Analysis of ram-jet engine performance including effects of component changes

RM E56D20

AP

NACA

RESEARCH MEMORANDUM

ANALYSIS OF RAM-JET ENGINE PERFORMANCE INCLUDING EFFECTS OF COMPONENT CHANGES By Richard J . Weber and Roger W. Luidens Lewis Flight Propulsion Laboratory Cleveland, Ohio

NATIONAL ADVISORY COMMITTEE

FOR AERONAUTICS

WASHINGTON October 29, 1976 Declassified July 22, 1959

NACA EM E56D20 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS RESEARCH MEMORANDUM ANALYSIS OF RAM-JET ENGINE PERFORMANCE INCLUDING EFFECTS OF COMPONENT CHANGES By Richard J. Weber and Roger W. Luidens SUMMARY Ram-jet engine performance data are presented over a range of en- gine design variables to aid in the selection and evaluation of a ram- jet engine configuration with particular emphasis on one suitable for a long-range supersonic missile. Calculated design-point performance of engines using JP-4 fuel is presented for a wide range of engine total- temperature ratios and combustion-chamber-inlet Mach numbers for flight Mach numbers from 1.5 to 4.0. The results include engine thrust, drag, fuel consumption, and area ratios, and are presented both with and with- out nacelle drag included. Maximum engine fuel specific impulse (in- cluding nacelle drag) is 1600 to 1700 pound-seconds per pound and occurs at a flight Mach number of 2.5 to 3.0. Over-all engine efficiency, how- ever, continues to increase to a flight Mach number of 4.Q, where it is 35 to 40 percent.

Important gains in both thrust coefficient and specific impulse may be achieved by improving the diffuser pressure recovery. Changes in flameholder pressure loss and combustor length have only small effects on engine performance. That these factors, however, influence combus- tion efficiency is significant, because the specific impulse varies di- rectly with the efficiency, although the thrust coefficient is practi- cally unaffected. Engine performance is very sensitive to changes in nozzle performance, a 1-percent variation in velocity coefficient often producing a 3-percent variation in engine thrust and specific impulse.

Some underexpansion of the exhaust gases is desirable to reduce nacelle drag whenever 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 can be obtained with the added complication of a translating-spike diffuser, although the specific impulse is poorer. Use of a movable plug to vary the throat area of the exhaust nozzle yields both thrust and specific impulse approaching those of a continuously variable geometry engine.

NACA RM E56D20.

INTRODUCTION The suitability of the ram-jet engine for the propulsion of high- speed aircraft has been generally recognized and accepted. The selec- tion of the proper engine for such applications must be based on many factors relating to the airframe-engine combination. The purpose of this report is to present calculated ram-jet engine performance data over a range of engine design parameters in order to aid in the selec- tion and evaluation of an engine design. General emphasis is placed on designs suitable for a long-range supersonic missile. A second purpose is to illustrate the relative importance of the different engine param - eters that influence the design of the ram-jet engine. Many other ther- modynamic cycle studies of ram-jet - engines are presented in the litera- ture (e.g., refs. 1 and 2). This report presents a wider range of oper- ating conditions, uses somewhat more advanced, but realistic, component characteristics, and demonstrates the effect of changes in these com- ponent characteristics.

The engine performance data are presented such that they may be used either with or without nacelle drag included and are therefore suitable for aircraft configurations with either internal or external engine installations.

The report has three major sections: (1) General design-point engine performance is presented for a wide range of engine total-temperature ratios and combustion-chamber-inlet Mach numbers for flight Mach numbers from 1.5 to 4.0. The fuel used is JP-4, and nominal assumptions are used for the component characteristics.

(2) The sensitivity of these design-point results to changes in the nominal assumptions is indicated by showing the effect of varying the different component parameters, one at a time, on the performance of se- lected engines. The parameters investigated are diffuser pressure re- covery, flameholder pressure loss, combustion efficiency, nozzle veloc- ity coefficient, nozzle expansion ratio, nozzle jet-deflection angle, and altitude. Calculations were also made comparing a high-energy fuel (pentaborane) with JP-4.

(3) Off-design performance is presented for an engine designed for efficient cruising at a flight Mach number of 3.5. Configurations hav- ing fixed geometry, continuously variable geometry, and two types of practically variable geometry are compared. Off-design performance is not emphasized, because results obtained in missile studies indicate..

that self-boosting capabilities are not important for ram-jet-powered long-range missiles using rocket boosters.

NACA EM E56D20 ANALYSIS The symbols used in this report are defined in appendix A.

A schematic diagram of a ram-jet engine is shown in figure 1. High- speed air enters the engine at station 1 and is decelerated to a low ve- locity at 2. Fuel is added, ignition takes place, and combustion is stabilized at the flameholders, between stations 2 and 3. Combustion occurs in a constant-area duct from stations 3 to 4, and the hot gases are, expanded and discharged through a convergent-divergent nozzle (sta- tions 4 to e).

The performance calculations were made on the basis of one- dimensional flow, using the equations of state, continuity, and conser- vation of momentum and energy. Reference 2 presents equations similar to those used in the present analysis, in which the values of y are based on the gas static temperature and composition at each station.

The problem of specifying the gas properties is discussed more fully in appendix B, and the assumed engine geometry and methOds used in calcu - lating the engine drags are detailed in appendix C. Engine performance data, which are generally presented for an altitude of 70,000 feet, may be used for any altitude in the isothermal region of the atmosphere with negligible error.

Engine performance is presented in this report in terms of the following: (i) Propulsive thrust coefficient CT, defined as engine thrust minus nacelle drag per unit cross-sectional area, divided by free-stream incompressible dynamic pressure. The cross-sectional area used is the diffuser capture area or the combustion-chamber frontal area, whichever is larger. This coefficient is a measure of the engine size required to produce a given amount of propulsive thrust.

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

Similarly, the net-thrust coefficient and specific impulse CF and IF are defined as above except that nacelle drag is not included.

Most of the various engine parameters fall into two groups: (A) those of major importance that cannot be finally specified without a complete flight analysis, and (B) those that can be realistically chosen from an engine study alone, or that are limited by what can practically be achieved. These major variables (group A) were taken as flight Mach number, combustion-chamber-inlet Mach number, and engine total-temperature

NACA EM E56D20 ratio. A complete set of design-point performance calculations was ob- tained for different values of these variables, based on nominal assump- tions made for the component parameters of group B. The range of calcu- lations for these major variables included flight Mach numbers from 1.5 to 4.0, combustion-chamber-inlet Mach numbers from 0.125 to 0.225, and engine total-temperature ratios corresponding to fuel-air ratios of ap- proximately 0.01 to stoichiometric, except where limited by thermal choking.

The following assumptions were used for the variables of group B in the design-point calculations: (1) Engines were considered with both single- and double-cone dif- fusers. The design-point engines operated critically (i.e., with the normal shock located at the inlet lip). For the single-cone diffuser, cone angle was varied with design flight speed to achieve maximum pres- sure recovery. For the two-cone diffuser, the cone angles were not se- lected for maximum pressure recovery but chosen to permit use of a low- drag cowl (low lip angle). Figure 2 shows the assumed variation of pres- sure recovery with flight Mach number for the two diffuser types. The illustrated single-cone values are in good agreement with the experimen- tal data for similar inlets reported in reference 3. Reference 4 shows that, in the present state of inlet development, the engine performance obtained with the single-cone inlet with low drag cowl is as good as that afforded by more elaborate diffusers such as the isentropic spike.

