variation of the mas flow per unit blade height along the middle st r eamline from the en tra n ce to th e exit value. If

O =d (Cz2) +CudCu+Cu2 d; =d (CZ)+2~ 2 cl (rCu)2 (4)

nece ary, the u tion- urface shape \V a modified to kerp the yelo ci ty on tb is urfaee nearly con tan t. . r 0 informa- If the moment of momentum icon tant, d(l'c )= O and C i tion wa obtained in thi fa bion about the aiJ-foi l no e or tbe u a therefore con tanto Tbe type of motion wher rc is a con- projecting uction ide of the blade ( ection A- B, fig . 1) u stan is de ignated free-vortex flow because the radial di - because the stream-filament theory of flow in channels is tribufiion of whirl velocity i the same as that for an isolated inapplicable in this region. Figme 1 sho"- the root ection vortex filament. of the .fir t tator ring.

~--s--~

~ /

..

Pressur e fOrces mduced by Flow near /nner shroud main stream flow Ma in stre om flow FIGURE I.-Cascade notation and Ilow chRractCl is tics of root sc ot'on of first stator ring of NACA two-stage turbine .

•

ANALY I OF P ERF ORi\VL,\ CE OF JET E~GINE FROM CHA R ACTERI TI CS OF OMPOK EKT-1 Construction .- T be turbi ne consist of two tage of rotor blades and t hr ee stages of tator bl ad es. R eact ion in both the rotor stages may be increa cd by the u of a final stator tage, wbich aloin LU' es efficient jet -nozzle ope ration ovcr a wide rang e of turbine and c ompr e SOl' operati.ng condition by eliminatillg th e rotation of the disc harg ed ga. A down- st ream view of tb fir t ring of stat or blades i hown in figme 2 . Th e ec ond ring (up strea m view) and th ird ring of tators (down tream view) are hown in fi gm es 3 and 4 , 1'e peet iv el y_ Tbe rotor is shown in fi gme 5. All rotor and tator blad es bad an inn er diam eter of 9 inche and au outcr diameter of 14 in ch s_ All blades had a radial tip clearance of 0.0 35 in cb. Th e rotor blad ar e fastened to th e wheel by a fil'-tree- ty pc blade ba c. For thi invcstigation, a et of slecyc bearings was u e el .

F IGU RE 4. -' J'bi r cl st aLOr I i og of X A C A tw o-stage Lurbin e. D o wn ~ lr c~lIn Yirw.

,, -- Co u p l ln q " ,--Journ a l-bearing s urfa ce FI (;("RE 2.- Fil "SL sL a L or rin g of N A C. \ two- stage L urbin e_ D o,,-n st rca m ,' iew. Journal-bear ing surfoce-- __ FI GURE 5. - RoLol of :'\ A A L\\"o-'tagc Wrbi n c_ F l m '- RE 3.- ccond stato r r in g Of N A CA Lwo-s t age L ur bi n . ps L rea m view_

J

REPOR'r NO . 7 - ATIOr AL AD VI ORY COM fl'l'TEE FOR ER ONA TIC A PP A RAT US charged from the stator ring and to find it effect on turbine p rforman e. The e mea mements wer e II ed to eval uat e Appara tu s for investigation of cascade ring .- The fu· t the turbine-design pro ced W" e and to sugge t improYed pro- tator ring wa mounted betw ee n two eonentrie p ipe with cedW"e when disagreement ex isted between theoretical and a b llmouth entranc and room air wa drawn throug h th e mea m·ed elo ci ty distribution.

ring. About 2} ~ inch es downstream of the ca ade, two B lade-surface boundary - layer survey .- Tb boundary- total-pre me tub and two flow-dire tion tube wel" lay er s W"v ey on th co nvex side of the blade at the tra iling mounted to pro\ide for radial urv ey. Th e who le ea eade edge ar hown in figure 7. Fo)" co mpari on, the momrntum cou ld be rotated lor tangential s ur vey. tatie-pre m ·e tap wer e lo cate d 2}~ inche down tream of t he cascade at 1.0 - u the inner and outer wa lls. In ot h er studie , th e boundary-

/~ --- ./"'

layer thickne on th e u ct ion su rfa ce of the blade wa mea-

w'ed about X inch from the LnliDnO" edge by mean of rake Ol / V

L .8 mall impact tube. A static -pre ure tube wa laid again t V- the b l ade. These boundary -I ayrr mea s ur e ment werr made at rad i al position }~ inch f r om th e blade r oot , 1%2 ineh e I from the outer radiu , and 7 \6 inch from the outer rad ius.

Apparatus for investi gation of turbine. - For over - all performance mea urement, til turb in e wa m unted a Dis fance from Momenfum Reynolds number hown in figure 6. The whole unit wa in serted into a clr um; ouler radius thickness, 6 (p c6! f1. )

L ~ -

( i n.) (m.)

the largr plat e at th e front formrd on end of thr drum. The 0 00066 6100 %.

rear rnd of the drum wa sealed by bolting th e rear flange of - '--0 3/00 - . 0028 1 %.

.00 17 2700 tbe turbine -ou tlet d u to th e edge of thr 11 01e in the rear 2~ " .2 plate of lhe drum. Th e entire drum \Va au-tig ht except for one larg e port in t he cy lin drical sur ra e, which served as the air inlet. Th r gas pa cd tbroug h a w ebbed e tion and the (Tc('n into the turbine.

o 02 .0 4 . 06 . 08 .10 .12 Normal distance from blade surface, in .

FI GU RE 7 .- Veloc it y dis tributi on in boundary la yer on blad e urfnce H i nc h fr om tr ailing edge of s tat or blade.

t hi e knrs \\"a a1 0 com putrcl fo)" a tU J" bulrnt houndary la yer on a fla L plate of chord equal to thr uction- urface arc l engt h. For all blade section , the rquivalent flat - plat e boundary-layer thieknr s ,, ·a about 0.0037 inch , which i ncar th average mea l\I"rcl valur for t be whole blade. B e- cause a trai l ing-edge thi c knr ss of 0.030 inch wa required to prcvcnL ,,· arpage of Lhe blades unc1rr h eat, the inCl"rmrnt in draO" cau rcl by the momentum thi ' kn e of thr boundary layer i mall. From the momrnLum rqllation, the formula for rnrrgy 10 in t he bladr wakr i F I Ge R>: 6.- 1nsla ll at ion of :\'A C A tw o· l aj(~ turbin ~ fO I co ld-air I' crforma n cc ill\ ·~s ti ga' i o n .

los. per ' lu g = fT d The power-ab orplion unil was a waler dynamomeLer.

Air flow Im s determined from an orifice m ter in Lhe intak(' where line. Total-pre me and tempera tur SUl"yey were made t fra t i Jl or a xial-f1011' area blockrc/ by trailing rclgr - of f lip trcam and down tream of tile turbine by mean of total- t blade , --- pre l\l"r lube and t brrmo coup le with velocity -r ecovery . co <P H head. Turbine powe1" output \\"a computed from th t blacle tUL iling -ecl O"e lhickne plu momentum thicknr ' measul"ed l ec1"ca e in t mperatuJ"e and rate of flow of the air.

of bounda ry layer, (ft) s blade piLch, ( ft ) RESULTS 'PN ang l between tra ilin g edgr and normal lo ea cade axi PERt ' O RMA NCE OF FI R T STATO R RI G R ga content , (ft- lb /C lu g) / ( OR » The fir t tator ring wa inve tigated to drtermine from 'Y ratio of pecific It aLs the boundary la yer on the blade s urface wbeLher the de i gn Thi eq uation i clrrivrd in apprndix B.

method atisfactorily ayo i<l ec! flow eparat ion and to find Computation for operation at th de i gn point a t th e l"oot- from thi boundary-layer SUl"vey the drag as ociated with mean- quare meli II g i ves a valu of f Td of] 60 foot- thi la yrr and its (,fl·ect on turbin rfficiency. A further pound per slug for an a umed boundary-layer thiclme of objr('t wa to survry the \Clocity di triblllion of the aa <Ii - 0.0040 in ch. For a rough (' tima te oJ tIl(' effect of thr blade ANALY I OF P ERF OR:\IA:C\ E OF JET EXGIKE FROM CHARACTERIS'r I C OF C OMPONENTS -I wake on turbine e ffi ciency, the averagc valu of f TclS blade wake on turbine e ffi ci n cy, th e m et hod of blad e- ection would be abou t 200 foot- pound s per slug (b ec ause of the de ign is co n idered atisfactory.

in crea e of c through the turbine) if the blad e were the Flow-direction surveys.- Dir ect ion-s ur vey data for 10 a arne for all tages. Becau e of th e varying numb er of meas ur eme nt in a space equal to on e blad e pit ch are shown blad e in each stage, f TdS is approx i mat ely equal to 2100 in figur e ; the surv ey w·ere mad e s imultan eou ly over foot-polmd p er lug for the five ets of blad es. B ec au e th e oppo ite s id e of the cascade ring. On each pl ot the de ign de ign work output is 1.255 X I0 foot-pounds per slug, the angle of flow for that radiu i hown ; the di ff erenc e in average lo ss in turbine e ffici ency ba sed on thi fa ct or i angle obtain ed in smveys on opposite id es of the cascade may result from va riations in blad e s pa cing and orientation.

