New Image - ONLY - Scan to PDF/67531/metadc60594/m2/1/high_res_d/19930088292.pdfTheoretical...

NACA RM E54F22a

NATIONAL ADVISORY COMMITTEE FOR AEBONAUTICS

RESEARCH MEMORANDUM

ANALYSIS OF ROCKET, RAM-JET, AND TURBOJET ENGINES FOR

SUPERSONIC PROPULSION OF LONG-RANGE MISSIUS

I - ROCKET-ENGINE PERFORMANCE

By Vearl N. Huff and Jack Kerrebrock

SUMMARY h

Theoretical performance charac te r i s t i c s and estimates of e f fec t ive spec i f i c impulse and weight a re presented f o r rocket engines serving both as main and as booster power p lan t s f o r t he missi les studied i n t h i s s e r i e s of repor ts . The propellants considered a r e JP4-oxygen and ammonia-fluorine. The t heo re t i c a l performance i s presented f o r a range of fuel-oxidant r a t i o s , expansion r a t i o s from 20 t o 300, and chamber pressures from 300 t o 1200 pounds per square inch absolute. Effect ive spec i f i c impulse i s estimated f o r t he fuel-oxidant mixture r a t i o t h a t gives near-maximum spec i f i c impulse f o r each propellant over a range of operating a l t i t udes from sea l e v e l t o i n f i n i t y (ze- ?o ambient pressure) f o r various engines designed f o r chamber pressures ?som 300 t o 1200 pounds per square inch absolute and exit-nozzle r sea r a t i o s f o r complete expansion a t severa l design a l t i t udes from sea Level t o 60,000 f e e t .

A t extremely high a l t i t udes , spec i f i c impulse depends primari ly on expansion r a t i o ; t h a t is, on design a l t i t u d e f o r a given chamber pressure. A t low a l t i t udes , spec i f i c impulse is not af fected g rea t ly by the design a l t i t u d e because of flow separation t h a t occurs i n nozzles designed f o r high a l t i t ude . Increases i n chamber pressure increase spec i f i c impulse f o r a l l conditions, the l a rge s t improvements occurring a t low a l t i t udes . Although increases i n e i t he r design a l t i t u d e or chamber pressure generally increase the spec i f i c impulse, they a l so in - crease the power-plant weight.

INTRODUCTION

The Complete Study

1, NACA RM E54F22a

The ro l e of guided missiles i n the nation's weapons system has received much a t ten t ion i n recent years. Latest advances i n research and development i n engines, aerodynamics, and guidance make practicable the u t i l i z a t i o n of these missiles f o r delivery of a warhead a t supersonic speeds t o a ta rge t thousands of miles d i s tan t . As an a i d t o the solut ion of development and design problems, it i s the purpose of t h i s s e r i e s of reports t o study the po ten t i a l i t i e s of various engines s u i t - able f o r supersonic propulsion of long-range missiles and t o determine those charac te r i s t ics which r e su l t i n the bes t over-all performance of the engine and missile combination. I n order t o keep primary emphasis on the charac te r i s t ics of the engine proper, the material on engine performance i s sepaqated from tha t which considers the over-all missile system. The rocket-engine performance i s presented herein, the study of the rocket-powered missile i s presented i n reference 1, and the performance of the ram-jet engine i s presented i n reference 2.

Continuing research indicates many improvements t h a t a r e possible i n some of the engine components. The performance of the components selected for--the engines i n t h i s analysis has e i t he r been demonstrated i n the laboratory or appears, from available data, t o be cer ta in of attainment within a reasonable time. Similarly, advanced features of airframe design tha t a re believed possible t o develop i n a comparable time were a l s o selected.

The pr inc ipa l mission t o which a t ten t ion has been directed i s tha t of a long-range s t ra teg ic bombardment missi$e. The configurations studied a re a l l l imited t o simple two-stage designs consisting of a rocket booster used only during the i n i t i a l phase of f l i g h t and a second stage tha t f l i e s the remaining distance under i t s own power. The rocket-propelled missiles a r e considered t o t r ave l along a b a l l i s t i c t ra jectory, even though there a r e serious problems of re-entry i n t o the atmosphere. Although gl ide and even skip rockets have frequently been proposed f o r t h i s application, the many problems and uncertainties associated with the aerodynamics of these air-borne types preclude them from the present study.

Air-breathing engines f o r long-range missile propulsion generally operate continuously a t t h e i r design conditions f o r the major portion of the f l i g h t time. Therefore, even though off-design engine performance i s considered i n these analyses, the study of the air-breathing engines can be based principally on design-point performance. On the other hand,

NACA RM E54F22a

rocket engines f o r long-range b a l l i s t i c missi les have very shor t oper- a t ing times ( 1 t o 3 min) and during t h i s time a re operating at continu- a l l y d i f f e r i ng f l i g h t conditions. The study of the rocket engine must, therefore, be based on a compromise design. Fortunately, however, the- study i s simplif ied, because t he performance of a rocket engine is prac t ica l ly independent of f l i g h t velocity.

Rocket-Engine Performance

The design and performance of rocket power plants have been d i s - cussed extensively i n the l i t e r a t u r e . For example, references 3 and 4 present de ta i l ed design s tudies of rocket power plants f o r miss i le applications. The purpose of t h i s repor t i s t o present t h e rocket- engine performance da ta t ha t were used t o design the rocket power plants and boosters of the long-range miss i le configurations of the present study. A secondhpurpose i s t o i l l u s t r a t e the r e l a t i v e importance of the major engine parameters t h a t influence t he design and resu l t ing performance of the rocket engine both f o r the long-range miss i le and f o r other applications.

Theoretical spec i f i c impulse, charac te r i s t i c velocity, and nozzle expansion r a t i o based on chemical equilibrium during expansion a re presented a t several chamber pressures f o r two propellant combinations. These data cover a wider range of nozzle expansion r a t i o s than had previously been avai lable f o r the two propellant conibinations. Equations a r e given f o r determining the performance f o r any chamber pressure a t constant expansion r a t i o .

The e f fec t ive spec i f ic impulse a t ta inable i n a missi le engine i s estimated, and t he power-plant weights based on estimates i n the l i t e r - a tu re a re presented. Data i n both tabular and graphical form are in - cluded on t h e e f f ec t i ve engine performance f o r off-design operation and f o r operation with flow separation i n t he nozzle.

The two propellants considered are ammonia-fluorine and JT4-oxygen. Although experience with t he ammonia-fluorine combination i s somewhat l imited, it is f e l t t ha t t he use of t h i s propellant i n an engine f o r a long-range miss i le application i s feas ible . Some experimental da ta have been obtained a t the NACA Lewis laboratory with ammonia-fluorine rocket engines of 100- and 1000-pound th rus t ( re f s . 5 and 6) . Hydrocarbon - liquid-oxygen rocket engines have, on the other hand, considerable his tory , and t he development of SUE& an engine f o r t h i s application i s thought t o present no spec ia l problems.

ANALYSIS

! 6

NACA RM E54F22a >$

Power -Plant Arrangement

The arrangement assumed f o r the power plant i s shown schematically i n f i gu re 1. The f u e l and oxidant are assumed t o be fed t o the rocket engine by cen t r i fuga l pumps driven by a turbine using the products of combustion of the propellants as a working medium. From the combustion c h d e r c the propellant gases pass through the minimum or th roa t area t and out t he nozzle e x i t e. With suf f ic ien t overexpansion, M

the flow of gases w i l l separate from the wal l of the nozzle a t some point s; otherwise, the flow w i l l continue t o follow the wal l t o the

D nozzle ex i t . The rocket engines are assumed t o be fuel-cooled; t h i s 1 has been accomplished experimentally f o r JP4-oxygen but has not ye t been f u l l y demonstrated with ammonia-fluorine.

I

Selection of Propellants

The theo re t i ca l specif ic impulse of several propellant combinations i s presented i n f igure 2 as a function of expansion r a t i o f o r optimum mixture rat% and f o r a chamber pres&e of 500 'pounds per square inch uf

absolute. These theore t ica l values are based on chemical equilibrium following combustion and during isentropic expansion t o the expansion r a t i o indicated. These propellant combinations can be grouped roughly i n two categories: (1) high-cost, high-specific-impulse combinations involving hydrogen or f luor ine and (2) low-cost, moderate-specif i c - impulse combinations. Inasmuch as it was not feas ib le t o consider a l l propellants i n t h i s analysis, one representative propellant of each of these categories was selected. They were (1) ammonia-fluorine NH3-FZ and (2) JP4-oxygen. High- spec i f ic -impulse combinations involving hydrogen as f u e l were not se lected because of the high s t ruc tu ra l weight of the miss i le due t o the low density of l i qu id hydrogen as well as the r e l a t i ve ly high cost of l iqu id hydrogen. The JP4-oxygen-fluorine combination, which may possess merit, was not considered, because suf f ic ien t information about it was not available a t the time of the select ion.

