1982012282staticperformance Sern

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TECH LIBRARY KAFB, NM

NASATechnicalPaper19621982

National Aeronauticsana Space Administrat ionScientific and TecnnicalInformation Branch

I1111111111Ill1lllIIIII1111I11111Ill

Static Internal Performanceof Single Expansion-RampNozzles With ThrustVectoring and ReversingRichard J. Reand Bobby L. BerrierLan gley Research CenterHampton Virginia


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SUMMARYA n investigation has been conducted at static conditions (wind off) in the

static-test facility of the Langley 16-Foot Transonic Tunnel. The effects of geo-metric design parameters on the internal performance of nonaxisymmetric singleexpansion-ramp nozzles were investigated at nozzle pressure ratios up to approxi-mately 10. Forward-flight (cruise), vectored-thrust, and reversed-thrust nozzleoperating modes were investigated.The results of this investigation indicate that single expansion-ramp nozzlepeak (on design) performance is not as high as peak performance for comparable non-axisymmetric convergent-divergent nozzles. However, at off-design nozzle pressureratios, single expansion-ramp nozzle performance is significantly higher than non-axisymmetric convergent-divergent nozzle performance. Test results also show that athrust-vectoring concept utilizing upper and lower nozzle flaps was a much moreeffective flow-turning device than a thrust-vectoring concept utilizing only a single

flap near the trailing edge of the upper expansion ramp. A l l thrust-reverser con-figurations investigated produced significant levels of reverse thrust, however, onlyone exhaust-flow blocker position provided a minimal normal-force component ofthrust.

INTRODUCTIONSince the advent of the turbojet engine, exhaust nozzles have traditionally beencircular in cross section to facilitate integration with the engine. Extensivedevelopment of the "round" nozzle concept has resulted in structurally and thermallyefficient exhaust systems with high internal performance. However, experimentalinvestigations (refs. 1 to 3) on current twin-engine fighter aircraft have shown that

sizable airplane performance penalties are associated with the installation of theexhaust system into the airframe. Most of the external installation penalty, formultiengine aircraft, probably results from the integration of "round" nozzles into a"rectangular" afterbody. (See ref. 4 . ) These configurations inherently have boat-tailed "gutter" interfairings or base regions on the afterbody.Recent studies on twin-engine fighter airplanes (refs. 5 to 13) have identifiedpotential benefits of nonaxisymmetric or two-dimensional nozzles. This nozzle con-cept is geometrically amenable to improved capability in the areas of improvedintegration for installed drag reduction; thrust vectoring for maneuver enhancementand short-field take-off and landing (STOL); and thrust reversing for improvedagility, ground handling, and reduced landing ground roll. One of the most promisingtypes of nonaxisymmetric nozzles identified in recent years is the single expansion-

ramp nozzle (SERN) (refs. 8 and 13 to 23). The SERN was originally developed with ajet deflector to provide high vector angles (up to llOo) for vertical take-off andlanding (VTOL) operations (refs. 15 to 18 and 20). However, system studies and windtunnel tests. have shown that the SERN is also competitive with other nozzle typesduring cruise and combat operating modes (refs. 8, 13, and 21 to 23). If conven-tional or moderate STOL performance is desired, the jet deflector can be removed fromthe SERN design to reduce nozzle weight and low vector angles can be achieved bydeflection of the nozzle expansion surfaces. Most of the experimental investigationsconducted on the SERN have concentrated on quantifying the uninstalled and installed


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performance of a s p e c i f i c n oz zl e des ign a t v a r i o u s n o z z l e p o w e r s e t t i n g s d u r in gc r u i s e and v e c t o r e d - t h r u s t o p e r a t i n g modes. T he se i n v e s t i g a t i o n s d i d n o t i n c l u d e ae v e r s e - t h r u s t o p e r a t i n g mode f o r t h e SERN. U n ti l now, l i t t l e e f f o r t h a s b ee nexpended on providing parametric data on the geometric v a r i a b l e s of i n t e r n a l n oz z ledes ign which could l ea d t o improved SERN des igns wi th h igh er performance and/or l o w es t r u c t u r a l w e ig h t. The e f f e c t of s i d e w a l l geometry on SERN performance i s r e p o r t e di n r e f e r e nc e 19 and a l i m i t e d amount of data on t h e e f f e c t o f nozzle aspect r a t i o onSERN performance i s c o n t a i n e d i n r e f e r e n c e 21.

T h i s p a p e r p r e s e n t s s t a t i c in te rn a l per formance of s in g le expansion-ramp noz zlesw i th ge o m et ri es r e p r e s e n t a t i v e of c r u i s e , v e c t o r e d - t h r u s t , a nd r e v e r s e d - t h r u s t oper-a t i n g modes. The e f f e c t s o f nozzle expans ion r a t i o , lower- f l ap l eng th , lower- f l apd i ve rgence ang l e , a nd s i d e w a l l c u t ba c k on i n t e r n a l pe rf or m an ce a r e p r e s e n t e d f o r t h ec r u i s e o r f o r w a r d - f l i g h t o p e r a t i n g mode. Two t h ru s t -vec t o r i ng s chemes w e r e i n v e s t i -ga ted a t des ign t h ru s t -ve c t o r ang l e s f r o m - loo t o 20.i s p r e s e n t e d a t a d e si g n t h r u s t - v e c t o r a n g l e e q u a l t o 20. For t h e r e v e r s e - t h r u s tope ra t i n g mode, t he e f f e c t of exhaust -f low b l ocke r pos i t i o n on t h ru s t and normalf o r c e i s p r e s e n t e d . Th i s i n v e s t i g a t i o n w a s c on du ct ed i n t h e s t a t i c - t e s t f a c i l i t y ofth e Langley 16-Foot Transonic Tunnel a t a Mach number of 0 and a t n o z z le p r e s s u r er a t i o s up t o approximately 10.

The e f f e c t o f s i d e w a l l l e n g t h

SYMBOLS AND A B B R E V I A T I O NA l l f o r c e s ( w i th t h e e x ce p ti on o f r e s u l t a n t g r o s s t h r u s t ) and a n g le s a r e

r e f e r r e d t o t h e model c e n t e r l i n e (body a x i s ) . A d e t a i l e d d i s c u s s i o n of t h e d a t a -r educ t i on and ca l i b r a t i o n p rocedu res as w e l l as d e f i n i t i o n s of f o r c e s , a n g l e s, a ndp r o p u l s i o n r e l a t i o n s h i p s us ed h e r e i n c an be fo und i n r e f e r e n c e 14.AR

e( Ae/At 1e( Ae/At 1iAPAtF

Fi

Frheht'2

n o z z l e - t h r o a t aspect ra t io , wt /h tn o z z l e - e x i t a r e a , cme x t e r n a l e x p an si on r a t i o f o r f u l l y e xp an ded f lo w ( A e measured a t endof nozzle expansion r a m p )i n t e r n a l ex pa ns io n r a t i o (A e measured a t end of nozzle lower f l a p )geometric area of reverser-port minimum, c m2

2n o z z l e g e om e tr ic t h r o a t area, cmmeasured th r u s t a long body ax i s , N

r e s u l t a n t g r o s s t h r u s t , v mn o z z l e - e x i t h e i g h t , c mn o z z l e - t h r o a t h e i g h t , cma x i a l l e n g th of n o z z l e f l a p , c m


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a x i a l l e n g t h of u pp er v e c t o r i n g f l a p , cmvfNP

P t , jP,p t or PtRS t a .T t , jwiWPWtX

XtY

Z

e

aY s ta t i cv

S u b s c r i p t s :

measured normal force, Nl oca l s t a t i c p r e s s u r e , Paj e t t o t a l p re s s u r e , Paambien t p r es su re , Papoint numbergas co ns ta nt , 287.3 J/kg-Kmode l s t a t i on , cmj e t t o t a l t e m p e r a t u r e , Ki d e a l mass-f low r a t e , kg/secmeasured mass-f low ra te , kg/secnozzle-throat width, 10.157 cma x i a l d i s t a n c e m easu red f rom n oz z le c on n ec t s t a t i o n ( p o s i t i v edownstream), cml e n g t h f r o m n o z z l e c on n ec t s t a t i o n t o n o z z l e - t h r o a t s t a t i o n , cml a t e r a l d i s t a n c e m ea sure d from model c e n t e r l i n e ( p o s i t i v e t o l e f tl ook i ng ups tr eam) , cmv e r t i c a l d i s t a n c e m ea su re d from model c e n t e r l i n e ( p o s i t i v e u p ) , c mv e r t i c a l d is t a n c e of n o z z l e - f l a p t r a i l i n g e dg e from model c e n t e r l i n e( p o s i t i v e u p ) , cmnozzle-f l ap t e r mi na l d ivergence angle , degr a t i o of s p e c i f i c h e a t s , 1.3997 f o r a i rr e s u l t a n t t h r u s t- v e c t o r a n gl e, t a n f , degd e s i g n t h r u s t - v e c t o r a n g l e m easu red f rom h o r i z o n t a l r e f e r e n c e l i n e( p o s i t i v e f o r downward d e f l e c t i o n a n g l e s ) , d eg

e x t e r n a li n t e r n a ll o w e rupper

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Conf i gurat i on desi gnat i ons:SERN si ngl e expansi on- ramp nozzl eFl , . . . , F6 f orward- f l i ght ( crui se) SERN conf i gurat i onsVF1( 6v) VF2( 6v) VF3( 6) vectored upper - f l ap SEKN conf i gurat i ons wher e6 = Desi gn t hrust - vector angl eV(6) ,V2( 6v) V3( 6) vectored upper - and l ower- f l ap SERN conf i gurat i ons6 = Desi gn thrust - vector angl ehereRl , . . . , E rever sed- t hrust SERN conf i gurat i ons

APPARATUS AND METHODSSt at i c- Test Faci l i t y

Thi s i nvest i gat i on was conducted i n t he st at i c- t est f aci l i t y of t he Langl ey16- Foot Transoni c Tunnel . The test i ng was done i n a roomw th a hi gh cei l i ng wheret he j et coul d exhaust t o atmosphere t hrough a l arge open doorway. Thi s f aci l i t yut i l i zes the same cl ean, dryai r suppl y as t hat used i n the 16- Foot Transoni c Tunneland a si ml ar ai r - cont rol syst em i ncl udi ng val vi ng, f i l t er s, and a heat exchanger(to operate the j et f l ow at const ant st agnati on temperature) . Data were recorded ona 96- channel , magnet i c- t ape data acqui si t i on system

Si ngl e- Engi ne Propul si on- Si mul at i on Syst emA sketch of t he si ngl e- engi ne ai r - powered nacel l e model on whi ch vari ous nozzl eswere mounted i s present ed i n f i gure 1 w t h a typi cal nozzl e conf i gurat i on at tached.The body shel l f orward of st at i on (Sta. ) 52.07 was r emoved f or t hi s i nvest i gat i on.An external hi gh- pressure ai r systemprovi ded a cont i nuous f l ow of cl ean, dryai r at a cont rol l ed temperature of about 300 K. Thi s hi gh- pressure ai r was var i ed upt o approxi matel y 10 atm ( 1 atm = 10 13 kPa) and was brought through the dol l y- mountedsupport st rut by si x tubes whi ch connect t o a hi gh- pressure pl enum chamber. As showni n f i gure 1, the ai r was then di scharged perpendi cul arl y i nt o the model l ow- pressurepl enum through ei ght mul t i hol ed soni c nozzl es equal l y spaced around the hi gh- pressurepl enum Thi s method was desi gned to mni mze any f orces i mposed by the t ransf er ofaxi al moment umas t he ai r i s passed f romt he nonmetr i c hi gh- pressure pl enum tothe met r i c ( mount ed t o the force bal ance) l ow- pressure pl enum Two f l exi bl e metalbel l ows are used as seal s and serve to compensat e f or axi al f orces caused by

pressur i zat i on.The ai r was t hen passed f romt he model l ow- pressure pl enum ( ci r cul ar i n crosssect i on) t hrough a t ransi t i on sect i on, choke pl at e, and i nst rument at i on sect i on whi chwere common f or al l nonaxi symmetr i c nozzl es i nvest i gat ed. The t ransi t i on sect i onprovi ded a smoot h f l ow pat h f or t he ai r f l ow f romthe round l ow- pressure pl enumt o therect angul ar choke pl ate and i nst rument at i on sect i on. The i nst rument ati on sect i on hada f l ow- path w dt h- t o- hei ght rat i o of 1.437 and was i dent i cal i n geomet ry t o t he noz-zl e ai r f l ow ent rance. Al l nozzl e conf i gurat i ons were att ached to the i nst rument at i onsect i on at model st at i on 104.47.