N e ar the inn er radius ( fig. (a)), the air i turned too f ar 0.002 1.255 X 10 wherea at a radius of 0 .44 foot ( fig. 8 (b)) the air i in- uffi cie ntly tu rn e d. From a radiu s of about 0.5 foot to a Ina mu ch as this co mputa t ion shows very little e fr e t of radius of 0.542 foot , th e turning is about 1 too low. Fi gme 9 show s ur veys a round a ector of the cascade; each ta tion 0 exper i mental is removed from th e n e xt by one blad e pa ce. At th e inner fIl Design 0 0 and puter radii, variation as high a 4 a round the a nnulu s 0 0 0 0 are pr esent . Th e radial di st ribu tion of turning -angle dis- crepan i es ob erved in the s urv ey over single blad e pa ces arc prese nt in th e survey over the whole ring. Both s ur veys show t hat the as llmpt ion of flow-dir ection di t ribution c or - rd.)

responding to the fr ee -vort ex co ndi tion i inadequat e fo r an acc urat e descrip tion of the flow .

0 0 0 0 70 0 0 ( 0 0 ( 0 0 Expenmental, Slqn

W I Di

(b) (a) 8D 0 0 0 0 0 0 (b)

. 60

(f) (c) ~80 ~ 1! 0 0 0 0 c s.. 70 Ie) 0 0 0 0 0 (d) (d) • 0 0 0 0 0 70 0 , 0 0 de ac f... - One b l ad e spacf ----'"

~ Ine bt r , ---->

Ie} I~ I'-- On e blade space (e) I I I 40 80 120 160 o 13 .3 18 D 193 . 3 Angular pos ition, degrees Angula r posilion , degrees (a) Radiu $, 00401 loot.

(a) Radiu s, 0.401 foot.

(b) Radius, 0.44 {oot.

(b) Raclius, 0.44 foot.

(c) Radius, 0.490 loot.

(c) Rad ius, 0.490 foot.

Cd) Radiu s, 0. 530 foot. (d) Radiu , O.n30 foot.

(e) R&dius, 0 . 5~2 fooi.

(e) Radius, 0.542 loot.

FIGURE 9.-Flow-dircciion surveys o\,er secto r 01 firsi stator ring.

FIGURE . -F low·direction survey in fir st stator rinl(.

6 RE POR T NO. 7 8-~ A' fIONAL AD\"! ORY COMMIT'l'EE FOR AERONAUTIC Velocity distributions.- T he gas ve lo citie were com pu ted ehalmels where it would cau e an increase in rC'l) but primarily on the assump tion of radial equilibrium. Th i condition can occurred out ide the nozzle cha nn el.

be tated a _36 ~

v

~ /

V

/

where a the local Olll C ve lo city in feet per econd.

~ .3 2 Because

/

/

. 28 ~

I ll'

a sub titution give ~ -'--...

~

I II

~ dp _ 21' [ (P T ) 'Y~ l 1 J . 2 dr 1'---0.

•. 24 - - -- - - lncp (5) P 1'-1 P r ~ d

!

Q 0" where 'I' i th angle between How direction and normal to

III

:;:'.20 o ca cade axi. The data obtained in th urvey were the l..

I

radial di tribuLion of the flow dU ' ec tion 'I' an 1 of the total )., ....

~

pressure PT' The sLatic pressure wa obtain el at th inner

<J

1'--1-

//

.'2 ./8 and outer radii. Thu cp and PT a function of r and the -0-...

QJ ::.

Lwo boundary values for P arc known. If the Picard method I

/I ~

o

of uccessive approxin1ations i u ed, the olution is obtained l<

1\

by assuming a function pet'), inscrtino- it into the right sid e, U

"" .12 integraLing to get a new functionp(t ), and repeating with th

\

II

new pC?). Th e initial point chosen " 'as (r T' p ,) , where the 1/ \ Rate of a ir f l ow subscr ipt r indicates the inner radiu. This so lution , ho\\ - ~ Lo 'w _08 o Intermed i a t e ever, re ult in a value for the tatic pre sure at th e ou tel" r:, High radius p t that doe not aOTee with Lhe mea med valu -. I - Becau e Lhe total ~ presure mea urements \\ -ere obtained with I

IP

.04 a claw tube, interferon c betwe n th tube made the Lotal ~ pres ure readings Ie s reliable than the cliJ' ect ion and s t atic ~

I

pres me mea urements. The equation was therefore u ed

If

to compute the hapc of thc pre me ~ gracliCJ)L curve, all o Root AD .44 .48 .52 . 56 value of which wer then multiplied by the ame factor Radius_ r . ft that mad J dp /p = log PI/P, equal to the m a me 1 value.

FI G\:I\ E IO. - R ad ial di s tribu l ion of axial \' el oc i ty downs lr eam of first sl alo r rin g.

2 2 The value of c /a obtained by use of equation (5 ) were u used with the mea ured va lu es of 'I' to compu tc the axial~ An ulcrease in 10w ~ enerO'y r eo- ion on the inner shroud occur velocity componenl. For a perfect isenCropic, i oenergetic 'with u1crease in mas flow. Because all flows are ubsonic, fluid pa ing through a ca cade of blade 0 de ia-ned that it i a umed that this is a Reynolds number effecL. For r tan 'I' icon tant (for this row of tator blade " tan '1' = hi gh flow dynamically imilar to low flow 1.535 ft ), the value of C and rc are co n stant over the radius a u regardless of the flow l-l ac h number if the now follow the desired direction and if radial equil ibrium is established. and The axial~vcloeity distribution arc sho"11 in rlgure ]0 as a funct ion of radiu for several raLe of ail' flo,,-. The thick, low-energy layer neal' the inner hroucl correspond to the wher Lis Lhc characteristic l ength and the ub cript hand region of overturning noted in the direction Ul'vey. Ne xL l indicate the hio·h-8.ow andlow~Dow condition , respeclively.

to Lhi region i a local region containino- a velocity maximum.

The di tance behind the blades rather than the blade height This reo-ion of extreme underlurning ,,-a noted in the clirec~ i elected as L becau e the viscous eLIects do noL extend from tion UlTey. Th e boundary lay er on the outer shroud is th e inner to the outer brond , although thi tate is abnost quite thin. The ploL of moment ~ of~momenLum parameter att.ained at the bi ghe t flow. The condition ju t cited imply rc / a1 ' (fig. 11 ) how the arne thick inne)' boundary layer that L, .< L which means that th SUl'V y tak en at high U 1, and th i11 ou tel' boundary layer_Th e region of high axial flow COlTe pond to the low ~ flow survey taken farther down- velocity doe not have a co rre poneling region of high moment tr am. This interpretation is u eful because the data for of momE'ntum, which ex plauls t11 w1de rtu rnin g in th is region. various flows at one position may be interpreted as cOl're~ Thl chscrepancy between exce ive axial-vcloclly component poneling to the arne flow at various urvey planes. Thi and low moment of momentum means that the flow into thi interpretation is not exact because dynamic simi larity implie region from the inner IU'oud, and h ence the build~up of the geometric imilarity, which i not maintained in the blade boundary lay er, did not take place mainly in iele the blade eetions.

-~

- - -. - --- - ~- ~- -- -~------- ANALY I OF PERFORUAX CE OF JET EXG IX E FRml CHARACTEIUSTI CS OF CO 1POXEXT -I P hysical interpretation of velocity and direction dis trib u- placed radi ally to a region of hi gh er mom ent of mom e ntum , tion ,- A c hang e from pot e ntial flow occ ur n eal' th e blade th e r es ultin g force on the fluid is n egat iv e and tend to send Ill' oud b ecause of the larg e vi cou forces. Th e co n can' th e particl e inw ard. Th e ta bilit y of the inner boundary mfa ce of the bl ade is a high - pr e L1r e r egion and the co m-ex l ayer a nd th e in tab ili ty of the outer boundar y l aye r are urfac e is a low-pres ure r eg ion (A-B , fig , 1) that exte nd thcreby explained. F u rth e rmor e, any parti cle of fluid in beyond the c hannel between Lh e blades. In t h e main body the main tream th at hav e a low mom e nt of mom e ntum of the flO\v (t he r egion not nea l' the blad e root nor ip) , t. h (s uch particl c may com e from th e blade wake 01' from the momentum is high en ough to ca rry the flow in a direction boundary layer of th e outer m:o ud ) 11,1 0 te nd to coll ect tran Ye l' e to th e pr e S Ul' e gra di en t. Adjacent to th e inner along th e inn er hroud , thu building up t hi boundary l aye r and outer hroud s i a reg ion of low mom ent um induced by at a gr eate r rate t han by fri ction alon e.

frictio n wi th these wall and by t urbulen t a nd vi eou hear- .40 ~ in g tre e . Thi low-mom entu m fluid flows almost dirertly

'\

V in the direction of th e pre m e gra di ent induced by the poL 'n -

----

ti al flow on th e blad e slll'faces, Th e velo city of t h e e low- ~ .36 en er gy boundary l ayers at tb e hI 'o uds ha s a c omponent opposed to the main ax ial-flow com pon ent, and 11, 1 0 a com-

V

pon en t in th e dir ect ion of rotation of th e main body of the ~

'\

V

fluid . Thi boundary l ayer at t be hroud s is therefore bu ilt L

.32

lip aft er di. c har ge from th e ch anne l section B-C , ( fig. 1) V

/

L althou gh orne build-up may ta k e place inside the e honn e l.

V

Thi laycr of ail' will therefore a pp ea l' to be oycrtmned ( fig.

