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(NACA-RM-E5UH03) ANALYSIS OF ROCKET,RAHJET, AND TURBOJET ENGINES FORSUPERSONIC PROPULSION OF LONG-RANGEMISSILES. 3: RAMJET ENGINE PERFORMANCE(NASA) 49 P

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RESEARCH MEMORANDUM

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

SUPERSONIC PROPULSION OF LONG-RANGE MISSILES

III - RAM -JET ENGINE PERFORMANCE

By Richard J. Weber and Roger W. Luidens

Lewis Flight Propulsion LaboratoryCleveland, Ohio

,0 ,

NATIONAL ADVISORY COMMITTEEFOR AERONAUTICS

WASHINGTON

NACA EM E54H03

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

RESEARCH MEMORANDUM

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

SUPERSONIC PROPULSION OF LONG-RANGE MISSILES

III - RAM-JET ENGINE PERFORMANCE

By Richard J. Weber and Roger W. Luidens

SUMMARY

Ram-jet engine performance data are presented over a range of enginedesign variables to permit selection and evaluation of a ram-jet engineconfiguration for a long-range supersonic missile. Calculated design-point performance of engines using JP4 fuel is presented for a vide rangeof engine totalTtemperature ratios and combustion-chamber-inlet Mach num-bers for flight Mach numbers from 1.5 to 4.0. The results includeengine thrust, drag, fuel consumption, area ratios, and weight, and aresuitable for use in design studies of missiles incorporating either in-ternally or externally mounted ram-jet engines. Maximum engine fuel spe-cific impulse (including nacelle drag) is approximately 1600 pound-seconds per pound and occurs at a flight Mach number of 2.5. Over-allengine efficiency, however, continues to increase to a flight Mach numberof 4.0, where it is 35 percent.

Important gains in both thrust coefficient and specific impulse maybe achieved by improving the diffuser pressure recovery. Changes inflame-holder pressure loss and combustor length have only small effectson engine performance. That these factors, however, influence combustionefficiency is significant, because the specific impulse varies directlywith the efficiency, although the thrust coefficient is practically un-affected. Engine performance is very sensitive to changes in nozzleperformance, a 1-percent variation in velocity coefficient often produc-ing a 3-percent variation in engine thrust and specific impulse. Someunderexpansion of the exhaust gases is desirable to reduce nacelle dragwhenever the nozzle-exit diameter exceeds that of the combustion chamber.

With a fixed-geometry configuration, a ram-jet engine does not oper-ate satisfactorily at off-design conditions. Somewhat better thrust canbe obtained with the added complication of a translating-spike diffuser,although the specific impulse is poorer. Use of a movable plug to varythe throat area of the exhaust nozzle yields both thrust and specificimpulse approaching that of a continuously variable-geometry engine.

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INTRODUCTION

The Complete Study

The role of guided missiles in the nation's weapons system has re-ceived much attention in recent years. Latest advances in research anddevelopment of engines, aerodynamics, and guidance make practicable theutilization of these missiles for delivery of a warhead at supersonicspeeds to a target thousands of miles distant. As an aid to the solution (

of development and 'design problems, it is the purpose of this series of <reports to study the potentialities of various engines suitable for the *supersonic propulsion of long-range missiles and to determine those char-acteristics which result in the best over-all performance of the engineand missile combination. In order to keep primary emphasis on the char-acteristics of the engine proper, the material on engine performance isseparated from that which considers the over-all missile system. Therocket-engine performance and the study of the rocket-powered missileare presented in references 1 and 2, respectively. The performance ofthe ram-jet engine is presented herein.

Continuing research indicates many improvements that are possible insome of the engine components. The performance of the components selectedfor the engines in Wiis analysis has either been demonstrated in the lab-oratory or appears, from available data, to be certain of attainmentwithin a reasonable time. Similarly, advanced features of airframe designthat are believed possible to develop in a comparable time were alsoselected.

The principal mission to which attention has been directed is thatof a long-range strategic bombardment missile. The configurations studiedare all limited to simple two-stage designs consisting of a rocket boosterused only during the initial phase of flight and a second stage that fliesthe remaining distance under its own power. Missiles propelled by theair-breathing engines are considered for cruise flight Mach numbers from2 to 4 at altitudes from 35,000 to 80,000 feet. The rocket-propelledmissiles are considered to travel along a ballistic trajectory, eventhough there are serious problems of re-entry into the atmosphere.Although glide and even skip rockets have frequently been proposed forthis application, the many problems and uncertainties associated withthe aerodynamics of these air-borne types preclude them from the presentstudy.

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Rocket engines for long-range ballistic missiles have very shortoperating times (l to 3 min) and during this time are operating at con-tinually differing flight conditions. The study of the rocket engine(ref. l) must, therefore, be based on a compromise design. Fortunately,however, the study is simplified, because the performance of a rocketengine is practically independent of flight velocity. On the other hand,air-breathing engines for long-range missile propulsion generally oper-ate continuously at their design conditions for the major portion of theflight time. Therefore, even though off-design engine performance isconsidered in these analyses, the study of the air-breathing engines canbe based principally on design-point performance.

Ram-Jet Engine Performance

The purpose of this report is to present sufficient ram-jet engineperformance data over a range of engine design parameters to permit se-lection and evaluation of a ram-jet engine configuration for a long-rangesupersonic missile. A second purpose is to illustrate the relative im-portance of the different engine parameters that influence the design ofthe ram-jet engine. Many other thermodynamlc cycle studies of ram-jetengines have been presented in the literature (e.g., refs. 3 and 4).This report presents a wider range of operating conditions, uses some-what advanced, but realistic, component characteristics, and demonstratesthe effect of changes in these component characteristics.

The missiles are considered to have externally mounted engines.Therefore, nacelle drag is included in the engine performance data tofacilitate separate consideration of airframe and engine. However,engine drag coefficients are tabulated so that the results may alsobe used without drag for other studies.

The report has three major sections:

(1) General design-point engine performance is presented for a widerange of engine total-temperature ratios and combustion-chamber-inletMach numbers for flight Mach numbers from 1.5 to 4.0. The fuel used isJP4, and nominal assumptions are used for the component characteristics.

(2) The sensitivity of these design-point results to changes in thenominal assumptions is indicated by showing the effect of varying thedifferent component parameters, one at a time, on the performance of se-lected engines. The parameters investigated are diffuser pressure re-,covery, flame-holder pressure loss, combustion efficiency, combustorlength, nozzle velocity coefficient, nozzle expansion ratio, nozzle jet-deflection angle, and altitude. Calculations were also made comparinga high-energy fuel (pentaborane) with JP4.

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(3) Off-design performance is presented for an engine designed forefficient cruising at a flight Macli number of 3.5. Configurations havingfixed geometry, continuously variable geometry, and two types of practi-cally variable geometry are compared. Off-design performance is notemphasized, because results obtained in missile studies indicate thatself-boosting capabilities are not important for ram-jet-powered long-range missiles.

ANALYSIS

The symbols used in this report are defined in appendix A.

A schematic diagram of the ram-jet engine is shown in figure 1.High-speed air enters the engine at station 1 and is decelerated to alow velocity at 2. Fuel is added, ignition takes place, and combustionis stabilized at the flame holders, between stations 2 and 3. Combustionoccurs in a constant-area duct from stations 3 to 4, and the hot gasesare expanded and discharged through a convergent-divergent nozzle (sta-tions 4 to 6).