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Nozzle DesignThe single expansion-ramp nozzle ( SERN) is a nonaxisymmetric, variable-area,internal/external expansion exhaust system. A photograph showing a typical SERN testnozzle installed on the single-engine propulsion-simulation system is shown in fig-ure 2. Basic nozzle components consist of (1 ) a 2-D variable-geometry convergent-divergent upper-flap assembly used to vary nozzle power setting (throat area), (2) a

2-D variable lower flap used to vary nozzle expansion ratio Ae/At, and ( 3) a 2-Dupper external expansion ramp. Note that the throat is forward of the variable lowerflap so that the power setting is independent of the lower-flap position orexpansion ratio Ae/At.be found in references 15 and 16. A l l test nozzles had a nominally constant exhaust-f l o w path width of 10.16 cm.interchangeable upper and lower nozzle flaps and sidewalls.

Additional details on nozzle operation and construction canParametric geometry changes were achieved by using

Figure 3 presents sketches showing the geometry of the six cruise or forward-flight SERN configurations tested. Important geometric parameters for these sixconfigurations are summarized in table I. Simulation of a variable lower flap (vari-able expansion ratio Ae/At) at a constant power setting was achieved by testingconfigurations F1, F2, and F3. The internal expansion ratio (Ae/At)i varied from1.097 to 1.391 for these configurations. Configurations F4 and F5 were used to studythe effect of lower-flap geometry changes and configuration F6 was used to investi-gate the effect of sidewall cutback. Configurations F2 and F6 have been previouslytested and data are reported in reference 19 as configurations SR4 and SR2,respectively.

Two thrust-vectoring concepts for SERN were studied during the current investi-gation. The first concept incorporates a variable flap in the trailing edge of the2-D upper external expansion surface. This thrust-vectoring concept results inexternal turning of the supersonic exhaust stream. Figure 4 presents a sketch show-ing the geometry of nozzle configuration vF1(6,), wherethrust-vector angle (which was varied from -100 (up) to 200 (down)). It should benoted that the unvectored or cruise nozzle configuration VFl(0) is nozzle configura-tion F6 shown previously in figure 3. Also shown in figure 4 is the geometry forconfigurations VF2(20) and VF3(20) which were used to investigate the effect ofsidewall length during vectored-thrust operation (6, = 20O).vectoring concept incorporates a variable full-length upper expansion surface used inconjunction with the existing variable lower flap. This thrust-vectoring conceptresults in internal turning of the supersonic exhaust stream. Figure 5 presents asketch of configuration Vl(6,) which simulates this thrust-vectoring concept atdesign thrust-vector angles from -loo to 200. The unvectored or cruise nozzle con-figuration Vl(0) is again configuration F6 shown previously in figure 3. The geom-etry for configurations V2( 20) and V3( 20), which were used to study the effect ofsidewall length during vectored-thrust operation, is also shown in figure 5.

6 equals the .design

The second thrust-

Sketches of SERN configurations in reverse-thrust operating modes are shown inThese configurations simulate a SERN reverse-thrust concept in which theigure 6.upper expansion ramp forms an exhaust-flow blocker .while simultaneously opening areverse-port exit on the nozzle upper surface. A parametric study of the exhaust-flow blocker position, illustrated by the sketches of figure 6(b), was conducted todetermine thrust-reverser efficiency (50-percent reverse thrust suggested as a goalin ref. 14) and potential impact on aircraft stability and control by examiningnormal force generated by each blocker position. The minimum open area of each port

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f or each bl ocker posi t i on i s shown i n f i gure 6(b). For al l bl ocker posi t i ons, thesum of the mni mumpor t areas was great er t han t he upst reamf orward- f l i ght ( crui se)geometr i c t hroat area. The i ncl uded angl e of the bl ocker f ace was 88.750 f or al lconf i gurat i ons. The geomet ry of the bl ocker af t of t he bl ocker f ace i s not i nt endedt o represent t he geometry of actual f l i ght hardware but was desi gned as shown f orease of st at i c- t est hardware f abr i cat i on.

I nst rument at i onA three- component st rai n- gage bal ance was used to measur e t he f or ces and momenton t he model downst reamof st at i on 52.07 cm. ( See f i g. 1 . ) J et t ot al pressure wasmeasured at a f i xed stat i on i n the i nst rument at i on sect i on ( see f i g. 1 ) by means of f our - probe rake through the upper surf ace, a three- probe rake t hrough the si de, anda three- probe rake t hrough the corner . A t hermocoupl e, al so l ocat ed i n t he i nst ru-ment at i on sect i on, was used to measure j et t otal t emperat ure. Mass f l ow of t he

hi gh- pressure ai r suppl i ed t o the nozzl e was determned f rompressure and t emperaturmeasurement s i n t he hi gh- pressure pl enum ( see f i g. 1 ) cal i brat ed w t h st andardaxi symmet r i c nozzl es. I nt ernal st at i c- pressure or i f i ces were l ocat ed on t he nozzl eupper and l ower f l aps and on t he bl ocker of r ever se- t hrust conf i gurat i on R 1 . Typi cai nt ernal st at i c-pressure i nst rument at i on i s i l l ust rat ed i n the sket ches of f i gure 7.Coordi nat es of t he st at i c- pressure or i f ces f or each conf i gurat i on are gi ven i nt abl e 11.

Dat a Reduct i onAl l data were recorded si mul t aneousl y on magneti c tape. Approxi matel y 1 1 f r ameof data, t aken at a r at e of 2 f rames per second, were used for each dat a poi nt;average val ues were used i n comput ati ons. Data were recorded i n an ascendi ng orderof Pt, j w th several r epeat poi nt s bei ng recorded as pt , j was decreased f romthemaxi mumval ue obtai ned. Wth the except i on of r esul t ant g r o s s t hrust Fr , al l f orce

dat a i n t hi s r epor t are ref erenced t o the model cent er l i ne.The basi c perf ormance paramet er used f or the present ati on of r esul t s i s t hei nt ernal t hrust r at i o F/ Fi , whi ch i s the rat i o of the actual nozzl e t hrust ( al ongt he body axi s) t o t he i deal nozzl e thrust. Actual nozzl e t hrust was obt ai ned f romthe bal ance axi al - f orce measurement corrected f or wei ght t ares and bal ance i nt er-act i ons. Al t hough the bel l ows ar rangement was desi gned t o el i mnate pressure andmoment um i nt eract i ons w th t he bal ance, smal l bel l ows t ares on axi al , normal , andpi t ch bal ance component s st i l l exi st. These t ares resul t f r oma smal l pressure di f -f erence bet ween the ends of the bel l ows when i nt ernal vel oci t i es are hi gh and al sosmal l di f f erences i n t he f orward and af t bel l ows spri ng const ant s when the bel l owsare pressur i zed. As di scussed i n ref erence 1 4 , t hese bel l ows t ares were determnedby runni ng. cal i br at i on nozzl es w th known perf ormance over a range of expectednormal f orces and pi t chi ng moment s. The bal ance data were then cor rect ed i n a manne

si m l ar t o t hat di scussed i n ref erence 1 4 .

RESULTS AND DI SCUSSI ONBasi c Data

Basi c dat a f or the SERN conf i gurat i ons i nvest i gat ed are present ed i n f i gures 8to 1 1 . Forward- f l i ght ( crui se) nozzl e dat a are present ed i n f i gure 8 vectored-6


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t h r u s t n o z zl e d a t a a r e p r e s e n t e d i n f i g u r e s 9 an d 10, a nd r e v e r s e d - t h r u s t d a t a a r ep r es e n te d i n f i g u r e 11. N oz zle i n t e r n a l t h r u s t r a t i o F /F i, r e s u l t a n t t h r u s t r a t i oF r / F i , and d is c h a r g e c o e f f i c i e n t wp/wis u r e r a t i o pt l j /pm f o r e ac h c o n f i g u r a t i o n i n v e s t i g a t e d .

a r e p r e s e n t e d a s a fun c t i o n of nozz le pres-

For s i ng le expansion-ramp nozzles , th e exhaust - f l o w expans ion process occursb o th i n t e r n a l l y a nd e x t e r n a l l y . I n t e r n a l ex p an si on o c c u rs from t h e t h r o a t up t h elower- f l ap ex i t . Ex ter na l expans ion occurs downs tream of the lower- f lap e x i t andbetween th e f i xe d upper boundary and th e f r e e ( f r e e s t ream/exhaus t ) lower boundary .Thus, performance i s i n f l u e n c e d by i n t e r n a l a nd e x t e r n a l e x pa ns io n r a t i o s and i sge ne ra l ly ch ar ac te r iz ed by some in d i ca t io n of two per formance peaks. Values of t hen o z z l e p r e s s u r e r a t i o r e q u i r e d f o r f u l l y expan ded f lo w ( d e s i g n ) a r e l i s t e d i n t h ef o l l o w i n g t a b l e f o r e ac h c r u i s e - n o z z l e e x p an si on r a t i o . G e n e ra l ly , f o r n o z z l e s w i t h

i n t e r n a l a nd e x t e r n a l e x pa ns io n r a t i o s , t h e f i r s t peak o c c ur s n ea r t h e d e s ig n p re s -s u r e r a t i o c o rr es p on d in g t o ( A e / A t ) i and i s lower i n magnitude th an t he secondpeak , which occu r s nea r t h e des ign p re s s u r e r a t i o co r re s pondi ng t o ( A e / A t ) e ( s e er e f . 1 9 ) . F or t h e n o z z l e s of t h e c u r r e n t i n v e s t i g a t i o n , t h e p er fo rm a nc e p ea ks arer e l a t i v e l y f l a t o ve r a l a rg e range of nozzle p r es su re r a t i o s when compared t o t y p i c a lconvergent -d ivergen t nozzles . As e xp ec te d, t h r u s t v e c t o r i n g d e c r e a s es t h e i n t e r n a lt h r u s t r a t i o F /F i (com pare f i g s . 9 and 10 t o f i g . 8 ( f ) ) s i n c e t h e t h r u s t v ec t o r i sb e i n g t u r n e d away f rom t h e a x i a l d i r e c t i o n a nd a l l r e v e r s e - t h r u s t c o n f i g u r a t i o n sp ro du ce n e g a t iv e v a l u e s of i n t e r n a l t h r u s t r a t i o ( s e e f i g . 1 1 ) .

The r e s u l t a n t t h r u s t r a t i o , shown by das hed l i n e s i n f i gu re s 8 t o 11, i s equalt o t h e i n t e r n a l t h r u s t r a t i o when t h e t h r u s t v e c t o r i s a l i g n e d w ith t h e t h r u s t o rbody a x i s . S i g n i f i c a n t d i f f e r e n c e s ca n be n o te d b etw ee n t h e i n t e r n a l and r e s u l t a n tt h r u s t r a t i o s shown i n f i g u r e s 8 t o 11, n o t o n ly f o r t h e v e c t o r e d - t h r u s t SERN b u ta l s o f o r t h e f or wa rd -f l i g h t ( u n ve c to r e d) c o n f i g u r a t i o n s shown i n f i g u r e 8. Thise f f e c t i s caused by changing wave pa t t e r ns impinging on th e expans ion su r fa ce s asn o z z l e p r e s s u r e r a t i o v a r i e s a nd t h e un eq ua l n orm al p r o j e c t e d areas of t h e upper andl o w e r f l a p s . Wave p a t t e r n s ( a n d r e s u l t i n g i n c l i n a t i o n of t h e e xh a u st stream) f o runderex panded and overexpan ded SERN ty pe n oz zl es are i l l u s t r a t e d i n r e f er en c e 24.R e s u lt a nt th r u s t- v e c to r a n g le c h a r a c t e r i s t i c s f o r SERN c o n f i g u r a t i o n s w i l l b e d i s -c u s s e d i n a l a t e r s e c t i o n of t h i s r e p o r t .

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M eas ured va l ues o f d i s c ha rge co e f f i c i e n t w p/w i are , as expected , less t h a n1 .0 for a l l n o z z l e s t e s t ed a nd , e x c ep t f o r t h e r e v e r s e - t h r u s t c o n f i g u r a t i o n s showni n f i g u r e 11, a re r e l a t i v e l y i n de pe nd en t of n o z z le p r e s s u r e r a t i o above t h e v a l ue f ochoked flow (ptvis co us effect s' imomentum and vena co nt ra c t a losses) which r educ e t h e amount of f l o wpas s i ng t hrough t h e t h ro a t . The re fore , t he s oni c -f l ow a r ea i s p r o p o r t i o n a t e l y l e s st h a n t h e g e o m et ri c t h r o a t area At by the r a t i o of measured mass-flow r a t e t o i d e a lmass - f low ra te w / w i . As shown i n f ig ur e 11, the m e a s u r e d d i s c h a r g e c o e f f i c i e n t sf o r t h e r e v e r s e - t E r u s t n o z z l e s are s u b s t a n t i a l l y l o w e r ( p a r t i c u l a r l y c o n f ig u r a ti o n sR1, R3, and R4) than tho se measured f o r th e forw ar d- fl ig ht and ve cto re d SERN c o n f i g -u r a t i o n s a n d are no t i ndependent of nozz l e p re s s u re r a t i o . The l o w values o f d i s -c h ar ge c o e f f i c i e n t i n d i c a t e a sonic-f low area which i s s u b s t a n t i a l l y less t h a n t h egeometric t h r o a t area u se d t o compute ideal mass-f low r a t ed i s c h a r g e c o e f f i c i e n t w it h n o z zl e p r e s s u r e r a t i o i n d i c a t e s a change i n th e son ic- f lowa r e a w i t h i n c r e a s i n g n o z z le pressure r a t i o . The minimum geometric flow-passage area( t h r o a t ) f o r t h e r e v e r s e - t h r u s t c o n f ig u r a ti o n s oc c ur s a t t h e same l o c a t i o n as f o r t hfo rwar d - f l i gh t and vec t o red SERN ( i .e . , t h e g e om e tr ic t h r o a t area i s l ess t h a n t h esum of the upper and lower r ev e r s e r e x i t ports ( see f i g . 6 (b ) ) . However , a p o s s i b l ec a us e f o r t h e t r e n d s o f t h e d i s c h a r g e c o e f f i c i e n t , shown i n f i g u r e 11, i s the forma-t i o n of s ep a ra t i on bubbl es on t h e fo rward s u r f ac es of t h e r e v e rs e r e x i t ports as t h eexhaus t f low turns th rough a s h a r p c o r n e r . The e x i s t e n c e o f s e p a r a t i o n b ub b le s a tt h e s e l o c a t i o n s co uld r e s u l t i n smaller f low areas i n t h e e x i t ports and caus e t hes ec o n f i g u r a t i o n s t o choke i n t h e e x i t p o r t s r a t h e r t h an a t t h e g e om e tr ic t h r o a t . Thes i z e of such sep ar a t io n bubbles would probably be dependent on nozzle p r es su re r a t io .