/ ) evcn though both ve loci ty com pon ent are 10\L The'

I /

buil d-up of this boundar y la yer at the hroud cau os a radial flow, ,,-hich in tlll'n induces a high axial ve lo ci ty in an ad j acent

I V

local region (fig. 10), and thus th a ir is und er turned ( fi g. ) alt hough it tangent ial c ompon e nt may be e qua l to the design I I ........

va lue. \

V

1 \

A radical difference i noted in the thickness and the I

lhi c kn e developme nt with vel ocity of the boundar y l aye r

I / \

on the inn er a nd outer s hroud ( fi g, 10 a nd 11 ) . I t may bc i mp ly de mon st rat ed that this offect is ca used by the ta bi li ty

I

\

, of th e inn er boundary la ye r and the in sta bility of th e outer

I

la ye r. Th e radial accele rating for ce on a fluid elem ent of ma ss pdt l'd x. is the differ ence b et ween the ce nkifugal f01' c0

I

( pd T 1'dX.) C,,2 / t and the pr ess ure- gradient force :

I

I

.08 Rate of air flow

1 / [; Lo w

who I' I'd x. is an elem en t of len gt h al ong cascad e fix-is aL o Inter me dt ate . Tl J ' 1 f .. h (rc ,Y 1 dp o High [ ra e HI . 1'. 1C raola orce p el' un it m ass IS t en - .3 - - l' .0 4 I P G r A tab le ro tat in g bod y of fluid h a a nct radial force of zero every wh er E'. If a parti cle of fluid at pos ition T wi th moment o Root .4 0 .56 Tip .44 .48 .5 2 of mom e ntum TC i di pIa ed to a position 1' <1 where the Il Rad i US , 7' , f'f preva iling mom e nt of mom en t um i (TC u) rl and ",h 0 1' e eq ui- Jo'I GU Il E IJ.- R a di a\ di s Lr i bution of m oment of m om e ntum (! o wn s tr ea m of fi rst stat or rin g.

l ibrium esta bli he a pr ess ure gra di ent of Thi s l'l'asoning i upported by figUl'e 10, which how s a thi ck inncr la yer and a thin outer la ycl'. A pr edicted, th e inner boundary l ayer build up and th e outer l ayer thins out with increa ing veloc i ty (which corre pond to incr ea ing t hen accordinO' to the principle of onsel'Vatioll of momentum distance from the ca cade). Th e arne genem l ch aracter j th e pal ·ticle \yill retain its original moment of momenLum.

h own in th e curve of the moment of mom entum ( fi g, 11).

Th e unb al anced force per uni t vo lum e on the particle in it For a ro tat ing in n er s hroud , th boundar y la yer i th er efore 11 e \\ - position in the pr e s ure field th erefore is un sta bl e, \\'h erea ,fo r the rotating outer s hroud , the la yer i sta bl e. A minimum thicknes in all boundar y l aye rs i th erefore obtained by ha vi ng a ro tat ing inn er sm:oud a nd a tation al'Y out er hl'oud a in the compl'e 01' component of If a particl e from th e low-veloci ty boundfll'Y laye r i d is- th e engine £or which thi tu rbin e was design d, ° 2~!)O S- ~ D- 2 REPORT XO. 7 -~A'r lO NA L ADnSORY CO J\L\ll T T EE FOR A EHOKAU Tl C in figure' la, ", b ic h bow th at the efl'ective angle of Relation of eascade performance to desi gn and turbine tmning i ma llet' th an the de ign angle.

p erformance .- The pUl'pO e' of tbe ca c ade i to impart a desired mom e nt of momentum to the air. For tu r bine /. 6 --- - - -- --.

----- -.--- - .- -- "D es i gn' powe r, the radial di tribution of moment of momentum i not : -----0-"- as ig n i fi cant as tbe ma s di tributio n of t he mo m ent of : '\ '\

-

p-- momentum , \\' hi ch i shown in figur e 12. Th e we igh L fl o \\ ' /

-

--- '"

V-

.40 \

\

~

v-

---

~

...-- 1\

~ Q)

\

~ \ ~ .8 :

/

.3 6

o \

Q.

I c: of aIr flow

Rofe .0 I-- .;::: I - ~ ~ a Low II .4 0 Intermedi a te Q) f\ , . 32 . l..

l> Hi gh p/' C5

----

/

Oesi~n .02 .0 4 .0 6 .08 .10 .12 o

I

Vari af i on of corrected m a ss flow, w/ gp r.,a T,3 . sq ft FIGURE 1 2. .- 1\lass disLribution of dire-ction parameter Te" / e".

In order to e timate the we ight flo\\' at Lhe de ign pr e s ur drop , usc i made of the fa cL t hat for th i turbine, the cor- rected we ig h t flow as a function of pr e ur e ratio is incl('- "- \ ( penden t of peed. Becau se of uberitical flow th e press ure ratio on r the nozzle i a funct i on only of th e ma -flow para- meter , w hi ch in turn i a function of the turbine over -all pre Ul 'e ratio and indepe n dent of peed, th e pre urr ratio of th e fir t tatol' i th erefore a fu n ct i on of th c pres me ratio of th (' w " ho le turbine and i in d ependent of perd. For this turb ine , t he relation of weigh t flo \\ ' and pr e ur e drop for de ign con ditions cl1n be c omputed e it l wr from co nditions at

the root-mean - qua re racliu .J~ (1'/+1'/) with the entire

Rate of air flow flow a rea or by co mputation and integ r ation over the whole Low - .DB bl ade heig h t. T h e pr essure r atio or the co rre ponding 0 In termedIate t:; High c/aT .3 at th (' root-mel1n-sq uar e racli u is th erefore taken a typ i ca l of thi tator. Th e d esig n pr('s Ul'e d rop over th e whole t ur bi ne j therefore a umed to prevail wh en c/aT.3 j .04 ('qual to the de i gn va lue at t he root-m e l1l1- quare radiu of t he fir t s tator.

The a rea of flow i blocked p rincipally at the inner broud.

I

o .02 .0 4 .06 .0 8 .10 .12 T be ai r fi o\\- at design pre sure drop i e tlmatecl by a uming Variation of' correc ted mass flo w, W! 9P TQ T, sq ft an efi'ecti\'e area d etcrmin('d from the e xperiment wit h th c I"IGUII~ 12 .-Mass di strib ution of moment of momrntum dowl1s trram of firs t stato r ring.

lo\\'c t flo \\, . Th e a ct ual veloc ity r atio - 1 w between t he inner sh r oud I1ncl a r ad ius r i th erefor e a 2 2 ...£= - Ic + C aT aT '\ a " function of r. Th c urves are more n el1 rl y con sta nt th an th e curve of figL Lt' e 11 , sh ow ing a \'Cry teep rise from zero at

imp li es a ce r ta in de n i ty rat io p/ PT fo r ise nt ropic fl ow. Tl le

both hr ouds. T h e desi gn va l ue of the ma -flow pammete r eR 'ecti ye flo \\ ' Mea A. i computed f r om W / gPT. 3 aT .3 i 0.0723 qua re foot , ligh tly lower th l1n th e a

W ( 7) ) (C )

lowest te t co ndition , which I\'a 0.0757 square foot. (TV, tota l gp TaT = A . PT aT weigh t flow th rough th e tator blades, Ib/sec; g, gravitat i onl1 1 and from tilt' d ata for t he lowes t- flo \\ ' conclition . From the factor; ub c ript 3 indicate tate of air enterino- t he fi r L set

yaille of Cla and piP ?' fo r t he de ign condition I1ncl t he

of tator blad es.) In order to c ompar e mea ured va lue of r efi'ectiY<' area, the flow at de ign pre ure ratio I1 nci tandard Te with d ign value , u e i mad e of the fact th aL , for a u a tmo ph e ri c co ncliL i on for the e nte ring s tag n at ion Late i per f ect fluid , if Te" and th e energy I1re c onstant for olle fl ow, -. ;) pound s per sl'eoncl, which i 95 perce nl of Lhe des i gn l'C" and CoL are c on sta n t over the radiu s for any ot h er flow ya i ll e. T he eR ' ect ive flow ar a i 7.5 p er cent of t il e aetual and rc,, /c is constanL for all flows and rad ii wit h eon Lant a ya i ll e. Th e a ump tion of free -vortex fl o \\ ' and uniform an o- Ie di st ribu tion and radial quilibriwn. Th e ma - axial w loe ity i th refor e lin atisfactory f or eSli matin g t he

averaged e wa co mputed and th c par am eLer rcufc wa

a a air-Ao\\ '- pr lir e-rat io rela t ion of the turbinC'.

plotLed again t thc co rr ected variation in ma f10W W/ gPT .3 aT ,3

I

I

_._._!

AI ALY IS OF P ERFORJ\IAXCE OF JET ENGL\TE FROM CHARACTERI TIC OF COMPONENT -I Turb i ne erTic i ency 5 6 7 8 9 10

I

'10 , , !,,':ppY'fl ()

I

//J; ~ I , ~ ;;

Wi

.5 I ~ " ~

~

~ ~. ' 0.: I ~ ~

,£4 p>

~

- - Corrected it ' ~> ~ -1-~--+--r-~- rotor sp eed -+--+--r- ~

~ Ai

'!..: n/ .ru;:; ' , Corrected .....