For the purpose of the present analysis, t he JP4-oxygen propellant i s considered a& a reference propellant. The density of t he JP4 i s 0.0278 pound per cubic inch; the heat of combustion i s 18,640 Btu per pound; and the hj.drogen-cazbon r a t i o by weight i s 0.163. The performance i s based or^. these values, but it i s not expected t o be especial ly sens i t ive t o the exact composition of t he fuel .

NACA RM E54F22a

General Assumptions

The t heo re t i c a l performance presented i n t h i s repor t i s based on chemical equilibrium following combustion and during expansion. I n addit ion, one-dimensional i sentropic flow i s assumed t o occur within the nozzle without heat t r ans fe r or f r i c t i o n , except f o r the case of sepa- r a t ed flow, when these conditions a re assumed t o hold t o the point of separation only. Performance with separated flow i s based on e q i r i c a l r e l a t i ons derived from experimental data. The off-design performance without separated flow i s calculated f romthe pressure difference and the e x i t area.

The estimated e f fec t ive performance, which includes t he losses due t o in&ff iciency of combustion, the propellant used f o r pumping the f l u id s i n t o t he chamber, and a l l other losses such as f r i c t i o n and three- dimensional e f f ec t s , i s assumed t o be r e l a t ed t o the t heo re t i c a l per- f ormance by an empirical equation.

THEORETICAL PERFORMANCE

Design-Point Operation

The rocket performance data f o r ammonia-fluorine were taken from references 7 and 8, and f o r JP4-oxygen were computed by t he technique described i n reference 9. The thermodynamic da ta used are taken from reference 7, except f o r H20 data, which a r e taken from reference 10.

The var ia t ions of t heo re t i c a l values of spec i f i c impulse, charac- t e r i s t i c velocity, and area r a t i o with t he weight-percent f u e l i n t he propellant f o r ammonia-fluorine and JP4-oxygen a re presented i n f igures 3 and 4, respectively. The spec i f ic impulse I and character- i s t i c veloci ty cw are defined by the equations

(symbols a re defined i n t he appendix. ) The charac te r i s t i c ve loc i ty serves as a coeff ic ient f o r determining throat area per un i t propellant flow r a t e .

Reference 11 shows tha t , f o r hydrazine-fluorine, the spec i f ic i m - pulse, charac te r i s t i c velocity, and area r a t i o (or t h e i r logarithm) a r e very nearly l inear functions of t he logarithm of the combustion pressure f o r f ixed fuel-oxidant r a t i o and expansion r a t i o . This same corre la t ion

MACA RM E54F22a

was found t o be s a t i s f ac to ry f o r both ammonia-fluorine and JP4-oxygen. Therefore, it i s possible t o express t h e i r va r ia t ion with chamber pressure by means of t he following equations:

where '3~0' czo0, and ( & / A ~ ) ~ ~ ~ a re the values of these parameters at

a chamber pressure of 300 pounds per square inch absolute f o r the desi red expangion r a t i o , and nl, n2, and n3 are the exponents f o r the

respective3aramete1-s. The values of n l , n2, and n3 a re given i n f igures 3 and 4 as a function of expansion r a t i o f o r both propellants. The values of nl are computed from equation (58) of reference 11, but the values of n2 and n3 shown at the top of f igures 3 (b) and (c) were computed f o r hydrazine-fluorine ( r e f . 11). A check at t he s to ich i - ometric mixture r a t i o indicates t h a t the same values a re s a t i s f ac to ry f o r ammonia-fluorine. The s imi l a r i t y between the two propellants and between t h e i r a rea - ra t io curves has lead t o t he assumption t h a t the same exponents w i l l be s a t i s f ac to ry f o r a l l mixtures. Any difference t h a t does e x i s t i s not expected t o lead t o a s ign i f ican t change i n performance.

The values of spec i f i c impulse f o r both ammonia-fluorine and JP4- oxygen are functions mainly of expansion r a t i o and the weight-percent f u e l i n the propellant . Although not shown d i rec t ly , the chamber pressure has only a very small e f f e c t on spec i f ic impulse f o r a given expansion r a t i o , as indicated by the low values of ( f igs . 3(a) and 4(a ) ) . However, va r ia t ions i n chamber pressure affec the expansion r a t i o f o r a given e x i t pressure. For ammonia-fluorine the weight- percent f u e l i n t he propellant t h a t gives maximum spec i f ic impulse i s very nearly equal t o the stoichiometric r a t i o of 23.01 f o r a l l except the low expansion r a t i o s ( f ig . 3 (a) ) . Even f o r an expansion r a t i o of 10, t he reduction i n spec i f ic impulse by operating at the stoichiometric r a t i o i s l e s s than 1 percent from the maximum. For JP4-oxygen, on the other hand, the weight-percent f u e l i n the propellant t ha t gives maximum speci$'?c impulse i s considerably higher (about 30 percent) than the stoichiom&tric r a t i o of 22.6 ( f ig . 4(a) ) . The maximum spec i f ic impulse i s from 3 t o 5 percent higher than t h a t obtained by operating a t stoichiometric r a t i o .

NACA RM E54F22a -.

Off-Design Operation

Without separation. - The design a l t i t u d e i s t h a t a l t i t ude f o r which the e x i t pressure pe of t h e nozzle is jus t equal t o t he anibient pressure pa. The t h ru s t of a rocket engine operating a t other than design e x i t pressure i s given by the equation

where I d i s t he value of the spec i f ic impulse f o r the design e x i t pressure. Subst i tu t ing equations (1) and (2) i n equation (6) leads t o t he following equation f o r spec i f i c impulse:

where Id, c*, and A ~ / A ~ correspond t o an isentropic expansion from

PC t o Pe*

With separation. - Separation i n t he nozzle of t he rocket tends t o reduce the o-verexpansion losses and thereby increase the performance. The t h ru s t of a ro,cket with separated flow i n t he nozzle at point s may be wr i t t en '"

Subst i tu t ion of equations (1) and (2) i n equation (8) leads t o the following equation f o r spec i f i c impulse:

The nozzle flow w i l l separate when the design e x i t pressure pd i s l e s s than the ambient pressure Pa by a ce r t a in c r i t i c a l r a t i o ps/pa found experimentally t o be i n the order of 0.5 t o 0.3. Thus, f o r separation t o occur,

NACA RM E54F22a

The value of ps/pa has been shown t o be subject t o considerable s c a t t e r (see r e f . 12). Performance calculations have been ca r r ied out Q

f o r th ree values of ps/pa, namely 0.5, 0.4, and 0.3. The values of the mean e f f ec t i ve pressure px were measured f o r a i r i n reference 1 3 and a r e given a s a function of nozzle area r a t i o and ambient pressure. I n order t o extrapolate these data t o higher area r a t i o s , Px/pa was

p lo t ted against At/Ae. A somewhat systematic s ca t t e r occurred, but a s ingle curve shown i n f igure 5 was f a i r e d through the data and used t o approximate the value of px/pa.

M CC) rl

The process used f o r computing separated performance i s admittedly M

approximate; nevertheless, the uncertainty i n the correction f o r sepa- r a t i on w i l l account f o r only a small percentage of the t o t a l impulse of a missi le. Additional research i s needed, however, t o secure r e l i a b l e data at the l a rge area r a t i o s and t o indicate t he proper method of computing the separated-flow performance under conditions other than those f o r which the data a r e taken, especia l ly where free-stream j e t i n t e r - ac t ion i s present.