/pa = 1 .8 9 ). D i sc h ar ge c o e f f i c i e n t s l e s s than 1.0 are caused by

w i . T h e v a r i a t i o n of

I n t e r n a l S t a t ic - P r es s u re D i s t r i b u t i o n sI n t e r n a l s t a t i c - p r e s s u r e data are p r e s e n t e d i n t a b u l a t e d f orm i n t ab l e s 111, IV,

and V f o r t h e f o r w a r d - f l i g h t , v e c to r ed , an d r e v e r s e d SERN c o n f i g u r a t i o n s , respec-t i v e l y . T yp ic al i n t e r n a l s t a t ic - p r e s s u r e d i s t r i b u t i o n s a r e p r e s en t e d i n f i g u r e s 12t o 15. The e f f e c t s o f expansi on r a t i o and lower-flap l e n gt h on i n t e r n a l f l a p s t a t i c -pressure d i s t r i b u t i o n s a re shown i n f i g u r e 12. P r e s s u r e d i s t r i b u t i o n l e v e l s on b o thf l a p s ( u p p e r - f l a p g eo metry f i x e d f o r a l l con f i g u ra t i o ns s hown) appea r t o be a func-t i o n of l ower -f l ap d i ve rgence ang l e r a t h e r t han expans i on r a t i o . F l a p s t a t i c p re s-s u r e g e n e r a l l y d e c r e a s e s w it h i n c r e a s i n g l o w er - fl a p d i ve r ge n c e a n g l e . S t a t i cpressures nea r th e t r a i l i n g edge of t he upper expansion ramp ( a f t of x / % , ~ J 1.4)on con f ig ura t io n F3 (a, = 13.5O) a c tu al ly produce a fo rc e component i n t he dragd i r e c t i o n as i n d i c a t e d by l o w e r v a l u e s of p / p t , j t h a n p,/pt j . T h is f a c t leadsone t o expec t i nc rea s i n g i n t e rn a l pe rformance w i t h dec reas i ng lower- f l a p divergencea n g l e. Almost i d e n t i c a l p r e s s u r e d i s t r i b u t i o n s w e r e measured on the l o w e r f l a pf o r SERN c o n f i g u r a t i o n s w i t h a lowe r-f lap diverge nce an gl e of approximately 40( c o n f i g u r a t i o n s F2, F4, and F5) even though th e i n te r n a l expans ion r a t i o var i ed f rom1.091 t o 1.389; t h e expan sion r a t i o f o r t h e s e c o n f i g u r a t io n s w a s se t by lower-f lapl e n g t h . S i m i l a r l y , p r e s s u r e d i s t r i b u t i o n s on t h e up pe r e x pa n si on ramp w e r e n e a r l yi d e n t i c a l f o r t h e s e c o n f i g u r a t i o n s up t o x / x t , u 1.4 on t h e u pp er f l a p . A f t oft h i s l o c a t i o n , e xp an sio n-ra mp s t a t i c p r e s s u r e s f o r c o n f i g u r a t i o n F4 ( s h o r t lo we rf l a p ) a r e lower than thos e measured on con f ig ura t io ns F2 and F5 ( lon ger lower f l a p s ) .This t r e n d i n d i c a t e s t h a t i n t e r n a l p er fo rm a nc e mig ht i n c r e a s e w i th i n c r e a s i n g l o w e r -f l a p l en g th . The Mach l i n e (no zzle assumed t o be ope ra t in g a t t h e d e s ig n i n t e r n a lexpansion r a t i o ) o r i g i n a t i n g fro m t h e s h o r t lo w e r -f la p t r a i l i n g ed ge of c o n f i g u r a t i o nF4 i n t e r s ec t s t he uppe r expans i on ramp a t From th e r u le of fo rb idden/xt ,u = 1.4.

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Forward-Fl ight (C ru is e) PerformanceThe e f f e c t s of e x pa n si on r a t i o ( lo w e r- f la p p o s i t i o n ) , l o w er - fl a p l e n g t h , ands i d e w a l l l eng th on s t a t i c in te rn a l per formance of f o rw ard- f l igh t SERN co nf i gu ra t ion sw e r e s t u d i e d d u ri n g t h e c u r r e n t i n v e s t i g a t i o n . A m o r e d e t a i l e d st u d y of s i d e w a l l

con t a i nmen t fo r S E W c o n f i g u r a t i o n s i s r e p o rt e d i n r e f e r e n c e 19. D a t a on configura-t i o n s F2 and F6 are r e p o r t e d i n r e f e r e n c e 19 a s c o n f i g u r a t i o n s SR4 and SR2, respec-t i v e l y . F i gu r e 16 presen t s a comparison of d a t a o b t a i n e d f o r c o n f i g u r a t io n F2 d u r i n gt h e c u r r e n t i n v e s t i g a t i o n w ith d a t a o bt a in e d f o r t h e s a m e c o n f i g u r a t i o n ( SR4) d u r i n gt h e i n v e s t i g a t i o n r e po r te d i n r e f e r e n ce 19. Except a t t h e h i g h e s t n o z zl e p r e s s u r er a t i o s i n v e s ti g a te d , t h r u s t r a t i o and d i s cha rge coe f f i c i en t da t a f rom t he t wo t e s t sagree t o w i t h i n 1/2 p e r c e n t .

E f fe c t o f expansi on r a t io . - The e f f e c t o f e xp a ns io n r a t i o on s t a t i c i n t e r n a lperformance i s p r e s en t e d i n f i g u r e 17. A t n o z z le p r e s s u r e r a t i o s below 7 .0 , t h r u s tr a t i o d e c r e a s e s w it h i n c r e a s i n g ex p an si on r a t i o . S i m i l a r t o o t h e r n o z z le t y p e s , SERNoverexpansion losses a re g r e a t e r a t low n oz z le p r e s s u r e r a t i o s f o r n o z z l e s h a v i n gl a rge expans i on r a t i o s . The r e s u l t s shown i n f i g u r e 17 a t pt ./pa = 5.98 a re con-s i s t e n t w it h t h e i n t e r n a l p r e s s u r e d i s t r i b u t i o n s shown i n f i g u r e 12. A t nozzle pres-s u r e r a t i o s a b o v e 7 .0 , the medium expansion r a t i o SERN ( c o n f i g u r a t i o n F2) producedt h e h i gh e s t t h r u s t r a t i o . A t n o z z l e p r e s s u r e r a t i o s a bo ve t h o s e t e s t e d , t he h i g h e rexpansi on r a t i o SERN con f i gu ra t i o ns ( co n f i gu ra t i on s F2 and F3) would be exp ecte d t oe x h i b i t s i g n i f i c a n t l y h i g h e r p er fo rm a nc e th a n t h e l o w expansion r a t i o SERN (c onf ig u-r a t i o n F1) because of s m al l er underexpansion losses. Figure 18 p r e se n t s t h e e f f e c to f e x pa ns io n r a t i o on r e s u l t a n t t h r u s t - v e c t o r a n g l e G s t a t i c . A s i s obvious fromt h e f i g u r e , s i n g l e ex pa nsio n-ra mp n o z zl e s p ro du ce s i g n i f i c a n t r e s u l t a n t t h r u s t - v e c t o rangles which are dependen t on nozzl e p re s s u re r a t i o , even fo r nozz l e s des igned fo runvectored (6, = Oo ) o p e r a t i o n (see r e f s . 14 and 1 9 ) . A r e s u l t a n t t h r u s t - v e c t o rangle o f Oo occurs a t on l y one nozz l e p re s s u re r a t i o f o r e a ch c o n f i g u r a t i o n t e s t e d .It can be deduced from th e wave pa t t e rn s shown i n r e f e r e n c e 24, t h a t t h i s n o z zl ep r e s s u r e r a t i o s hou ld co r re s pond c l o s e l y t o t h e d e s ig n n o z z le p r e s s u r e r a t i o f o r t h en o z zl e e x t e r n a l e x pa n si on r a t i o . A t a l l o t h e r n o z z l e p r e s s u r e r a t i o s , a t h r u s tper formance pen al t y would be ass oc ia te d wi th th e nonzero va lues o f measured re su l t a n tt h r u s t -v e c t o r a n g le , s i n c e t h e t h r u s t v e c t o r i s tu rn ed away from the t h r u s t (body)ax i s . The magnitude of th i s pe na l ty can be as s e s s ed by comparing i n t e rn a l t h ru s tr a t i o s w ith t h e r e s u l t a n t t h r u s t r a t i o s shown i n f i gu re 8 . Thrus t lo ss es f rom 0 t o1.5 p e r c e n t a r e shown i n f i g u r e 8 f o r t h e r e s u l t a n t t h r u s t - v e c t o r a n g l e s shown i nf i g u r e 18. I n a d d i t i o n t o t h e t h r u s t l o s s e s d i s c u s s e d a bo ve , n on ze ro v a l u e s o fr e s u l t a n t t h r u s t - v e c t o r a n g l e w ould a l s o cause a t h r u s t induced pi tc h in g moment whichmay have t o be trimmed ou t w i th ae rodynamic con t ro l s u r f ac es , or conversely be usedt o augment aerodynamic co n t r o l s u r f ac es f o r a i rp l a ne t r i m , dependi ng on t h e f l i g h tc o n d i t i o n s . These d a t a s u g g e s t a n ee d f o r i n t e g r a t i o n o f a SERN t h r u s t - v e c t o r i n gm echanism i n t o an i n t e g r a t e d f l i g h t / p r o p u l s i o n c o n t r o l s ys te m t o el im in at e unwantedr e s u l t a n t th r u s t - v e c to r a n g l es o r t o o p ti m iz e t h r u s t - v e c t o r a n g l e f o r a p a r t i c u l a ra i r p l a n e f l i g h t c o n d it io n .

87

E ff e c t of lower-f lap geometry.- Figure 19 p r e s e n t s t h e e f f e c t of l o w er - fl a pgeometry on SERN s t a t i c i n t e r n a l p e rf or m an ce a nd f i g u r e 20 p r e s e n t s t h e e f f e c t ofl o w er - fl a p l e n g t h on r e s u l t a n t t h r u s t - v e c t o r a n g le . D a t a a re shown f o r t w o nominallyc o n s ta n t i n t e r n a l e xp an sio n r a t i o s For a c o n s ta n t i n t e r n a lexpans ion r a t i o , i nc rea s i n g lower- f l a p l e n d h ( d e c r e a s i n g lo we r-f l a p divergencea n g l e ) in c r e a se d t h e t h r u s t r a t i o ac r os s t he nozz l e p re s s u re r a t i o r ange shown. Thee f f e c t o f l ower - fl ap geometry on r e s u l t an t t h ru s t -ve c t o r ang l e w a s g e n e r a l l y small.

( A e / A t ) . = 1 . 1 and 1.39.

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Ef f ect of si dewal l l ength. - The ef f ect of si dewal l l ength on stat i c i nt ernalper f ormance i s present ed i n f i gure 21 and on resul t ant thrust - vector angl e i n f i g-ure 22. For t he amount of si dewal l cutback empl oyed i n the current i nvest i gat i on,onl y smal l ef f ects on F/Fi and Gstat i c were measured. Consi st ent w th resul t srepor t ed i n ref erence 19, whi ch examned a broader range of si dewal l geometry, t henozzl e pressure rat i o f or peak F/Fi t ends t o shi f t t o a l ower val ue w th si dewal lcutback. Thi s ef f ect probabl y resul t s f roman ef f ect i ve reduct i on i n ext ernal expan-si on rati o (Ae/ At)e when si dewal l cont ai nment of the exhaust f l ow i s reduced.