~ / (rps) +-+--+--+----1 d lotor speed 102. I o n/-IB;; 12 49 +

~

(rps)

t I

~-4--+--+-~--+- D 13 I. (j -+--+--+--1-----j

~ ' '

~

, .. ,,' '\) 0 1021 1 40.8 q, <>

~

124.9 + ..... c; 1 499

d

()2 0 131.6 16/./ -I--+--+--1-----j , , ~~--+--+-~-~I- ~ q, v:

~ 140.8

170.4 t; l. 14 9,9 /-" I 8/.5 +---:-7:- ~ ____i-_t- -I ~ 'V 16/./ c3 / $ Des i gn IJH ./ B T•3 ~ 170. 4 0."

• IJH/B T,3 ",,' o 'l 1 81.5 "

I

.

4 8 12 16 20 24 28-10 Corrected enthalpy drop, LlH / gBT,] , ft -Ib/lb I x 3 o 4 8 12 16 20 24 l0 FI GUI< E l !i.- lse ntr o pic a nd act ua l en t ha lp y cha nge through NAC'A two- s l ag~ t urhi ne.

Corrected isentro p ic entha l py drop. I1U / g8 ,3. ft -Ib/lb S T FIOl ' HE 14 .- Variaii on of weig ht fl ow with ise ntr o pic ent h alpy drol) of MACA two-stage Lurbin e.

If th e mean ax ial-veloe i ty co mp onen t c i d ec l' eased in t:;,H s i ent ropic ent halpy d rop th rough tu rbine, (ft-lbl lug) a the ratio O. 75 to accoun t for th e ar ca blockage, th cn the n rotor p ee d, ( rp s) va lu e of TC ,,/C is ch anged from 1. 34 to 1.540, which cIo ely ubscrip t : a approxim ate th e de ign va lu e of 1.535 . Thu the under - 3 t urbine -i.nl et co ndi tion turning of th e a il' i almo t exactly acco unted for by he st standa rd- ail' condit ion blockage of fl ow at t he blade root with the de i gn va lue of FigUl'e 14 show th at the t urbine behaves like a nozzle with momen t of momentum. Thi underturning may be explained no effect of r otH ti ve speed. The design point computed Oil by ass uming that most of th e build- up of th e inne!' boundary th e ass ump tion of an efficiency of 0.90 j also shown. Th laye !' ta k es pla ce after di sc harge from th e nozzle by fl ow we igh t flow at de ign pr ess ure dl: Op is about 96.4 percent of t be de i gn alue, rath er th an 95 pe rcent as pr edicted from toward the uC'tion urfaee of th e blade, which projects the cascade performance; the agreement of fl ow pr e di cted beyond th e guid ed channel sect ion. Th e ma in effect of these ph enome na i to inc l' ea e th e axial-v elo c it y co mp onents from cascade data with t Ul'bine performan ce is good. Thi s over the pa rt of the blade ju st out ide the s hroud boundary increase in air flow may be ca used by the influence of the layer and to redu ce the a il' flow from th e des ign va lu e. Th e rotatillg set of blad es , which might r e nd er the inn er boun d- pOOl' angle of a tac k at t he ro tor-blade r oot is relatively ary l ayer un tab le and t hu destroy it, Tbi influence may in ignifican t because of the small part of the fl ow in th at be felt to orne extent by the l ayer ju t down tream of the region, bu t the deviation from d es ign angle ar e rel at ively fir t row of nozzle , which become th inner alld thu r eel uces ig nifi cant in the pot en tia l-H ow region adjacent to the inner the flow obstruction. Figul'e 15 show the co rr ected isen- hl'oud . Accurate d es ign procedul' req uire the develop- tropic en thalpy drop of the a il' as a fun ct ion of the co n ected m ent of a m et hod of predicting these e ff ect neal' the s hr o ud . enthalpy drop; the e ffi ciency contoUl'S are straig h t ela hed line thro u gh the origin of lope eq ual to the r ec iprocal of TURBINE PERFORM A C E the efficiency, A peak efficiency of O. 75 is noted. Th e ent halpy cur ves show nearly constant efficie ncy over a w iel e Th e relaLion between the CO l'rected weigh t flow of the r ange of sp ee d an 1 power out pu t. At the desi gn va lli e for t urbine W 1 (ur ,3 O r,3), the co rr ected turbine ro tor speed peed and work outp ut pel' pound of ail', th e ffi cien cy is 2

n/ -/ O ,3, a nd corrected isent ropic ent ha lp y drop t:;,H .I goT,3

r i given in figure 14 where perce nt rat her than 90 per ce nt , which v\ Ta u eel in the cit' i gn lr wei ght fl ow of ga t hr ough co mpre SO l' or tu rbine, process. At tbe cO l'l' es pondinO' i ent ropic e nthalpy drop , which is 901 2 tim es the des i gn valu e, the air H ow i on ly 1.7 (Ib l ec) percent lower than the de i O' n va lue of 6. 1 pound pe l'

u ratio of densi ty to normal gas den i ty , p/ P s t

o sq uare of ra io of onic speed to onic peed for econd , Thi s de ign point i al 0 shown on figure 14.

normal air, a /a ./ (referred to a co rr ected tem - Wh en the turbine operate in the engine. it will handl e pe r ature ratio he ca usc of reta Lion li ghtly more O'a than indicated from the e data beca ll e of

- I

I

REPOR'l ' " 0. 8 i -N ATIONAL ADVJ ORY COMM I TTEE FOR AERONA UT I C

!

the e xpan ion of th e clearanc es und er the action of th e hot r ec ted weight-Bow param eter, both of which ar c useful in ga e . Th e agreemen t b etw~e n de ign and actua l air flow finding the m atch in g and the int e ra ct ion of the till'bine and at de ign work output can th er efore be r egarded as satis - the com pr e SOl' as com pon e nts of a j et engine. Lin e of fa ctory. c onstan t c orr ected rotor peed and of constant turbine A plo t of the over -all tmbine performance in figur e 16 e ffi cie ncy ar e hown as well a th e lo cat ion of the d es ign hows a corrected torqu e parameter plott ed against a cor- poi nt. Th e design point is not th e point of highest effic ien cy C orrect ed rotor ..nJ!,ee d Corrected n / 'B r. 3 x/OJ temperature (rps) ratio B T,3I B T,1 I/O 1 20 1 30 14 0 I 0 45 , -t 4.0 I Tur b i ne

!

3.5 !

_____ .80

!

erf ici ency --.

3 .0 I

---- ~ - ,

I I I

6 2.5 j- - , , 2.0 "," .... I <J ,

I

17 1.5 ,

I J- .. -

I

, , I , Des i gn po i nt III , 16l I 1 70 I , ,

i

-

I .82 I !/ ,

-

,I . 84

tt

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, ~ .85 .. .. - ..

,,'r

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V I I --1:: .

24 . 86 - ,

-- ~ ' - .8 7

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p, I ~ ,

dP d ~ ~

, , , ~ ;/" ~ ,

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V ~ ~ / //

Q.2D , ' , / ,

.., /

1/1

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V /

VJ /

, / , '. 8 7 /, 1/ ,

Vi

V V I r- // /

"" ': -- - ... _-- ,I

I :' ' 86

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1 /1 ,'

lif ... .............. ... ~ .

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j

V

1 .:' if

- - -- - ...

I

'/

/

-J

~ I Y

./ : / .' 5

-'-lf

" 1 / I

" y;

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1(----

// 1/ --1''1

vi J: / L. ---- - --

I

, ... ----

/ .I

[/--- .82

:'j /

/1 / : - -- -'

/ I

/

,i-

: / / _J - ' .80

k

--

--_ ...

II

:; --- /

/ /,.1.- -

/

. ---/

V -" - - .. -

;/--

_.-- ---

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_--i / -- -

, -- - - ---" , ,

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--- -;- V·

/ / -".7 5

/1

------7

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'It ~~- --. -

- --' , . _ _ __ -r ;' ;'

i _ . --

/ I..~ / 8 , , .- - --_ .. - - ,

/----

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;/ ~ -- .. 70 .... ---- ----- --

;- --j/

" /- /---

,/ --;./ --

, /----

.. ..... - .-- .. -- - -- , __ r-- .. ----- / _-:T ,/ / ,/ _.' ,/ ,/

-- --'7

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/

-/---- - 60 / ,/

, V:---

/ -_ ./ .. -- .. ..-- - -

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-- -,-/ - / -_ ..... - -

/.--

/ / y/-' -;~ ;/ / V'-·- . ' D 3 4 5 6 7 8 9 ID II We i gh t-f'/ ow pa r ameter, w:,n / O' T, J B T,3. Ib / sec' FI GUR E 16. - Matching char.L for NACA tw o·stage t urbille.

ALYSI OF PERFORMAL'l"CE OF JET E ' OINE FROM HARA TERI 'TIC OF CO IPONENT -I then ina much as thi efficiency wa about O. 23 as co mpar ed WIn 'Y 3PT,3 H'3 n with the peak valu of O. 75 at a peed of 1 0 revolution (7) IJT,02T,2 'Y2PT.2(1 +f) IJT. 30 T.3 per econd. Thi discrepancy in peed indicate that an analytical determination of efficiency is requir ed in order to which relate the tUl'bine and eompre or ga flows in terms produ ce th mo t efi'eetive deigns with minimum losses at of param eters that are r e duc ed to tandard-air values.

the design poi nt. large range of high efficiency i avail- The pow er equation is able, however , for use at points other th an the des ign point .