(2) Flameholder total-pressure loss was taken as.twice the incom- pressible dynamic pressure at station 2. Combustion of the fuel (JP-4 with 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 relation between ¶ (engine total-temperature ratio) and fuel-air ratio f/a for different flight Mach numbers is shown in figure 3. Reference 5 reports the 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 of about 1 atmosphere.

(3) The nozzle velocity coefficient was taken as 0.975. Values of this magnitude have been obtained experimentally for convergent-divergent nozzles at nozzle pressure ratios P4 /p 6 of about 15 (ref. 6). At flight Mach numbers of 2.5 and higher, the nozzle-exit diameter is gen- erally the largest diameter 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 unpublished

NACA RN E56D20 data obtained in long-range missile studies showing the effect of expan - sion ratio on missile range, the optimum expansion ratio is roughly gen- eralized by the empirical formula A = 1 + O.55[() - i] (1) A3 A6\ where ( is the ratio of nozzle-exit to combustion-chamber area

f -1

A3j for complete expansion. This expression was used for the design-point engine calculations whenever the nozzle-exit diameter exceeded that of the combustion chamber. In all other cases the nozzle was made com- pletely expanding. - The sensitivity of the design-point results to changes in these assumed values of the various component parameters was indicated by cal - culating the effect of varying these parameters, one at a time, at flight Mach numbers of 2.5 and 3.5. At each speed, two values of 'r were con- sidered, a low value for good cruising performance and a higher value to give increased thrust for acceleration.

The off-design performance of engines designed for cruising at a flight Mach number of 3.5 was also evaluated. Engines equipped with the following 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 coefficient and specific impulse are shown in figure 4 for the single-cone diffuser as functions of flight Mach number M 0 , ratio of combustion-chamber-exit to -inlet total temperature 'r, and combustion-chamber-inlet Mach number M2 . These data, as well as engine area ratios and drag coefficients, are

NACA RM E56D20 listed in table I. Similar data are listed in table II for the two-cone diffuser. The values of and I include nacelle drag. The corre- CT sponding values without nacelle drag may be obtained by the relations (2) CF=CT+CD C (3) T Performance of engines having velocity coefficients other than 0.975 may be calculated from the following formula: CV (4) + 2(] - - 2() C CD CD T = 0.975 00.975 + which is based on the assumption that the jet thrust is directly propor- tional to the velocity coefficient and that the nacelle drag does not change. The change in I is directly proportional to the change in CT.

Performance can also be computed for values of combustion efficiency T, the thrust coefficient re- other than 0.90. At any constant value of mains essentially constant with changes in combustion efficiency, and specific impulse and fuel-air ratio are given by (5) 0.90 1Q9Q Tic f (6) a 0.90 \a/090 The effect of changes in diffuser pressure recovery may be approxi- mated by the following expressions A6/A3 (Ps - + A/A + C) 0), + CT =__= - CD 2 T M6 (7) CT (P2/ P O)' (8) I = I T (A 1/A3 ) (P2/P0) (9) A1/A3 = (p2/P0)'

NACA RN E56D20 in which (P2 /P0 )' denotes the single-cone pressure recoveries given in figure 2, and Crji , I', and (A 1 /A3 ) 1 are the values listed in table I.

Equations (7) to (9) are based on the assumptions that the inlet capture area is varied with pressure recovery and nacelle drag and nozzle exit area are constant. The data of table I and equations (7) to (9) were used to compute the performance presented in table II for the low-cowl- drag two-cone diffuser. (Note that eqs. (7) and (8) require that CT be based on A3.)

The remaining discussion, except where noted, is based on the low- cowl-drag single-cone diffuser. Although the actual level of perform- ance may be somewhat different with other diffuser types, all the trends are expected to be the same.

Figure 4 shows that high thrusts are obtained at the high values of -r and maximum specific impulses at intermediate values of

t. Raising

-r (at a constant N,3 and M2 ) 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 'r is raised, the fuel flow increases at a greater rate than the jet thrust, so that, after the constant loss of the inlet momentum drag is sufficiently overcome, the specific impulse reaches a maximum and then decreases. When nacelle drag is included, the value of ¶ for maximum specific impulse is raised.

The effect of flight Mach number on over-all engine efficiency and specific impulse is shown in figure 5, in which the value of ¶ is var.- led to provide maximum I and E at each flight speed. Combustion- chamber-inlet Mach number is generally 0.200, except for N0 above 3.5, where it was necessary to reduce M2 to prevent the diffuser-inlet diam- eter from exceeding that of the combustion chamber. Maximum I (1600 lb-sec/lb including nacelle drag) occurs at N 0 of 2.5. This flight Mach: number, however, may not be optimum for a missile, because missile range is more nearly related to the over-all engine efficiency, which in turn is proportional to the product of specific, impulse and flight velocity rather thnto specific impulse alone. Maximum E of the or- der of 0.35 isrealized at M 0' near 4, while the highest efficiency ob- tainable at M0 of 2.5 is only 27 percent. For engines with a two-cone diffuser, the maximum values of I and E are 1700 and 40; respectively.

(Still higher values of E would be expected for M O greater than 4.)

The effect of combustion-chamber-inlet Mach number- M 2 is indi- cated in figure 4 but is more readily apparent in a cross plot of some of these data (fig. 6). The thrust coefficient increases with 142 be- cause of the essentially linear increase in air flow to the point where the inlet capture area becomes equal to the combustion-chamber area.

The value of at which these areas are equal is higher than the M2

NACA RN E56D20 region of interest shown in figure 6, but is a function of the flight speed and the diffuser pressure recovery. Raising M 2 also increases both the flameholder pressure loss and the momentum pressure loss due to heat addition. If nacelle drag is not included, the specific impulse de- creases with increasing values of M 2 . However, higher values of N2 reduce the diameter of the combustor and nozzle relative to the diffuser capture area and so result in lower nacelle drag per pound of air (pro- vided the capture area remains smaller than the combustion-chamber area).

Because of these two opposing effects, the specific impulse including drag is fairly insensitive to variations in M2 for the conditions of figure 6.

Effect of Variations in Design-Point Assumptions Diffuser pressure recovery. - Diffuser total-pressure ratio is used in this report as a measure of the efficiency with which the diffuser converts the kinetic energy of the captured airstream to pressure. Lines of constant kinetic-energy efficiency superimposed on the curve of pres- sure recovery against flight Mach number (fig. 2) show that the lower numerical values of total-pressure ratio at high flight Mach numbers do not necessarily mean lower diffuser efficiency.

The nominal diffuser assumed for the design-point calculations is an oblique-shock inlet with a single-cone spike centerbody. Figure 7 shows the effect on engine performance of changes in the assumed values of pressure recovery. (This performance is based on the drag of a low- angle cowl at all pressure recoveries.) The engine air flow per unit combustion-chamber area increases linearly with pressure recovery, so that the propulsive thrust coefficient (based on combustion-chamber area) also increases nearly linearly. As pressure recovery is increased, the diffuser capture area enlarges relative to the combustion chamber in At high flight order to handle these larger air flows at constant 142 .

Mach numbers and high pressure recoveries, the resulting capture area often becomes greater than the combustion-chamber area. The size of the engine required to produce a given thrust is then indicated by basing the thrust coefficient on diffuser capture area. At a flight Mach num- ber of 2.5, the combustion chamber is always the larger for the range of pressure recoveries considered. At a flight Mach number of 3.5 and M2 of 0.20, the capture area becomes the larger at pressure recoveries greater than 0.43, which causes the sharp break in thrust coefficient observed at thi.s point in figure 7. The engine specific impulse in- creases with increasing pressure recovery because of the higher pressure ratio across the exhaust nozzle. The higher air flow also improves the specific impulse because of the lower nacelle drag per pound of air.