Perf ormance compar i son~ ____ w th nonaxi symmet r i c convergent - di vergent nozzl es. - Acompar i son of SERN conf i gurat i on F1, whi ch has hi gh i nt er nal per f or mance, w th t wononaxi symmet r i c convergent - di vergent nozzl es reported i n ref erence 19 ( conf i gura-t i ons C1 and C9) , i s present ed i n f i gure 23. Unl i ke t he SERN, nonaxi symmetr i cconvergent - di vergent nozzl es do not have a f ree- j et boundary and have onl y one per-f ormance peak rel ated t o an i nternal expansi on r at i o %At. Conf i gurat i on C1(ref. 19) has an expansi on rat i o cl ose t o t he i nt ernal expansi on r at i o (Ae/+iof SERN conf i gurat i on F1. Conf i gurat i on C9 ( ref . 19) has an expansi on rat i o cl oseto the ext ernal expansi on rat i o ( At)e of SERN conf i gurat i on F1. The data i nf i gure 23 i ndi cat e t hat SERN i nt ernal per f ormance i s sl i ght l y l ower , general l y l essthan 1/2 percent , t han nonaxi symmet r i c convergent - di vergent nozzl e i nt ernal per f or -mance ( w th si ml ar expansi on rat i os), when operat i ng near the desi gn nozzl e pressurerat i o (2. 97 and 5.41 f or conf i gurat i ons C1 and C9, respect i vel y). However , at of f -desi gn nozzl e pressure rat i os, the SERN conf i gurat i on has si gni f i cant l y l ower over -expansi on l osses than conf i gurat i on C9 ( ref . 19) at l ow nozzl e pressure rat i os, andsi gni f i cant l y l ower underexpansi on l osses than conf i gurat i on C1 ( ref . 19) at hi ghnozzl e pressure rat i os. These data i ndi cate that si ngl e expansi on- ramp nozzl es havehi gh st at i c i nt ernal perf ormance over a broader range of operat i ng nozzl e pressurerat i os than comparabl e nonaxi symmet r i c convergent - di vergent nozzl es. Thi s resul tsuggest s that one mght consi der t he use of a f i xed SERN or one w th l i mted var i abl egeomet ry i n pl ace of a var i abl e- geomet ry convergent - di vergent nozzl e i n order t oreduce wei ght and provi de si mpl i ci t y. For exampl e, i f one consi der s the nonaxi symmet r i c convergent - di vergent nozzl e conf i gurati ons shown i n f i gure 23 t o represent avar i abl e- geomet ry nozzl e desi gn w th an expansi on rati o range f rom 1.089 to 1.397( per f ormance envel ope obtai ned by f ai r i ng a l i ne between two per f ormance peaks), andt he SERN conf i gurat i on t o represent a f i xed- geomet ry nozzl e desi gn, i t i s apparentthat SERN per f ormance i s onl y 0.2 to 1.6 percent l ower t han the convergent - di vergentnozzl e per f ormance t hroughout t he nozzl e pressure r ati o range. Thi s perf ormancepenal t y coul d be t raded f or si mpl i ci t y and reduced wei ght .

Vectored- Thrust Per f ormanceAf t - f l ap thrust vectori ng. - The ef f ect on t hrust r at i o of thrust vector i ng bydef l ect i on of an upper , af t f l ap on the SERN expansi on ramp i s presented i n f i g-ure 24. As expect ed, t he hi ghest i nternal perf ormance was obt ai ned on t he unvectored(6, = O o ) or f orward- f l i ght SERN conf i gurat i on. Thrust r at i o was decreased by ei ther

negat i ve or posi t i ve f l ap def l ect i ons ( posi t i ve def l ect i on def i ned as t rai l i ng edgedown i n order to produce posi t i ve thrust - vector component i n the normal - f orce di rec-ti on). The loss i n t hrust rat i o dur i ng vectored- thrust operat i on resul t s f romt wosources. Fi arst, dur i ng vectored- t hrust operat i on, the thrust vector i s turned awayf romthe body or thrust axi s. Thi s l o s s i s merel y a t r i gonomet r i c f unct i on of t heresul t ant t hrust - vector angl e. An appreci at i on of the magni tude of t hi s l oss can be

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ob t a i ne d by compari ng t h r u s t r a t i o w it h t h e r e s u l t a n t t h r u s t - r a t i o d a t a i n f i g u r e 9.The second source f o r t h r u s t loss d u r i ng v e c t o r e d - t h r u s t o p e r a t i o n i s exhaust-f lows e p a r a t i o n a nd /o r l o w e r pressures on t h e f l a p . For p o s i t i v e f l a p d e f l e c t i o n s , t u r n -t u r n i n g losses. F or n e g a t iv e f l a p d e f l e c t i o n s , t u r n i n g losses r e s u l t f rom f l owi n g losses r e s u l t f r o m a s h o c k o r i g i n a t i n g a t t h e f l a p hi ng e l i n e . A n a p p r e c i a t i o nof t h e magnitude of t h i s loss can be o b t a i n e d by c om pa rin g t h e r e s u l t a n t t h r u s t - r a t i od a t a i n f i g u r e s 9 ( c ) and 9 ( d ) wi th r e s u l t a n t t h r u s t - r a t i o d a t a f o r t h e u n ve cto re don r e s u l t a n t t h r u s t - v e c t o r a n g l e i s shown i n f i g u r e 2 5 . A s e x p e c t e d , r e s u l t a n t( SV = O o ) c o n f i g u r a t i o n F6 i n f i g u r e 8 ( f 1t h r u s t - v e c t o r a n g l e i n c r e a s e s w i t h i n c r e a s i n g d e s i g n t h r u s t - v e c t o r a n g l e .

The e f f e c t of d e s i g n t h r u s t - v e c t o r a n g l e

Upper- and lower-flap t h ru s t vec to r i ng .- F i gu r es 26 and 27 p r e s en t the e f f e c t ofupper- and lower-f lap t h r u s t v e c t o r i n g ( d e f l e c t i o n ) on t h r u s t r a t i o and r e s u l t a n tt h r u s t - v e c t o r a n g l e , r e s p e c t i v e l y . The d a t a t r e n d s f o r t h i s t h r u s t - v e c to r i n g c on ce ptconcept. However, a comparison of the v e c to r e d r e s u l t a n t t h r u s t r a t i o s shown i n f i g -u r e 10 wi t h t he unvect o red ( co n f i g u ra t i on s V l ( 0 ) and F6 are i d e n t i c a l ) r e s u l t a n tt h r u s t r a t i o s shown i n f i g u r e 8 ( f ) i n d i c a t e s t h a t most of t h e t h r u s t r a t i o loss dur-i n g vectored o p e r a t i o n f o r t h i s c o nc ep t ( u pp er - a nd l ow e r- fl ap d e f l e c t i o n ) r e s u l t sf ro m t u r n i n g t h e t h r u s t v e c t o r away from t h e t h r u s t a x i s ; e xh au st -f lo w t u r n i n g lossesw i th t h i s v e c t o r i n g co n ce p t are s m a l l . The d i f f e r e n c e i n e xh a us t- fl ow t u r n i n g lossesbet ween t h e two t h ru s t - ve c t o r i n g concep t s i s i nd i ca t ed by compari son of t h e r e s u l t a n tt h r u s t r a t i o s f o r e ac h v e c t o r e d c on ce pt ( co mp are f i g . 9 w i th f i g . 1 0 ) .

are s i m i l a r t o t h o s e d i s c u ss e d p r e v i o u s l y f o r t h e u p pe r, a f t - f l a p t h r u s t - v e c t o r i n g

Ef fe c t o f s i dewa l l l eng t h on vec t o re d - t h ru s t pe rformance .- The e f f e c t o f s i de -w a l l l e n g t h on no z z le i n t e r n a l p er fo rm a nc e an d r e s u l t a n t t h r u s t - v e c t o r a n g l e d u r i n gv e c t o r e d - t h r u s t o p e r a t i o n ( 6, = 2 0 ) i s p r es e nt e d i n f i g u r e s 28 and 29 , r e s pe c t i ve l y .Re s u l t s on bo t h t h ru s t -ve c t o r i ng concep t s are shown. Sidewal l l eng th ge ne ra l ly hadonly a s m a l l e f f e c t ( less t h a n 1 p e r c e n t o v e r t h e n o z z le p r e s s u r e - r a t i o r an g e t e s t ed )o n t h r u s t r a t i o f o r e i t h e r t h r u s t - v e c t o r in g c on ce pt ( see f i g . 2 8 ) . A t nozzle pres-s u r e r a t i o s g r e a t e r t h a n 4.0, t he cu t back - s i dewa l l nozz l e s gene r a l l y p roduced t h eh i g h e s t t h r u s t r a t i o s an d t h e e x t en d ed - si de w a ll n o z z l e s g e n e r a l l y p ro du ce d t h e l o w e s tt h r u s t r a t i o s . However, an exami na ti on o f t h e r e s u l t an t t h ru s t r a t i o s shown i n f i g -u re s 9 ( e ) and l O (c ) i n d i c a t e s t h a t t h e h i g h e s t r e s u l t a n t t h r u s t r a t i o s are o b t a i n e dwi t h t he bas e l i ne and ext ended - si dewa l l nozz l e s . These t r ends cou l d on l y occur i ft h e l o n g er - si d ew a l l n o z z l e s p ro du ce d h i g h e r v a l u e s of r e s u l t a n t t h r u s t - v e c t o r a n g le .This r e s u l t , an i n c r e a s e i n r e s u l t a n t t h r u s t - v e c t o r a n g l e w it h i n c r e a s i n g s i d e w a l ll e n g t h , i s c l e a r l y i n d i c a t e d i n f i g u r e 29, p a r t i c u l a r l y f o r t h e a f t , u pp er -f la pt h r u s t - v e c t o r i n g c o n c e p t . This t r en d on t h e upper - and l ower - f lap t h r u s t -ve c t o r i n gconcept w a s i n d i c a t e d by t h e i n t e r n a l s t a t i c - p r e s s u r e d i s t r i b u t i o n s shown i n f i g -u re 14 and d i s cus s ed p re v i ou s l y . Thus, a l t hough h i ghe r va l ue s o f t h ru s t r a t i o can beob t a i ned w i t h cut back s i d ew a l l s a t a g i ven va l ue o f des ign t h ru s t -v ec t o r ang l e , al o w e r r e s u l t a n t t h r u s t - v e c t o r a n g l e ( an d t h u s no rm al f o r c e or l i f t ) i s a l s o o b t a i n e d .To ach ieve a g iv e n l e v e l of r e s u l t a n t t h r u s t - v e c t o r a n g l e w i t h c u tb a ck s i d e w a l l s , al a r g e r v a l u e o f geometric ve cto r an g le must be used and , as d i s c u s s e d p r e v i o u s l y ,l a rge t h r u s t - r a t i o losses w i l l occur.

E f fe c t o f t h ru s t -ve c t o r i ng concept .- A c om p ar is on of t h r u s t r a t i o and r e s u l t a n tt h r u s t r a t i o f o r t h e t w o t h r u s t - v e c t o r in g c o nc e pt s i n v e s t i g a t e d i s p r e s en t e d i n f i g -u re 30.and 20 (down). As e xp ec te d, l a r g e l o s s e s i n a x i a l t h r u s t (see f i g . 30(a ) ) occur a tb o t h n e g a t iv e an d p o s i t i v e v a l u e s of d e s i g n t h r u s t - v e c t o r a n g l e s i n c e the t h r u s tv e c t o r i s t u r n e d away from t h e t h r u s t ( bo dy ) a x i s d u r i n g v e c t o r e d - t h r u s t o p e r a t i o n .R e s u l ta n t t h r u s t - r a t i o d a t a (see f i g . 3 0 ( b )) i n d i c a t e t h a t most of the a x i a l t h r u s tloss f o r t h e u pp er- a nd lo w e r -f la p t h r u s t - v e c t o r i n g c o nc e pt r e s u l t s from t h i s

Comparisons are made a t c o n s t a n t d e s ig n t h r u s t - v e c t o r a n g l e s of - loo ( u p ) -

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e f fe c t . For t h e uppe r - and l ower- f lap t h r u s t -ve c t o r i n g concep t , the r e s u l t a n t t h r u s tr a t i o d u r in g v e c t o r e d o p e r a t i o n ( c o n f i g u r a t i o n s V l (- 1 0) and V l ( 2 0 ) ) i s g e n e r a l l yw i t h i n 1 p e r c e n t of t h e un v ec to r ed ( c o n f i g u r a t i o n V l ( 0 ) ) r e s u l t a n t t h r u s t r a t i o , t h usi n d i c a t i n g o nl y s m a l l i n t e r n a l t h r u s t l o s s e s a s s o c i a t e d w ith t u r n i n g th e e x h au s tflo w. L ar ge r i n t e r n a l t h r u s t lo s s e s , p a r t i c u l a r l y a t 6, = 200 , are i n d i c a t e d by t h er e s u l t a n t t h r u s t r a t i o s f o r t h e upper, a f t -f l a p t h r u s t -v ec t o r i ng concep t . Forexample, a t & = 20 and p t , j /p, = 5, t h e u p pe r, a f t - f l a p t h r u s t - v e c t o r i n g co n ce p ts u f f e r s a 5 -p er ce nt i n t e r n a l t h r u s t loss as compared t o an 0 .8-percen t i n t e rn a lt h r u s t loss f o r t h e upper - and l ower- f lap t h ru s t -v ec t o r i ng concep t . The l a r ge t h r u s tloss f o r t h e up pe r, a f t - f l a p t h r u s t - v e c t o r i n g c on ce pt a t p o s i t i v e d e s ig n t h r u s t -v e c t o r a n g l e s i s probably caused by a sh oc k which o r i g i n a t e s a t t h e f l a p h in g e l i n ea nd ca u se s s t a t i c - p r e s s u r e c ha ng es on t h e a f t f l a p .