ESTIMATED EFFECTIVE SPECIFIC IMPULSE

The t heo re t i c a l spec i f i c impulse must be reduced by a fac tor t o account fo r combustion inefficiency, nozzle f r i c t i o n , and s imilar losses. I n addition, some propellant may be used i n a gas generator t o supply con t ro l power and t o pump the propellants i n t o the chaniber. These f l u i d s are not e n t i r e l y spent when exhausted from the turbine and, a t l e a s t at high a l t i t ude , would be used t o secure addi t ional t h ru s t . As an approximation, t h e e f fec t ive spec i f ic impulse was assumed t o be given by t he following equation:

The second term i n parentheses, which var ies with chamber pressure and propellant density, accounts f o r the propellant used t o supply pumping work. The v a l i d i t y of t h i s correction at large expansion r a t i o s (approx. 300) i s uncertain, and experimental da ta i n t h i s range a r e needed.

The e f fec t ive value of cha rac t e r i s t i c ve loc i ty was obtained by a similar equation:

NACA RM E54F22a

A more de ta i l ed treatment could be devised (see r e f . 14, e.g. ) t h a t would use a smaller correction f ac to r f o r c* than t h a t used f o r I. The value of c*, howeyer, a f f ec t s only t he engine weight by the f a c t t ha t it determines the th roa t area; and, inasmuch as the uncer ta int ies i n t he assumed engine weights are greater than the e r rors i n weight due t o uncer ta int ies i n c*, the same correction is used as f o r spec i f i c impulse. A separate fac tor f o r obtaining the e f fec t ive area r a t i o s from the t heo re t i c a l values coula a l so be included; however, because experimental measurements of the area r a t i o s required f o r expansion r a t i o s i n the order of 300 a r e unavailable, the t heo re t i c a l area r a t i o s have been used without correction.

A' fuel-oxidant mixture w a s se lected f o r each propellant t o give near-maximum performance over a range of expansion r a t i o s . The values se lected f o r the weight-percent f u e l f o r both propellants a re given i n the following tab le :

A l l subsequent calculat ions a re based on these values. I n t he case of ammonia-fluorine, t h e high cost of f luor ine might lend some advantage t o t he use of a mixture containing more fue l , but no attempt was made t o optimize the mixture r a t i o f o r minimum cost .

Propellant

Ammonia-f luorine

JP4 -oxygen

The estimated e f fec t ive spec i f ic impulse f o r the se lected fue l - oxidant r a t i o s i s given i n t ab le I fo r both design-point and off-design engine operation, including conditions with flow separation i n the nozzle. These "effective" values were obtained by multiplying t he t heo re t i c a l values by t he following fac tors i n accordance with equation (11) :

Weight-percent f u e l

23.01

27.64

Average density, P 9

~ b / c u in .

0.04335

,03637

Propellant

Ammonia-fluorine

JP4-oxygen i

Ratio of e f f ec t i ve t o t heo re t i c a l spec i f i c impulse, 1ef / ~ t h

Chamber pressure, pc, lb/sq i n . abs

1200

0.9155

.9127

800

0.9203

.9 185

300

0.9264

.925 7

400

0.9252

.9242

600

0.9228

.9214

Design-Point Operation

NACA RM E54FZ2a

The estimated effective specific impulse fo r the design point i s shown as a function of design a l t i tude and chamber pressure i n figure 6. A gr id of expansion r a t i o i s superimposed. The very small slope of these gr id l ines shows tha t the specific impulse i s principally a function of expansion r a t io . The s l igh t decrease i n specific impulse with increasing chaniber pressure f o r a given expansion r a t i o i s due t o the pumping work tha t increases with chamber pressure.

Off - ~ e s i g n Operation

The off-design effective specif ic impulse i s plotted i n f igure 7 f o r a ser ies of f ixed engine designs. The effect ive specific impulse i s plot ted wainskt a l t i tude fo r chamber pressures from 300 t o 1200 pounds per square inch absolute and a t design a l t i tudes from sea leve l t o 60,000 fee t . The overexpanded and underexpanded specific-impulse curves are shown on separate graphs t o reduce the cross-over of l ines . I f the design a l t i tude of a nozzle is suff ic ient ly higher than the operating afiitude, the flow w i l l separate from the nozzle walls. The variat ion of specific impulse with a l t i tude i s shown by the solid: l ines f o r the unseparated condition and by the dashed l ines fo r the separated condition fo r various values of ps pa. The specific impulse varies with a l t i tude depending on the ps 1 pa value a t which the nozzle operates. However, as a l t i tude increases, the separation point moves toward the ex i t of the nozzle and w i l l arrive a t the end of the nozzle at the same a l t i t ude a t which the dashed curve intersects the sol id curve corresponding t o the design a l t i tude of the nozzle. A t higher a l t i tudes the flow does not se,parate and the specific impulse follows the so l id curve corresponding t o the design a l t i tude of the nozzle. The specific impulse does not change much above 100,000 f e e t fo r any engine shown, because the atmospheric pressure becomes essent ial ly zero a t t h i s a l t i tude .

Figure 7 shows tha t the specif ic impulse fo r separated flow i s independent of design a l t i tude for the same chamber pressure and value of ps/pa. Table I, however, shows s l ight ly different values fo r specific impulse under these conditions fo r different design al t i tudes. These differences, which are too small t o show on figure 7, are depend- ent on the variat ion of Px/pa with the area. r a t i o A~/A, as shown i n f igure 5. It i s important t o note that , because of separation of the flow, an engine designed- f o r high a l t i tude may be operated at sea M

l eve l without large losses. For example, an engine designed f o r any a l t i t ude above sea l eve l may be operated a t sea leve l with l e s s than

NACA RM E54F22a

6-percent loss i n impulse i f the value of Ps/pa i s equal t o 0.4. On the other hand, an engine designed f o r sea l eve l when operated a t a high a l t i tude may e n t a i l much greater losses. For a chaniber pressure of 300 pounds per square inch absolute and operation a t 120,000 fee t , an engine designed f o r sea level has about 15-percent-lower specific impulse than one designed f o r 60,000 fee t .

Increases i n chamber pressure a t a constant design a l t i tude increase w the specific impulse a t a l l a l t i tudes, as may be noted from table I. P 0-2 The increase i s greater fo r operation a t low al t i tudes than fo r high W al t i tudes. Increases i n chamber pressure a t constant expansion r a t i o

increase the specif ic impulse for operation a t low a l t i tude but have pract ical ly no effect fo r extremely high al t i tudes. Inasmuch as the power-plant weight and t rajectory also affect the selection of design a l t i t ude and chamber pressure, optimum values of these parameters can- not be found without a detailed missile design and f l i g h t analysis. An analysis of t h i s type is presented i n reference 1 for a specific configuration.

Nozzle-Throat Area and Area Ratio

The variation of nozzle 'area r a t i o with chamber pressure and design a l t i tude i s shown i n figure 8, and the variat ion of effective charac- t e r i s t i c velocity wSth chamber pressure i s shown i n figure 9. From these two figures, the throat and ex i t area of the rocket nozzle may be found f o r a given flow ra te .

ESTIMATED POWER -PLANT WEIGHT

The following equation (given i n r e f . 3) was used f o r calculating engine weights:

where L* was assumed t o be 45 inches.

NACA RM E54F22a

The weight of the auxi l i a r ies WaUx, consist ing of the pumping plant, piping, and re la ted equipment, was estimated from the data of reference 15. The following empirical equation was f i t t e d t o these data:

This equation does not apply f o r values of w below 50 pounds per second.

The estimated t o t a l weight of the rocket power plant i s shown i n f igures 10 and 11 as a function of propellant flow r a t e , design a l t i tude , and chamber pressure. This weight includes the rocket th rus t chamber and nozzle, turb?pumps, gas generator, and piping and represents the sum of equations (13) and (14). It does not include weight f o r swiveling the engine t o obtain d i rec t iona l control .

Figures 10 and 11 show tha t the weight of the power plant increases more than proportionately with the propellant flow ra te , which indicates t h a t one power plant of a given flow r a t e would be heavier than two smaller power plants having the same t o t a l flow. There is reason t o believe, however, t h a t higher specif ic impulse can be obtained from large engines than from small ones. The increased nozzle length permits a c loser approach t o equilibrium expansion i n the nozzle; the more favorable surf ace-volume r a t i o of the larger engine simplif i e s cooling problems; and the use of fewer engines s impl i f ies control problems. For these reasons, a s ingle engine was used i n each of the bodies i n t he b a l l i s t i c missiles and boosters considered i n t h i s s e r i e s of repor ts .

The f r ac t i on of the power-plant weight represented by the pumping plant is shown i n f igure 12 as a function of flow r a t e f o r the two propellant systems fo r a f ixed design a l t i t ude of 20,000 f e e t . The scale e f f ec t a s the propellant flow r a t e var ies may be noted as wel l as the e f f ec t of ch-er pressure.