T RBI E-COM PRE OR M AT C HIN G or Th e turb ine c hara cte ri tic arc now u cd to detrrrnine how well they match the character istics f th ompl'essor where with whj ch the tLU'bine is to be us ed . Th e tUl'bine may be o. ) , p. .. auxi l iary-power consumption ( bea r in (It-Ib l ec) xp ted Lo b c ha '''P omcwhat differently than predict d by 6.H enlbalpy drop through Lurbille, HT , 3- lI T ,4 tbe cold - air data when in talled in the e ngin e becau e of the challO'ed propel'tie of the worki ng fluid , the clearance ex- Thi s equation can b conve rted into L relat.ion between the pan ion, the nonuniform 'emp erat me di tribution in the ompre or and turbine torque in e'qui\~ale'nt va riabl es: incoming stream, and the combu tion in Lhe tUl'bine in some condit ion s of opera Lion. Another difference may be x- pected becau e Lhe data available fol' the co mpr e or were obLained with a scroll-eli cha rg e collector rather than the ( ) axial-eli charge colle ctor LbaL will be 1.1 cd in the engine.

Another unknown is the co mbu tion-chamber Lota l-pr e SUTe For Lhe combu Lion c hamb e' r, the pressure-loss fun ction is los , which is assumed to be 5 percent of the ab oluLe tota l a sL;med to be in the form pre Ul'e ddivered by Lhe compre SOl'.

RELAT I ON BETWEEN TU RBI E A 0 COM P R" SO R VARIABLES W 2 )

function of 1, W f (9 )

p ( PT, 2PT .2 Th e maLching of the turbine and compres or components of the engine i delel'mlned by related parameters of tho and Lhe combust ion dficiency ompre 01' and lhe turbine. For examp l e, the pe'ed of the turbine is eq ual to that of tbe' comp ressor and the relation (10) between the' equiya l ent spee'cl i glven a (6)

7) = function of ( lIT ,3, co ndition at stat ion 2) ( 11 )

= [unction of U, condition at tation 2)

where the subs ript 1 indicate state at compre SOl' inlet.

wher e C mpre or and Lurbine ga flow are related by the equation lI b e nthalpy of fuel enLcl'ing combustlon e hamh cr , 1 F 3= (1 +f ) lC (It-lb / lug ) \"heref is Lhe fuel-air ratio. The n healing yalLle of fuel, (ft-Ib / lu g) h Win = 1 lV IJ7 '.3 OT ,3 3n CO MPRE SSO R AND TU R BIN" MATCHJNG C HARTS

IJT ,z O T,2 1 + f 7r T.3 07', 3 IJT ,2 OT. 2

Exccpt for sma ll co rr ectio ns for fuel input , be'aring powe'r, where Lhe ubscl'ipL 2 indicale . sLaLe al the compressor pre ur c 10 in the combustion chamber , and change in 'Y ouLlet.

from tation 1 lo staLion 4 , the torque pa ram ete r lV6.lI l (nIJO ) equation ( ) i the arne for thc turbine' and for the eom- Beeau e pre or under any eng ine ope'l'ation condition. Th same eq uality hold for Lbe air -n ow pflxamelcr W n ( IJO ), as eq nalion (7) shows. If th e tU I·bine and comp l' e'ssol' perfo rman ce arc and plotted in tcrm of the e yariables and Lhe charts super-

o 'Y 3PT ,3

im.posed , one point indicate both the turbine and compre or IJT. 3 7' .3= 'Y " Pst RE POR'l ' KO . 7 - XATIOKAL AD \'ISOR Y C Q:\HIl TT EE FOR AE RONAU TI ope rating ta te when th ey a rc oper ating a compone nt s or a for each operat ing poin t. The engin - c hara cter i Li c arc j et ngin. A c ha r t of t he compre OJ" performance i.n te rms now refined Lo ta ke into a cc ou nt losse and ch an ge in ga of th c e variable i hown in fi gurc 17 for con tant va lue proper tic . Th e bear ing pow l' P A ma y be found from the of n / O T ,l ' The e dat a for th com pr e or wit h a croll op rat ion p ee d . Th en approxi matel y collec tor wer e obta ined from references 2 a nd 3. ome H r.l) - j _ (H T ,a - 6 H c difference is to b expec ted b et w ee n the performance 0 ( 12 ) - TJh - (H T, a- H T.I ) de t r min ed and th e perform an cc ofh c compre 01' when From the dat a on the compl' es o r- di chal'g a nd burn er c har - t raight e nin g vane ar c ub tiLu te d fo r the croll for u e in t he engine. A similar c hart for the t urbine i hown in act eI ·i tic , TJ a nd j can be compu ed from equ at ion ( 11 ).

T his value of j wiL h O T .a/ Or , I and O T , I pe rmit the cl eLe rmina- fi g ur e 16 for con t ant va lue of n / O T,a . If the char t for thc t urbine and th e c ompr e or ar e up rimpo ed, it c an be tion of 'Y a hl an 1 T r ,3/ T T, I' uffi cien t data ar c then ava ilable see n wh et her th hi O" h- e ffi ciency region fo r th e t urbine over- L o find the value of PT .a/ PT , 2.

lap th e h igh-e ffi cicncy r gion for th e compre or. If they Th e L ur bin e torqu and air- fl ow requireme nt ma y now be o mpu ted to include th e e ff ect of compr es O l" , combu tion- do not , th e re ultan jet engine i pr even cd from reac hin g c hamb er pr es ure los and e ffi ien cy, and bearing r equire- its maA'imum pos ible e ffi ciency.

m e nt by th e appl1ca lion oJ equ ation (7) and ( ) for veral The over-all ngin c p erforman ce c an also be est imat ed point on each compressor- p eed curve. T he e point ar e from th e e c har t, and th rela L ion of cach componen t to th e over-all engine p erfor man ce can b e dt e nn in d . T hi re la - connec ed by a c mv for a gi ven p ee d . The in ter ection tion will indi cate the mo t approp ria te modifi cat ion of of the e c ur ve of turbine requireme nt with the proper L m b in e and comp re or Lo obtain b ette r over-all engine per- peed c ur ve of turbine performan ce give turbine opera ting formance. F ix L , a rough approximation i made by as um- point th at can be co rr ected by qua tion (7) and ( ) L o give ing no bearing 10 e, no combu tion- hamb er pr e s ur e loss, L he corre ponding compr es or ope ra ting poi nt . Th e e re- a nd no fuel a dd ed. If a valu e for the C OIT e ted tem pe ra t ur e ult h ould b e of L he de U· d a cc uracy bu t hould be checked ra tio O T ,a/ O T ,I i a um cd , the ra Lio of Lurbine to c ompr e or Lo ee t ha t they fall on th e orig in al compre or c ur ve. Equ a- tion (J 2) i u cd wi th lhe burn er char t (equ at ion (J 1)) to sp ee d i fi xed for thi value of O T,a/ OT ,1 by e qu at ion (6 ). By up erimpo ing the t wo ch art a nd choo ing a par ticular com- fmd f. A ch eck on the acc uracy can be mad e by recompu t- pre 01'- p ee d lin , Lh e in ter ection of thi lin e with a turbine- in g. the in te r ection poin L wi th the n ew valu e f or .f and speed line having th e corre t ra t io of t mbin e p ee d to th impr oved valu e for the bea l'U lg co rrection and Pr,a/ Pr ,2' In co mpr e or sp ee d determine an eng in e opera tion poin t. the exa mpl e being co mpu te 1, i t was a s um ed th at TJ = 0 .9 Th e cho ic f ano th er co mpr e or sp e d determine another and P7 ' ,a/ PT,z= 0.95. Th e bearin O" were a um ed to u e a point. In thi mann er, an oper at ion curve c an b ob tained L orque of 7 inch- pound and th e compl'es or-inlet condition for each te mp er at ure rat io. Th e fl ow and th e talc of L he con e ponded to an alti tu de of 30, 00 0 feeL and a Oi O" h L pe d a il' el i char ge d from th compre or can then b e o bL a in ed of 470 mile pe l" h o ur .

I

C orrected

L o

---

r o tj -s pee d

::::--

h/ O T ,l .

~

:::::::====

( rp s) ~

I

=-

-

~

--- r---

c89-

:::::::::-

p- c 74

~

~

~

:::::::: ~ r--::: :::::::: E58 .....

;:;20 ~ Q:) N

y f---

~ .

--

~

----

s::

:::::: -- ~

/

~

-- ./

'£ /6

--

'-- 1 83 ~

--

Surg e lin e - -- - --

/

I ~ V /" /

//

/

12 2/ 9 /0 1/ X / 0' 3 4 5 8 7 8 We i ght - f l ow p ar a m eter, W n/ d r, 2 8 T,2, l bjsec' l F I Gl:R E Ji.- :\I afch ing ch art for ::\ AC A eight·stage com pressor. ( Data fr om ref renee 2 and 3.)