NACA EM E56D20 9 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 im- proved pressure recovery may be largely offset by the resulting engine drag increase. Figure 8 shows engine performance at a flight Mach num- ber 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 and represents the best performance attainable at any value of pressure recovery. Figure 8 indicates the penalties in drag rise that are acceptable to obtain better engine performance as a result of im- proved pressure recovery. Calculations based on the experimentally meas- ured pressure recovery and cowl drags reported in reference 3 confirm the conclusion that currently available high-recovery inlets do not yield better over-all engine performance than does the single-cone type. Al- though the single-cone inlet was used to give performance representative of that available with other current inlet types, the advanced inlets have greater potentialities for improvement, as indicated in figure 8.

Other factors must also be considered, of course, in comparing different diffuser designs. For example, a single-cone inlet may be easier to de- sign and manufacture and is less sensitive to angle of attack than are more elaborate types. On the other hand, the higher pressure provided by an advanced inlet may increase combustion efficiency and prevent blow- out.

The effects of variations discussed in the following sections are based on the use of a single-cone diffuser.

Combustion efficiency. - If 'r 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 this effect lies in the fact that the range of a ram-jet missile varies di- rectly with the specific impulse, if all Other factors do not change.

Flameholder pressure loss. - The purpose of the flameholder is to ensure the ignition and efficient burning of a fuel-air mixture moving at several hundred feet per second when the laminar flame speed of the mixture may be in the order of only 5 feet per second. Increased flow blockage and turbulence often improve the combustion efficiency but in- troduce pressure losses detrimental to the thrust output of the engine.

A compromise is often necessary between these opposing factors. The change in propulsive thrust and specific impulse with the flaineholder, cold-flow pressure-drop coefficient is indicated in figure 9 for a con- stant combustion efficiency.

Fuel type. - Another combustor variable that may be changed to im- prove performance is the fuel used. High-energy fuels permit raising both thrust and specific impulse, but they are generally more expensive

NACA RN E56D20 than hydrocarbon fuels, or they may have other undesirable characteris- tics such as pumping or storage problems. Calculations were made for pentaborane (B5 119 ) as a typical high-energy fuel frequently mentioned for rain-jet applications. Figure 10 shows the propulsive thrust coef- ficient and specific impulse of an engine designed for flight Mach num- ber of 3.5 for pentaborane and JP-4. These calculations for B5 H9 were made with the assumption of equilibrium composition of the exhaust gases and with expansion to the same area assumed with JP-4. Data for these calculations were taken from reference 7. These curves are for a com- bustion efficiency of 0.95 for the pentaborane and 0.90 for the JP-4 fuel.

For the same thrust coefficient, a specific impulse with penta- borane of more than 150 percent of that with JP-4 is indicated at low fuel-air ratios up to those that give maximum specific impulse. The improvement is less at high fuel-air ratios that give near maximum thrust coefficient a Nozzle area ratio. - The effect of nozzle area ratio is presented in figure 11. Very little loss in propulsive thrust coefficient and specific impulse is suffered by cutting back the nozzle area as much as 30 percent from that required for complete expansion. In fact, for smaller amounts of underexpansion, gains of 1 or 2 percent may be real- ized, because reducing these areas reduces the external nacelle drag sufficiently to compensate for the lower internal thrust. In addition, since the nozzle was assumed to have a velocity coefficient less than 1.0, a small amount of underexpansion results in a very small increase in internal thrust. It is sometimes proposed that the nozzle-exit area not be permitted to exceed the combustion-chamber area. This condition (A6 = A3 ) is marked on the curves of figure 11. It is apparent that this amount of underexpansion results in appreciable losses, particularly at the higher flight speed. The performance of a convergent nozzle (A6 = A5 ) is seen to be very poor at both speeds.

Nozzle velocity coefficient. - The velocity coefficient (defined as the actual velocity at the nozzle exit divided by the ideal isentropic velocity at the nozzle exit for the same pressure ratio) is used to in- dicate the amount of the nozzle internal flow losses. These losses, which reduce the total pressure, are due to shocks, turbulence, and vis- cous effects-within the gas stream and to wall friction at the gas bound- aries. The effect on engine performance of a variation in the nozzle aSince the calculations for figure 10 were completed, revised data have beóome available for the combustion products of B5 119 . The curve presented, therefore, is only indicative of the general improvement pos- sible with B5 H9 ; the absolute magnitudes may be somewhat in error. (Ref.

8 presents charts and tables which incorporate these revised combustion data and which may be used for cycle calculations with pentaborane fuel.)

NACA RM E56D20 velocity coefficient from the assumed value of 0.975 is indicated in figure 12. A 1-percent change in velocity coefficient changes the thrust and specific impulse from 2 to 3 percent for the indicated values of Mach T.

number and There are other sources of thrust losses through the nozzle that do not affect total-pressure loss. In addition to the flow losses treated through the application of a nozzle velocity coefficient, the assumption of one-dimensional flow implies that all exhaust gases are discharged axially and that there are no radial gradients in velocity. Neither of these implications is necessarily true. A nonuniform temperature dis- tribution at the combustor exit would result in radial velocity gradi- ents. Calculations indicate that all reasonable temperature distribu- tions, such as a parabolic profile, result in thrust losses of less than 2 percent. Losses due to nonaxial discharge from a conical nozzle with a half-angle of 15 0 would be of the order of 1.5 percent. Use of a smaller angle or changes in nozzle contour would reduce this loss, although possibly at the expense of increased manufacturing cost and nozzle length.

Nozzle jet-deflection angle. - An interesting possibility for im- proving the performance of a rain-jet missile lies in turning the jet thrust of the engine downward. This slightly decreases the forward thrust and specific impulse but provides some lift, thereby permitting the use of a smaller wing and lowering the missile weight and drag.

Figure 13 presents the effect of jet-deflection angle on engine perform- ance, in which CT,v represents the component of vertical thrust di- vided by the free-stream dynamic pressure q and the engine cross- sectional area A,. These data are based on the assumption that nacelle drag does not 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 thrust coefficient and specific impulse through the Reynolds number effect on nacelle skin-friction drag coefficient. Below the tropopause, in addi- tion to this Reynolds number effect, the changing ambient temperature significantly affects ram-jet performance. In this region more fuel is required to maintain a design 'r as the altitude is reduced. This ex- tra mass addition, although it raises the thrust coefficient slightly, lowers the specific impulse considerably. This same increase in fuel consumption is felt by the over-all engine efficiency; however, the in- creased flight velocity (at constant flight Mach number) reduces, the magnitude of the effect. These considerations combine to produce the variations in propulsive thrust coefficient, specific impulse, and over- all efficiency shown in figure 14. Also important is the effect of flight altitude (not shown) on combustion efficiency through changes in ambient pressure and temperature, which in turn establish the tempera- ture, pressure, and velocity at the combustor inlet.

NACA RM E56D20 Off-Design Performance All the previous discussion has been concerned with a continuously variable-geometry engine or a series of fixed-geometry design-point en- gines. Thus, it is implied that the inlet capture area is sized to avoid subcritical spillage, the diffuser cone angle is selected for optimum pressure recovery, the diffuser spike can be translated for correct posi- tioning of the oblique shock upon the cowl lip, and the nozzle-throat area and area ratio are optimum. A practical engine incorporating such variable components is not yet available.