CONCLUDING REMARKS

The theore t ica l performance of ammonia-fluorine and JP4-oxygen propellants has been presented over a wide range of expansion r a t i o s and f o r a range of fuel-oxidant mixture r a t i o s . Estimates of the ef- f ec t i ve specif ic impulse t h a t can be obtained i n ac tua l missiles were given both i n tabular form and i n graphs f o r se lected fuel-oxidant mixture r a t i o s . These estimates a re based on currnet developments of fu l l - sca le engines or components. Although t h i s performance may not

NACA RM E54FZZa

be available a t the present time f o r the particular propellants chosen, it i s believed t o be attainable with reasonable development e f for t . The mixture r a t io s selected give near-maximum specific impulse fo r large expansion ra t ios . They were 23.01-percent f u e l by weight f o r ammonia- fluorine and 27.64-percent fue l by weight fo r JL'4-oxygen. The estimated weights of the power plants based on information cbtained from the l i t e r - ature were a l so presented.

A t extremely high al t i tudes, the specific impulse depends primarily on expansion rat io; tha t is, on design a l t i tude fo r a given chamber pressure. A t low al t i tudes, on the other hand, the specific impulse i s not affected greatly by design a l t i tude for a given chamber pressure because of flow separation tha-t occurs i n nozzles designed f o r high a l t i tude . Increases i n chamber pressure increase the specific impulse f o r a l l con- dit ions, the largest improvements occurring a t low al t i tudes. Although increases i n e i ther design a l t i tude or chamber pressure generally increase the specific impulse, they a lso increase the power-plant weight.

Lewis Flight Propulsion Laboratory National Advisory Committee fo r Aeronautics

Cleveland, Ohio, July 8, 1954

NACA RM E54F22a

AF'PrnIX - SYMBOLS

The following symbols are used i n t h i s report:

A area of nozzle, sq in .

c* charac te r i s t i c velocity, f t / sec

F th rus t , l b

g f t - l b (mass) g rav i ta t iona l constant, 32.174

sec l b (force)

I specif ic impulse, l b (f orce) -sec/lb (mass)

L * charac te r i s t i c length, in .

P pressure, lb/sq in . abs

p, meaneffective pressure i n r o c k e t nozzle downstreamof separated flow, lb/sq in. abs

W weight, l b

w propellant flow ra te , lb/sec

P average density of propellant , lb/cu in .

Subscripts :

a ambient

aux auxi l i a r ies

c combustion chamber

d design

e nozzle e x i t

ef e f fec t ive

m engine

s nozzle separation point

t nozzle th roa t

NACA RM E54F22a

t h theore t ica l

Exponents f o r correla t ion :

nl fo r specif ic impulse

n2 f o r charac te r i s t ic velocity

n 3 f o r nozzle area r a t i o

1. H u f f , Vearl N., and Kerrebrock, Jack L.: Analysis of Rocket, Ram- J e t , and Turbo j e t Engines f o r Supersonic Propulsion of Long-Range Missiles. &I - Rocket Missile Performance. NACA RM E54129a.

2. Weber, Richard J., and Luidens, Roger W.: Analysis of Rocket, Ram- J e t , and Turbo j e t Engines f o r Supersonic Propulsion of Long-Range Missiles. I11 - Ram-Jet Engine Performance. NACA RM E54H03.

3. Gendler, S. L., e t a l . : Long-Range Surface-to-Surfaee RocKet and Ramjet Missiles. Rep. R-180, The Rand Corp., May 1, 1950. (US&? Proj. RR 1 . )

4. Wilson, E. M., Deeney, D. M., Eaton, C. B., and Kaelin, W. H.:

I/ Propellant Consideration fo r the Power Plant Design Study of a Long-Range Rocket Vehicle. Aerojet, Eng. Corp., Nov. 2, 1951. (contract AF 33 (038) -19956, Pro j . h-1593. )

5. Rothenberg, Edward A., and Douglass, Howard W. : Investigation of Liquid Fluorine - Liquid Ammonia Propellant Combination i n a 100- Pound-Thrust Rocket Engine. NACA RM E53E08, 1953.

6. Douglass, Howard W.: Experimental Performance of Liquid Fluorine - Liquid Ammonia Propellant Combination i n 1000-Pound-Thrust Rocket Engines. NACA RM E54C17, 1954.

7. Gordon, Sanford, and Huff, Vearl N. : Theoretical Performance of Liquid Ammonia and Liquid Fluorine as a Rocket Propellant. NACA RM E53A26, 1953.

8. Gordon, Sanford, and Huff, Vearl N.: Theoretical Performance of Mixtures of Liquid Ammonia and Hydrazine as Fuel with Liquid Fluorine as Oxidant f o r Rocket Engines. NACA RM E53F08, 1953.

NACA RM E54F22a

9. Huff, Vearl N., Gordon, Sanfard, and Morrell, Virginia E.: General -I' Method and Thermodynamic Tables f o r Computation of Equilibrium

Composition and Temperature of Chemical Reactions. NACA Rep. 1037, 1951. (supersedes NACA TN1s 2113 and 2161.)

10. Glat t , Leonard, Adam, Joan H., and Johnston, Herriek L.: Thermo- dynamic Properties of $he H20 Molecule from Spectroscopic Data. Tech. Rep. 316-8, Cryogenic Lab., Dept. Chem., Ohio S ta te Univ., June 1, 1953. ( ~ a v y Contract N6onr-225, Task Order X I I , ONR Proj . NR 085-005.)

- 11. Gordon, Sanford, and Huff, V e a l N. : Theoretical Performance of Liquid Hydrazine and Liquid Fluorine a s a Rocket Propellant. NACA RM E53E12, 1953.

,y 12. Green, Leon, Jr. : Flow Separation i n Rocket Nozzles. Jour. Am. Rocket S O C . ~ vol. 23, no. 1, Jan. - Feb., 1953, pp. 34-35.

13. Meleney, R . H., and Kuhns, R. M.: Flow Separation i n Over-Expanded W' Supersonic Nozzles. RT-115, Prog. Rep. No. 1, Consolidated Vultee

Ai rc ra f t Corp., Oct. 23, 1951.

14. Sutton, George P.: Rocket Propulsion Elements. John Wiley & Sons, Inc., 1949, pp. 68-70.

15. Colvin, D., Fyff e, R . J., and Sackson, M. : The Effect of Selected Parameters on the Design of Rocket Engine Pumping Plants. Res. and Dev. Rep. SPD 230, The M. W. Kellogg Co., May 15, 1949. (U. S. A i r Forces Contract W-33-038-ac-14221.)

I Desian altitude. 30.000 ft: seoaratlon at D,/D. = 0.3 I

I DBsirrn altitude. 30.000 ft: seoaration at os/oa = 0.4 I

Design altitude, 30,000 ft; separatlon at ps/pa = 0.5

2 6 4 . 1 2 6 9 . 1 2 7 4 . 0 2 7 7 . 7

2 7 4 . 0 2 7 8 . 5 2 8 3 0 2 8 6 : 3

2 4 2 . 8 2 4 8 . 8 2 5 4 8 2 5 9 1 2

2 3 2 5 2 3 9 : 0 2 4 5 . 4 2 5 0 . 2

O O Q 5 , 0 0 0

1 0 . 0 0 0 1 3 , 7 3 7

2 5 5 9 2 6 1 : 3 2 6 6 . 6 2 7 0 . 6

2 7 9 9 2 8 7 : 5 2 9 4 . 8 3 0 0 . 3

3 1 8 8 3 2 2 : 4 3 2 7 . 8 3 3 1 . 8

3 2 8 2 3 3 3 : s 3 3 7 8 3 4 1 : 2

2 9 2 0 2 9 8 : 9 3 0 5 . 7 3 1 0 . 7

3 0 7 . 3 3 1 3 . 4

::$';

NACA RM E54F22a 19

TABLE I. - CONCLUDED. ESTIMATED EFFECTIVE SPECIFIC IMPULSE OF AMMONIA-FLUORINE AND JP4-OXYGEN PROPELLANTS

[mlues obtalned from t h e o r e t l ~ a l va lues by 1.f = I t h (0.93 - 0.0000005235 +I] Altitude,

ft

0 0 0 5 ' 0 0 0

1O:OOO 1 5 0 0 0 2 0 ' 0 0 0 2 5 : 0 0 0 3 0 , 0 0 0 35 0 0 0 4 0 : 0 0 0 4 5 3 0 0 0 5 0 , 0 0 0 6 0 0 0 0 ~ O : U O O 8 0 9 0 0 0