A NALY I OF P ERFO RlI AKCE OF J E'f ENG l "E FR OM CH AR A ' fEIU TI CS OF COM PO NENTS-I Th e e ompJ" e or-ope ratio n c ur ve for con tan t c orr ected p re s ur e r at io i no t do e to th e e tim a ted va lu e und er th e e t mp e ra t ur e ratio fi T ,3 / fi T ,[ ar e hown in figure 1 a nd th e c ir c um ta n ee (m eas ur ed e ffi cien cy, O. 2; design e ffi cien cy, c orr ected te mp e ra t ur e-ratio line a rc ho\"\"n on L h e t urbin e 0.90), Ie PI' ur e will b e available for th e j et nozzle, which c bart ( fi g. 16 ). Tll e ' ompr es or a nd th e tU 'rbine arc no t mu st th er efore be larger than first es tima ted .

p e rf ec tly mat ch ed a hown in fi gul' . 16 by th e fa ct t ha t non e JET -ENG I NE P E RFORM ANCE COMPUTATIO , S of th e fi T ,3/ fi T ,I lin e pa t hrou gh Lh e r egion of maxinmm t urbin e e ffi cien cy. Th high est c ompr e S Ol' e ffi cien cy is I n ord r to c ompu te h j et -eng in e p e rforman ce at a gi ven being u cd wh en fi T ,3/ fi 7' ,[ =3.5 an d n/-hT, 1 = 274 rev olu tion al tit ud e and peed , th e ram pr css ur (g n erally C OLT cted p er econd. nd e !' Lh e e condition th e t urbin e i oper at ing for du ct los c bu t no t in t hi s e xampl e) s. nd th e te mp e ra t u re at anffi cien cy of only O. 2. Th e ope ration c ur ve cove l' at th e c ompr e or inlet ar c c ompu ted a nd from th em V/ fi T. 1 all mod e of ope ra tion of th e engine wi th arbitrar y ram a nd a nd PT. l/ PO a t' d ete rmin ed. Th e fli gh t peed is V a nd Po e mau t pr es ur e an d di ch arge-j et noz zl e iz e, bu t only i th e frec- tr eam pres ur e. If th e ub sc rip t 4 in di cate a mall par i of th e en t ir e t urbin p e rforman ce ran ge of good t urbin e-ou tl et ta te, th en th e j et pr e ur r at io rna be eff iC ien cy . Dat a ob tained from exp erime nt s wi th t hi s j et wri tten eng in e a a omplete unit th er efore c annot be e :.-q )ected to PT,4 = PT,lPT,4 C O ve r a ran ge lar g nough to llldicate wh er e th e region of Po Po PT.)

p e ak t urbin e e ffi cien cy i a nd wh eL h er th compon ents ar c well ma tc h ed .

wh er e PT ,4/ P1',) i pr e um ed known from pl'eviou engine Th e e ff ect of th e discr cpan ei b et ween de ign e tima te co mpu tat ion _ If tb e va lu e of 1' 4 a nd T T , 4 ar c I mo w n, the a nd t urblne pe rforman e on engin e ope ra tion is minor in o far co rr ected j et veloci ty c s/ fi T, l ma y b e c ompu ted from a th e c ompr es or-ope ra tion s tat es ar e co nce rn ed, b ec au se of good c orr e lation be t" -ee n air flow e tim ate d and m ea ured at th e de ign va lu e for t ur b in e ,,- ork p e l' poun d of a il' at design p ee d . Th ese thr ee variabl es ar e enough to deter min e th at th e com pr e 01' will opera t a t d sign a i1' ~ f l ow condi tion for th e de ir d p eed a nd te mp er at u re ra t i o. B ec au se tb e t urbine wh er e t h e ub sc l'ip t 5 indi cate pr o pul ion-n oz zl e co ndi tion .

I I Corr e ct ed rOTor ~ed S.8 ~--~-- --~-- ~ ~--~---- +----4---- 4- n ! V8T.1 --~----~---+ ----4--- ~~---r ----+----i---- ~ (rps) 289p~ , Co m pressor

"

Corr e cted ,/ e ffi ci enc y ~~.

V

5.0 ~--l-- tempera t ure ---I---4---4-----/ 7C74 ' .... ". ' ;;O / f~ ',,_ V ,_ _ " I' n "" " r.1 /' " " -', f .... - Y .

o 4.5 - .l-~4/.· ~_:~.::',:....J- -r>:~ ,j.,.,.. :...., ~',,::+.- --+--~--+--1--_t--_i 6 ~ : g d /! \. /~" ~ 835" ~:""l) .

... -

o 3.0 2S.9~:-: ..... . ,; ~ . > .....

~42 J-- -.....J.

A OJ c.5 V "i tI ' V ' ',' 2.0 ,.. ......... .. ........ ~ .. " .........

r.:- 1. 5 ~ -......... ... ..... ~ ...... ............ .. ........ L.

A.

..j. ;/' " -- ' -..:~ ',---- ~ .....

~~ o I..

t 3.4

~ I/) I/)

'"

cl:: F -- . __ __ . '.......------f--- . _.

--·-_1 -- ~.-.- 1.0 ~--- 3L- ---L---- 4 L----L~· - ~5 L----1---- 6 L---~----~7----~--- 8 ~--~---- ~9 ----~---/ ~0 ~--~ { l x 10 We i g h t- fl ow para m eter , W ,n / 0 r. 2 (J r.2, I bjsec' FIGl'RE) .-Estimated operati on of compressor in jet engine.

REPORT NO. 7 -~ATIO~AL ADYI ORY COMMITTE E FOR AEROKA T I C 1 /0 0 / 1 00 Co r recfed .l Co rrected !.

' rotar spee d temperature ratio , n /v'B;; ,

8 /e r. t · , __ •• J /

, (rps )' "4 5 1 000 C or r ected

j

Q rot or s peed 27 4 n / ~

1\ "

, (rps) 900 900 , ,\ 28 9

/ \

4 .0 !- '

, ' , , ,

L , I

,

\ / '\

80 0 BOO " \V ~74 r.

q ~~ Corrected ~ , ' temperat u re rot lo / !59 -0 B /8 ......

3.~\ , '- T,) 7.1 \, , ..

. 'l '

!

r:r, Q 70 0 , ~ , , , 45 , ,

, , I 1 /

', j

'\) h il ti , b.

' , c;:- ' , I '. / --S O 1", I

I '"

, '0' , I

l~n

'- 05 60 0 600 ~ ' , ' J: , 259 J: t 'l ' ,: ., .. :

I

' ' 2 44 :EO I , ~," ~ 3.0 , , " 4 0 " ,

'X "

" ;g 500 5 00 ~ , Sur ge line ·,.

~ ' f( i '" " , .....

" I "

15'

'" ..

-i- ~ ..

, '-

1 ;4 1J

// , : .

CJ ~ 400 40 0 " ' .

] I

, . S

~ / I

'f 0-

: I I J/:'

" l.cJ ~

L V' V,f S ur ~e line . JL. ,f,,'

t...J 300 ,I)" 1'-' \ 213 //

. l/

6P'

.' 1 /

/'

/ V

~ g , 2 1 3,,-

~ .

200 - - 200 t--- ~r;3 /

U1 s

- -

- -

~ 1

: ~

/'

.r _

- l Oa I--

~~ O

0- ~ (b) ( a. )

o

+

0. 3. 8 .5 6 .7 .8 .9 /.0. 1.1 1.2 2 . .4 .5 .6 .7 . .9 E qu i valen t s pec if ic th rust, F -v?J;; /36D0 w, .r. Ib /(I b/ h r ) Cqu lv a l ent spec if ic t hrust, F,;e;; f36 00 w.,;: Ib j(l bjhr ) (8) EQlli " alent specific thrust: flight speed . 0 miles per hour; pressure BltiLUde. 26.000 fe~t.

(h) EOJllh'al~nt specific thrllst: flight speed. 4iO miles per hour; pr ess u" e altitude. ~3,OOO fe et.

FIGL"Rll19.- Estimated characlcristic or jet engine .

Th e minu tc e fr ect of va ri at ion in 'Y du ring lh e nozzlc-

3600 ( L) ( WI )

cxpc uL ion pr oce j negl ecl d. Th e c ompr c or ch ar acter - _ 01',1 P (f1'. l"\ 01'.1_ (l b) / (h p -h r) i ti c g i\ 'c WI ,a nd f is kn o wn for each p o in l. Th e ~r.1 (01',1)3/2 (fr. I , Or. I e ql liYalen L thru st i Fr om lh e weig hl fl ow a nd lh e out lel c ondili on , th e a r ca of l h (' lhrll l no zzle c an al 0 be com pul ed for each ope ratin g a

_ F =~ ( ~" _ I ) [ (l +J) ( C ) _ V ] (lb)

poi nt an d th e co rr ccL nozzle elected [ I' any cl esi re cl co nd itio n.

(fr. 1 1', 1 g (fr. 1 , 0;; \ 01',1 , 01',1 Th e o mpu tee! engine perfo rm a n ce i h O \\" 11 for ze ro II igh t p e dinfi g ul' c 19 (a),w llich gi vc cq ui , "a len L La tic t111'u lan d T h e cquiv alen t po wer is ('Cju ival l' nl sp ec ifi c lh rus l for co n lan L va Iu(' of cO l'l' ecl('d r oto r peed and cor rected l0 mp ('J'alure ra t i o. A imil ar cha l' L i h o wn in fL g m e 19 (b) for a [Ji gh s p ('c d o f 470 m ile pN llOur al an a ltilud e co rr e pon ding to th e am e co mpr e 01'- inlet pr e surc . .At th e am e fli g ht p ee d a nd altitud e, fi o- L1r e Th c p ec ific thru L is 19 (c) 11 0\ th c p ccific fu el con u mpli on. Th e minim um e t im a lcd p ec ifi c fuel co ns umplion a t 470 miles per h o ur - JI O ' ) / [ : 3600 ( WI_ ) (/ ) ] (lb/( lb/ br )) ( j O. 5 po und p er h o I' epo \\ "e r-bour al 55 0 po und Cj lli va lcn L (f r.lr,1 (f r,I , 01'.1 1'.1 lh rLl t , a te mp e ralur e rati o of 3.35, a co rr ecled co mpr e or sp ec d of 2 74 r evoluti on P (, l' ccond , and pr ll re ra tio of 4,4 .