This invariance of geometry is of no concern if the engine can al- ways be operated at its design or cruise point. Design-point engine operation is possible for a ram-jet missile that cruises along a Breguet flight path, provided the missile is fully boosted to its cruising Mach number and altitude by some other means. Even after starting cruise flight, however, some corrective action may be required and off-design engine operation may be necessary. Moreover, rain-jet thrust may be de- sired during the boost phase of the flight. In order to include engine performance for these flight conditions, some off-design engine calcula- tions were also made. Because it was desired to indicate trends rather than absolute magnitudes, a constant value of y of 1.30 for the ex- haust gas was used for ease of computation of the off-design performance.

Figure 15 shows the propulsive thrust coefficient and specific im- pulse of a fixed-geometry engine designed to operate at M0 of 3.5, M2 of 0.200, and w of 2.25. Because the combustor must now operate over a wide range of flight conditions, the combustion efficiency (0.87) was assumed to be slightly lower than that for the design-point case (0.90).

Along each line of constant M0 , the parameter ic is raised to increase the thrust coefficient. For any given 'r there is a single unique value of M2 due to the choked fixed-nozzle throat area. At M 0 of 3.5 and values of 'r below 2.25, M 2 is greater than 0.2 and the diffuser oper- ates supercritically, with a severe loss in pressure recovery and a con - sequent adverse effect on thrust and specific impulse. As 't is raised by burning more fuel, M 2 is reduced to its design value, and the dif- fuser then operates critically, with the normal shock positioned at the diffuser lip.

This condition corresponds to the sharp break in the curve. Further increase of r causes subcritical diffuser operation.

Although the external shock or "bow wave" so generated does not neces- sarily reduce the diffuser pressure recovery severely, it spills air that would normally enter the engine and causes large additive-drag losses. With subcritical operation and no loss in pressure recovery, a small gain in thrust is obtainable over critical operation, but the specific impulse drops markedly. In addition to inefficient operation,

NACA EM E56D20 subcritical operation often results in instability of flow or "buzzing," which can, in severe cases, even blow out the combustor flame or damage the diffuser structure. In general, then, subcritical operation is undesirable.

For speeds less than design, best engine performance is also gener- ally obtained with the value of -r chosen to give critical diffuser operation. However, as flight speed is reduced, the value of M 2 for critical 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 various types of geometry variation is shown in figure 16 as a function of flight Mach number. Performance is shown for the engines operating at their maximum thrust condition. Also included are data for critical operation of a fixed-geometry engine obtained by cross-plotting the peaks of the curves from figure 15. The performance of an engine with both continuously variable inlet diffuser and exit nozzle is obtained with a wide-open exhaust nozzle and a stoichiometric fuel-air ratio.

Extremely large penalties in thrust are suffered with the fixed-geometry engine, with a thrust at flight Mach number 2.5 of Only 15 percent of that available from an engine equipped with a continuously variable in- let and outlet. These large thrust losses are mainly due to the neces- sity of reducing 'r to prevent subcritical operation. The ability to burn more fuel without being forced into the subcritical region explains why the continuously variable engine can produce more thrust than the fixed-geometry engine even at the design Mach number of 3.5.

Equipping an engine with either a movable-spike inlet or a variable- area exit nozzle, both of which are currently feasible, results in con- siderable gain over fixed-geometry engine performance. With a movable- spike inlet, the spike is translated axially so that all air spillage occurs behind an oblique shock. The flow behind the oblique shock re- mains supersonic, and the additive drag is not as severe as in the case of a bow wave. This spillage permits r to be increased without caus- ing subcritical operation. Thrust increases over the fixed configura- tion of 50 to 100 percent are possible, but the specific impulse is very low.

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

NACA EM E56D20 CONCLUDING REMARKS The calculated design-point performance of ram-jet engines using JP-4 fuel is presented for a wide range of engine total-temperature ratios and combustor-inlet Mach numbers for flight Mach numbers of 1.5 to 4.0. The results, which include engine thrust, drag, fuel consump- tion, and area ratios, are given in both graphical and tabular form.

Maximum engine specific impulse (including nacelle drag) is approxi- mately 1600 to 1700 pound-seconds per pound and occurs at a flight Mach number of about 2.5 to 3.0. Over-all engine efficiency, however, con- tinues to increase to a flight Mach number of 4.0.

Calculations are also presented which indicate the sensitivity of the design-point results to changes in diffuser pressure recovery, flame- holder pressure loss, combustion efficiency, fuel type, nozzle expansion ratio, nozzle velocity coefficient, nozzle jet-deflection angle, , and altitude. Significant gains in both thrust coefficient and specific im- pulse may be achieved by improving the diffuser pressure recovery. How- ever, presently available inlet designs that provide high recovery also have high cowl pressure drags which largely offset this potential gain.

Changes in flameholder pressure loss have only small effects on engine performance. This factor may, however, influence combustor efficiency and the resulting range. Engine performance is very sensitive to changes in nozzle performance, a 1-percent variation in velocity coef- ficient often producing a 3-percent variation in engine thrust and spe- cific impulse. Some underexpansion of the exhaust gases is desirable to reduce nacelle drag whenever the nozzle-exit diameter exceeds that of the combustion chamber.

Satisfactory off-design operation of a ram-jet engine is not pos- sible with a fixed-geometry configuration. Somewhat better thrust can be obtained with the added complication of a translating-spike diffuser, although the specific impulse is poorer. Use of a movable plug to vary the throat area of the nozzle yields both thrust and specific impulse approaching those of a continuously variable-geometry engine. In con- sidering engines designed for good cruise performance at flight Mach number 3.5 but operating at flight Mach number 2.5, the maximum thrusts are 15, 37, and 74 percent of that available with continuously variable geometry for engines with fixed-geometry, translating-spike diffuser, and movable-plug nozzle, respectively.

Lewis Flight Propulsion Laboratory National Advisory Committee for Aeronautics Cleveland, Ohio, April 25, 1956

NACA RM E56D20 15 APPENDD( A SYMBOLS The following symbols are used in this report: A area, sq ft diffuser capture area A1 or combustion-chamber , area A3 , which- An ever is larger, sq ft 'nacelle drag coefficient, D/qA CD net-thrust coefficient, F/q0A CF propulsive thrust coefficient, CF - CD CT nozzle velocity coefficient Cv D drag, 1b over-all engine efficiency, (F - D)V0/JHwf E F net thrust, m V 6 - m0V0 + A6 (p6 - p0 ), lb f/a ' fuel-air ratio lower heating value of fuel, Btu/lb H I fuel specific impulse, (F - D)/wf , lb-sec/lb fuel specific impulse not including drag, F/w f , lb-sec/lb.

mechanical equivalent of heat, 778 ft-lb/Btu J M Mach number . ...

mass-flow rate, slugs/sec total pressure, lb/sq ft P static pressure, lb/sq ft .. ... .. .

p incompressible dynamic pressure, PV'/2., lb/sq ft , q gas constant, 53.4 ft-lb/(lb)(°R) R total temperature, 0R T

16 NACA RN E56D20 static temperature, °R t V velocity, ft/sec wf fuel-flow rate, lb/sec ratio of specific beat at constant pressure to specific heat at y constant volume combustion efficiency, wf,jd/wf,ac jet-deflection angle, deg X density, lb/cu ft P engine total-temperature ratio, T4/T3 Subscripts: ac actual effective ef fr friction id ideal nom nominal v vertical free stream diffuser inlet combustion-chamber inlet (upstream of flameholder) 3 combustion-chamber inlet (downstream of f1aneho1der) 4 combustion-chamber exit 5 nozzle throat nozzle exit

NACA RM E56D20 17 APPENDIX B THERMODYNAMIC ASSUMPTIONS Assigning correct gas properties and maintaining high computational accuracy are very important in any rain-jet engine analysis, because small changes in the calculated jet thrust may be magnified 3 or 4 times in the net propulsive thrust. Specification of the gas properties involves re- alistic choice of 1, R, and 'r as functions of temperature, fuel-air ratio, and pressure (if there is appreciable dissociation).