F i gu re 31 p re s en t s a comparison a t c o n s t a n t d e s ig n t h r u s t - v e c t o r a n g l e s ofr e s u l t a n t t h r u s t - v e c to r a n g le as a f u n c t i o n of n o z z le p r e s s u r e r a t i o f o r t h e twot h r u s t - v e c t o r i n g c o n ce p t s i n v e s t i g a t e d . F i g ur e 32 p r e s e n t s a s i m i l a r co m pa ris on a tc o n s t a n t n o z zl e p r e s s u r e r a t i o s f o r v a r y i n g d e s i g n t h r u s t - v e c t o r a n g le . D a t a showni n bo th f i g u r e s i n d i c a t e t h a t t h e u pp er - a nd lo w e r -f l ap t h r u s t - v e c t o r i n g c on ce pt i s amuch more ef fe c t i v e f low-turn ing dev ice a t b o t h p o s i t i v e a n d n e g a t i v e d e s i g n t h r u s t -v e c t o r a n g l e s t h a n t h e up p er , a f t - f l a p t h r u s t - v e c t o r i n g c o nc e pt . This r e s u l t w a sa l s o i n d i c a t e d by t h e p r e s s u r e d i s t r i b u t i o n s shown i n f i g u r e 13. A t 6, = 20 , t h eupper a f t - f l a p t h r u s t - v e c t o r i n g c o nc e pt ne ve r r e a l i z e s t h e d e s i g n go a l of a 20r e s u l t a n t th r u s t - v e c t o r a n g l e f o r t h e n oz z le p r e s s u r e r a t i o ra ng e t e s t e d . The d a t ao f f i g u r e 32 can be u s ed t o i nd i c a t e t he des i gn t h ru s t -ve c t o r ang l e r equ i r ed by eacht h r u s t - v e c t o r i n g c o n c e p t t o produce a d e s i r e d r e s u l t a n t t h r u s t - v e c t o r a n g le . F orexample, a tupper, af t -f l a p Ehrus t -vec t o r i ng concep t t o produce the same r e s u l t a n t t h r u st - v e ct o ra n g l e ( l l o ) as a des ign th ru s t - ve c to r ang le of 110 f o r th e upper- and lower- f l apt h r u s t -v ec t o r i ng concept . Thes e des i gn t h r u s t -v ec t o r ang l e s would p roduce a t h r u s tr a t i o o f 0.974 (see f i g . 1 0 ( b ) ) f o r t h e up pe r- a nd lo w e r -f l ap t h r u s t - v e c t o r i n gconcept and a t h r u s t r a t i o of 0.940 (see f i g . 3 0 ( a ) ) f o r t h e u pp er, a f t - f l a p t h r u s t -v e c t o r i n g c on ce pt a t ~ , , ~ / p , 6.0.concept would su f f e r a 3 . - p e rc e n t a x i a l t h r u s t loss t o a ch i e ve t h e same r e s u l t a n tt h r u s t - v e c t o r a n g l e as th e upper- and lower- f lap th r us t -v ec tor ing concept a t t h e t e s tc o n d i t i o n s c i t e d .

p t , . /pa = 6 .0 , a des i gn t h ru s t -v ec t o r ang l e of 200 i s r eq u i r e d by t he

T hus, t h e u p pe r , a f t - f l a p t h r u s t - v e c t o r i n g

E f f e c t of a programmed vector f lap.- As d i s c u s s e d p r e v i o u s l y , a t h r u s t p e n a l tywould be a s s o c i a t ed w it h t h e nonze ro va l ues o f r e s u l t an t t h ru s t -v ec t o r ang l e meas uredon t h e f o rw a r d - f l i g h t n o z z l e c o n f i g u r a t i o n s . I f a t h r u s t - v e c t o r i n g c o n c e p t i sinc luded as p a r t of t he SERN des ign , it can be used i n con junct ion w i th a f l i g h t com-p u t e r t o e l i m i n a t e o r n u l l n o nz er o v a l u e s of r e s u l t a n t t h r u s t - v e c t o r a n g l e d u ri ngc r u i s e f l i g h t . F i g u r e 33 p r e s e n t s a compar is on o f des i gn t h ru s t -v ec t o r ang l e , r e s u l -t a n t t h r u s t - v e c t o r a n g l e , a nd t h r u s t r a t i o f o r SERN c r u i s e c o n f i g u r a t i o n F6 ( o rVF1( 0) with a f i x e d ( 6, = O o ) v e c t o r f l a p an d w it h a va r i ab l e vec t o r f l a p programmedt o n u l l o u t n on ze ro r e s u l t a n t t h r u s t - v e c t o r a n g l e s. The u pp er , a f t - f l a p t h r u s t -vec t o r i ng concep t w a s s e l e c t e d f o r t h i s c o mp ar is on b ec au se d a t a w e r e o b t a i n e d a t mored e s i g n t h r u s t - v e c t o r a n g l e s f o r t h i s t h r u s t - v e c t o r i n g c on ce pt th a n f o r the conceptu t i l i z i n g u pp er a n d l o w e r f l a p s . A s imilar comparison can he made with the upper-and l ower- f lap t h r u s t -v ec t o r i ng concep t bu t more d a t a i n t e r p o l a t i o n w i l l be requ i red .F i gu re 33(aY shows des i gn and r e s u l t an t t h ru s t -v ec t o r ang l e s fo r nozz l e con f i g u ra t i on swi th f ix ed and programmed vec tor f l ap s . The f i xe d ve c to r - f l ap nozzle had a con s tan tdes ign t h ru s t -v ec t o r ang l e o f Oo and p roduced r e s u l t an t t h ru s t -ve c t o r ang l e s from - 8 Ot o about 5 O o v er t h e n o z z l e p r e s s u r e r a t i o r an ge i n v e s t i g a t e d ; t h e s e d a t a w e r e shownp r e v i o u s l y i n f i g u r e 21 ( c o n f i g u r a t i o n F6) a n d f i g u r e 25 ( c o n f i g u r a t i o n VF1( 0) . Theprogrammed vec t o r - f l ap con f i gu ra t i o n (das hed l i n e i n f i g . 33) had a des i gn t h ru s t -

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v e c t o r - f l a p s c h ed u l e w hic h v a r i e d f r o m - lo o t o 9 O and produced a c o n s t a n t r e s u l t a n tt h r u s t - v e c t o r a n g l e e q u a l t o O o o v er t h e n o z z l e p r e s s u r e r a t i o r a n g e i n v e s t i g a t e d ;t h e s e d a t a w e r e o b t a i n e d by i n t e r p o l a t i o n o f t h e d a t a s hown i n f i g u r e 25. A compar-i s o n of t h r u s t r a t i o s f o r t h e s e no z zl e c o n f ig u r a t i o n s i s shown i n f i g u r e 3 3 ( b ) ; d a t af o r t h e f i x e d v e c to r f l a p are shown i n f i g u r e 8 ( f ) ( c o n f i g u r a t i o n F 6) a n d f i g u r e 24( c o n f i g u r a t i o n VFl(0)); d a t a f o r t he programmed ve c t o r f l a p w e r e o b t a i n e d by i n t e r -po l a t i o n o f da t a f rom f i gu re 24. Th rus t r a t i o s fo r t h e p rogrammed vec t o r - f l apcon f i gu ra t i o n r anged f rom 0 t o 0.9 p e r c e n t lo we r th a n t h e f i x e d v e c t o r - f l a p c o n fi g u -r a t i o n . This r e s u l t w a s e x p ec t ed s i n c e t h e d a t a of f i g u r e 24 show t h a t t h e h i g h e s tt h r u s t r a t i o s w e r e always ob ta ine d wi th a d e si gn t h r u s t - v e c t o r a n g l e e q u a l t o 00.The a x i a l t h r u s t g a in a c hi e ve d by e l i m i n a t i n g n on ze ro v a l u e s of r e s u l t a n t t h r u s t -v e c t o r a n g l e i s more th a n o f f s e t by t h e i n t e r n a l t h r u s t l o s s a s s o c i a t e d w i th t u r n i n gt h e exhaus t f low when t he uppe r , a f t - f l a p t h r u s t -ve c t o r i n g concep t i s u t i l i z e d t otrim o u t r e s u l t a n t t h r u s t - v e c t o r a n gl e. The i n e f f i c i e n t t h r u s t- v e c t o r i n g p e r f o r-mance of t h e uppe r, a f t - f l ap t h ru s t -v ec t o r i ng concep t w a s d i s c u s s e d p r e v i o u s l y . Itshould be no t ed t h a t a l t hough t he u s e o f a program med up p er , a f t v e c t o r - f l a p r e s u l t si n a s m a l l t h r u s t p e n a l t y ( l e s s t han 1 pe rc en t ) , t h e norma l t h ru s t -ve c t o r componenth a s been e n t i r e l y e l i m i n a t e d and c ou ld r e s u l t i n a r e d u c t i o n of a i r p l a n e t r i m drag.

D ata f rom r e f e r e n c e 14 i n d i c a t e t h a t it i s p o s s i b l e t o a c hi ev e h i gh e r t h r u s tperformance by u t i l i z i n g a programmed ve ct or ed -t hr us t mechanism on SERN nozz les ;maximum r e s u l t a n t t h r u s t r a t i o w a s a c hi ev e d a t r e s u l t a n t t h r u s t - v e c t o r a n g l e s from-50 t o -7.5O. Examination of f ig ur e 26 in d i ca te s t h a t th e use of the upper- andl o w e r- f la p t h r u s t - v e c t o r i n g co n ce p t t o t r i m o u t n on ze ro r e s u l t a n t t h r u s t - v e c t o ra n g l e s co ul d r e s u l t i n a t h r u s t - r a t i o g a in i n a d d i t i o n t o e l i m i n a t i o n of t h e n orm althrus t -vec tor component . A t P,,*/P, l e s s than 4 .5 , a d e s i g n t h r u s t - v e c t o r a n g l ee q u al t o -100 g e n e r a l l y pr od uc ed h i g h e r t h r u s t r a t i o s t h a n t h e u n v ec t or e d c o n fi g ur a -t i o n . U n f o r t u n a t e l y , a desig n thru st -v ec to r an gle of -5O w a s n o t t e s t e d with t h i st h r u s t - v e c t o r i n g c o n c e p t . The more e f f i c i e n t t h r u s t - v e c t o r i n g p er fo rm an ce of t h i sc on ce pt r e l a t i v e t o t h e u pp er , a f t vec t o r - f l ap concep t has been d i s cus s ed p re v i ou s l y .I n t e r p o l a t i o n of t h e l i m i t e d d a t a shown i n f i g u r e s 26 an d 27 i n d i c a t e s d e s ig n t h r u s t -vec t o r ang l e s f rom abou t - 5 O t o 6 O would be required t o t r i m o u t t h e r e s u l t a n tt h r u s t - v e c t o r a n g l e s shown f o r t h e u n ve c to r ed c o n f i g u r a t i o n a nd t h a t s m a l l t h r u s t -r a t i o improvements do occur a t n o zz le p re s s u r e r a t i o s l e s s than 4.5.

Reversed-Thrust PerformanceThe e f f e c t o f e x t e r n a l ex h au s t- fl ow b l o c k e r p o s i t i o n on t h e i n t e r n a l pe rf or m an ce

of a r e v e r s e d - t h r u s t n o z z l e i s pre s en t ed i n f i gu re 34. The exhaus t -f l ow b l ock e rwould be deployed from th e a f t por ti on of th e upper ramp of th e SERN downstream oft h e fo rwa rd - f l i gh t geometr i c t h r oa t . The r e s u l t i n g uppe r and l ower ports d i f f e r e d i narea and p a ss a ge a n g l e , a nd t h e t o t a l p o r t a r e a w a s g r e a t e r t h an t h e f o r w a r d - f l i g h tg e o m e t r i c t h r o a t ( see f i g . 6 ) .