The performance calculations were made on the basis of one-dimensional flowy using the equations of state, continuity, and conser-vation of momentum and energy. Reference 4 presents equations similarto those used in the present analysis, in which the values of f arebased on the gas static temperature and composition at' each station.The problem of specifying the gas properties is discussed more fully inappendix B, and the assumed engine geometry and methods used in calcu-lating the engine drags are detailed in appendix D. Engine performancedata, which are generally presented for an altitude of 70,000 feet, maybe used for any altitude in the isothermal region of the atmosphere withnegligible error.

Engine performance is presented in this report in terms of thefollowing:

(1) Propulsive thrust coefficient Crp, defined as engine thrustminus nacelle drag per unit cross-sectional area, divided by free-streamincompressible dynamic pressure. The cross-sectional area used is thediffuser capture area or the combustion-chamber frontal area, whicheveris larger. This coefficient is a measure of the engine size requiredto produce a given amount of propulsive thrust.

(2) Specific impulse I, defined as engine thrust minus nacelledrag divided by engine fuel-flow rate. At any given flight speed, thisparameter is a measure of the efficiency with which thrust is produced.

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Appendix C describes a simple method of estimating engine weight,from which it was concluded that ram-jet engine weight per unit cross-sectional area is approximately constant.

Most of the various engine parameters fall into two groups: (A)those of major importance that cannot be finally specified without acomplete missile flight analysis, and (B) those that can be realisticallychosen from an engine study alone, or that are limited by what can prac-tically be achieved. These major variables (group A) were taken asflight Mach number, combustion-chamber-inlet Mach number, and enginetotal-temperature ratio. A complete set of design-point performancecalculations was obtained for different values of these variables, basedon nominal assumptions made for the component parameters of group B.The range of calculations for these major variables included flight Machnumbers from 1.5 to 4.0, combustion-chamber-inlet Mach numbers from0.125 to 0.225, and engine total-temperature ratios corresponding tofuel-air ratios of approximately 0.01 to stoichiometric, except wherelimited by thermal choking.

The following values were used for the variables of group B inthe design-point calculations:

(1) Diffuser pressure recoveries were assumed for a single-conespike diffuser with a kinetic-energy efficiency of 90 percent in thesubsonic portion. Cone angle was varied with design flight speed toachieve maximum pressure recovery. The design-point engines operatedcritically with no spillage. Reference 5 shows that, in the presentstate of inlet development, the engine performance obtained with thissingle-cone inlet with low-drag cowl is as good as that afforded by moreelaborate inlets such as the isentropic spike. Figure 2 shows theassumed variation of pressure recovery with flight Mach number for crit-ical operation. These values are in good agreement with the experimentaldata for similar inlets reported in reference 6.

(2) Flame-holder total-pressure loss was taken as twice the incom-pressible dynamic pressure at station 2. Combustion of the fuel (JP4with a lower heating value H of 18,640 Btu/lb) took place from sta-tions 3 to 4 with an assumed efficiency of 0.90. The resulting relationbetween T (engine total-temperature ratio) and fuel-air ratio f/a fordifferent flight Mach numbers is shown in figure 3. Reference 7 reportsthe achievement of about 0.95 efficiency with the same amount of flame-holder loss in tests of a 16-inch combustor at a combustor pressure ofabout 1 atmosphere. The combustor pressure, however, in an engine forlong-range missiles may for some flight paths be subatmospheric.

(3) The nozzle velocity coefficient was taken as 0.975. Values ofthis magnitude were obtained experimentally in large-scale tests ofconvergent-divergent nozzles at nozzle pressure ratios P /Pe of about

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5 (ref. 8). Recent unpublished results indicate that this value may beapproached even at high nozzle pressure ratios. At flight Mach numbersof 2.5 and higher, the nozzle-exit diameter is generally the largestdiameter of the engine. To reduce nacelle drag in these cases, the nozzle expansion ratio was made less than that required for complete expansion of the gases to ambient pressure. From data obtained in missilestudies shoving the effect of expansion ratio on missile range, theoptimum expansion ratio is roughly generalized by the empirical formula

•r^ = 1 + 0.55A3

te\^ 3'p =p

- 1

where ( T~ ) is the ratio of nozzle-exit to combustion-chamber area

for complete expansion. This expression was used for the design-pointengine calculations whenever the nozzle-exit diameter exceeded that ofthe combustion chamber. In all other cases the nozzle was made com-pletely expanding.

The sensitivity of the design-point results to changes in theseassumed values of the various component parameters was indicated bycalculating the effect of varying these parameters, one at a time, atflight Mach numbers of 2.5 and 3.5. At each speed, two values of Twere considered, a low value for good cruising performance and a highervalue to give increased thrust for missile acceleration.

The off-design performance of engines designed for cruising at aflight Mach number of 3.5 was also evaluated. Engines equipped with thefollowing features were considered:

(1) Continuously variable diffuser and nozzle

(2) Variable-throat-area nozzle with fixed diffuser

(3) Translating-spike diffuser with fixed nozzle

(4) Fixed diffuser and nozzle

RESULTS AND DISCUSSION

Design-Point Performance

The calculated design-point values of propulsive thrust coefficientand specific impulse are shown in figure 4 as functions of flight Machnumber MQ, ratio of combustion-chamber-exit to -inlet total temperatureT, and combustion-chamber-inlet Mach number Mg. These data, as well as

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engine area ratios and drag coefficients, are listed in table I. Thevalues of Cm and I include nacelle drag. The corresponding valueswithout nacelle drag may be obtained by the relations . '

Cm + CTJ (2)

(3)

.Performance of engines having velocity coefficients other than0.975 may be calculated from the following formula:

y°T ~ 0.975 (Cm)T'0.975

which is based on the assumption that the jet thrust is directly propor-tional to the velocity coefficient, and that the. nacelle drag does notchange. . . , .

Performance can also be computed for values of combustion efficiencyother than0.90. At any constant value of T, the thrust coefficientremains essentially constant with changes in combustion efficiency, andspecific impulse and fuel-air ratio are given by

0.90T

0.90 (5)

fa (6)

Figure 4 shows that high thrusts are obtained at the high values ofT and maximum specific impulses at intermediate values of T. RaisingT (at a constant MQ and Mg) increases the exit momentum of the gases,mainly because of the higher jet velocity and, to a lesser degree, be-cause of the increased fuel mass flow. However, as T is raised, thefuel flow increases at a greater rate than the jet thrust; so that,after the constant loss of the inlet momentum, drag is sufficiently over-come, the specific impulse reaches a maximum and then decreases. Whennacelle drag is included, the value of T for maximum specific impulseis raised.

The effect of flight Mach number on:over-all engine efficiency, pro-pulsive thrust coefficient, and specific impulse is shown in figure 5, inwhich the value of T is varied to provide maximum I and E at eachflight speed. Combustion-chamber-inlet Mach number is generally 0.200,except for MQ above 3.35, where it was necessary to reduce Mg to pre-vent the diffuser-inlet diameter from exceeding that of the combustion

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chamber. Maximum I (1600 Ib-sec/lb including nacelle drag) occurs atMQ of 2.5. This flight Mach number, however, may not be optimum for amissile, because missile range is more nearly related to the over-allengine efficiency, vhich in turn is proportional to the product of spe-cific impulse and flight velocity rather than to specific impulse alone.Maximum E of the order of 0.35 is realized at MQ near 4, while thehighest efficiency obtainable at MQ of 2.5 is only 27 percent.