And th c p ecific fu el c on umpLi on is ANALYSI OF PERFORl\IAl TCE OF JET ENGINE FROM CHARACTERISTIC OF C OMPONENT - I eng in e is a hot- ga producel', for which th e matching c harts Corre c ted r otor spe ed will determine the tate of the discharged ga. If thi ga n/ ...;e:;:-: 1 f i di charged in to a reheat er and from there into a po, er 900 _ ( rps ) _0 Lmbine, the matching e bart c an be II cd to find the over-all .. J '\ ·· .. 289 :

I

I I performance for an engine of Lhi type. In th e D"eneral ca e I Corrected

~

I \, of the turbine-propeller engine with jet power, a chart simi- 800 temperature rat io ' 8, .• /8 T ., lar to the impl j t -engine chart may be u cd with a difrere nt .~ 1 2~:t

\

I

, , vertical shift of th e cales for each \ralue of prop eller torque.

, , I

\

Another Lype of gen ralization i po ible by the 11se of 4.5 259, t }'I :8 differe nt mat ch ing funcLion. For exampl e, if th e Lurbi ne ,

\

, i geared to th e compres OJ" Lhe gear ratio may be so in cor- \ : d m..

, porated into the function that th e tmbine and com pr e or BOO , , ,: , "0 , fun ct ion mat ch. Th e engine with a ingle power t mbin e : j ~

\

I

1<;- and no jet power may be t lldied by u of the isenLropic- ..: ' ,

" V 4.0

244J " , ~ 500 ent halpy-drop factor in Lead of the torque factor, which , ... , " , -c \ A permits a matching of th e pre me drop. In till ca e, a

.... \

3.5 I .....

, vertical logarithmic calc i advi ed bec au e a simple hift f, , , I

S 400

I '- in the vertical direction will O"ive maLching requir eme nt 0 \~ ,.

, , ~ with variou ram-pre sme ratio .

\ ;'\ """ 0- ", ~ , " l.::i 300 SUMMARY OF RESULTS \',:, ~ ~ '" 3 .0 Th e following 1"e ult s were obtained from an inv e tigation

I'--- 213 0

of the performance with cold air of the ACA two- Luge -......

"'"

turbine anci the fir t stao r-ring componenL:

----- '

2 . ~

r--- r------

1. Th e st r ea.m-filame nL me thod of ch eking turbine -blade

----

-- r--L-B~

pressme di tribution gave blade velocity distributions th at g nerated boundary la yer of mom e ntum thickness of about 0.0037 inch for the uction urfa ce .

( c) o 2. Th e energy los in th e wake of the blad es engendered .8 .9 /.0 1.1 1.2 1.3 1.4 1.5 by th blade e dg e and the boundary-layer momentum Specific fuel co ns umption. Ib/hp - hr thicknes caused an e t imat ed decrea e in Lmbine e ffi ciency (c) Specific fuel consu mpi iou : flight speed. 470 m il es per hour; press lH c a ltiiu de, 33,000 fc et.

of 0.2 percent . The incre ment in ell'ag c aLI cd by boundary FlO U RE 1 9.-Concluded.

layer at the trailing dg j negligible.

An esti mat e wa mad e of Lhe change in performan ce for an 3. Th e boundary lay er at the hroud built up to om e improvement in the matching of the tmbine with Lhe com- extent ins id e the c hannel ection of the nozzle but mainly pro or. At the point whoro th tati thrust wa 7 pound down tr e am of the nozzle tlu·oat. Thi s pJ"oce s wa a ct i va ted and the pecilic thrust 1.024 pound pel' pound fuel pel' hom, chiefly by the low pre m e on th e projecting mia ce of the the compTe or speed was 2 9 revolutions per econd, the blade.

corrected t mperatme ratio was 3.5, and the tmbine effi- 4. Th e boundary lay er on th e tat ionary inn er lu'oud was ciency, O. 2. Th e assumption was made that the hanD"ed thick compared with that on the outer lu'oud, wa stab le, tmbine D"ave the peak effi iency of O. 75 at that corre pond- and. built up with increa inD" air flow . Th e boundar y lay er ing point on the tmbine matching c hart . Th e tlu ·u twas on the outer she ud was t hin , unstable, and decrea ed in Lhic lrnes a th e air flow wa in cl" a cd.

increa ed to 26 pound and the specific thru t to 1.073 5. Th e boundary lay er at th e inn er slu'oud blocked part pound per pound fuel per hom , an improvement of 4.7 of the flow ar a and e tabli hed high axial velocitie in the percent . Tl:-c improvement at 470 miles per hoUl' wa about 4.7 pel' e nt in all pe rforman ce parameters. region adjacent to the inner boundary lay er but down tream A tudy of the problem of eng in e adju tment for better of the ca cade. Th e boundary lay er a ppar e ntl y had no matchinD" i required in order to apply the knowledge other e ff ect on the velocity di tribution indu ced by the gained from the matching c hart . 'rh e manner in which the blade .

t,ur bin e and compressor performance c haract eri tics mu t 6. Th e e ff ective annular area wa about 0.875 of the actual At the design pres m e ratio, the computed flow was be altered in order to get fLn exact superpo ition of the area.

0.95 and the measured flow 0.964 of de ign. At de ign ma..\':imum-efficiency region of turbine and compre or with ent halpy drop, the flow wa 0.9 of the design va lu e. Th e optimum engine performance mu be determined .

difference between the flow reduction and the aTea reduction OT H ER APPLICATIONS OF MATCm G CHART wa probably caused by the build-u~ of the boundary lay er of the inner IU'oud on the proj ect ing u cL ion urfa ce of the The matching chart described ca n be applied to engine other than the simple j et engin e. Es entially the jet blad e without greatly affecting the flow in the nozzle tlu·oat.

j RE POR ' l' TO. 7 - NATION AL ADYI 'ORY COM111T'J. 'EE F OR AE RO N AU' rI C 7. A de i o- n valu e of t h e e quival e nt torqu and th e pr od- forman ce was abou t 4.7 p Ol'ce n t for all param ete rs at fii o- hl u ct of e quiva l ent air flo \ an 1 q uivalen t rotor sp ee 1 speeds of 0 and 470 mile per hour. Thi i mpro vem en t ( liV 3n / UT , 36 T, 3, wh er e Wi ga flow, n i rotativ e p ee d, (J and might be re gard ed as available through impl'o, 'e cl mat c hin g- 6 arc th e density and te mp e ra t ur e C OlT ct ion , r esp ect ive ly , of th e t, 0 engine c ompon en t .

and T ignifie total and 3 th e turbin e inlet ), th e e ffi cien cy ONCLUSIO S wa O. 23 a c ompar d with tb e pe ak of O. 75 at a p eed f 1 0 r e volution per ec ond , which wa th e prin c ipal di cr e p- Thi inv e Li gat ion indi ca ted th prob a bl e general va lidit y ancy b et w ee n tb le ign and m a ur ed 1' e ult .

of th e following onelu ion : . A e of ch a rt s wa d ev lop ed, wbich p rmil an es ti- 1. Th e tr ea m-filam nt m elll o cl of ch ec kin o- t urbin e-blad e mat of j L- eng in e p el'forman e from th e p el'fol'manc of Lh e pr es w'e dis tribu t ion prov e at i fa ct or y fol' obtainin g hi g h- co mpon e nt and a dete rmin a tion of th e cl egre of m atc hin g olidity blad e in a pr e sm e -drop flow with out tbi ck bo und - of tll c ompon en ts .

ary l ayers . Di ch arg g uid ance in th e bl ade gi ves des ired 9. Th e ma tc hin g c har ts s how ed tha t th e be t compl'e 01'- ave ra ge mom en t of momentum , bu t in c orr ect an gles nc ar e ffi cien cy r eg ion did no t c oin cide wit h th e be t L Lu-bin e- L h e bl ad e rooL .

e ffi cien cy r eg ion wh en th e I \VO c ompon e nt were 11 e el a a 2 . Tb e ass ump t lon of fr ee -v ort ex flow a nd unifo rm axial j et eng in e. Th e pe ak c ompr e 01' e ffi cien cy ,m O . 4 a nd veloci ty be w en blad e row i in adeq ua ie Jor e Limating the pe ak tmbin e e ffi ci n cy O. 7 5. Th e p ak c ompr e 0 1' fl ow angle or weight-flow pr e m e -rati o r ela ti on bU L i e ffi iency o CC UlT ed at a c orr e ted te mp e ra L LL t'C. ratio of 3.5 aLi f act or y for e t im a tin g weight-flow work-outpu t rela tions a nd a con e ted r ot or p ee l of 274 r ev olution p el' ec ond .

and i lh erefor e aL i fa ctory for e t im at ing t h op er ati ng L thi s p iu t, th t urbin e op e rat ed a t an efficien cy of only poin t of t h e c ompr e or . For acc w' aL e d esi o- Il , th e area O. 2. Th e p oin t of minimum pec ifi fu el c on umption of blocked by th e bounda ry la ye r in th e nozzle and t he radi al th e eng in e at 47 0 mile p er h our and 33, 000 fee l i, O. 5 flow ca u cd by th e bo undar y-l aye r thi cke nin g do wn lr ea m of p o und p er b orsepowe r-hour with a co rr ecte d thru st of 550 Lh e stat or s hou ld b e t ak en in to acc unt o orne m et h od po und s.

mu st be ev olved for predi ct ing th e e e ff ect from de ign da ta .