A l l exhaust -f low b l ock e r po s i t i o ns p roduced u s e fu l amounts of r ev e r s e t h ru s t(where an F/F i value of - 0 - 5 i s c o ns id e re d d e s i r a b l e a t l o w n o z z l e p r e s s u r er a t i o s ) . However, due t o th e d i f f er en ce between upper and lower po r t a r ea s and pas -sage ang les , co ns i de ra t ion mus t be g iven to t he m agni tude of th e normal- force compo-n e n t of t h e r e s u l t a n t t h r u s t w it h t h e de plo ye d b l o c k e r i n e ac h p o s i t i o n . F i g ur e 35p r es e n t s t he e f f e c t o f b l ocke r po s i t i on on meas ured normal fo rce . Con f i gu ra ti on R5(b loc ke r lowered) had the l e a s t impact on normal fo r ce and R4 (b loc ke r ra i s ed ) hadt h e l a r g e s t i m pa ct on n or ma l f o r c e . I n f a c t , c o n f i g u r a t i o n s R2 and R4 pr od uc edenough normal fo rc e t o cause t h e n o zz le p r e s s u r e r a t i o t e s t r an ge t o be t runca t ed due

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t o f or ce bal ance l i mt at i ons i n pi t chi ng moment. I n some appl i cat i ons i t coul d bebenef i ci al to generat e normal f orce dur i ng t hrust r eversal f or aerodynamc t r i mpurposes, however, generati on of a l arge, uncont rol l ed normal - f orce component woul dprobabl y be undesi rabl e.The smal l est amount of reverse thrust was produced by conf i gurati ons R 2 and R4( f i g. 3 4 ) . These conf i gurati ons are the onl y ones t hat gave any i ndi cat i on of chok-

i ng (soni c f l ow on upper ramp onl y) at the f orward- f l i ght geomet r i c t hroat ( seef i g. 15). I n addi t i on, conf i gurat i ons R2 and R4 had t he l argest normal - f orce t hrustcomponents. The l argest amount of reverse t hrust was produced by conf i gurat i on R 3and thi s conf i gurat i on was t he f ur t hest f romchoki ng at t he f orward- f l i ght geomet r i ct hroat ( see f i g. 15). These resul t s tend to i ndi cat e t hat i mproved reverse- thrustper f ormance can be accompl i shed by bl ocki ng and turni ng a l ow vel oci t y exhaust st reamand al l ow ng choked condi t i ons to occur at t he rever ser por t exi ts.Dur i ng the thrust - rever ser i nvest i gat i on, consi derabl e nozzl e vi brat i on wasencount ered and i s probabl y att r i but abl e to f l ow unst eadi ness caused by separat i on att he ent rance corner s of the reverser passages as di scussed i n t he sect i on on i nt ernalstat i c-pressure di st r i but i ons. For practi cal appl i cat i on of thi s t ype of t hrust -reverser ar rangement , vi brat i on woul d have to be el i mnated.The pract i cal i t y of a t hrust reverser i s dependent on possi bl e ef f ects onengi ne (and ai rpl ane) st abi l i t y and not sol el y on t he ef f i ci ent product i on of r eversethrust. A change i n back pressure due to depl oyment of a r everser can resul t i nengi ne st al l or over speed i f the reverser por t area i s not proper l y si zed (seeref . 26).The l i kel i hood of back pressure ef f ects af f ect i ng engi ne st abi l i t y can beassessed by examni ng the di scharge coef f i ci ent whi ch i s a measure of nozzl e nor-mal i zed f l ow rat e at a par t i cul ar nozzl e pressure rat i o. Theref ore, a change i ndi scharge coef f i ci ent , when based on a const ant geometr i c t hroat area, i s t he sameas a change i n f l ow rate unl ess a compensat i ng change i n t hroat area i s made. Thereversed- thrust di scharge coef f i ci ent s present ed i n f i gure 34 are based on the

f orward- f l i ght t hroat area and range f rom0.66 t o 0.94. Conf i gurati ons R2 and R4,whi ch gave an i ndi cat i on of some soni c f l ow at the f orward- f l i ght geomet r i c throat ,have t he hi ghest di scharge coef f i ci ents. Even at t he hi ghest di scharge coef f i ci entof 0.945, t hese conf i gurati ons have about a 3 t o 4 percent l ower f l ow rat e t han at ypi cal f orward- f l i ght SEW. Thi s i ndi cates that a 3- t o 4- percent i ncrease i nreverser t hroat ( soni c) area woul d be necessary to el i mnate an i ncrease i n backpressure on t he engi ne i n the reversed- t hrust mode.The ot her r eversed- t hrust conf i gurat i ons, whi ch as i ndi cat ed by t he i nt ernalpressures are unchoked at t he f orward- f l i ght geomet r i c t hroat , have much l ower di s-char ge coef f i ci ents. Thi s i ndi cat es t hat t he f l ow i s probabl y choked at t he reverserpor t s at a si gni f i cant l y smal l er ef f ecti ve t hroat area than t he f orward- f l i ght geo-met r i c t hroat and that a si gni f i cant i ncrease i n rever ser por t area woul d be requi red

to prevent dr i vi ng the engi ne t oward st al l ( see ref . 26).CONCLUSIONS

A n i nvest i gat i on has been conducted at stat i c condi t i ons ( w nd of f ) i n t hestat i c- test f aci l i ty of t he Langl ey 16- Foot Transoni c Tunnel . The ef f ect s of geo-metr i c desi gn parameters on t he i nt ernal per f ormance of nonaxi symmetr i c si ngl e

15


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expansion-ramp nozzles w e r e i n v e s t i g a t e d a t n o z zl e p r e s s u r e r a t i o s up t o approxi -mate ly 10. Forward - f l i gh t ( c ru i s e ) , VeCtOred- th rUSt, and r ev e r s e d - t h ru s t o pe ra t i ngmodes w e r e i n v e s t i g a t e d . R e s u l ts of t h i s s t u d y i n d i c a t e t h e f o l lo w i n g c o n cl u si o ns :

1. Sin gle expans ion-ramp nozz les have h igh s t a t i c i n t e r n a l p e rf o rm a n ce o v e r a

2. Si dewa l l l eng t h has l i t t l e e f f e c t o n n o z zl e t h r u s t p er fo rm a nc e o r r e s u l t a n tt h r u s t - v e c t o r a n g l e f o r t h e f o r w a r d - f l ig h t ( c r u i s e ) n o z z l e g eo me tr y.

lower-f lap d i ve rgence ang l e .

b r o a d e r r an g e of o p e r a t i n g n o z z l e p r e s s u r e r a t i o s than nonaxisymmetric convergent-d i ve rg en t nozz l e s w i t h comparabl e expans i on r a t i o s .

3. Thrus t r a t i o w a s i n c r e a s e d by i n c r e a s i n g lo w e r - f la p l e n g t h a nd d e c r e a s i n g

4. A t h r u s t - v e c t o r i n g c o n ce p t u t i l i z i n g up pe r a nd l ow e r n o z z l e f l a p s w a s a muchmore e f f e c t i v e f l ow- t u rn i ng dev i ce t han a t h r u s t - v e c t o r i n g c o nc e pt u t i l i z i n g on ly as i n g l e f l a p n e a r t h e t r a i l i n g ed ge of t h e u p pe r e x p a n si o n ramp.

5 . For vec t o r ed - t h ru s t ope ra t i on , r educed s i de wa l l con ta i nment t ended t o r educer e s u l t a n t th r u s t - v e c t o r a n gl e.

6. U s e of a programmed th r us t -v ec tor ing mechanism can e l i m ina te un des i re dr e s u l t a n t t h r u s t - v e c t o r a n g l e s d u r i n g c r u i s e f l i g h t . The e f f e c t of t h e program medv e c t o r f l a p on t h r u s t r a t i o d epends on t h e e f f i c i e n c y of t h e t h r u s t - v e c t o r i n gmechanism. Duri ng t h e cu r re n t i nv es t i g a t i on , s m a l l t h r u s t - r a t i o l o s s e s ( l e s s t h a n1 p e r c e n t ) o c c u r r e d when t h e u p pe r, a f t f l a p w a s u t i l i z e d f o r t h i s p u rp o se . H ow evert h e d a ta i n d i c a t e t h a t small t h r u s t - r a t i o g a i n s may b e p o s s i b l e w i t h t h e more e f f i -c i en t uppe r - and l ower - f l ap t h ru s t - vec t o r i n g concep t .

7 . Duri ng r ev e r s e - t h ru s t ope ra t i on , a l l b l o c k e r p o s i t i o n s t e s t e d p r od uc ed u s e f uamounts of re ve rs e th ru st . However, only t h e l owered b l ocke r p os i t i on had l i t t l eo r no e f f e c t on n or ma l f o r c e . I n a d d i t i o n , a l l e x ha u st -f lo w b l oc k e r p o s i t i o n s t e s t e dp ro d uc e d lo we r d is c h a r g e c o e f f i c i e n t s t h a n t h e f o r w a r d - f l i g h t c o n f i g u r a t i o n s a ndwould require a n i n c r e a s e i n r e v e r s e r p o r t area t o p r e v e n t d r i v i n g t h e e n g in e t ow a rds t a l l .

Langley Research CenterNa t i ona l Aeronau t i c s and space Admi n i s t r a t i onHampton, VA 23665January 20, 1982

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REFERENCES1. Schmeer, J a m e s W.; Lauer, Rodney F., Jr . ; and B e r r i e r , Bobby L.: Performanceof Blow-in-Door E j e c t o r N o z z l e s I n s t a l l e d on a Twin-Jet Variable-Wing-Sweep

F ig h te r A ir p la n e Model. NASA TM X-1383, 1967.2. Reubush, David E.; and Mercer, Charles E.: Ef f e c t s of Nozz le I n t e r f a i r in g Modi-

f i c a t i o n s o n L o n g i t u d i n a l A erodyn am ic C h a r a c t e r i s t i c s of a Twin-Je t , Va r ia b le -Wing-Sweep F i g h t e r Model. NASA TN D-7817, 1975.3. Maiden, Donald L.; and B er r i e r , Bobby L.: E ff ec t of Air frame Mo dif ica t ions on

Lon g i tu d ina l Aerodynam ic C ha r a c t e r i s t i c s of a Fixed-Wing, Twin-Jet F ig h te rA i r p l a n e Model. NASA TM X-2523, 1972.

4. Maiden, Donald L.; and P e t i t , John E.: I n v e s ti g a ti o n of Two-Dimensional WedgeExhaus t Nozz les f o r Advanced Ai rc ra f t . J. A irc r . , vol . 13, no. 10, O c t . 1976,pp. 809-816.

5 . Martens, Richard E.: F-15 Nozzle /Afterbody In te gr a t io n . J. Airc r . , vol. 13,no. 5, May 1976, pp. 327-333.

6. Capone, Francis J.: Summary of P ro pu ls iv e- Li f t Research i n th e Langley 16-Ft.Transonic Tunnel . J. A i r c r . , vol. 13, no. 10, O c t . 1976, pp. 803-808.

7. Hiley, P. E.; Wallace , H. W.; and Booz, D. E.: Nonaxisymmetric Nozz les In s ta l l e di n Advanced F ig h t e r A i r c r a f t . J. A ir cr . , v ol . 13, no. 12, D e c . 1976,pp. 1000-1006.

8. Sedgwick, T. A.: In v e s ti g a t io n of Non-Symmetric Two-Dimensional NozzlesI n s t a l l e d i n Twin -Eng ine T a c t i c a l A i r c r a f t . A I A A Paper N o . 75-1319,Sept.-Oct. 1975.

9. Berrier, Bobby L.; Pa lcza , J. Lawrence; and Rich ey, G. Keith: NonaxisymmetricNozzle Technology Program - A n O v e r v i e w . AIAA Pa pe r 77-1225, Aug. 1977.

10. F-15 2-D Nozzle System In te gr a t io n S tudy. Volume I - Technical Report .NASA CR-145295, 1978.

11. Stevens, H. L.: F-l5/Nonaxisymmetric Nozzle System In te g ra t i o n Study SupportProg ram . NASA CR-135252, 1978.

12. Bergman, D.; Mace, J. L.; and Thayer, E. B.: Non-Axisymmetric Nozzle Conceptsf o r an F-111 T e s t Bed. AI Paper N o . 77-841, J u l y 1977.

13. Wasson, H. R.; H a l l , G. R.; and Pa lcza , J. L.: R e su l t s o f a F e a s i b i l i t y s t ud y t oAdd Canards and ADEN Nozzle t o t h e YF-17. AIAA Pa pe r 77-1227, Aug. 1977.

14. Capone, Fr anc i s J.: S t a t i c Performance of Five Twin-Engine Nonaxisymmetr icNoz zles w ith V ec to ri n g and Rev ersi ng C ap ab il it y . NASA TP-1224, 1978.

15. Lander, J. A.; and Pa lcza , J. Lawrence: Exhaust Nozzle De fle ct or Systems f o rV/STOL Fi gh te r A ir c ra f t . A I A A Paper N o . 74-1169, O c t . 1974.

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Nozzl e (ADEN) Desi gn f or Fut ure Fi ghters. AI AA Paper No. 75- 1318,Sept . -0ct. 1975.7. Nash, D 0. ; Wakeman, T. G; and Pal cza, J . L.: St ruct ural and Cool i ng Aspectsf the ADEN Nonaxi symmetr i c Exhaust Nozzl e. Paper No. 77- GT- 110, Ameri can SOC.