Data for octane (ref. 2), which include dissociation effects, were converted to JP-4 and used in constructing figure 3, which gives r as R. Sim- a function of MO and f/a for an ambient temperature of 392 0 ilar curves were constructed for altitudes under the tropopause where the ambient temperature is different from 392 0 H. The very high temper- of atures plus the changes of composition due to burning cause the i the combustion gases to vary appreciably from 1.40 if equilibrium is reached. These equilibrium values, as a function of temperature and f/a and for a pressure of 1 atmosphere, were obtained from reference 9, which includes avery appreciable effect of dissociation. Molecular equilibrium is not necessarily maintained during the expansion of the gas through the nozzle. However, considerations of heat-capacity lag and chemical-reaction rates indicated that the process is probably closer to equilibrium than to "frozen" conditions. After trying several different methods, it was found that specifying an effective y for the nozzle by (i + 16) Tef - gave best results as checked by equilibrium calculations using refer- ences 10 and 11. The deviations in net thrust were generally found to be less than 3 percent. According to reference 9, this means of spe- cifying Tef is also best for use in the isentropic equation = (E' T P \, The value of R for the airstream was taken as 53.4 ft-lb/(lb)(°R).

The same value was used for the exhaust gas with small error (ref. 12).

NACA RN E56D20 APPENDIX C ENGINE DRAG The engine thrust is defined in terms of the total-momentum changes occurring between the free-stream tube ahead of the engine and the ex- haust at the end of the engine. The drag must, therefore, include all the external forces acting on the stream tube and engine between the same two points. These forces are composed of pressure forces acting perpendicular to the stream tube and engine, and a friction force act- ing parallel to the engine nacelle due to the viscosity of the air. The pressure (or wave) drag may be further broken down into the part acting directly on the nacelle and the additional, imaginary part acting on the stream tube because of the way the thrust was defined. The latter force is termed additive drag, and was calculated by the method of reference 13.

The nacelle friction drag was calculated from the following equa- tion, which is based on the flat-plate formula of reference 14: Aw 0.0306 K CD,fr A 5/7 Re'/(l + - 1 where Aw is nacelle skin area, K is a shape factor taken as 1.05 for a 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 theory from reference 15. For the low-speed cases when the exit area was smaller than combustion-chamber area, data for boattail drag for a 7•040 cone were used from the same source. The diffuser cowl was assumed con- ical, with no added pressure drag incurred from a curved lip.

The engine was assumed to have a fineness ratio (length divided by combustion-chamber diam.) of 9, the diffuser being nominally 4, com- bustion chamber 3, and nozzle 2. The appearance of the engine as a

NACA 1RM E56D20 function of flight speed is as shown in the following sketch (not to scale): Low MO (1.5 - 2.0) Medium M0 (2.0 - 3.0) High M0 (3.0 - 4.0) REFERENCES 1. Cleveland Laboratory Staff: Performance and Ranges of Application of Various Types of Aircraft-Propulsion System. NACA TN 1349, 1947.

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

3. Bernstein, Harry, and Haefeli, Rudolph C.: Investigation of Pressure Recovery of a Single-Conical-Shock Nose Inlet at Mach Number 5.4.

NACA EM E53Al2, 1953.

4. Conners, James F., and Woollett, Richard R.: Performance Character- istics of Several Types of Axially Symmetric Nose Inlets at Mach Number 3.85. NACA EM E52115, 1952.

Cervenka, A. J., Dangle, E. E., and Friedman, Robert: Effect of 5.

Inlet-Air Temperature on Performance of a 16-Inch Ram-Jet Combustor.

NACA EM E53103, 1953.

NACA RN E56D20 6. Steffen, Fred W., Krull, H. George, and Schmiedlin, Ralph F.: Effect of Divergence Angle on the Internal Performance Characteristics of Several Conical Convergent-Divergent Nozzles. NACA RN E54H25, 1954.

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

8. Hall, Eldon W., and Weber, Richard J.: Tables and Charts for Thermo- dynamic Calculations Involving Air and Fuels Containing Boron, Car- bon, Hydrogen, and Oxygen. NACA RN E56B27, 1956.

9. Bahn, G. S.: Thermodynamic Properties of Combustion Gases. Preprint No. 53-S-39, A.S.M.E., 1953.

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

11. English, Robert E., and Wachtl, William W.: Charts of thermodynamic Properties of Air and Combustion Products from 300 to 35000 R.

NACA TN 2071, 1950.

12. Henry, John B., and Bennett, J. Buel: Method for Calculation of Ram- Jet Performance. NACA TN 2357, 1951.

13. Sibulkin, Merwin: Theoretical and Experimental Investigation of Additive Drag. NACA RN E51B13, 1951.

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

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

NACA RN E56D20 TABLE I. - DESIGN-POINT RAM-JET ENGINE PERFORMANCE WITH SINGLE-CONE DIFFUSER Flight Mach number, M0 I I 1.5 2.0 Combustion-chamber-inlet Mach number, M2 = 0.150 A1/A3 0.287 A1/A3 = 0.382 I I ¶ CD A6/A3 A5/A3 CT CD A6/A3 AS/A3 - CT 2.0 0.023 152 0.186 0.468 0.395 2.5 0.291 1274 0.118 0.750 0.450 .210 907 .175 .585 .499 3.0 .428 1372 .009 .840 .499 3.0 4.0 .383 1054 .161 .699 .590 3.5 .551 1400 .098 .925 .548 4.0 .670 1393 .086 1.005 .595 5.0 .533 1080 .143 .812 .690 4.5 .780 1360 .087 1.085 .643 6.0 .698 1056 .122 .931 .794 .882 998 .109 1.060 .909 5.0 .880 1307 .088 1.174 .696 7.0 7.32 .945 975 .109 1.106 .945 5.5 .990 1227 .090 1.275 .751 5.96 1.096 1139 .092 1.380 .807 Combustion-chamber-inlet Mach number, M2 = 0.175 A1/A3 = 0.334 A1/A3 0.444 2.0 0.055 418 0.175 0.550 0.465 2.5 0.365 1426 0.104 0.874 0.530 3.0 .282 1043 .158 .694 .590 3.0. .524 1508 .086 .985 .593 .660 1488 .084'1.086 .654 4.0. .471 1139 .138 .825 .713 3.5 4.0 .780 1438 .085 1.180 .720 5.0 .635 1106 .113 .970 .843 a60 .780 984 .109 1.124 1.000 4.5 .895 1369 .087 1.287 .790 5.0 1.007 1288 .089 1.400 .863 5.5 1.122 1197 .092 1.527 .940 a585 1.206 1130 .094 1.618 1.000 Combustion-chamber-inlet Mach number, M 2 = 0.200 A1 /A3 = 0.379 A1/ = 0.505 2.5 0.225 996 0.150 0.726 0.620 2.25 0.347 1433 0.091 0.941 0.581 2.50 .440 1498 .081 1.009 .620 3.0 .344 1131 .137 .808 .697 .454 1177 .121 .896 .779 2.75 .520 1527 .082 1.072 .660 3.5 4.0 .550 1178 .103 .986 .865 3.00 .598 1519 .083 1.139 .700 4.5 .625 1136 .100 1.080 .952 3.25 .672 1502 .084 1.194 .743 3.75 .804 1448 .087 1.324 .832 a477 .659 1065 .101 1.132 1.000 4.25 .927 1371 .090 1.460 .929 84.60 1.006 1312 .093 1.560 1.000 Combustion-chamber-inlet Mach number, M 2 = 0.225 A1/A3 = 0.564 A1/A3 = 0.424 2.50 0.266 1079 0.130 0.835 0.719 2.25 0.399 1469 0.081 1.078 0.675 2.75 .348 1151 .122 .87E .766 2.50 .488 1492 .083 1.152 .721 3.00 ' .400 1180 .111 .931 .819 2.75 .574 1497 .084 1.226 .770 3.25 .452 1177 .099 .988 .870 3.00 .657 1481 .086 1.302 .822 3.25 .733 1457 .087 1.378 .879 3.50 .499 1144 .097 1.040 .928 3.50 .801 1423 .089 1.456 .940 8380 .540 1047 .099 1.110 1.000 1 a372 .863 1377 .091 1.530 1.000 a The1 choking