The effect of combustion-chamber-inlet Mach number M2 is indicatedin figure 4 but is more readily apparent in a cross plot of some of thesedata (fig. 6). The propulsive thrust coefficient increases with VLbecause of the essentially linear increase in air flow to the point wherethe inlet capture area becomes equal to the combustion-chamber area. Thevalue of Mj> at which these areas are equal is higher than the region ofinterest shown in figure 6, but is a function of the flight speed and thediffuser pressure recovery. Raising Mg also increases both the flame-holder pressure loss and the momentum pressure loss due to heat addition.If nacelle drag were not included, the specific impulse would decreasewith increasing values of Mg. However, higher values of VL reducethe diameter of the combustor and nozzle relative to the diffuser capturearea and so result in lower nacelle drag per pound of air (provided thecapture area remains. smaller than the combustion-chamber area). Becauseof these two opposing effects, the specific impulse is fairly insensitiveto variations in M2 for the conditions of figure 6.

Effect of Variations in Design-Point Assumptions

Diffuser pressure recovery. - Diffuser total -pressure ratio is usedin this report as a measure of the efficiency with which the diffuserconverts the kinetic energy of the captured air stream to pressure.Lines of constant kinetic -energy efficiency superimposed on the curve ofpressure recovery against flight Mach number (fig. 2) show that the lowernumerical values of total -pressure ratio at high flight Mach numbers donot necessarily mean lower diffuser efficiency.

The nominal diffuser assumed for the design-point calculations isan oblique-shock inlet with a single-cone spike centerbody. Figure 7shows the effect on engine performance of changes in the assumed valuesof pressure recovery. (This performance is based on the drag of a low-angle cowl at all pressure recoveries.) The engine air flow per unitcombustion-chamber area increases linearly with pressure recovery, sothat the propulsive thrust coefficient (based on combustion-chamber area)also increases nearly linearly. As pressure recovery is increased, thediffuser capture area enlarges relative to the combustion chamber in orderto handle these larger air flows at constant Mp . At high flight Mach num-bers and high pressure recoveries, the resulting capture area often be-comes greater than the combustion-chamber area. The size of the engine

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required to produce a given thrust is then indicated by basing .the thrustcoefficient .on diffuser capture area. At a flight Mach number of 2.5,the combustion chamber is always the larger for the range of pressure re-coveries considered. . At a flight Mach number of 3.5 and Mg of 0.20,the. capture area becomes the larger at pressure recoveries greater than0.43, which causes the sharp break in thrust coefficient observed at thispoint in figure 7. The engine specific impulse increases with increasingpressure recovery because of the higher pressure ratio across the exhaustnozzle. The higher air flow also improves the specific impulse becauseof the lower nacelle drag per pound of air.

In general, however, diffuser designs that result in improved pres-sure recoveries have associated with them high engine-cowl pressure drags.Consequently, the gain in engine performance resulting from improved pres-sure recovery may be largely offset by the resulting engine drag increase.Figure 8 shows engine performance at a flight Mach number of 3.5 as a - ..function of both pressure recovery and engine nacelle drag coefficient.The-dotted line repeats the low-angle-cowl drag values from figure 7 andrepresents the best performance attainable at any value of pressure.re-covery. Figure 8 indicates the penalties in drag rise that are.acceptableto obtain better engine performance as a result of improved pressure re-covery. Calculations based on the experimentally measured pressure re-covery and cowl drags reported in reference 5 confirm the conclusion thatcurrently available high-recovery inlets do not yield better over-all en-gine performance than does the single-cone type assumed throughout thisanalysis. Although the single-cone inlet.was used to give performancerepresentative of that available with other current inlet types, the ad-vanced inlets have greater potentialities for improvement, as indicatedin figure 8. Other factors must also be considered, of course, in com-paring different diffuser designs. For example, a single-cone inlet maybe easier to design and manufacture and is less sensitive to angle ofattack than are more elaborate types. On the other hand, the higher pres-sure provided by an advanced inlet may increase combustion efficiency andprevent blow-out. . .. .

Combustion efficiency. - If T is held constant in an engine, var-iations in combustion efficiency have only a negligible effect on engine.thrust. However, fuel flow and hence specific impulse are directly pro-portional to the combustion efficiency. The great importance of thiseffect lies in the fact that the range of a ram-jet missile variesdi-.rectly with the specific impulse, if all other factors do not change.

Flame-holder pressure loss. - The purpose of the flame holder is toensure the ignition and efficient burning of a fuel-air mixture movingat several hundred feet per second when the laminar flame speed of themixture may be in the order of only 5 feet per second. Increased flow .blockage and turbulence often improve the combustion efficiency but intro-duce pressure losses detrimental to the thrust output of the engine. Acompromise is often necessary between these opposing factors. The changein propulsive thrust and specific impulse with the flame-holder cold-flow

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pressure-drop coefficient is indicated in figure 9 for a constant com-bustion efficiency.

Combustion-chamber length. - Improved combustion efficiency may alsoresult from lengthening the combustion chamber to obtain more completeburning; however, this results in a heavier engine and increased drag.The effect of increased drag on the propulsive thrust coefficient andspecific impulse due to lengthening the engine is shown in figure 10 ata flight Mach number of 3.5 (for constant combustion efficiency). Thecorresponding change in engine weight is also indicated. As describedin appendix D, the design-point engine calculations assumed a nominalcombustor length equal to 3 diameters of the combustion chamber, witha total engine length of 9 diameters. Doubling the combustor lengthfrom 3 to 6 diameters (at constant T) reduces Crp and I by less than2 percent but, according to the weight estimates of appendix C, increasesthe installed engine weight by 24 percent.

Fuel type. - Another combustor variable that may be changed to im-prove performance is the fuel used. High-energy fuels permit raisingboth thrust and specific impulse, but they are generally more expensivethan hydrocarbon fuels, or they may have other undesirable characteristicssuch as pumping or storage problems. Calculations were made for penta-borane (BgHg) as a typical high-energy fuel frequently mentioned for ram-jet applications. Figure 11 shows the propulsive thrust coefficient andspecific impulse of an engine designed for flight Mach number of 3.5 forpentaborane and JP4. These calculations for BgHg were made with theassumption of equilibrium composition of the exhaust gases and with ex-pansion to the same area assumed with JP4. Data for these calculationswere taken from reference 9. These curves are for a combustion effic-iency of 0.95 for the pentaborane and 0.90 for the JP4 fuel.

For the same thrust coefficient, a specific impulse with pentaboraneof more than 150 percent of that with JP4 is indicated at low fuel-airratios up to those that give maximum specific impulse. The improvementis less at high fuel-air ratios that give near maximum thrust coefficient.Because of other factors, however, such as different fuel densities,missile range is not necessarily improved in the same proportion.

Nozzle area ratio. - The effect of nozzle area ratio is presentedin figure 12. Very little loss in propulsive thrust coefficient andspecific impulse is suffered by cutting back the nozzle area as much as30 percent from that 'required for complete expansion. In fact, forsmaller amounts of underexpansion, gains of 1 or 2 percent may be real-ized, because reducing these areas reduces the external nacelle dragsufficiently to compensate for the lower internal thrust. In addition,since the nozzle was assumed to have a velocity coefficient less than1.0, a small amount of underexpansion results in a very small increasein internal thrust. It is sometimes proposed that the nozzle-exit areanot be permitted to exceed the combustion-chamber area. This condition(Ag = Aj) is marked on the curves of figure 12. It is apparent that*

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this amount of underexpansion results in appreciable losses, particularlyat the higher flight speed. The performance of a convergent nozzle(Ag = A^) is seen to be very poor at both speeds.