10. An e tim a te of t he i mproy em e nt in oyer-all engine Thl ck boundar y l aye r ar e no t exp ecte d do wn tr e am ot pe rf o rm an ce was mad e for en o- ine opel'ftt ion at a c orr ected r t or .

te mp e ra t ur e ra ti o of 3.5 and a c orr ec ted n gine p ee d of 2 9 r evoluLion pC I' second , und er tb as umption that t he t ur - FL IG H T P ROP LSIOK R ESEAR H L .\ BORATORY, b ine couJd be a dju sted to op erate a t ils p e ak e ffi cien cy of TA 'l'I OKA L ADV ISORY CO :\L\IIT' l'EE FOR A EROXA ' TI , O. 75 in t ad of lh e tim a ted op ra t ing e ffi cien cy of O. 20 CL EVE L .u m , OH IO, J une 6, 1947.

fo r lhi engine condi tion . Th e improv em n t in en o- in e p e r- r-~ --- ~ -- APPENDIX A SYMBOL Th e following ymho l arc used in this report: i: = t /Cs co 'P/>;) 17 fligh t sp ('e d , It/ ec e£fecti \Te flow area down tream of fir t turbine _ tator A.

11 ' total weight Bow of gas, Ib/ ec row , q ft w weighL fl o \\ ' of ga in annulus bowlCled bv inn er hi' nd a oni velocity of gas, H/ ec of ea cade ring a nd r ael ius r, lb / ee L standa rd-air onic vclority, 1116.3 Et l c 'Y ratio of pecific h eat of ga

era vdoc i ty, it/

o momcntum Lhiekne s of bound ary 1a y('1', in.

rna -an'raged axial-velocity co mpon en t, it/ ec

TI eomb u sLio n-eh a mb('r e ffi cien cy p me h ea t of gas at con tanL pressml', It-Ib /( hw) 0= a /a s / (OF) f-L abso lut e visco ity of ga , s lu gJ fL- e t hru t of engine, Ib P ga de n ity , lu g/ eu It fud-a ir ratio 2 Ps t stan da rd- ai l' d ens it y, 0.00237 s lu g/ eu Ii tandard g ravitational acceleration, 32. 174 ft l ec (T p/ Pst e ntbalp y, It -Ib/ lu g 'P angle between normal to cascade ax is a nd fl o \l - direction e nthalpy of fuel enLe rin g com bu tion c hamber , of ga or eli c har ge angle of stator bl ades, c1eg It-Ib/ lu g tagnaLion e nthalpy drop in turbine , ft-lb / lu g ub cripts: sLagn a tion e nthalpy rise in co mpre ssor , ft-Ib /s hw

o free- tr ea m co ndition

i en Lropic drop in tagllation enLhalpy through turbine, 1 com pr e so r-inl et cond iLion ft-Ib / lu g 2 com pr e or-outlet co nlition h eat in g value of fuel, f t-Ib/slug 3 tmbine-inlet cond i tion rotative p ed of t urbin e, rp t hru L hor se pow r f j et ngi.ne 4 t urbin e -outl et co ndi t ion au.xil i ary-power co n umption ( bearin g ), ft-Ib / ec 5 propu ls ion-nozzle co ndition ga pr e s ure , lb / sq It a axial-velocity co mpon ent ga co n Lant, ft-llJ / ( lug)(OR ) T con d i tion in nozzle Lhroat of blade ca cacle r distance [rom axis of annular c hannel , It l' blade-root co n lition ga enLropy, ft -Ib/ ( lug )(O R ) st tandar J-aiJ' c ondition bl ad e pitch , It s T tagnation con l ition gas temperature, oR T t blad e -tip co nd i tion blade tra iling-edge th ic kn e plus momentum thickne t of boundar y lay (' l' , It u ta ngen tial- ve lo c it y co mpon ent

j

I

APPEND IX B TRAILING- E DG E MO ME TUM LO S A uniform parallel flow of gas ,, - ith pre s me P N, te mp e ra -

\

tur T N, den ity P N, and velocity C N flow b etween an a

fTd =~ C ( :v -1 ) ( ~ ) (B )

PN 2 l - i/ l - i/

infmite cL of traight vane of thic kn e t, pitch (al ong j

ca cad e axi ) , and angle ({IN ,, - ith 1' e pect to th e normal to t he ca cadc axis. Th e ga disc harg e into a pa ce wi th no

I

From th e e quation of t at e, en rgy, and c on t inuity vane an I at t ain a final tat e of p, T , P with direc tion angl e ({J and velocity C of a)..-ial c omponent C and tangential com- a pon en Cu. The c ontinuity eq un,tion i P NCN co ({I N ( s - -- t- ) = PC a cos ({I N The fraction of flow ar ea blocked i t Wh en thi pr e s ur e difference i quat ed to that found t /= --- co ({I N from th e mom e ntum e qu a tion and p/P N i e limina ted by u e of t he variabl e [(p/P N) / (I - t/ ) ]-I , a qua dra tic e quation i a nd th e continuity e quation is obtain ed with th e e xa ct olution PNC N co ({IN (1 - t /)= pc ( Bl ) a Th mom e ntum e quation for component s normal to th e ea cade axis is PN -p = pC co ({I N) = p SC (1 - ; /P 7) ( B2 ) a (Ca-CN a B ec au c th e flow i i ocn crgctic Th e 10 in av ailable ener gy is mea m ed by the h e at- di ipa,tion int gml th e approximat s olution is s

10 s p er slug of fluid = r Td (B4)

j SN

L _ l_ _ l ~ ( ~ )

( B9 ) PN (1- t )) ~ l - -yM /(1- k) where S i th e entropy. From th e rmodynami cs

s JT j' P dp I P dp

Equation ( B9 ) i ub s titu ted in e quation (B ) toge th er Td = cp dT - - =cp( T - T N) - - ( B5 ) SN TN P.v P PN P

l

with p/P N= 1 for the fir t fa ct or to obtain t he a pproximat e an we I' The mom e ntum equation for compon nt s along th e ascade rec/uce to ( B6 ) p

The in tegral r dp i approximat ed by

j PN P p ( BID )

r dp =1:. (1:.+ 2. ) (P- P N) ( B7 )

j PN P 2 P PN From eq uation ( B2 ) REFER E ES p 2 a 1. Sinn et te, John T ., Jr. , Schey, 0 c ar W. , and Kin g, J . Au st in : P er-

r dp = P- PN (1 + L ) = c ( :N -1 ) (1 +L)

j PN P 2p PN 2 I-t/ P N formanc e of "ACA Eigh t-Stage Axial-Fl ow Com pr e s or D e igned on th e Ba i of Airfoil Th or y . NACA Rep. No . 75 , 1943.

2. ilm ette , John T ., Jr., and Vos , William J.: E x te n ion of U eful ubstitution of till relation as well as eq us tion s (B3) Operating Rang e of Axial -Flow Compr essors by se of Adju t- and ( B6 ) into e quation ( B5 ) give able ta t or Blade. ACA ACR No . E6E02 , 1946.

3. King , J . Austi n, and R e gan, Owen W .: P erfo rman ce of N ACA 2 2 2 a a Eigh t- tag e Axial-Flow Compr e or a t imula te d Al t it ud es.

f Td = C .N -C Ca (L. _l _ _ 1)(I+ L)

2 2 P N I - t/ PN ACA ACR "0. E4L21, 1944.

4. Stodola, A. : St e am and Ga s Turbin e . Vol. II . M c Graw-Hill Th e quantity C a.N i e liminat ed by means of the c ontinuity Book Co. , In c ., 1927, pp . 992- 994. (R eprin Le d, P eL e l' mi th ( ew York ), 1 9<15. ) eqnation ( Bl ) U. S, GOVERN MENT PRINTING OFFICE : 1 94$1

y

z Positive directions of axes and angles (forces and moments) are shown by arrows Angle Velocities Axis Moment about axis Force (parallel Linear to axis) Sym- Sym- Positive Designa- Sym- (compo- Designation symbol Designation Angular bol bol direction tion bol nent along axis) Rolling _____ __ RoIL _ ______ LongitudinaL ______ X L Y---tZ X u p cf> LateraL ___ _ ___ _ ______ Pitching _ __ _ __ Pitch _ ____ _ __ Y Y M Z---tX v g N ormaL _____________ Yawing _ __ _ ___ Yaw __ ______ Z Z N X~Y y., w r Absolute coefficients of moment Angle of set of control surface (relative to neutral

L M position), o. (Indicate surface by proper subscript.)

0,= qbS Om= qcS (rolling) (pitching) 4. PROPELLER SYMBOLS Diameter D p

Power, absolute coefficient Op= ~D6

Geometric pitch pn P Pitch ratio 5 j--VS plD O. Speed-power coefficient=-V ~n2 Inflow velocity

V'

Slipstream velocity V.

Efficiency Revolutions per second, rps n

T Thrust, absolute coefficient OT= ;D4

pn Effective helix angle=tan-1(z.!:.n)

Q Torque, absolute coefficient OQ= 9n.~

pnLF 5. NUMERICAL RELATIONS 1 hp=76.04 kg-m/s=550 ft-lb/sec 1 lb=0.4536 kg 1 metric horsepower=O.9863 hp 1 kg=2.2046 lb 1 mi=1,609 . 35 m=5,280 ft 1 mph=0.4470 mps 1 m=3.2808 ft 1 mps=Z.2369 mph