22 NACA RM E56D20 TABLE I. - Continued. DESIGN-POINT RAM-JET ENGINE PERFORMANCE WITH SINGLE-CONE DIFFUSER Flight Mach number, N0 2.5 3.0

II

Combustion-chamber-inlet Mach number, M2 = 0.150 A1/A3 = 0.505 A1/A3 = 0.626 -r I A6/A3 A5 /A3 t I A6/A3 A5/A3 CT CD CT CD 2.0 0.284 1441 0.076 0.960 0.397 2.00 0.390 1522 0.061 1.177 0.398 2.5 .469 1555 .072 .453 1.052 2.25 .507 1565 .062 1.235 .429 3.0 .638 1546 .073 1.125 .501 2.50 .620 1566 .063 1.290 .456 3.5 .795 1510 .074 1.193 .552 2.75 .730 1550 .064 1.344 .481 4.0 .960 1432 .075 1.275 .606 3.00 .834 1516 1.402 .065 .506 4.5 1.132 1329 .077 1.371 .661 3.25 .951 1474 .066 1.466 .537 4.80 1.250 1249 .078 1.436 .697 3.50 1.079 1419 .069 1.540 .559 3.96 1.349 1300 .073 1.701 .619 Combustion-chamber-inlet Mach number, M2 = 0.175 A1/A3 = 0.586 A1/A3 = 0.727 2.0 0.348 1512 0.070 1.062 0.468 2.00 0.458 1537 0.058 1.305 0.472 2.5 .554 1594 .071 1.138 .534 2.25 .591 1576 .061 1.370 .507 3.0 .749 1565 .073 1.246 .598 2.50 .722 1574 .063 1.430 .538 3.5 .934 1508 .075 1.338 .665 2.75 .851 1551 .066 1.499 .571 4.0 1.125 1406 .077 1.432 .734 3.00 .972 1515 .067 1.567 .606 4.5 1.302 1299 .079 .810 1.535 3.25 1.105 1462 .069 1.644 .641 4.80 1.420 1212 .081 1.600 .860 3.50 1.249 1402 .072 1.732 .674 3.96 1.546 1266 .078 1.942 .747 Combustion-chamber-inlet Mach number, M2 = 0.200 A1/A3 = 0.666 A1/A3 = 0.826 2.0 0.400 1537 0.071 1.158 0.545 2.00 0.520 1531 0.065 1.425 0.545 2.5 .630 1597 .072 1.262 .625 2.25 .657 1561 .067 1.502 .590 3.0 .850 1566 .074 1.363 .706 2.50 .801 1555 .068 1.578 .633 3.5 1.052 1501 .076 1.470 .793 2.75 .953 1533 .070 1.652 .673 4.0 1.250 1396 .079 1.589 .888 3.00 1.091 1496 .072 1.727 .714 a445 1.420 1287 .082 1.710 1.000 3.25 1.239 1444 .074 1.822 .763 1 3.50 1.390 1375 .076 1.908 .811 3.96 1.692 1220 .084 2.162 .918 Combustion-chamber-inlet Mach number, M2 = 0.225 A1/A3 = 0.745 A1/A3 = 0.923 2.00 0.439 1519 0.071 1.240 0.625 2.00 0.589 1551 0.053 1.553 0.629 2.25 .565 1556 .073 1.301 .675 2.25 .748 1556 .055 1.628 .680 2.50 .689 1565 .074 1.360 .722 2.50 .900 1544 1.714 .072 .730 2.75 .810 1555 .075 1.421 .775 2.75 1.052 1513 .074 1.817 .787 3.00 .920 1527 .076 1.486 .829 3.00 1.197 1465 .076 1.901 .840 3.25 1.028 1487 .077 1.551 .897 3.25 1.351 1410 .078 2.022 .901 a3.

a358 1.201 1400 .080 1.669 1.000 1.584 1314 .083 2.168 1.000 a Thel choking

NACA RN E56D20 TABLE I. - Concluded. DESIGN-POINT RAM-JET ENGINE PERFORMANCE WITH SINGLE-CONE DIFFUSER Flight Mach number. M,0

I I

3.5 I II 4.0 I Combustion-chamber-inlet Mach number, M 2 = 0.125 0.618 A,/A3 = 0.743

II 1

T I C5 A6/A3 A5 /A3 -r I C5 A6/A3 A5/A3 CT CT 1.75 0.271 1349 0.055 1.209 0.303 1.50 0.162 954 0.047 1.362 0.281 2.00 .388 1411 .056 1.275 .329 1.75 .334 1255 .050 1.457 .308 2.25 .505 1428 .057 1.341 .355 2.00 .493 1324 .052 1.543 .334 2.59 .628 1422 .058 1.406 .376 2.25 .654 1334 .054 1.627 .356 2.75 .759 1398 .059 1.488 .400 2.50 .838 1310 .058 1.804 .383 3.00 .900 1353 .062 1.615 .426 2.75 1.047 1218 .064 2.048 .412 3.25 1.059 1276 .064 1.744 .451 Combustion-chamber-inlet Mach number, M 2 = 0.150 Al/A = 0.740 Al/A = 0.890 1.75 0.341 1375 0.054 1.358 0.370 1.50 0.213 1045 0.049 1.536 0.399 2.00 .470 1441 .056 1.437 .401 1.75 .403 1263 .052 1.653 .373 225 .617 1450 .058 1.515 .430 2.00 .592 1329 .055 1.762 .403 2.50 .755 1442 .060 1.606 .459 2.25 .784 1329 .058 1.880 .435 2.75 .908 1412 .062 1.695 .487 2.50 1.001 1314 .063 2.086 .466 3.00 1.076 1360 .066 1.856 .519 2.75 1.254 1217 .071 2.356 .501 3.25 1.255 1266 .070 2.015 .549 Combustion-chamber-inlet Mach number, M2 = 0.175 A1/ = 0.858 = 1.032 1.75 0.389 1410 0.058 1.524 0.438 1.50 0.244 1035 0.055 1.730 0.401 2.00 .553 1452 .060 1.609 .474 1.75 .467 1263 .057 1.844 .438 2.25 .720 1462 .062 1.691 .507 2.00 .687 1329 .061 1.986 .477 2.50 .887 1450 .064 1.805 .544 2.25 .906 1335 .064 2.125 .513 2.75 1.060 1415 .067 1.912 .578 2.50 1.158 1310 .069 2.352 .551 3.00 1.240 1353 .072 2.104 .620 2.75 1.449 1213 .078 2.680 .598 3.25 1.440 1250 .077 2284 .662 Combustion-chamber-inlet Mach number, M2 0.200 = 0.976 1.75 0.428 1375 0.063 1.665 0.505 2.00 .610 1420 .65 1.768 .551 2.25, .800 1436 .667 1.871 .594 2.50 .995 1426 .069 1.991 .638 2.75 1.195 1394 .072 2.118 .683 3.00 1.400 1340 .077 2.311 .732 3.25 1.634 120 .084 2.560 .790

24 NACA RM E56D20 TABLE II. - DESIGN-POINT RAM-JET ENGINE PERFORMANCE WITH TWO-CONE DIFFUSER [Note: Values of CD, A6/A3 , and A5/A3 are assumed to be the same as those in table I.]