Nozzle velocity coefficient. - The velocity coefficient (defined asthe actual velocity at the nozzle exit divided by the ideal isentropicvelocity at the nozzle exit for the same pressure ratio) is .used to indi-cate the'amount of the nozzle internal flow losses. These losses, whichreduce the total pressure, are due to shocks, turbulence, and viscous'effects within the gas stream and to wall friction at the gas boundaries.The effect on engine performance of a variation in the nozzle velocitycoefficient from the assumed value of 0.975 is indicated in figure 13.A 1-percent change in velocity coefficient changes the thrust and spe-cific impulse from 2 to 3 percent for the indicated.values of Mach num-ber and T. .

There are other sources of thrust losses through the nozzle that donot affect total-pressure loss. In addition to the flow losses treatedthrough the application of a nozzle velocity coefficient, the assumptionof one-dimensional flow implies that all exhaust gases are dischargedaxially and that there are no gradients in radial velocity. Neither ofthese implications is necessarily true. A nonuniform temperature dis-tribution at the combustor exit would result in radial velocity gradientseven with a nozzle designed for axial discharge. Calculations indicatethat all reasonable temperature distributions, such as a parabolic pro-'file, result in thrust losses of less than 2 percent. Losses due tononaxial discharge from a conical nozzle with a half-angle of 15° wouldbe of the order of 1.5 percent. Use of a smaller angle or changes innozzle contour would reduce this loss, although possibly at the expenseof increased manufacturing cost and nozzle length.

Nozzle Jet-deflection angle. - An interesting possibility for im-proving the performance of a ram-jet missile lies in turning the jetthrust of the engine downward. This slightly decreases the forwardthrust and specific impulse but provides some lift, thereby permittingthe use of a smaller wing and lowering the missile weight and drag.Figure 14 presents the effect of jet-deflection angle on engine perform-ance, in which Cy v represents the component of vertical thrust dividedby the free-stream dynamic pressure qg and the engine cross-sectionalarea A^. These data are based on the assumption that nacelle drag doesnot change with deflection angle.

Altitude. - In the stratosphere (between 35,332 and 105,000 ft),changing flight altitude has only a small effect on propulsive thrustcoefficient and specific impulse through the Reynolds number effect onnacelle skin-friction drag coefficient. Below the tropopause, in addi-tion to this Reynolds number effect, the changing ambient temperaturesignificantly affects ram-jet performance. -In this region more fuel isrequired to maintain a design T as the altitude is reduced. This

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extra mass addition, although it raises the thrust coefficient slightly,lowers the specific impulse considerably. This same increase in fuelconsumption is felt by the over-all engine efficiency; however, the in-creased flight velocity (at constant flight Mach number) reduces themagnitude of the effect. These considerations combine to produce thevariations in propulsive thrust coefficient, specific impulse, and over-all efficiency shown in figure 15. Also important is the effect offlight altitude (not shown) on combustion efficiency through changes inambient pressure and temperature, which in turn establish the temperature,pressure, and velocity at the combustor inlet.

Off-Design Performance

All the previous discussion has been concerned with a continuouslyvariable-geometry engine or a series of fixed-geometry design-point en-gines. Thus, it is implied that the inlet capture area is sized toavoid subcritical spillage, the diffuser cone angle is selected foroptimum pressure recovery, the diffuser spike can be translated for cor-rect positioning of the oblique shock upon the cowl lip, and the nozzle-throat area and area ratio are optimum. A practical engine incorporatingsuch variable components is not yet available.

This invariance of geometry is of no concern if the engine canalways be operated at its design or cruise point. Design-point engineoperation is possible for a ram-jet missile that cruises along a Breguetflight path, provided the missile is fully boosted to its cruising Machnumber and altitude by some other means. Even after starting cruiseflight, however, some corrective action may be required and off-designengine operation may be necessary. Moreover, ram-jet thrust may bedesired during the boost phase of the flight. In .order to include en-gine performance for these flight conditions, some off-design enginecalculations were also made. Because it was desired to indicate trendsrather than absolute magnitudes, a constant value of f of 1.30 forthe exhaust gas was used for ease of computation of the off-designperformance.

Figure 16 shows the propulsive thrust coefficient and specific im-pulse of a fixed-geometry engine designed to operate at MQ of 3.5, Mgof 0.200, and T of 2.25. These conditions are shpwn__in missile stud-ies to result in good cruise performance. Because the combustor mustnow operate over a wide range of flight conditions, the combustion effi-ciency (0.87) was assumed to be slightly lower than that for the design-.point case (0.90). Along each line of constant MQ, the parameter iis raised to increase the thrust coefficient. For any given T thereis a single unique value of M2 due to the choked fixed-nozzle throatarea. At MQ of 3.5 and values of T below 2.25, M2 is greater than

W.CA EM E54H03 'I ^ ^ ^ HI 13

0.2. and the diffuser operates supercritically, with a severe loss inpressure recovery and a-consequent adverse effect on thrust and specificimpulse. As T is raised by burning more fuel, Mg is reduced to itsdesign value, and the diffuser then operates critically, with the normalshock positioned at the diffuser lip. This condition corresponds to thesharp break in the curve. Further increase of T causes subcriticaldiffuser operation. Although the external shock or "bow wave" so gen-erated does not necessarily reduce the diffuser pressure recoveryseverely, it spills air that would normally enter the engine and causeslarge additive-drag losses.. With subcritical operation and no loss inpressure recovery, a small gain in thrust is obtainable over criticaloperation, but the specific impulse drops markedly. In addition to in-efficient operation, subcritical operation often results in instabilityof flow or "buzzing," which can, in severe cases, even blow out the com-bustor flame or damage the diffuser structure. In general, then, sub-critical operation is undesirable.

For speeds less than design, best engine performance is also gener-ally obtained with the value of T chosen to give critical diffuseroperation. However, as flight speed is reduced, the value of Mg forcritical operation is raised.

The off-design performance of several engines designed for effi-cient cruising at a flight Mach number of 3.5 and incorporating varioustypes of geometry variation is shown in figure 17 as a function offlight Mach number. Performance is shown for the engines operating attheir maximum thrust condition. Also included are data for criticaloperation of a fixed-geometry engine obtained by cross-plotting thepeaks of the curves from figure 16. The performance of an engine withboth continuously variable inlet diffuser and exit nozzle is obtainedwith a wide-open exhaust nozzle and a stoichiometric fuel-air ratio.Extremely large penalties in thrust are suffered with the fixed-geometryengine, with a thrust at flight Mach number 2.5 of only 15 percent ofthat available from an engine equipped with a continuously variableinlet and outlet. These large thrust losses are mainly due to thenecessity of reducing T to prevent subcritical operation. The abilityto burn more fuel without being forced into the subcritical region ex-'plains why the continuously variable engine can produce more thrustthan the fixed-geometry engine even at the design Mach number of 3.5.

Equipping an engine with either a movable-spike inlet or avariable-area exit nozzle, both of which are currently feasible, resultsin considerable gain over fixed-geometry engine performance. With amovable-spike inlet, the spike is translated axially so that all airspillage occurs behind an oblique shock. The flow behind the obliqueshock remains supersonic, and the additive drag is not as severe as inthe case of a bow wave. This spillage permits T to be increased with-out causing subcritical operation. Thrust increases over the fixedconfiguration of 50 to 100 percent are possible, but the specific im-pulse is very low.

14 *m ^ ^ Hr MCA EM E54H03

Thrust levels approaching the continuously variable case with aboutthe same specific impulse can be achieved with an engine having a fixedinlet and a movable-plug nozzle. Although the nozzle throat area isvariable, the nozzle-exit diameter is fixed and the nozzle expansionratio cannot be independently chosen. At a flight Mach number of 2.5,the thrust is 74 percent that of the continuously variable engine.