1 0 0 ~ 0 0 0 1 2 0 3 0 0 0 9 9 9 , 9 9 9

0 0 0 5 , 0 0 0

1 0 O O e 1 5 : 0 0 0 1 8 , 6 5 0

0 0 0 5 , 0 0 0

1 0 0 0 0 1 5 ' 0 0 0 2 0 : 0 0 0 2 5 , 0 0 0 2 5 . 4 0 0

0 0 0 5 0 0 0

1 0 : 0 0 0 1 5 , 0 0 0 2 0 , 0 0 0 2 5 , 0 0 0

' 3 0 , 0 0 0 3 0 . 3 8 5

0 0 0 5 , 0 0 0

1 0 0 0 0 1 5 ' 0 0 0 2 0 : 0 0 e 2 5 0 0 0 3 0 ' 0 0 0 3 5 ' 0 0 0 4 0 : 0 0 0 4 5 . 0 0 0 5 0 , 0 0 0 6 0 0 0 0 7 0 : 0 0 8 8 0 , 0 0 0

1 0 0 0 0 0 1 2 0 : 0 0 0 9 9 9 , 9 9 9

0 0 0 5 , 0 0 0

1 0 , 0 0 0 1 5 0 0 0 2 0 ' 0 0 0 2 5 ' 0 0 0 3 0 : 0 0 0 3 4 , 6 9 6

0 0 0 5 , 0 0 0

1 0 . 0 0 0 15:OOO 2 0 , 0 0 0 2 5 , 0 0 0 3 0 > 0 0 0 3 5 , 0 0 8 4 0 0 0 0 4 0 : 8 0 6

0 0 0 5 . 0 0 0

1 0 , 0 0 0 1 5 , 0 0 0 2 0 9 0 0 0 2 5 0 0 0 3 0 : 0 0 @ 3 5 , 0 0 0 4 0 , 0 0 0 4 5 , 4 4 6

- Estimated effective specific

Ammonia-fluorine, 23.01 percent fuel by weight

Chamber pressure, pc, lb/sq in. abs

separation

impulse, Ief, lb-sec/lb for-

JP4-oxygen, 27.64 percent fuel by weight

Chamber pressure, pc, lb/sq in. abs

800 600 300 1200 400 300

ft; ---c

2 8 6 4 3 0 2 ' 8 3 1 6 : 8 3 2 8 . 8 3 3 9 . 1 3 4 7 . 7 3 5 4 . 9 3 6 0 . 9 3 6 5 . 8 3 6 9 6 3 7 2 1 6 3 7 6 9 3 7 9 1 5 3 8 1 . 2 3 8 2 . 8 3 8 3 . 4 3 8 3 . 8

ft; separation 3 1 7 . 3 3 2 2 . 7 3 2 7 . 8 3 3 2 8 3 3 6 1 5

ft; separation 3 2 4 . 3 3 2 9 . 4 3 3 4 . 3 3 3 8 . 9 3 4 3 . 5 3 4 8 . 0 3 4 8 . 3

ft; separation 3 2 8 . 2 3 3 3 0 5 3 7 1 8 3 4 2 . 3 3 4 6 . 7 3 5 0 . 9 3 5 5 . 1 3 5 5 . 4

60,000 ft;

2 2 8 . 8 2 5 5 . 9 2 7 9 2 2 9 9 ' 2 3 1 6 1 1 3 3 0 . 4 3 4 2 . 3 3 5 2 . 3 3 6 0 . 3 3 6 6 . 7 3 7 1 . 7 3 7 8 . 7 3 8 3 . 1 3 8 5 . 8 3 8 8 . 5 3 8 9 . 6 3 9 0 . 2

ft; 3 1 7 3 3 2 2 1 7 3 2 7 . 8 3 3 2 . 8 3 3 7 . 8 3 4 2 . 7 3 4 7 . 4 3 5 1 . 9

ft; 3 2 4 . 4 3 2 9 . 4 3 3 4 . 3 3 3 8 . 9 3 4 3 . 5 3 4 7 . 9 3 5 2 . 3 3 5 6 . 7 3 6 0 8 3 6 1 1 5

ft; 3 2 8 . 2 3 3 3 . 0 3 3 7 . 8 3 4 2 . 3 3 4 6 . 7 3 5 0 9 3 5 5 : l 3 5 9 . 2 3 6 3 . 2 3 6 7 . 2

800 400 1 600

altitude, 45,000

2 6 8 9 2 8 7 ' 7 3 0 4 : O 3 1 7 . 8 3 2 9 . 6 3 3 9 . 6 3 4 7 . 9 3 5 4 8 3 6 0 : 4 3 6 4 9 3 6 8 1 3 3 7 3 . 2 3 7 6 . 3 3 7 8 . 2 3 8 0 . 1 3 8 0 . 8 3 8 1 . 2

45,000 3 0 4 . 2 3 1 0 5 3 1 6 1 6 3 2 2 . 5 3 2 6 . 6

45,000 3 1 2 . 3 3 1 8 . 1 3 2 3 . 8 3 2 9 . 4 3 3 4 . 7 3 3 9 . 9 3 4 0 . 3

45,000 3 1 6 . 8 3 2 2 . 3 3 2 7 . 8 3 3 3 . 1 3 3 8 . 3 3 4 3 . 3 3 4 8 . 1 3 4 8 . 5

altitude,

2 0 2 . 6 2 3 3 . 8 2 6 0 . 7 2 8 3 . 6 3 0 3 . 1 3 1 9 . 5 3 3 3 . 3 3 4 4 7 3 5 4 1 0 3 6 1 . 3 3 6 7 . 1 3 7 5 . 2 3 8 0 . 2 3 8 3 . 3 3 8 6 . 4 3 8 7 . 6 3 8 8 . 4

60,000 3 0 4 . 2 3 1 0 . 5 3 1 6 . 6 3 2 2 . 5 3 2 8 . 1 3 3 3 . 7 3 3 9 . 1 3 4 4 . 3

altitude, 60,000 3 1 2 . 4 3 1 8 . 1 3 2 3 . 8 3 2 9 . 3 3 3 4 . 7 3 3 9 . 9 3 4 4 . 9 3 4 9 . 8 3 5 4 . 6 3 5 5 . 3

altitude, 60,000 3 1 6 . 8 3 2 2 . 4 3 2 7 . 8 3 3 3 . 1 3 3 8 . 3 3 4 3 . 3 3 4 8 . 1 3 5 2 . 7 3 5 7 . 3 3 6 1 . 9

2 1 2 6 2 3 8 ' 8 2 6 1 1 4 2 8 0 7 2 9 7 ' 1 3 1 0 1 9 3 2 2 . 5 3 3 2 1 3 3 9 : 9 3 4 6 1 3 5 0 : 9 3 5 7 7 3 6 2 : 0 3 6 4 . 6 3 6 7 . 2 3 6 8 2 3 6 8 1 9

2 6 2 . 3 2 7 0 6 2 7 8 : 9 2 8 7 1 2 9 2 : 9

2 7 3 . 6 2 8 1 . 4 2 8 9 . 1 2 9 6 . 6 3 0 4 . 0 3 1 1 . 3 3 1 1 . 9

2 7 9 . 8 2 8 7 3 2 9 4 1 6 3 0 1 . 8 3 0 8 . 9 3 1 5 . 9 3 2 2 . 8 3 2 3 . 3

1 1 9 . 8 1 6 3 . 4 2 0 0 9 2 3 2 ' 9 2 6 0 1 1 2 8 3 0 3 0 2 ' 2 3 1 8 ' 2 3 3 1 : 2 3 4 1 . 4 3 4 9 . 4 3 6 0 . 7 3 6 7 . 8 3 7 2 . 1 3 7 6 . 5 3 7 8 . 1 3 7 9 . 2

2 6 2 3 2 7 0 : 6 2 7 8 . 8 2 8 6 . 9 2 9 4 9 3 0 2 ' 8 3 1 0 : 4 3 1 7 . 6

2 7 3 . 7 2 8 1 . 4 2 8 9 . 0 2 9 6 . 6 3 0 4 0 3 1 1 : 2 3 1 8 . 3 3 2 5 . 2 3 3 2 0 3 3 3 1 0