Mech. Ehg., Mar. 1977.18. Schnel l , W C ; Grossman, R L.; and Hof f , G E: Compari son of Non- Axi symmetr i cand Axi symmetr i c NoZZl eS I nst al l ed on a V/ STOL Fi ght er Model . [ Prepr i nt ]770983, SOC. Automot. Ehg., Nov. 1977.19. Berr i er , Bobby L.; and Re, Ri chard J.: Ef f ect of Several Geometr i c Parameters on

NASA TP- 1468, 1979.t he Stat i c I nt ernal Per f ormance of Three Nonaxi symmet r i c Nozzl e Concepts.

0. Schnel l , W C. ; and Grossman, R L.: Vector i ng Non- Axi symmetr i c Nozzl e J etI nduced Ef f ects on a V/ STOL Fi ghter Model . AI AA Paper 78- 1080, J ul y 1978.21. Hut chi nson, R A ; Pet i t , J . E. ; capone, F. J . ; and Whi t taker , R W: I nvest i ga-t i on of Advanced Thrust Vect ori ng Exhaust Syst ems f or H gh Speed Propul si veLi f t. AI M- 80- 1159, J une/ J ul y 1980.22. Hi l ey, P. E.; and Bowers, D L.: Advanced Nozzl e I ntegrat i on f or Supersoni cSt r i ke Fi ghter Appl i cat i on. AI AA- 81- 1441, J ul y 1981.23. Capone, Franci s J . ; Hunt , Br i an L.; and Poth, Greg E.: Subsoni c/ Supersoni c Non-vectored Aeropropul si ve Character i st i cs of Nonaxi symmet r i c Nozzl es I nst al l ed onan F-18 Model . AI AA- 81- 1445, J ul y 1981.24. Fer r i , Antoni o: El ements of Aerodynamcs of Supersoni c Fl ows. Maani l l an Co.,1949, p. 171.25. Von Karman, Theodore: Supersoni c Aerodynamcs - Pr i nci pl es and Appl i cat i ons.J . Aeronaut . Sci . , vol . 14, no. 7, ' J ul y 1947, pp. 373- 409.26. Wl l ard, C . M; Capone, F. J . ; Konarski , M; and St evens, H L.: St at i c per f or -mance of Vectori ng/ Reversi ng Non- Axi symmetr i c Nozzl es. AI AA Paper 77- 840,J ul y 1977.

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C o n f i g u r a t i o nF1F2F3F4F5F6

26.16826.11126.11126.16826.16826.111

TABLE 1.- SUMMARY OF FORWARD-FLIGHT NOZZLE GEOMETRY

1.0971.2151.3911.0911.3891.215

( A / A )e t e1.4071.5101.6651.4761.5581.510

cmf, u8.328.328.328.328.328.32

cmf,Z2.362.362.361.094.012.36

aut deg2.52.52.52.52.52.5

-3.04.0

13.54.44.54.0

A R3.943.953.953.943.943.95

Sidewal lbase l i nebase l i nebasel neba sel i ebase l i necu tback


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TABLE 11.- INTERNAL STATIC-PRESSURE:

0.8880.9541.0081.0631.1291.1841.2501.3161.3831.4491.5221.6061.691

ORIFICE LOCATIONS

0.000XXXXXXXXXXXXX

(a) Configurations F1 and F3

0.500

X

X

. .-Upper flapYl(WtI2>

0.750

X

X~~

XXXX

- .0.450

X

XXXX

XX

0.875

XX

~~

I Lower f l a pI

0.881,9411.0011.0191.0491.0791.1211.1571.199

0.000 0.250

20

Y l (wt/2)0.875 0.950

X

X


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TABLE 11.- Continued(b) Configurations F2, F6, VF1(0),and Vl(0)

x/xt,

0.888.9541.0081.0631.1291.1841.2501.3161.3831.4491.5221.6061.691. .

Upper f l a p

0.000XxXXXXXXXXXXX

Y l (wt/2)0.450

XXXXXXXXXXXXX

0.875XXXXXXXXXXXX

0.8811.0011.0431.0791.127

~1.168

,947

Y 1(wt/2). -0.000 0.450 0.8751

X

21


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

x / x t ,

0 . 888. 9541 . 0 0 81 . 0 6 31 . 1 2 91 . 1 8 41 . 2 5 01 . 3 1 61 . 3 8 31 . 4 4 91 . 5 2 21 . 6 0 61 . 6 9 1

TABLE 11.- Continued( c ) Configuration F4

Y/ Wt 2_____

0.000 0 . 4 5 0 0 . 8 7 5XXX X XXX X XXX X XX X xXXXX X XX 1 X X

I Upper f l a p i

x/ xt, I

0 . 8 8 1. 9 4 1

1 . 0 0 11 . 0 1 91 . 0 4 91 . 0 7 9

Y / Wt 2 )0.000 0 . 2 5 0 0 . 5 0 0 0 . 7 5 0 0 . 8 7 5 0 . 9 5 0

XXX X X X X XXXX _ _ .__

22


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TABLE I1.- Continued( d ) Conf i gu ra t i on F5

. -

X/Xt,u

0 . 8 8 8. 954

1 . 0 0 81 . 0 6 31 . 1 2 91 . 1 8 41 . 2 5 01 . 3 1 61 . 3 8 31 . 4 4 91 . 5 2 21 . 6 0 61 . 6 9 1

~

x/xt,

0.881. 9 4 1

1 . 0 0 11 . 0 1 91 . 0 4 91 . 0 7 91 . 1 2 11 . 1 5 71 . 1 9 91 . 2 5 91 . 3 1 9

-0.000

XXXXXXXXXXX

. .0 . 250

U pp er f l a p.

-0.000

XXXXXXXXXXXXX

Y 1 wt12)~ .

0 . 450 0 . 875

~L o w e r f l a p

Y/ Wt /2)0-5000

XIX1XXX

23


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TABLE I1.- Continued

0.000 0.250XXXX XXXXXX XXXXXXXX XX ____

( e ) Configurations VF1(-10), VF1(-5), VF1(5), VFl(101,and VF1( 20)

0.500

X

X

X~~

x /x t uF-- ~~ 0.750X

X

X

0.888.924.9661.0081.0511.0871.1291.1901.2501.3221.3891.4491.5101.5701.6301.6911.751

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0. 875

X

X

TABLE 11.- Continued(f) Configurations ~l(-lO), Vl(111, Vl(201, V2 20), and V3(20)

0. 950

X

X

x/xt,

0.8880.9240. 9661.0081. 0511.0871.1291.1901. 2501.3221. 3891.4491. 5101. 5701. 6301.6911. 751..._

Upper f l ap

0.000XXXXXXXXXXXXXXXXX*. . . . ..~

0.250

X

X

X~ ~.

0. 500

X

X

X-

0. 750

X

X

X

0. 875

X

X

X

0. 950

X

X

X

. .

I0. 8810. 9411. 0011.0191. 0491. 0791. 1211. 157. 199

0. 750

' *Conf i gurati ons V1(20), V2(20), and V3(20) do not have ori f i cex / x ~ , ~1. 751.n upper f l ap at

25


28/144

TABLE 11.- Concluded4)Conf i gu ra t i ons R1, R2, R3, R4, and R5

xxt, u0.9540.9781.0021.0271 .051

Y/ (wt/2)0 . 0 0 0

XXXXx.

x/xt,L

0.9590.9831.0071 .0311 .055

Bl ocke r s u r f ace*I 11

- - .

Y/ (wt/2)0.000

XXXXX

/ht

0.7450.3450.000

-0.498-0.996-1.345-1.745

*B lo ck er o r i f i c e s o n c o n f i g u r a t i o n R 1 on l y .

0.000XXXXXX

~~ x__

26


29/144

1 1 , 0 0 12 1.9933 2.9944 2.9885 3.9946 4.9837 5.9838 5.9639 6.95510 7.97211 7 . 9 5 112 8 .955

13 9 .95714 9 .87615 9 .9511 6 , 9 9 8

Pt Pt,jlP,1 1 .0012 1 . 9 9 33 2.9944 2.9885 3.994b 4.9837 5.9838 5 .9639 6 .955

10 7.97211 7.95112 8.9551 3 9 . 9 5 714 9.87615 9 .9511 6 . 9 9 8

T A B L E 111.- C O M PU T ER P R I N T O U T O F R A T I O O F I N T E R N A L S T A T I C P R E S S U R E T O J E T T O T ALPRE SSU Re FOR FORWARD-FLIGHT SIN GLE EXPANSION-RAMP NOZZLES

( a ) C o n f i g u r a t i o n F1t.jpper-flap static-pressure ratio, p/p .y/(wt/2) = 0.000

0.888- 9 9 6

792,794.794, 7 9 3.793, 7 9 3,793

792,792-792, 7 9 2.792,792- 7 9 1

1.002

0.954.999- 5 7 2, 5 7 0- 5 7 0,569~ 5 7 0,569,569,570.570,570- 5 7 1, 5 7 1- 5 7 1- 5 7 1

1.002

1.008, 9 9 9,246. 247.247, 2 4 7- 2 4 60 2 4 5,245.245.244. ? 44.244,244.244.244

1.002

1.0631 . 0 0 1,238

. 2 3 7, 2 3 7, 2 3 7, 2 3 7. ? 35, 2 3 5. 2 3 4- 2 3 3. ? 3 3. 233, 2 3 3, 2 3 3.233

1.001

1.129 1.1841 .000 . 999

- 2 8 4 - 3 1 9-289 , 317,289 . 317,290 -315.291 , 314- 2 9 1 , 3 1 3,291 , 314,291 . 313, 2 9 0 , 313- 2 9 0 - 3 1 3.291 . 312,29 1 ~ 3 1 1, 2 9 1 - 3 1 1.291

1.250, 9 9 8

506- 3 2 8- 3 2 8- 3 2 7.326,326, 3 2 6.3? 5- 3 2 5- 3 2 5- 3 2 5, 3 2 5,325, 3 2 5

1.002

1.316 1.383. 997 , 999600 -609

, 3 3 2 -314,332 ,314.331 -314- 3 3 1 -313. 3 3 1 - 3 1 3,331 -313.331 ,313- 3 3 0 ,313,330 - 3 1 3.330 -313.330 , 313- 3 3 0 .313,330 e 3131.004 1.002

Upper-flap static-pressure ratio, p/~,,~-y/(wt/2) = 0.450 P

1.008 1.129 1.250 1.316 1.606 1.691,999 .999 .999- 2 4 5 . 2 8 9 508,245 ,288 . 3 2 7, 2 4 6 . 2 P P . 327-245 .289 ~ 3 2 6-244 , 2 8 8 - 3 2 4, 2 4 3 . 2@7 , 3 2 4, 243 . 7 8 8 , 3 2 4, 242 .287 a 324.241 .286 ,323.241 ,286 , 3 2 4- 2 4 1 - 2 8 6 - 3 2 3-240 .2Ph , 3 2 3, 240 ,286 323.240 . 2 8 6 , 3 2 3

1.001 1.002 1 .002

1 , 0 0 0.bo5, 3 4 1- 3 4 1.339, 3 3 7. 3 3 1.337. 337.337, 3 3 7, 3 3 7. 3 3 7. 3 3 1

1 .003

. 3 3 e

l . @ O O. 561.485- 4 0 6, 217, 210. 211.211.211.211.211. Z l l, 711.212.211

1 .004

.999

.546,432,430.394,171,172,172-177- 1 7 2. I 7 2172- 1 7 2-172.172

1 .001

1.449.999-536-392,395.25v.228-209,210- 1 9 9- 1 9 1- 1 9 1-186-184.185,185

1.003

1.522, 998,562,532,532,269-268, 2 6 8- 2 6 8- 2 6 8,268, 2 6 8.2 68- 2 6 8.268, 2 6 8

1 .003

1.606 '1.691.999, 5 6 1, 4 9 5.496.214- 2 1 4, 2 1 5, 2 1 5, 2 1 5.215, 2 1 5, 2 1 5.215.215.215

1 .002

,999'. 549,427.425- 4 0 0- 1 7 5- 1 7 5- 1 7 5.176-176- 1 7 6,176- 1 7 6, 1 7 6.17b, 9 9 9

1.008 1.129 1.250 1.316 1.606 1.691. 999 , 999, 2 4 8 - 2 8 9.247 , 291,247 . 291, 2 4 6 .2vo.244 , 2 8 8- 2 4 3 , 287, 2 4 3 - 2 8 7, 7 4 2 -286,241 eZR5

241 , 285241 e 284- 2 4 2 , 2 8 3. 2 4 2 , 2 8 3- 2 4 2 .2R4

1 .001 1 .002

.998

.533, 3 2 2, 3 2 2, 3 2 0

. 318- 3 1 8.318

' - 3 1 7.317.317.317.317.317

, 1 . 003

,317

. Q ~ R .99R , 9 9 8, 5 7 9 , 5 5 3 - 5 0 1,376 .457 .334,327 .457 .334,325 .216 .250, 3 2 3 , 2 1 1 , 2 0 1.322 . 211 - 1 6 7- 3 2 2 .211 , 168- 3 2 1 . 2 1 1 - 1 4 4-320 .210 , 1 2 5.3?0 . 210 , 126-320 -205 . 112,319 , 199 . l o oe 319 . z o o .101- 3 1 9 . zoo ,100