CONCDJDING REMARKS

The calculated design-point performance of ram-jet engines using<JP4 fuel is presented for a wide range of engine total-temperatureratios and combustor-inlet Mach numbers for flight Mach numbers of 1.5to 4.0. The results, which include engine thrust, drag, fuel consump-tion, area ratios, and weight, are given in both graphical and tabularform. These data are suitable for use in design studies of ram-jetmissiles incorporating, either internally or externally mounted engines.Maximum engine specific impulse (including nacelle drag) is approxi-mately 1600 pound-seconds per pound and occurs at a flight Mach numberof about 2.5. Over-all engine efficiency, however, continues to in-crease to a flight Mach number of 4.0. It is not possible on the basisof engine performance data alone to determine best flight Mach numberand fuel-air ratio for maximum missile range.

Calculations are also presented which indicate the sensitivity ofthe design-point results to changes in diffuser pressure recovery, flame-holder pressure loss, combustor length, combustion efficiency, fueltype, nozzle expansion ratio, nozzle velocity coefficient, nozzle jet-deflection angle, and altitude. Significant gains in both thrust coef-ficient and specific impulse may be achieved by improving the diffuserpressure recovery. However, presently available inlet designs that pro-vide high recovery also have high cowl pressure drags which largelyoffset this potential gain. Changes in flame-holder pressure loss andcombustor length have only small effects on engine performance. Thesefactors may, however, influence combustor efficiency and the resultingmissile range. Engine performance is very sensitive to changes in noz-zle performance, a 1-percent variation in velocity coefficient oftenproducing a 3-percent variation in engine thrust and specific impulse.Some underexpansion of the exhaust gases is desirable to reduce nacelledrag whenever the nozzle-exit diameter exceeds that of the combustionchamber.

Satisfactory off-design operation of a ram-jet engine is not pos-sible with a fixed-geometry configuration. Somewhat better thrust canbe obtained with the added complication of a translating-spike diffuser,although the specific impulse is poorer. Use of a movable plug to vary

NACA EM E54H03 15

the throat area of the nozzle yields both thrust and specific impulseapproaching those of a continuously variable-geometry engine. In consid-ering engines designed for good cruise performance at flight Mach number3.5 but operating at flight Mach number 2.5, the maximum thrusts are15, 37, and 74 percent of that available with continuously variablegeometry for engines with fixed-geometry, translating-spike diffuser,and movable-plug nozzle, respectively.

Lewis Flight Propulsion LaboratoryNational Advisory Committee for Aeronautics

Cleveland, Ohio, August 5, 1954

16 ^ ^ ^ ^ NACA RM E54H05^ ^ ^ ^ ^ ^ ^ ^ ^ W

APPENDIX A

SYMBOLS

The following symbols are used in this report:

area, sq ft

diffuser capture area A^ or combust ion-chamber area A^, jwhichever is larger, sq ft i

CD nacelle drag coefficient,

Cji net thrust coefficient,

Cm propulsive thrust coefficient, Cp - C-Q

Cy nozzle velocity coefficient

D drag, Ib

d diameter, ft

E over-all engine efficiency, (F - D)VQ/JH wf

F net thrust, mgVg - H VQ + Ag(p6 - pQ), Ib

f/a fuel -air ratio

H lower heating value of fuel, Btu/lb

I fuel specific impulse, (F - D)/wf, Ib-sec/lb

Iji fue]. specific impulse not including drag, F/w , Ib-sec/lb

J mechanical equivalent of heat, 778 ft-lb/Btu

I combustion-chamber length, ft

M Mach number

m mass-flow rate, slugs/sec

P total pressure, Ib/sq ft

p static pressure, Ib/sq ft

MCA RM E54H03 JJ ^ ^ ^ ^ M, 17

o

q. incompressible dynamic pressure, pV /2, Ib/sq ft

R gas constant, 53.4 ft-lb/(lb)(°R)

T total temperature, °R

t static temperature, ^

V velocity, ft/sec

Wf fuel-flow rate, Ib/sec

T ratio of specific heat at constant pressure to specific heat atconstant volume

T]_ combustion efficiency, \rf . ,,/w> „„C X • 1Q* X • £LC

X jet -deflect ion angle, deg

p density, Ib/cu ft

T engine total-temperature ratio,

Subscripts:

ac actual

ef effective

fr friction

id ideal

nom nominal

v vertical

0 free stream

1 diffuser inlet

2 combustion-chamber inlet (upstream of flame holder)

3 combustion-chamber inlet (downstream of flame holder)

4 combustion-chamber exit

5 nozzle throat

6 nozzle exit

18 ^ ••• k MCA EM E54H03

APPENDIX B

THERMODYMMIC ASSUMPTIONS

Assigning correct gas properties and maintaining high computationalaccuracy are very important in any ram-jet engine analysis, "becausesmall changes in the calculated jet thrust may be magnified 3 or 4 timesin the net propulsive thrust. Specification of the gas properties in-volves realistic choice of r , R, and T as a function of temperature,fuel-air ratio, and pressure (if there is appreciable dissociation).

Data for octane (ref. 4), which include dissociation effects, wereconverted to JP4 and used in constructing figure 3, which gives T asa function of Mg and f/a for an ambient temperature of 392° R. Sim-ilar curves were constructed for altitudes under the tropopause wherethe .ambient temperature is different from 392 R. The very high temper-atures plus the changes of composition due to burning cause the y ofthe combustion gases to vary appreciably from 1.40 if equilibrium isreached. These equilibrium values, as a function of temperature andf/a and for a pressure of 1 atmosphere, were obtained from reference 10,which includes a very appreciable effect of dissociation. Molecularequilibrium is not necessarily maintained during the expansion of thegas through the nozzle. However, considerations of heat-capacity lagand chemical-reaction rates indicated that the process is probablycloser to equilibrium than to "frozen" conditions. After trying severaldifferent methods, it was found that specifying an effective r for thenozzle by

gave best results as checked by equilibrium calculations using refer-ences 11 and 12. The deviations in net thrust were generally found tobe less than 3 percent . According to reference 10, this means of spe-cifying Tef is also best for use in the isentropic equation

- ~T

The value of R for the air stream was taken as 53.4 ft-lb/(lb)(°R).The same value was used for the exhaust gas with small error (ref. 13).

MCA BM E54H03 a ^ ^ ^ H 19

APPENDIX C

ENGINE WEIGHT

The engine was assumed to be constructed entirely of stainlesssteel with a density of 490 pounds per cubic foot of material. Theallowable stress was 100,000 psi in the diffuser and 50,000 psi in thecombustion chamber and nozzle. The engine was designed to withstand apressure of 110 psig, which would be obtained at MQ = 3.5 and an alti-tude of 35,000 feet. The diffuser island was made the same gage as thediffuser shell and the nozzle the same as the combustion-chamber wall.The external nacelle thickness was taken as> 0.020 inch. An allowanceof 50 pounds per square foot of combustion-chamber area was made forfuel systems and controls. After making arbitrary allowances for stif-feners and supports that were felt to be conservative, the weight oftypical engines designed for several flight speeds was calculated. Inall cases the calculated weight was very nearly 180 pounds per squarefoot of combustor cross-sectional area. Because missile studies showthat ram-jet engine weight is of secondary importance, it was assumedthat the value of 180 pounds per square foot was sufficiently accuratefor all engines"considered.