Flight Mach number, M13 2.0 2.5 3.0 Combustion-chamber-inlet Mach number, N 2 = 0.150 A1/A3 = 0.557 A1/A3 = 0.758 A1/A3 = 0.392 r -I: I I I CT CT CT 2.5 0.309 1319 2.0 0.344 1581 2.00 0.525 1690 2.5 .344 1652 2.25 .668 1704 3.0 .451 1406 3.5 .577 1429 3.0 .550 1621 2.50 .810 1684 4.0 .700 1417 3.5 .738 1571 2.75 .943 1652 1483 1.071 1607 4.5 .814 1382 4.0 .913 3.00 .918 1327 4.5 1.097 1372 3.25 1.215 1555 5.0 5.5 1.032 1245 4.80 1.289 1287 3.50 1.373 1491 3.96 1.706 1358 5.96 1.141 1155 Combustion-chamber-inlet Mach number, M 2 = 0.175 A1/A3 = 0.456 A1/A3 = 0.646 A1/A3 = 0.880 1469 2.0 0.416 1639 2.00 0.611 1692 2.5 0.386 3.0 .550 1541 2.5 .645 1683 2.25 1705 .774 3.5 .691 1516 3.0 .863 1635 2.50 .736 1684 4.0 1462 3.5 1.069 1565 2.75 1.095 1648 .815 4.5 .934 1391 4.0 1.283 1453 3.00 1.244 1601 1.408 1545 5.0 1.050 1308 4.5 1.480 1339 3.25 5.5 1.170 1215 1.612 1248 3.50 1.586 1470 4.80 a585 1.257 1146 3.96 1.954 1321 Combustion-chamber-inlet Mach number, M2 = 0.200 A1/A3 = 0.519 A1/A3 = 0.735 A1/A3 = 1.100 2.25 0.368 1479 2.0 p .476 1658 2.00 0.691 1680 2.50 .464 1538 2.5 .761 1678 2.25 .860 1687 2.75 .547 1563 3.0 .917 1632 2.50 1.037 1663 3.00 .627 1552 3.5 1.203 1556 2.75 1.224 3.25 .704 1532 4.0 1.424 1442 3.00 1.394 1579 a445 3.75 .841 1474 1.615 1327 3.25 1.577 1518 4.25 .969 1395 3.50 1.763 1440 a460 1.051 3.96 2.139 1274 Combustion-chamber-inlet Mach number, M2 = 0.225 A1/A3 = 0.579 A1/A3 = 0.822 A1/A3 = 1.118 2.25 0.422 1514 2.00 0.521 1633 2.00 0.695 1688 2.50 .515 1532 2.25 .661 1651 2.25 .870 1670 .604 1533 2.50 2.75 .800 1647 2.50 1.040 1644 3.00 .690 1514 2.75 .935 1627 2.75 1:208 .768 1487 3.25 3.00 1.058 1542. 3.00 1.368 1546 3.50 .839 1452 3.25 1.178 1545 3.25 1.539 1482 a372 a355 a358 1 .893 1388 1.372 1450 1.796 1,376 aThel choking.

NACA RN E56D20 TABLE II. - Concluded. DESIGN-POINT RAM-JET ENGINE PERFORMANCE WITH TWO-CONE DIFFUSER [Note: Values of and A5/A3 CD, A6/A are assumed to be the seine as those in table I.]

Flight Mach number, M,0 3.5 4.0 Combustion-chamber-inlet Mach number, M 2 = 0.125 A1/A3 = 0.834 A1/A3 = 1.048 I I CT CT 0.435 1602 1.50 0.284 1243 1.75 2.00 .595 1604 1.75 .520 1452 2.25 .756 1584 2.00 .738 1472 2.50 .926 1552 2.25 .959 1452 2.75 1.106 1509 2.50 1.214 1410 3.00 1.303 1451 2.75 1.507 1302 3.25 1.523 1359 Combustion-chamber-inlet Mach number, M 2 = 0.150 A1/A3 = 0.999 A1/A3 = 1.256 1.75 0.535 1597 1.50 0.300 1311 2.00 .713 1619 1.75 .518 1445 2.25 .915 1593 2.00 .735 1468 2.50 1564 2.25 .955 1441 1.106 2.75 1.317 1517 2.50 1.206 1409 3.00 1.551 1452 2.75 1.501 1296 3.25 1.801 1346 Combustion-chamber-inlet Mach number, N 2 = 0.175 A1/A3 = 1.456 A1/A3 = 1.158 1.75 0.525 1631 1.50 0.304 1287 2.00 .720 1621 1.75 .530 1432 2.25 .918 1598 2.00 .754 1459 2.50 1.117 1566 2.25 .978 1440 2.75 1.323 1515 2.50 1.237 1399 3.00 1.542 1443 2.75 1.538 1288 3.25 1.783 1327 Combustion-chamber- inlet Mach number, M2 = 0.200 A1/A3 = 1.318 1.75 0.507 1589 2.00 .697 1584 2.25 .895 1567 2.50 1.099 1538 2.75 1.309 1490 3.00 1.526 1426 3.25 1.775 1315

26 NACA RN E56D20

(0

lID 11) tID

a)

a)

4) (I

a)

(a ND Cd

v v v v

0) Id Cd a)

a)

a) C44 •r-1 4) Cl)

NACARM E56D20 ci) ci) Cl) ci) 4-4 P r4 ci) DH U) cus 4-I 4.) I-4 Cl-I 0) 0(.)

•1-4 H •i-1' 'rj 4-3 4- 0 r 1) 0)'- H Cd rl o .1-I o 0)4.)

+) 0 (I) I 0)00 H 0+).r I bO cnq-4 •r-1 0 0 0) Id 0 CIDE-io 0) 0) ci) r ci 0 4.)

H ci) 4-I cl-I 4.)

// op ci) cl-I 4-4 1:rl C\) .-1 C') ci) H rI '1)0 bD H r.x nfl H

'LIA03aJ a mss a id .isnjjp

NACA RN E56D20 _Flight Mach number, MO Ui I) ('I U) 2.5 3.0 Cd 3.5 2.0 4.0 U) ° 2 I I I I I I I I I I I I I .04 0 .01 .02 .03 .05 .06 .07 .08 Fuel-air ratio, f/a Figure 3. - Effect of fuel-air ratio on combustion-chamber total-temperature ratio for JP-4 fuel (heating value, 18,640 Btu/lb). Ambient temperature, 392 0 R; combustion efficiency, 0.90.

NACA RN E56D20

1.2001

'25

Combustion-chamber-

a)

inlet Mach number, .150

I I U)

M2 -

H H

a 800

H C 'H a.)

0 Thermal choking

'H

a)

0) C,) 1.0 0.

.8 C.)

a)

c- .6

a) 2

0 S.

U) .4 a) U, H 0) It

.2

4 5 6 7 8

2 3

Engine total-temperature ratio, w

(a) Flight Mach number, 1.5.