2 8 0 . 0 2 8 7 . 4 2 9 4 . 6 3 0 1 . 8 3 0 8 . 9 3 1 5 9 3 2 2 : 7 3 2 9 . 4 3 3 5 . 8 3 4 2 . 3

1200

2 2 6 8 2 4 4 ' 3 2 5 9 : 3 2 7 2 2 2 8 3 ' 1 2 9 2 : 3 3 0 0 . 0 3 0 6 4 3 1 1 1 7 3 1 5 8 3 1 9 1 0 3 2 3 . 5 3 2 6 . 4 3 2 8 . 1 3 2 9 . 9 3 3 0 . 5 3 3 1 .O

2 6 2 . 1 2 6 7 . 1 2 7 2 . 0 2 7 6 8 2 8 0 : 3

2 6 9 . 9 2 7 4 . 5 2 7 9 . I 2 8 3 7 2 8 8 12 2 9 2 . 6 2 9 3 .O

2 7 4 . 0 2 7 8 5 2 8 3 1 0 2 8 7 . 4 2 9 1 . 7 2 9 6 . O 3 0 0 . 2 3 0 0 . 6

1 5 6 . 5 1 8 7 . 1 2 1 3 . 4 2 3 5 . 9 2 5 5 . 0 2 7 1 . 1 2 8 4 . 6 2 9 5 8 3 0 4 : 9 3 1 2 . 1 3 1 7 . 7 3 2 5 . 7 3 3 0 . 6 3 3 3 . 7 3 3 6 . 7 3 3 7 . 9 3 3 8 . 7

2 6 2 2 2 6 7 : 1 2 7 2 . 0 2 7 6 . 8 2 8 1 . 6 2 8 6 . 3 2 9 1 . 0 2 9 5 . 4

2 6 9 . 9 2 7 4 . 5 2 7 9 . 1 2 8 3 . 7 2 8 8 . 2 2 9 2 . 6 2 9 7 . 0 3 0 1 . 4 3 0 5 5 3 0 6 1 2

2 7 4 . 1 2 7 8 . 5 2 8 3 . 0 2 8 7 . 4 2 9 1 . 7 2 9 6 0 3 0 0 1 2 3 0 4 . 4 3 0 8 . 5 3 1 2 . 7

2 3 1 . 0 2 5 4 9 2 7 5 : s 2 9 3 0 3 0 8 : O 3 2 0 . 6 3 3 1 . 1 3 3 9 . 9 3 4 7 . 0 3 5 2 . 6 3 5 7 . 0 3 6 3 . 3 3 6 7 . 1 3 6 9 . 5 3 7 1 . 9 3 7 2 . 8 3 7 3 . 4

2 7 6 . 0 2 8 3 . 7 2 9 1 3 2 9 8 ' 8 3 Q 4 : 2

2 8 6 . 3 2 9 3 . 5 3 0 0 . 5 3 0 7 . 5 3 1 4 . 3 3 2 1 .O 3 2 1 . 5

2 9 2 . 0 2 9 8 8 3 0 5 : 6 3 1 2 . 2 3 1 8 8 3 2 5 1 1 3 3 1 . 4 3 3 1 . 9

1 4 7 . 1 1 8 6 . 7 2 2 0 . 7 2 4 9 . 7 2 7 4 . 4 2 9 5 . 2 3 1 2 . 6 3 2 7 1 3 3 8 1 9 3 4 8 . 2 3 5 5 . 5 3 6 5 . 7 3 7 2 . 1 3 7 6 . 1 3 8 0 . 0 3 8 1 . 5 3 8 2 . 5

2 7 6 0 2 8 3 : 7 2 9 1 . 3 2 9 8 . 7 3 0 6 . 1 3 1 3 . 2 3 2 0 . 2 3 2 6 . 6

2 8 6 . 4 2 9 3 . 5 3 0 0 . 5 3 0 7 . 4 3 1 4 . 2 32'0. 9 3 2 7 . 4 3 3 3 . 7 3 3 9 . 7 3 4 0 . 6

2 9 2 . 0 2 9 8 . 8 3 0 5 . 6 3 1 2 . 2 3 1 8 . 7 3 2 5 . 1 3 3 1 . 3 3 3 7 . 4 3 4 3 . 2 3 4 9 . 0

without separation

1 6 5 . 3 1 9 0 . 3 2 1 1 . 7 2 3 0 1 2 4 5 1 6 2 5 8 . 8 2 6 9 . 8 2 7 8 . 9 2 8 6 . 4 2 9 2 . 2 2 9 6 . 8 3 0 3 . 3 3 0 7 . 3 3 0 9 . 8 3 1 2 . 3 3 1 3 . 3 3 1 3 . 9

at ps/pa 2 1 5 . 5 2 2 2 . 6 2 2 9 . 7 2 3 6 . 6 2 4 1 . 7

at ps/pa 2 2 6 . 6 2 3 3 . 2 2 3 9 . 8 2 4 6 . 3 2 5 2 . 8 2 5 9 . 2 2 5 9 . 7

at p,/pa 2 3 2 . 5 2 3 8 9 2 4 5 1 2 2 5 1 . 5 2 5 7 . 8 2 6 4 . 0 2 7 0 . 1 2 7 0 . 6

without separation

6 5 . 8 1 0 9 . 4 1 4 6 . 8 1 7 8 . 8 2 0 6 . 0 2 2 8 . 9 2 4 8 . 1 2 6 4 1 2 7 7 1 0 2 8 7 . 2 2 9 5 . 2 3 0 6 . 6 3 1 3 . 6 3 1 7 . 9 3 2 2 . 3 3 2 3 . 9 3 2 5 . 0

at p,/pa 2 1 5 . 6 2 2 2 . 6 2 2 9 . 6 2 3 6 . 6 2 4 3 . 4 2 5 0 . 2 2 5 7 . 0 2 6 3 . 5

separation at ps/pa

2 2 6 . 6 2 3 3 . 2 2 3 9 . 8 2 4 6 . 3 2 5 2 . 8 2 5 9 . 1 2 6 5 . 5 2 7 1 . 8 2 7 7 . 9 2 7 8 . 9

separation at ps/pa

2 3 2 . 6 2 3 9 . 0 2 4 5 . 3 2 5 1 . 5 2 5 7 . 8 2 6 3 9 2 7 0 : O 2 7 6 . 1 2 8 2 . 0 2 8 8 . 1

Design

2 5 4 5 2 7 5 ' 3 2 9 3 : 2 3 0 8 . 6 3 2 1 . 6 3 3 2 . 5 3 4 1 . 7 3 4 9 4 3 5 5 : 6 3 6 0 . 5 3 6 4 . 3 3 6 9 7 3 7 3 : l 3 7 5 . 1 3 7 7 . 2 3 7 8 .O 3 7 8 . 5

Design altitude, 2 9 3 . 4 3 0 0 3 3 0 7 : 0 3 1 3 . 6 3 1 8 . 3

Design altitude, 3 0 2 . 4 3 0 8 . 7 3 1 5 . 0 3 2 1 . 1 3 2 7 . 1 3 3 2 . 9 3 3 3 . 3

Design altitude, 3 0 7 . 3 3 1 3 . 4 3 1 9 . 4 3 2 5 . 2 3 3 0 . 9 3 3 6 . 5 3 4 2 . 0 3 4 2 . 4

Design

1 8 1 . 5 2 1 5 . 9 2 4 5 5 2 7 0 : 7 2 9 2 . 2 3 1 0 . 3 3 2 5 . 5 3 3 8 1 3 4 8 : 4 3 5 6 . 4 3 6 2 . 8 3 7 1 . 7 3 7 7 . 3 3 8 0 . 7 3 8 4 . 1 3 8 5 . 4 3 8 6 . 3

Design altitude, 2 9 3 4 3 0 0 : s 3 0 7 . 0 3 1 3 . 5 3 1 9 . 9 3 2 6 . 0 3 3 2 . 0 3 3 7 . 7

Design 3 0 2 . 4 3 P 8 . 8 3 1 5 . 0 3 2 1 . 1 3 2 7 . 0 3 3 2 . 8 3 3 8 . 4 3 4 3 . 8 3 4 9 0 3 4 9 : 8

Design 3 0 7 . 3 3 1 3 . 4 3 1 9 . 4 3 2 5 . 2 3 3 0 . 9 3 3 6 . 5 3 4 1 . 9 3 4 7 . 1 3 5 2 . 0 3 5 7 . 1