20 ••••IV' MCA RM E54H03

APPENDIX D

ENGINE DRAG

The engine thrust is defined in terms of the total-momentum changesoccurring between the free-stream tube ahead of the engine and the ex-haust at the end of the engine. The drag must, therefore, include allthe external forces acting on the stream tube and engine between thesame two points. These forces are composed of pressure forces actingperpendicular to the stream tube and engine, and a friction force actingparallel to the engine nacelle due to the viscosity of the air. Thepressure (or wave) drag may be further broken down into the part actingdirectly on the nacelle and the additional, imaginary part acting on thestream tube because of the way the thrust was defined. The latter forceis termed additive drag, and was calculated by the method of reference 14.

The nacelle friction drag was calculated from the following equa-tion, which is based on the flat-plate formula of reference 15:

„ AW 0.0306 K

where A^ is nacelle skin area, K is a shape factor taken as 1.05 fora cylindrical nacelle, and the Reynolds number Re is based on free-stream conditions with a nominal length of 30 feet and a nominal alti-tude of 70,000 feet.

The nacelle pressure drag was obtained from the linearized theoryfrom reference 16. For the low-speed cases when the exit area wassmaller than combustion-chamber area, data for boattail drag for a7.04° cone were used from the same source. The diffuser cowl was assumedconical, with no added pressure drag incurred from a curved lip.

The engine was assumed to have a fineness ratio (length divided bycombust ion-chamber diam.) of 9, the diffuser being nominally 4, com-bustion chamber 3, and nozzle 2. The appearance of the engine as afunction of flight speed is as shown in the following sketch (not toscale):

NACA RM E54H03 21-

Low MQ (1.5 -.2.0)

Medium MQ (2.0 - 3.0)

High (3.0 - 4.0)

REFERENCES

1. Huff, Vearl N., and Kerrebrock, Jack: Analysis of Rocket, Ram-Jet,and Turbojet Engines for Supersonic Propulsion of Long-RangeMissiles. I - Rocket-Engine Performance. NACA RM E54F22a, 1954.

2. Huff, Vearl N., and Kerrebrock, Jack: Analysis of Rocket, Ram-Jet,and Turbojet Engines for'Supersonic Propulsion of Long-RangeMissiles. II - Rocket Missile Performance. NACA RM E54I29a.

3. Cleveland Laboratory Staff: Performance and Ranges of Applicationof Various Types of'Aircraft-Propulsion System. NACA TN 1349, 1947.

4. Douglass, Win. M.: Supersonic Ram Jet Performance. USCAL Rep. 2-4,Aero. Lab., Univ. of Southern Calif., May 27, 1946. (Navy ContractN0a(s)7598.)

5. Conners, James F., and Woollett, Richard R.: Performance Character-istics of Several Types of Axially Symmetric Nose Inlets at MachNumber 3.85. NACA RM E52I15, 1952.

22 idOTIMK NACA RM E54H03

6. Bernstein, Harry, and Haefeli, Rudolph C.: Investigation of PressureRecovery of a Single-Conical-Shock Nose Inlet at Mach Number 5.4.NACA RM E53A12, 1953.

7. Cervenka, A. J., Dangle, E. E., and Friedman, Robert: Effect ofInlet-Air Temperature on Performance of a 16-Inch Ram-Jet Com-bust or. NACA RM E53I03, 1953.

8. Krull, H. George, and Steffen, Fred W.: Performance Characteristicsof One Convergent and Three Convergent-Divergent Nozzles. NACARM E52H12, 1952.

9. Huff, Vearl N., Gordon, Sanford, and Morrell, Virginia E.: GeneralMethod and Thermodynamic Tables for Computation of EquilibriumComposition and Temperature of Chemical Reactions. NACA Rep. 1037,1951. (Supersedes NACA TN's 2113 and 2161.)

10. Bahn, G. S.: Thermodynamic Properties of Combustion Gases. PreprintNo. 53-S-39, A.S.M.E., 1953.

11. Hottel, H. C., Williams, G. C., and Satterfield, C. N.: Thermo-dynamic Charts for Combustion Processes, Pts. I and II. JohnWiley & Sons, Inc., 1949.

12. English, Robert E., and Wachtl, William W.: Charts of ThermodynamicProperties of Air and Combustion Products from 300° to 3500° R.NACA TN 2071, 1950.

13. Henry, John R., and Bennett, J. Buel: Method for Calculation of Ram-jet Performance. NACA TN 2357, 1951.

14. Sibulkin, Merwin: Theoretical and Experimental Investigation ofAdditive Drag. NACA RM E5IB13, 1951.

15. Tucker, Maurice: Approximate Calculation of Turbulent Boundary-Layer Development in Compressible Flow. NACA TN 2337, 1951.

16. Jack, John R.: Theoretical Wave Drags and Pressure Distributionsfor Axially Symmetric Open-Nose Bodies. NACA TN 2115, 1950.

NA.CA KM E54H03 23

TABLE I. - DESIGH-FOIST RAM-JET ENGINE PERFORMANCE

Flight Mach number, MQ

1.5 | 2.0

Combustion-chamber-inlet Mach number, Mg = 0.150

A.J/AJ = 0.287

T

2.03.04.05.06.07.07.32

CT

0.023.210.383.533.698.882.945

• I .