Figure 4. - Design-point performance of ram-jet engine with single-cone

diffuser.

30 NACA EM E56D20 H a) C') Combustion-chamber- I-1 .225 \ ,, inlet Mach number, a) CD Of 200 M2 H E •'- 1200 C-) CH 0 II ° 75 a) co 1.2 1.0 E C-) 4) a) .8 Cf-I a) 4) 0) Thermal choking I .6 a) CD -1 .4 I I I I 1I 1I I I .21 4 6 2 3 5 Engine total-temperature ratio, 'r (b) Flight Mach number, 2.0.

Figure 4. - Continued. Design-point performance of ram-jet engine with single-cone diffuser.

NP1CA PM E56D20 - 1600 U) U) '-4 Combustion-chamber- inlet Mach number, -4 M2 C CO 1.6 1.4 1.2 C) U) ..-, 1.0 C.-.

C.-.

a) C U) 0 Thermal choking

tt

.4 .21 2.0 2.5 3.0 3.5 4.0 4.5 5.0 Engine total-temperature ratio, -r (c) Flight Mach number, 2.5.

Figure 4. - Continued. Design-point performance of ram-jet engine with single- cone diffuser.

NACA RN E56D20 -C) - Combustion-chamber- inlet Mach number, M2 a' 1400 Ca .175 C C) a) CO 1.8 .225 1.6 1.4 C-) a) C) 1.2 U) C-) + (a 4-, 1.0 a) (a 0 Thermal choking .8 .6 4I I I I I I I I I 2.0 2.5 3.0 3.5 4.0 4.5 Engine total-temperature ratio, 't (d) Flight Mach number, 3.0.

Figure 4. - Continued. Design-point performance of ram-jet engine with single-cone diffuser.

I'TACA RM E56D20 1:00 amber- nber, C- a) C, 0.

0.1751 U C.-.

C) C) P4 CI) 1.8

MI

1.6 0.175 1.4 d111 .150 C) 1.2 4-) a) C) -I C.-) C- a) 0 125 C) 1.0 4-) a) '-4 Co - 4 .8 It .4 I I I I II I I 21 I 1.5 2.0 2.5 3.0 3.5 1.5 2.0 2.5 3.0 Engine total-temperature ratio, 'r (e) Flight Mach number, 3.5. Flight Mach number, 4.0.

(f) Figure 4. - Concluded. Design-point performance of ram-jet engine with single-cone diffuser.

NACA RME56D20 With nacelle drag Without nacelle drag -T- C)

V -

ci) H N H

N

ci) CD H , c-i C) Cl) .4

-

—

Pq C-, .3 ci) r4 U c-i a) H H Cd Q I I I I I I I I 1.5 2.0 2.5 3.0 3.5 - 4.0 Flight Mach number, M0 Figure 5. - Effect of flight Mach number on design-point performance of ram-jet engine. Engine total-temperature ratio chosen for maxi- mum efficiency.

NACA RM E56D20 35

With nacelle drag Without nacelle drag Engine total-

p

-temperature ratio,- -r k.50 1 I-I - Cd I-4 U) ' 1400 U '-4 U a ' 1200 1.6 4.50 1.4 1.2 c El .: U '-4 9-4 9-4 0) U +1 .8 2.50 4___- • - .20 .22 .24 .12 .14 .16 .18 Combustion-chamber-inlet Mach number, M2 - (a) Flight Mach number, 2.5.

Figure 6. - Effect of combustion-chamber-inlet Mach number on ram-jet engine performance.

NACA RN E56D20 With nacelle drag Without nacelle drag Engine total- temperatLu'e ratio,

flit

-'C-) (QU) 2.25 - I OH r '0 3.25 C)) H 1.8 3.25 1.6 C) / 1.4 , H . 1.2

1/

CH a -I-, 1.0 12.25 :8

I-----

.12 .14 .16 .20 .18 Combustion-chamber-inlet Mach number, M2 (b) Flight Mach number, 3.5.

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

NACA EN E56D20

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TQACA EM E56D20 CD - - -_-_ ----------- ----------- H V--, 1-4 W a) H H --i Low-angle cowl CO / - - - 0 Assumed single-cone inlet 1.4 1.2 C) a) C) 1.0 4-, a) "-4 H .6 41 I I I I I .2 .3 .4 .5 .6 .7 Diffuser pressure recovery, - Figure B. - 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-temperature ratio, 2.50.

NACA RM E56D20 1.04 total- Engine ratio, - temperature 1.02 Flight Mach number, C') .__ MO CH C') 1.00 4.)

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1 2 3 4 5 6 Flameholder loss,iP/q2 Figure 9. - Effect of flameholder pressure loss on ram-jet engine performance. Combustion-chamber-inlet Mach number, 0.200; combustion efficiency, 0.90. (Specific impulse is affected in same proportion as thrust.)

NACA RM E56D20

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Figure 10. - Comparison between performance of engines using pentaborane

and JP-4 fuel. Flight Mach number, 3.5; combustion-chamber-inlet Mach

number, 0.200.

NACA EM E56D20 Li (0 P4 1.0 Engine total- 4) temperature ratio, Cd S __ +) .9 'C + ci) .8 (0 H .7 r1 4) cii .4 .6 .8 1.0

Area ratio

Area ratio at p6 = p0

Figure 11. - Effect of nozzle area ratio on ram-

jet engine performance. Combustion-chamoer-

inlet Mach number, 0.200. (Specific impulse

is affected in same proportion as thrust.)

NACA RM. E56D20 r1 i c-i Hc.

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NACA RN E56D20 43 1.2 Engine total- mperature ratio, i 2.50 I 1.0 2.25 C) Cd jet

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1.0 a C) " a.soi - (I = 1433 CT) 2.251 (i = 1791 CT) ' 2.001 (i = 2324 CT) .4 16 20 4 8 12 Jet-deflection angle, 1, deg Figure 13. - Effect of jet-deflection angle on ram-jet engine performance.

Flight Mach number, 3.5; combustion-chamber-inlet Mach number, 0.200.

NACA RN E56D20 1.2 1.1

N

7.0, 000 o 1.0 EQ cdO - 0 C /1/170000 .8 '-7 • 0 20 40 60 80x103 Altitude, ft Figure 14. - Effect of altitude on ram-jet engine performance. Flight Mach number, 3.5; combustion- chamber-inlet Mach number, 0.200; engine total- temperature ratio, 2.50.

IN

NACA RM E56D20 160( Flight Mach number, MO 3.0 4.0 H C) a) H a) 800 H r4 C) c'-4 C) a) co 0 Design point 1.0 1.2 Propulsive thrust coefficient, CT Figure 15. - Off-design performance of fixed-geometry ram-jet engine designed for flight Mach number of 3.5, combustion-chamber-inlet Mach number 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.

NACA RM E56D20 it00 Design point o ,- / -- - .- --- F-I / C-, -'-I co Translating-spike diffuser - --Fixed geometry (critical operation) -Continuously variable Movable-clug variable- [!1 area nozzle 2.0 1.6 El (-) S --I C) 3.

2.4 1.6 2.0 1.2 Flight Mach number, M0 Figure 16. - Off-design performance of various fixed- and-variable-geometry ram-jet engines operating at maximum thrust. Engines designed for flight Mach number of 3.5, combustion-chamber-inlet Mach number of 0.200, and engine total-temperature ratio of 2.50. Combustion efficiency, 0.87; ratio of specific heats for exhaust gases, 1.30.

NACA - La;igky Field. Va.