1 9 9 3 2 2 0 ' 3 2 3 8 : 3 2 5 3 . 8 2 6 6 . 8 2 7 7 . 9 2 8 7 . 1 2 9 4 . 8 3 0 1 . 1 3 0 6 0 3 0 9 1 9 3 1 5 3 3 1 8 1 7 3 2 0 . 8 3 2 2 . 9 3 2 3 . 7 3 2 4 . 2

2 4 1 . 6 2 4 7 . 5 2 5 3 . 4 2 5 9 3 2 6 3 : 5

2 5 0 . 9 2 5 6 . 5 2 6 2 0 2 6 7 : 4 2 7 2 . 9 2 7 8 . 3 2 7 8 . 7

2 5 5 . 8 2 6 1 . 2 2 6 6 . 6 2 7 1 . 8 2 7 7 . 1 2 8 2 . 3 2 8 7 . 4 2 8 7 . 8

1 1 5 . 9 1 5 2 . 4 1 8 3 . 9 2 1 0 . 7 2 3 3 . 5 2 5 2 . 8 2 6 8 . 9 2 8 2 . 3 2 9 3 . 2 3 0 1 . 8 3 0 8 . 5 3 1 8 . 0 3 2 3 . 9 3 2 7 . 6 3 3 1 . 2 3 3 2 . 6 3 3 3 . 5

2 4 1 . 6 2 4 7 . 5 2 5 3 . 4 2 5 9 . 3 2 6 5 . 0 2 7 0 . 8 2 7 6 . 4 2 8 1 . 8

2 5 0 . 9 2 5 6 . 5 2 6 2 . 0 2 6 7 . 4 2 7 2 . 9 2 7 8 . 2 2 8 3 . 6 2 8 8 . 8 2 9 3 . 9 2 9 4 . 8

2 5 5 . 9 2 6 1 . 3 2 6 6 . 6 2 7 1 . 8 2 7 7 . 1 2 8 2 . 2 2 8 7 . 4 2 9 2 . 5 2 9 7 . 4 3 0 2 . 5

1 8 0 2 2 0 3 : 4 2 2 3 . 4 2 4 0 . 5 2 5 5 . 0 2 6 7 . 2 2 7 7 . 5 2 8 6 . 0 2 9 2 . 9 2 9 8 4 3 0 2 : 6 3 0 8 7 3 1 2 1 4 3 1 4 . 8 3 1 7 . 1 3 1 8 .O 3 1 8 . 6

= 0.3 2 2 7 . 0 2 3 3 . 6 2 4 0 1 2 4 6 ' 6 2 5 1 : 3

= 0.4 2 3 7 . 3 2 4 3 . 4 2 4 9 . 6 2 5 5 . 7 2 6 1 . 7 2 6 7 . 6 2 6 8 . 1

= 0.5 2 4 2 . 8 2 4 8 . 7 2 5 4 . 6 2 6 0 . 5 2 6 6 . 3 2 7 2 . 1 2 7 7 . 8 2 7 8 . 2

0 8 7 . 7 1 2 8 . 2 1 6 3 . 1 1 9 2 . 8 2 1 8 . 1 2 3 9 . 4 2 5 7 . 3 2 7 2 . 2 2 8 4 . 2 2 9 3 . 7 3 0 1 . 2 3 1 1 . 7 3 1 8 . 2 3 2 2 . 3 3 2 6 . 3 3 2 7 . 9 3 2 8 . 9

= 0.3 ,

2 2 7 0 2 3 3 1 6 2 4 0 . 1 2 4 6 . 5 2 5 3 . 0 2 5 9 . 3 2 6 5 . 6 2 7 1 . 6

= 0.4

2 3 7 . 3 2 4 3 . 5 2 4 9 . 6 2 5 5 . 6 2 6 1 . 6 2 6 7 . 6 2 7 3 . 5 2 7 9 . 4 2 8 5 . 0 2 8 5 . 9

= 0.5

2 4 2 . 8 2 4 8 . 8 2 5 4 . 7 2 6 0 . 5 2 6 6 . 3 2 7 2 0 2 7 7 : 7 2 8 3 . 4 2 8 8 . 9 2 9 4 . 5

2 1 1 . 6 2 3 1 . 0 2 4 7 . 8 2 6 2 1 2 7 4 1 2 2 8 4 . 5 2 9 3 . 1 3 0 0 . 2 3 0 6 . 0 3 1 0 . 6 3 1 4 . 2 3 1 9 . 2 3 2 2 . 4 3 2 4 . 3 3 2 6 . 3 3 2 7 . O 3 2 7 . 5

2 5 0 . 8 2 5 6 . 3 2 6 1 . 8 2 6 7 . 2 2 7 1 . 2

2 5 9 . 4 2 6 4 . 6 2 6 9 . 7 2 7 4 . 8 2 7 9 .9 2 8 4 . 8 2 8 5 . 2

2 6 4 . 1 2 6 9 . 1 2 7 4 . 0 2 7 8 . 9 2 8 3 . 8 2 8 8 . 6 2 9 3 . 3 2 9 3 . 7

1 3 3 . 9 1 6 7 . 8 1 9 7 . 1 2 2 2 . 0 2 4 3 . 2 2 6 1 . 1 2 7 6 . 1 2 8 8 . 6 2 9 8 . 7 3 0 6 . 6 3 1 2 . 9 3 2 1 . 7 3 2 7 . 2 3 3 0 . 6 3 3 4 . 0 3 3 5 . 3 3 3 6 . 1

2 5 0 . 8 2 5 6 . 3 2 6 1 . 8 2 6 7 . 2 2 7 2 . 6 2 7 7 . 9 2 8 3 . 1 2 8 8 . 1

2 5 9 . 5 2 6 4 . 6 2 6 9 . 7 2 7 4 . 8 2 7 9 . 9 2 8 4 . 8 2 8 9 . 8 2 9 4 . 6 2 9 9 . 4 3 0 0 . 1

2 6 4 . 1 2 6 9 . 1 2 7 4 . 0 2 7 8 . 9 2 8 3 . 8 2 8 8 6 2 9 3 : 3 2 9 8 . 0 3 0 2 . 6 3 0 7 . 3

Nozzle

Nozzle exit, e

Figure 1. - Schematic diagram of liquid-propellant rocket engine.

NACA RM E54FZZa

0 80 160 240 320 400 Expansion ratio, pC/p,

Figure 2. - Theoretical specific impulse of several propellants. Optimum mixture ratio; isentropic expansion assuming equilibrium composition. Chamber pressure, 500 pounds per square inch absolute.

NACA RM EW22a

Oxidant-fuel weight ratio

(a) Specific impulse. I = 1 (p /300)~l. 300 C

Figure 3. - Theoretical performance of liquid ammonia and liquid fluorine as a rocket propellant. Isentropic expansion assuming equilibrium composition. Chamber pressure, 300 pounds per square inch absolute.

18 22 2 6 30 34 38 42 46 50 Fuel in propellant, percent by weight

4 3 2.5 2 1.5 1.25 1 Oxidant-fuel weight ratio

n2 (b) Characteristic velocity. c* = ~&~(~~/300) . Figure 3. - Continued. Theoretical performance of liquid ammonia and liquid fluorine as a rocket propellant. Isentropic expansion assuming equilibrium composition. Chamber pressure, 300 pounds per square inch absolute.

3 2.5 2 1.5 1.25 Oxidant-fuel weight ratio

( c) Nozzle area ratio. Ae/At = (&/At) 300(~c/3~~)n3.

Figure 3. - Concluded. Theoretical performance of liquid ammonia and liquid fluorine as a rocket propellant. Isentropic expansion assuming equilibrium composition. Chamber pressure, 300 pounds per square inch absolute.

(a) Specific impulse. I = 1 ~ ~ ~ ( ~ ~ / 3 0 0 ) ~ ~ .

Figure 4. - Theoretical performance of JP4 and liquid oxygen as a rocket propellant. Isentropic expansion assuming equilibrium composition. Chamber pressure, 300 pounds per square inch absolute.

Fuel in propellant, percent by weight L 8 8 I I

4 3 2.5 2 1.5 Oxidant-fuel weight ratio

(b) Characteristic velocity. c' = ~ g * 0 ~ ( ~ ~ / 3 0 0 ) ~ ~ .