152907

105410801056998975

CD

0.186.175.161.143.122.109.109

AS/AS0.468

.585

.699

.812

.9311.0601.106

AS/AS

0.395.499.590.690.794.909.945

A-j^/Aj = 0.382

T

2.53.03.54.04.55.05.55.96

CT

0.291.428.551.670.780.880.990

1.096

I

12741372140013931360130712271139

V0.118

.009

.098

.086

.087

.088

.090

.092

AG/AS0.750

.840

.9251.0051.0851.1741.2751.380

AS/AS

0.450.499.548.595.643

. .696.751.807

Combustion-chamber-inlet Mach number, Vl^ = 0.175

A-L/Aj = 0.334

2.03.04.05.0

*6.0

0.055.282.471.635.780

418104311391106984

0.175.158.138.113.109

0.550.694.825.970

1.124

0.465.590.713.843

1.000

A^Ag = 0.444

2.53.03.54.04.55.05.5

*5.85

0.365.524.660.780.895

1.0071.1221.206

14261508148814381369128811971130

0.104.086.084.085.087.089.092.094

0.874.985

1.0861.1801.2871.4001.5271.618

0.530.593.654.720.790.863.940

1.000

Combustion-chamber-inlet Mach number, Mg = 0.200

AI/AS = °*379

2.53.03.54.04.5

*4.77

0.225.344.454.550.625.659

99611311177117811361065

0.150.137.121.103.100.101

0.726.808.896.986

1.0801.132

0.620.697.779.865.952

1.000

AI/AS = °-505

2.252.52.753.03.253.754.25

*4.60

0.347.440.520.598.672.804.927

1.006

14331498152715191502144813711312

0.091.081.082.083.084.087.090.093

0.9411.0091.0721.1391.1941.3241.4601.560

0. 581.620..660.700.743.832.929

1.000

Combustion-chamber-inlet Mach number, fL = 0.225

AI/AS = °-424

2.502.753.003.253.50

*3.80

0.266.348.400.452.499.540

107911511180117711441047

0.130.122.111.099.097.099

0.835.876.931.988

1.0401.110

0.719.766.819.870.928

1.000

A-j^/Aj = 0.564

2.252.502.753.003.253.50

^3.72

0.399.488.574.657.733.801.863

1469149214971481145714231377

0.081.083.084.086.087.089.091

1.0781.1521.2261.3021.3781.4561.530

0.675.721.770.822.879.940

1.000

•Thermal choking

24 NACA EM E54H03

TABLE I. - Continued. DESIGN-POINT RAM-JET ENGINE PERFORMANCE

Flight Mach number, MQ

2.5 || 3.0

Combustion- chamber- inlet Mach number, Mg = 0.150

A-^Aj = 0.505

T

2.02.53.03.54.04.54.80

CT

0.284.469.638.795.960

1.1321.250

I

1441155515461510143213291249

CD

0.076.072.073.074.075.077.078

A6/A3

0.9601.0521.1251.1931.2751.3711.436

AS/AS0.397

.453

.501

.552

.606

.661

.697

A-j/Aj = 0.626

T

2.002.252.502.753.003.253.503.96

CT

0.390.507.620.730.834.951

1.0791.349

I

15221565156615501516147414191300

CD

0.061.062.063.064.065.066.069.073

AS/AS

1.1771.2351.2901.3441.4021.4661.5401.701

AS/AS0.398

.429

.456

.481

.506

.537

.559

.619

Combustion-chamber-inlet Mach number, Mg *» 0.175

Aj/Aj = 0.586

2.02.53.03.54.04.54.80

0.348.554.749.934

1.1251.3021.420

1512159415651508140612991212

0.070.071.073.075.077.079.081

1.0621.1381.2461.3381.4321.5351.600

0.468.534.598.665.734.810.860

A-j/Aj = 0.727

2.002.252.502.753.003.253.503.96

0.458.591.722.851.972

1.1051.2491.546

15371576157415511515146214021266

0.058.061.063.066.067.069.072.078

1.3051.3701.4301.4991.5671.6441.7321.942

0.472.507.538.571.606.641.674.747

Combustion-chamber-inlet Mach number, Mg = 0.200

A /A_ = 0.666

2.02.53.03.54.0

*4.45

0.400.630.850

1.0521.2501.420

153715971566150113961287

0.071.072.074.076.079.082

1.1581.2621.3631.4701.5891.710

0.545.625.706.793.888

1.000

Combustion-chamber-inlet

A-j/Aj = 0.745

2.002.252.502.753.003.25

*3.66

0.439.565.689.810.920

1.0281.201

1519155615651555152714871400

0.071.073.074.075.076.077.080

1.2401.3011.3601.4211.4861.5511.669

0.625.675.722.775.829.897

1.000

A^A^ = 0.826

2.002.252.502.753.003.253.503.96

0.520.657.801.953

1.0911.2391.3901.692

15311561155515331496144413751220

0.065.067.068.070.072.074.076.084

1.4251.5021.5781.6521.7271.8221.9082.162

0.545.590.633.673.714.763.811.918

Mach number, Mg = 0.225

A-L/AJ = 0.923

2.002.252.502.753.003.25

*3.58

0.589.748.900

1.0521.1971.3511.584

1551155615441513146514101314

0.053.055.072.074.076.078.083

1.5531.6281.7141.8171.9012.0222.168

0.629.680.730.787.840.901

1.000

'Thermal choking

MCA EM E54H03 25

TABLE I. - Concluded. DESIGN-POINT RAM-JET ENGINE PERFORMANCE

Flight Mach number, MQ

3.5 4.0

Combustion-chamber-inlet Mach number, Mg = 0.125

A-L/Ag = 0.618

T

1.752.002.252.502.753.003.25

CT

0.271.388.505.628.759.900

1.059

I

1349141114281422139813531276

CD

0.055.056.057.058.059.062.064

V^S

1.2091.2751.3411.4061.4881.6151.744

y^0.303

.329

.355

.376

.400

.426

.451

Combustion- chamber- inlet

A^y^ = 0.740

1.752.002.252.502.753.003.25

0.341.470.617.755.908

1.0761.255

1375144114501442141213601266

0.054.056.058.060.062.066.070

1.3581.4371.5151.6061.6951.8562.015

0.370.401.430.459.487.519.549

Combustion-chamber-inlet

A^y^ = 0.858

1.752.002.252.502.753.003.25

0.389.553.720.887

1.0601.2401.440

1410145214621450141513531250

0.058.060.062.064.067.072.077

1.5241.6091.6911.8051.9122.1042.284

0.438.474.507.544.578.620.662

Combustion-chamber-inlet Machnumber, Mg = 0.200

A-j/Aj = 0.976

1.752.002.252.502.753.003.25

0.428.610.800.995

1.1951.4001.634

1375142014361426139413401240

0.063.065.067.069.072.077.084

1.6651.7681.8711.9912.1182.3112.560

0.506.551.594.638.683.732.790

Al/^ = °'743

T

1.501.752.002.252.502.75

CT

0.162.334.493.654.838

1.047

I

95412551324133413101218

CD

0.047.050.052.054.058.064

A6/A3

1.3621.4571.5431.6271.8042.048

AS/AS0.281

.308

.334

.356

.383

.412

Mach number , M« = 0 . 150

A1/A3 = 0.890

1.501.752.002.252.502.75

0.213.403.592.784

1.0011.254

104512631329132913141217

0.049.052.055.058.063.071

1.5361.6531.7621.8802.0862.356

0.399.373.403.435.466.501

Mach number, Mg = 0.175

A., = 1-032

1.501.752.002.252.502.75

0.244.467.687.906

1.1581.449

103512631329133513101213

0.055.057.061.064.069.078

1.7301.8441.9862.1252.3522.680

0.401.438.477.513.551.598

26M

CA

B

M E

54H03

NA.CA EM E54H03 27

<aoo0)!H

CQ0}a;

a;w

a]o•H-p•Hfi

1.0

ni

: Cc«

^X

\*^N.

^s

N

ingle-cone inletsnstant kinetic- energyefficiency (over-all .diffuser)

V\\

^^

\

\

•\V

\X

\\\

\

kx:

0.95

.90

1 2 3 4Flight Mach number, MQ

Figure 2. - Effect of flight Mach numberon critical diffuser pressure recovery.Single-cone spike inlet.

28 NACA BM E54E03

.Flight Machnumber,

•1.5

f•*o

1<U

•pi.

2.0

2.5

3.0

§•rl-P(03

4.0

.01 .02 .03 .04 .05Fuel-air ratio, f/a

.06 .07 .08

Figure 3. - Effect of fuel-air ratio on combustion-chamber total-temperatureratio for JP4 fuel (heating value, 18,640 Btu/lb). Ambient temperature,392° R) combustion efficiency, 0.90.

NACA EM E54H03

1200

oVa

<uCO

CO

-PS

£

29

1000

800

600

400

i.o r

Combustion-chamberinlet Mach number,

0.150

3 4 5 6 7Engine total-temperature ratio, T

(a) Flight Mach number, 1.5.

Figure 4. - Design-point performance of ram-Jet engine.

30 KA.CA BM E54H03

1600

o0)m

o•H

•HO

1

01oo

aI

1400

1200

1000

1.2

1.0

.8

.6

.4

.2

Combustion-chamber-inlet Mach number,

«2

.150

.175

y/7

,200

.175

150

O Thermal choking

2 . 3 4 5 6Engine total-temperature ratio, T

(b) Flight Mach number, 2.0.

Figure 4. - Continued. Design-point performance of ram-Jet engine.

NACA EM E54H03 31

I

<H•HO

o

£<uoo

^

£

1600

1400

1200

1.6

Combustion-chamberinlet Mach number,

"2 .

1.4

1.2

1.0

.8

.6

.4

X

/

.225

0.20

.150

.175

O Thermal choking

2.0 2.5 3.0 3.5 4.0Engine total-temperature ratio, T

4.5 5.0

(c) Flight Mach number, 2.5.

Figure 4. - Continued. Design-point performance of ram-Jet engine.