1 .002 , 1 .001 , 999


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TABLE 111.- Continued( a ) Concluded

p t P , , , k1 1.0012 1.9933 2.9944 2.9885 3.9946 4.9831 5.9838 5.9639 6.95510 7.97211 7.95112 8.95513 9.95714 9.8761 5 9.95116 ,998

Pt Pt, jlP,1 1.0012 1.9933 2.9944 2.9885 3.9946 4.9837 5.9838 5.9639 6.95510 7.91211 7.95112 8.95513 9.95714 9.87615 9.95116 ~ 9 9 8

Lower-flap static-pressure ratio, p l pyl(wt/2) = 0 . 0 o o d ~

0.881.999- 8 4 6,844.a44.a44.a44,844,844.a44.e44, 8 4 4.e44,845, 8 4 5.a451.001

0.9411.001,740.739.739,739-739.138,738,738.738.738.138.738,7381.001.73a

1.001.99b,614.613.613-611,611-611.611,611.bll,611.611.b11.bll,6111.006

x'xt ,I

1.019 1.0491,001 1.000599 - 5 6 1,591 .563,597 -564591 .563597 . 5 6 2

0 591 563-591 -563# 597 .563.591 -564.597 -564,596 ,565.596 ,566.596 .5 66.596 ,5661.001 1.000

1.0791.000,530528,528.527-528,528- 5 2 8-529-530,530,531,531.531-5311.001

1.121.999,468- 4 6 8- 4 6 8, 4 6 8, 4 6 8- 4 6 8- 4 6 8,469.469.469-469-469-469.4691.002

t , jower-flap static-pressure ratio, plp

*---------- X/Xt,l = 1.001Yl(Wt/2)

0.250 0.500 0.750 0.875 0.950.999. 620,617,617-615,615,615-615-615.615,615,615.b16-615a b 1 51.001

1.005,619,615-615.614,413.6 1 3.613,613-613-613,613.613,612.612,996

1.000,614,610.611- 6 1 0,610,610,610,610,611-611,611.612.612,6121.001

,999,614b o t.bo6.bo2,601600600.599.599,599,599.599,599* 5991.001

,999~ 6 2 3,619-619a61R,618-619619,619a618a618,619.610e 619.6191.002

1.1571.000.411.412- 4 1 2-411-410,410-409-410- 4 1 0.410-410-410-410.4101.001

1.199. 9 w-409,363,363-361-361, 3 6 0e360-360- 3 4 0.360,360.360,360- 3 6 01 . 0 0 2

-IXt,, - 1.121 _____tY/ wt12) 0.875 0.950.250 0.500 0.750,999 1,000.410 o 467.468 ,466- 4 8 .466-468 -464, 4 6 8 . 4 6 4.468 - 4 6 4. 4 6 8 ,464.469 -465.469 -465.469 -465, 4 7 0 ,465.410 e 4 6 6,470 .465,470 -4651.001 1 . 0 0 0

,999470- 4 6 7.468.466-466.46b466.461- 4 6 8.468.469,469-469. 4 69,001

.997,460,456.457.455,455.455,455.455. 4 5 5.455,456. 4 5 7,457.4511 . 0 0 4

1.001,469-466,466-465-465-464-465,465-463. 4 6 3. 463.463- 4 6 3-4631.000

. .


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Pt Pt,,IP,

(b) Configurat ion F2

X'Xt,u

0.888 0.954 1.008 1.063 1.129 1.184 1.250 1.316 1.383 1.449 1.522 1.606 1.691

Upper-flap static-p ressure ratio, p/pt J4 yl(wt/2) = 0.000 t

1234567891011121 314

,9991.9902.9994.0014.9925.9905.9956.9556.9627.9889.0108.9949.9961.000

Pt

567891011121314

1.001.793.794-792.792-791e791-790,790-790e 790,790.7901.001

1.000 1.000 1.001 1.001 1,000 1.000a570 , 2 4 3 229 - 2 5 6 . 2 8 1 ~ 4 2 3,568 ,244 ,228 .261 -263 , 2 4 2a567 ,244 .22R ,263 . 2 6 4 ,241,566 ,243 .22P -2 63 ,263 ,240,566 .242 .227 -263 - 2 6 2 . 2 4 0m566 . 2 4 2 .227 -263 , 262 , 2 4 0-566 .241 . 2 2 6 ,263 . 262 -239e566 . 2 4 1 . 2 2 6 . 2b3 2 6 7 . 2 4 0-566 ,241 .225 .2b3 ,262 .239,566 -240 ,224 -263 ,262 -239-566 . 2 4 0 . 2 2 4 ,263 . 2 6 2 -239-567 ,240 ,224 -263 - 2 6 2 .2391.000 1.000 1.000 .999 .999 1.000

1.001-463-229. 22Re 2 2 6- 2 2 5-225-2252 2 5. 2 2 4- 2 2 4. 2 2 4. 2 2 41.001

1.001 1,001,551 .595-237 ,389-233 .227e 232 ,227-231 , 226-231 . 2 2 6-230 - 2 2 6-230 -226.?29 -225-229 -225-229 - 2 2 51.001 1.001

e230 ,225

1.001. 5 8 5, 4 2 8- 2 1 7,217-216.216,216-216e216-216-216,2161.000

1.000 1.006-569 - 5 5 2,494 -469. 2 0 5 -335-205 e192-205 ,192-205 ,192- 2 0 5 ,192e205 e192-206 ,192,206 e192- 2 0 6 e1931.001 .997

. 2 0 5 -192

I Upper-flap static-pressure ratio, p/p t.jd */(wt/2) = 0.450.

.999 1.0001.990 ,7932.999 ,7934.001 .7934.992 -7 925.990 ,7925.995 ,7926.955 -7926.962 7927.988 .7929.010 -7918.994 ,7919.996 .7911.000 1.000

0.9541.004,580.577-576,576,576,576,576,576.576,576.5761.001

,578

1.0081 o o o. 242,241-240-239,238,238-237,237.237~,236.236, 2 3 61.000

1.0631.001-229229,229.229, 2 2 8,228,227,227.227~,227, 2 2 6- 2 2 61.001

1.1291.001.262, 2 6 2- 2 6 2.Zbl, 2 6 0,260

a 2 6 0, 2 6 0-259-259-259,2591 ooo

1.184 1.2501.000 1.000, 2 6 5 ,421.263 . 2 4 4. 2 6 2 243- 2 6 0 .242.259 -241.259 . 2 4 1,259 -241-259 ,241- 2 5 8 . 2 4 0-258 -240. 2 5 8 .240,258 2 4 01.000 1.000

1.3161.000,475-234- 2 3 3-232.232,232.232.232-232.232,2321,001

233

1.3831.001,577,238.23t,237.?37,237-237- 2 3 7- 2 3 7,236.237,2371,000

1.4491.000,593.385-234,233-233-233-233-233,233,233-233,2331.000

1.5221.001,575.440-217s216- 2 1 6

e 2 1 6.215-216. 2 1 5,215-2152 1 51.001

1.6061.001,565,506,205-204-203203e203.to3.202.202.202,2021.001

1.6911.001-546- 4 5 6e351-186.186,185-185-185-185,185,185,1861,000


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W

Pt Pt.jlPm

TABLE 111.- Continued

0.888 0.954 1.008 1.129 1.184 1.250 1.316 1.383 1.449 1.522 1.606 1.691

(b) Continued

.jpper-flap static-pressure ratio, p/pt 1\ y/(wt/2) = 0.875XIX,, u

12345618910111 21 31 4

, 9 9 91 . 9 9 02 9994 . 0 0 14.9925.9905.9956.9556.9627.9889 . 0 1 08 . 9 9 49 . 9 9 61.000

. 9 9 9 1 . 0 0 17 9 0 , 5 6 8,789 ,564,788 ,562, 7 8 7 , 5 6 1, 7 6 7 -5 6 0. 7 8 7 -5 6 0.187 .559-7 8 7 . 5 5 9.786 .559-7 8 6 . 5 5 8. 7 8 t , 5 5 8,786 .5581.001 1.000

1.000, 247.246.245- 2 4 2-241. 2 4 1,240,240- 2 4 0.?39- 2 3 9,2391 ooo

1 . 0 0 1.25P- 2 5 8.257- 2 5 6,255,255,254.255,254.253.253.2531.000

1.001.266.262, 2 6 1, 2 6 1.260- 2 6 0.260n260. 259,259- 2 5 9- 2 5 91 ooo

1 . 0 0 1.433,240.239,238, 237- 2 3 7,237.237- 2 3 7.236,236.2361 . 0 0 1

1 . 0 0 0,498- 2 3 4- 2 3 3, 2 3 2, 2 3 1- 2 3 1.230.230- 2 3 0- 2 3 0- 7 3 0, 2 2 91 . 0 0 1

Lower-flap static-pressure ratio, p/py/(wt/2) = 0.000

XIX,, 1

Pt Pt,j/P, I 0.881 0.947 1.001 1.043 1.079 1.127 1.168 I12345618910111 21 3

1 4

, 9991 . 9 9 02.9994 . 0 0 14.9925 . 9 9 05.9956.9556 . 9 6 27.9889.0108 . 9 9 49 . 9 9 61.000

, 9 9 8- 8 4 2,840.840- 8 4 0- 8 4 0.E40- 8 4 0, 8 4 0.E41.E41, 8 4 1, 8 4 11 . 0 0 4

1 . 0 0 4- 6 9 5- 6 9 3, 6 9 2-690, 689.689,689,689~ 6 8 6,688,688e687,998

.9985 2 9- 5 2 8- 5 2 7- 5 2 7. 5 2 1.527. 5 2 1. 527- 5 2 7,527,527- 5 2 71.003

1 . 0 0 1,434.433, 4 3 3. 433,433,433.433.433,432.432- 4 3 2,4321.000

1 . 0 0 1,423, 4 2 3, 4 2 1- 4 2 0- 4 2 0,420- 4 2 0. 420.421~ 4 2 1, 4 2 1, 4 2 11 . 0 0 1

1 , 0 0 0,376.314,372,370.310,370, 3 7 03 7 0, 3 7 0, 3 7 0.310,3701 . 0 0 0

1 . 0 0 0.3343 3 4, 3 3 3, 3 3 3.333,333.333.333.333,333.333,3341.000

1 . 0 0 1.5332 3 4.233- 2 3 2- 2 3 1- 2 3 1- 2 3 1- 2 3 1-230,230- 2 2 91.000

2 3 0

1 . 0 0 1, 5 6 0- 3 8 0,230-230- 2 9 9- 2 2 9- 7 2 9-229- 2 7 9,229, 2281 . 0 0 1

2 2 9

1.000- 5 6 2.445,215, 2 1 4, 2 1 4, 2 1 4,213- 2 1 3, 2 1 3,213- 2 1 3.212.999

1 . 0 0 1- 5 5 6459.2b4e 2 0 3. 202,202, 202. 2 0 2.t02, 2 0 2, 2 0 2, 2021 . 0 0 0

1.000.537.434. 3 4 5.19b.188.188,187,187,187,187- 1 8 7,1871 . 0 0 1


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Lower-flap static-pressure ratio, PIP,, j- y/(wt/2) = 0875~-X/xt, 1

k

Pt Ptyj/P, 0.881 0.947 1.001 1.043 1.079 1.127 1.168

(b) Concluded

1 .9992 1.9903 2.9994 4.0015 4.9926 5.9907 5.9958 6.9559 6.96210 7.98811 9.01012 8.9941 3 9.99614 le000

1.000e 8 3 2.833.e338 3 4. e 3 3. e 3 3. e 3 3,833,833.e33. a 3 3e 8 3 21 ooo

ower-flap static-pressure ratio, p/pt ,j

1/(wt/2) = 0.4500.947 1.001 1.043 1.079 1.127 1.168.999- 7 0 3e7020 7 0 27 0 1e700700- 7 0 070C.699

e 6 9 9.e99.e991.001

1.001e 5 3 3530m 5285275260 5 2 6526526e 5 2 60 5 2 6,526- 5 2 51.001

1.002,432,430426e 424- 4 2 4424e 4 2 3e423.423

e 423423- 4 2 41 coo

1.000.423e420- 4 1 8a417- 4 1 6e416e410- 4 1 6- 4 1 6e416- 4 1 6- 4 1 61.000

1 e 000e 3 8 2e381.3R1a380- 3 8 0380380

m 3 8 03803R0380e3811.001

1.001. 3 3 5336.334333a 3 3 3.333.333.333e 3 3 3. 3 3 3,333.3341 000

1 .9992 1.9903 2.9994 4.0015 4.9926 5.9907 5.9958 6.9559 6.962.10 7.98811 9.01012 8.99413 9.99614 1.000

1 ooo.844e844, 8 4 4.844, 8 4 4.844.844.844eP44e844.e441 eOG2

1982012282staticperformance Sern

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