Figure 4. - Continued. Theoretical performance Of JP4 and liquid oxygen as a rocket propellant. Isentropic expansion assuming equilibrium composition. Chamber pressure, 300 pounds per square inch absolute.

20 24 28 3 2 36 40 Fuel in propellant, percent by weight

I I I I

4 3 2.5 2 1.5 Oxidant-fuel weight ratio

(c) Nozzle area ratio. ~ ~ 1 % = (Ae/At) 300(pc/3~~)n3.

Figure 4. - Concluded. Theoretical performance of JP4 and liquid oxygen as a rocket propellant. Isentropic expansion assuming equilibrium composition. Chamber pressure, 300 pounds per square inch absolute.

Nozzle-throat area At 9 - Nozzle-exit area A,

Figure 5. - Ratio of mean effective pressure acting downstream of separation point to ambient pressure as function of nozzle area ratio. Data are for air (ref. 16).

NACA RM E54F22a

Figure 6. - Effective spec i f ic impdse estimated f o r design-point operation f o r ammonia-fluorine and J'P4-oxygen f o r various chamber pressures.

Altitude, ft

(a) Overexpandedj chamber pressure, 300 pounds per square inch absolute.

Figure 7. - Estimated effective specific impulse of ammonia-fluorine and JP4-oxygen. Nozzle area ratio A,/A~ to give complete expansion at indicated design altitude.

Altitude, ft

(b) Underexpandedj chamber pressure, 300 pounds per square inch absolute.

Figure 7. - Continued. Estimated effective specific impulse of ammonia- fluorine and JP4-oxygen. Nozzle area ratio Ae/At to give complete expansion at indicated design altitude.

NACA RM E54FZ2a

380 . I Design altitude,

ft

360 .. Ps/Pa for separated flow

0 10 20 30 40 50 60x10~ Altitude, ft

(c) Overexpanded j chamber pressure, 400 pounds per square inch absolute.

Figure 7. - Continued. Estimated effective specific impulse of ammonia- fluorine and JF'4-oxygen. Nozzle area ratio Ae/At to give complete expansion at indicated design altitude.

NACA RM E5432Za

Altitude, ft

(d) Underexpandedj chamber pressure, 400 pounds per square inch absolute.

Figure 7. - Continued. Estimated effective specific impulse of ammonia- fluorine and JP4-oxygen. Nozzle area ratio A,/A~ to give complete expansion at indicated design altitude.

0 10 20 30 40 50 60 Alti~ude, ft

(e) Overexpanded; chamber pressure, 600 pounds per square inch absolute.

Figure 7. - Continued. Estimated effective specific impulse of ammonia- fluorine and JP4-oxygen. Nozzle area ratio Ae/At to give complete expansion at indicated design altitude.

NACA RM E54F2Za

400

380

5 360 aJ

I

5 - t.1

340 - aJ m rl

ii E! .rl

0

d 320 . r i 0 a,

4 $ .rl :: aJ 300 k k W

280

2 60 o 20 40 60 80 100 120x103 Altitude, ft

(f) Underexpanded j chamber pressure, 600 pounds per square inch absolute.

Figure 7. - Continued. Eetimated effective specific impulse of ammonia- fluorine and JP4-oxygen. Nozzle area ratio Ae/At to give complete expansion at indicated design altitude.

(g) Overexpanded; chamber pressure, 800 pounds per square inch absolute.

Figure 7. - Continued. Estimated effective specific impulse of ammonia- fluorine and JP4-oxygen. Nozzle' area ratio A,/A~ to give complete expansion at indicated design altitude.

Altitude, ft

(h) Underexpandedj chamber pressure, 800 pounds per square inch absolute.


NACA RM E5B22a

380

3 60

340

3 20

300

280

260 0 10 20 30 40 50 6 0 M

Altitude, ft

(i) Overexpandedj chamber pressure, 1200 pounds per square inch absolute.


NACA RM E54FZa

( j) Underexpanded j chamber pressure, 1200 pounds per square inch absolute.

Figure 7. - Concluded. Estimated effective specific impulse of ammonia- fluorine and JP4-oxygen. Nozzle area ratio A,/A~ to give complete expansion at indicated design altitude.

Figure 8. - Variation of nozzle area ratio with design altitude and chamber pressure for ammonia-fluorine and JP4-oxygen.

200 400 600 800 1000 1200 Chamber pressure, pc, lb/sq in. abs

Figure 9. - Effective characteristic velocity of ammonia-fluorine At

and JP4-oxygen. c* = gp, ;.

0 200 400 600 800 1000 Propellant flow rate, w, lb/sec

(a) Chamber pressure, 400 pounds per square inch absolute.

Figure 10. - Variation of estimated weight of rocket power plant with propellant flow rate and design altitude f ~ r ammonia-fluorine at various chamber pressures. Average propellant density, 0.04335 pound per cubic inch; weight-percent fuel, 23.01.

Propellant flow rate, w, lb!sec

(b) Chamber pressure, 600 pounds per square inch absolute.

Figure 10. - Continued. Variation of estimated weight of rocket power plant with propellant flow rate and design altitude for ammonia-fluorine at various chamber pressures. Average propellant density, 0.04335 pound per cubic inch; weight-percent fuel, 23.01.

Propellant flow rate, w, lb/sec

(c) Chamber pressure, 800 pounds per square inch absolute.

Figure 10. - Continued. Variation of estimated weight of rocket power plant with propellant flow rate and design altitude for ammonia-fluorine at various chamber pressures. Average propellant density, 0.04335 pound per cubic inch; weight-percent fuel, 23.01.

NACA RM E5$F22a, is

(d) Chamber pressure, 1.200 pounds per square inch absolute.

Figure 10. - Concluded. Variation of estimated weight of rocket power plant with propellant flow rate and design altitude for ammonia-fluorine at various chamber pressures. Average propellant density, 0.04335 pound per cubic inch; weight-percent fuel, 25.01.

-A


(a) Chamber pressure, 400 pounds per square inch absolute.

Figure 11. - Variation of estimated weight of rocket power plant with propellant flow rate and design altitude for JP4-oxygen at various chamber pressures. Average propellant density, 0.03637 pound per cubic inch; weiuhf . -ner~nnt f'?~nl . 77 fib

(b) Chamber pressure, 600 pounds per square inch absolute.

Figure 11. - Continued. Variation of estimated weight of rocket power plant with propellant flow rate and design altitude for JP4-oxygen at various chamber pressures. Average propellant density, 0.03637 pound per cubic inch; weight-percent fuel, 27.64.

NACA RM E54FZZa


(c) Chamber pressure, 800 pounds per square inch absolute.

Figure 11. - Continued. Variation of estimated weight of rocket power plant with propellant flow rate and design altitude for JP4-oxygen at various chamber pressures. Average propellant density, 0.03637 pound per cubic inch; weight-percent fuel, 27.64.


(d) Chamber pressure, 1200 pounds per square inch absolute.

Figure 11. : Concluded. Variation of estimated weight of rocket power plant with propellant flow rate and design altitude for JP4-oxygen at various chaiuber pressures. Average propellant density, 0.03637 pound per cubic inch; weight-percent fuel, 27.64.


(a) Ammonia-f luorine . Figure 12. - Variation of ratio of auxiliary weight to power-plant weight with fuel flow and chamber pressure. Design altitude, 20,000 feet.

.90

.85 . \

\

.80 \ \

.75

.70

.65

-60

.55 0 200 400 600 800 1000

Propellant flow ra te , w, lb/sec

(b ) JP4-oxygen.

Figure 12. - Concluded. Variation of r a t i o of auxi l iary weight t o power- plant weight with f u e l flow and chamber pressure. Design a l t i tude , 20,000 f e e t .

NACA RM E54F22a

Unclassif ied when detached from r e s t of repor t

Vearl N. Huff Aeronautical Research Sc i en t i s t

Rocket Propulsion Theory

Jack Kerrebrock

Approved :

d& M- K A Eldon W. Hal l

Aeronautical Research Sc i en t i s t Propulsion Systems

9&-444~/ Bruce T. Lundin

Chief / Engine Research Division

New Image - ONLY - Scan to PDF/67531/metadc60594/m2/1/high_res_d/19930088292.pdfTheoretical...

Documents

Transcript of New Image - ONLY - Scan to PDF/67531/metadc60594/m2/1/high_res_d/19930088292.pdfTheoretical...