32 MCA EM E54H03

Ib-s

ec

o£fto&

1600£ O

N o

#

i

coe

ve

CDH

CT>

.225

/

0.200

.ITS

.150

O Thermal choking

3.0 2.5 3.0 3.5Engine total-temperature ratio, T

4.0 4.5

(d) Flight Mach number, 3.0.

Figure 4. - Continued. Design-point performance of ram-jet engine.

NACA EM E54H03 33

£a<uCO

3 1400

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a?(QHa•H 1200o

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0.125.200

amber-mber,

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\ 0.175

1.8

1.6

1.4

1.2

1.0

.8

.6

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,0.200

.175

.150

.125

I1L

77

7

7

7

77

0.175

.150

.125

2.0 2.5 3.0 3.5 1.5 2.0Engine total-temperature ratio, T

2.5 3.0

(e) Flight Mach number, 3.5. (f) Flight Mach number, 4.0.

Figure 4. - Concluded^ Design-point performance of ram-jet engine.

34

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S3

1400

1200

1000

MCA BM E54H03

w

tJ(U

I1.5 2.0 2.5 3.0

Flight Mach number,3.5 4.0 4.5

Figure 5. - Effect of flight Mach number on design-point performance ofram-Jet engine. Engine total-temperature ratio chosen for maximumefficiency.

NACA EM E54H03 35

1600

10

£>.

I

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&03

EHO

1I)Oo•pCO

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1400

1200

1.6

1.4

1.2

1.0

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12.85 IEngine total-

_temperature ratio,

4.45

4.45

2.85

.12 .14 .16 .18 .20Combustion-chamber-inlet Mach number, Jt,

(a) Flight Mach number, 2.5.

Figure 6. - Effect of combustion-chamber-inlet Mach number onram-Jet engine performance.

36 MCA EM E54H03

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,0

4>mH

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I

-pa<u

Voo

1600

1400

1200

1.8

1.6

1.4

1.2

1.0

.8

.6

Engine total-- temperature ratio,

T

2.50

3.25

3.25

2.50

.12 .14 .16 .18 .20Combustion-chamber-inlet Mach number, Mg

(b) Flight Mach number, 3.5.

Figure 6. - Concluded. Effect of combustion-chamber-inletMach number on ram-jet engine performance.

MC

A

EM

E54H

0337

°J/ 2<ptre

/e sarr[B

A

03.q.sTuqq. aAtsindoad

jo

38

o•H<H

0)PiCO

1700

1500

1300

1100

900

Nacelle drag coefficient,

KA.CA EM E54H03

• Low-angle cowlO Assumed single-cone Inlet

<H"Hvoo

aI

1.4

1.2

1.0

.8

.6

.2

A

.20

.3 .4 .5Diffuser pressure recovery, P2/P0

.6 .7

Figure 8. - Effect of diffuser pressure recovery and engine drag coef-ficient on ram-Jet engine'performance. Flight Mach number, 3.5;combustion-chamber-inlet Mach number, 0.200; engine total-temperatureratio, 2.50.

NACA EM E54H03 39

1.04

1.02oCM

VlO

1.00

-P•H

-PCO

O•P

-PIQ

oo

.98

.96

.94

.92

Engine total-temperature ratio,

/-4.45

Flight Mach number,

"o3.52.5

2.50

2.85s*

\

0 1 2 3Flame-holder loss,

Figure 9. - Effect of flame-holder pressure loss on ram-Jet engineperformance. Combustion-chamber-inlet Mach number, O.ZOO; combustionefficiency, 0.90. (Specific impulse is affected in same proportionas thrust.)

40 MCA EM E54H03

0(0

<u-p oCO

•H -PCO Q)

1.02

1.00

.98

1.3

1.1

2 4Combustion- chamber length-

diameter ratio,

I$<H

<D

0) "S

<U

o•H

.7

Figure 10. - Effect of combustion-chamberlength on performance and weight ofram- jet engine. Flight Mach number,3.5; combustion- chamber- inlet Machnumber, 0.200; engine total- temperatureratio, 2.50; combustion efficiency,0.90. (Specific impulse affected ins_ame proportion as thrust.)

NACA KM E54H03 41

oHi01

<uCOH

I

2600

2200

1800

1400

1000

Fuel

--- JP4

Combustionefficiency,

\0.95.90

1.6

-p<u•HO•H<H

£•P

•HCO

a

1.2

.01 - .02 .03Fuel-air ratio, f/a

.04 .05

Figure 11. - Comparison between performance of engines using pentaboraneand JP4 fuel. Flight Mach number, 3.5; combustion-chamber-inlet Machnumber, 0.200.

42 KA.CA BM E54H03

COP<

•PW

•HM

O

O•H-P

temperature ratio,T

.6Area ratio

Area ratio at p_ = p.O U

Figure 12. - Effect of nozzle area ratio on ram-jet engine performance. Combustion-chamber-inlet Mach number, 0.200. (Specific impulseis affected in same proportion as thrust.)

MC

A EM

E54H

0343

+>cfl

-p•a•HHft

COo

CO

LO00

**

ID

into oo

\

CD

CD

O-P0)•H

CO

OCD

-H

• SH

CD

OOH0)NO

CDLOCO

00

CD

o

0) O

tOH

5L6'Q

JO

Djo

44 MCA EM E54H03

EHo

1.2

1.0

.8

.4

y

/

Engine total-_temperature , ratio,

2.50

2.25

2.00

1.0

-pc0)

<H01O

8 12 16Jet-deflection angle, \, deg

20

Figure 14. - Effect of jet-deflection angle on ram-jet engine performance.Flight Mach number, 3.5; combustion-chamber-inlet Mach number, 0.200.

KA.CA EM E54H03 45

ooo

40 60Altitude, ft

Figure 15. - Effect of altitude on ram-jet engineperformance. Flight Mach number, 3.5; combustionchamber-inlet Mach number, 0.200; engine total-temperature ratio, 2.50.

46 NACA EM E54H03

1600

Flight Mach number,

"o3.5

.4 .6 .8Propulsive thrust coefficient,

1.2

Figure 16. - Off-design performance of fixed-geometry ram-jet enginedesigned for flight Mach number of 3.5, combustion-chamber-inlet Machnumber of 0.200, and engine total-temperature ratio of 2.25. Combus-tion efficiency, 0.87; ratio of specific heats for exhaust gases, 1.30.

KACA EM E54H03 47

1600

o 1200

I

O

&co

800

400

X/"

O Design point

^

^*»«*" /

,''

//

*

— • —

//

//

^/

/

~T^

^

Fi:0]

— Moiai

/'

"•~^^

^^

—

— ~

— n

- •

_^ •

insisting- spike diffuserted geometry (criticalDeration)itinuously variable^able-plug variable-•ea nozzle

-pc

2.0

1.6

1.2

1.2 1.6 2.0 2Flight Mach

.4 2.8number, M«

3.2 3.6

Figure 17. - Off-design performance of various fixed- and variable-geometryram-jet engines operating at maximum thrust. Engines designed for flightMach number of 3.5, combustion-chamber-inlet Mach number of 0.200, and enginetotal-temperature ratio of 2.50. Combustion efficiency, 0.87; ratio ofspecific heats for exhaust gases, 1.30.

NACA RM E54B03

Unclassified when detached from rest of report

Richard J. WeberAeronautical Research Scientist

Propulsion. Systems

Roger W. LuidensAeronautical Research Scientist

Aerodynamics

Approved:

Eldon W. HallAeronautical Research Scientist

Propulsion Systems

Bruce T. LundinChief

Engine Research Division

maa - 8/5/54