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Number: Title: Menghapus Jejakmu (Dengan Chord Gitar) Album: Hari Yang Cerah Artist: Peter Pan Genre:	Lyrics: intro:C D Bm Em 2x C D terus melangkah melupakan mu, Bm Em lelah hati perhatikan sikapmu, C D jalan pikiran mu buat ku ragu, Bm Em tak mungkin ini tetap bertahan. C D perlahan mimpi tak biasa menganggu, Bm Em kucoba untuk terus menjauh, C D perlahan hatiku terbelenggu, Bm Em kucoba untuk lanjutkan itu. C D engkau bukanlah segalaku, Bm Em bukan tempat tuk hentikan langkahku, C D usai sudah semua berlalu, Bm Em biar hujan menghapus jejakmu. C D terus melangkah melupakan mu, Bm Em lelah hati perhatikan sikapmu, C D jalan pikiran mu buat ku ragu, Bm Em tak mungkin ini tetap bertahan. C D perlahan mimpi tak biasa menganggu, Bm Em kucoba untuk terus menjauh, C D perlahan hatiku terbelenggu, Bm Em kucoba untuk lanjutkan itu. C D engkau bukanlah segalaku, Bm Em bukan tempat tuk hentikan langkahku, C D usai sudah semua berlalu, Bm Em biar hujan menghapus jejakmu. C D lepaskan segalanya, Bm Em lepaskan segalanya, C D engkau bukanlah segalaku, Bm Em bukan tempat tuk hentikan langkahku, C D usai sudah semua berlalu, Bm Em biar hujan menghapus jejakmu. nanananana   Hari Yang Cerah Untuk Jiwa Yang Sepi (Dengan (Peter Pan)    Lyrics: Intro : Am F [2x] Am pagi biar kusendiri F jangan kau mendekat Am wahai matahari Am dingin hati yang bersedih F tak begitu tenang mulai terabaikan Int: Am F Dm F C Am C hari yang cerah untuk jiwa yang sepi Am C begitu terang untuk cinta yang mati Am F C Bes F C ah... ku coba bertahan dan tak bisa Int : Am F [2x] Am biru langit kelabuku F tak begitu luas seperti memudar Am kini tak terulang lagi F di hari yang cerah dia telah pergi Am C hari yang cerah untuk jiwa yang sepi Am F C Bes F C ahh... ku coba bertahan dan tak bisa Am F C Bes F C ahh... mencoba melawan ku lepas Am C hari yang cerah untuk jiwa yang sepi... Am C begitu terang untuk jiwa yang mati Am C hari yang cerah untuk jiwa yang sepi Am F C Bes F C ahh... ku coba bertahan dan tak bisa Am F C Bes F C ahh... mencoba melawan ku lepas Bes F C semua telah hilang .... Bes F C semua telah ....    Lirik / lyric Sally Sendiri Biar Sally mencariku Biarkan dia terbang jauh Dalam hatinya hanya satu Jauh hatinya hanya ku Katakan ku takkan datang Pastikan ku takkan kembali Lalu biarkan dia menangis Lalu biarkan dia pergi Sally kau selalu sendiri Sampai kapanpun sendiri Hingga kau lelah menanti Hingga kau lelah menangis Sally kau selalu sendiri Sampai kapanpun sendiri Hingga kau lelah menanti Hingga kau lelah menangis Biar Sally mencariku Biarkan dia terbang jauh Dalam hatinya hanya satu Jauh hatinya hanya ku Katakan ku takkan datang Pastikan ku takkan kembali Lalu biarkan dia menangis Lalu biarkan dia pergi Sally kau selalu sendiri Sampai kapanpun sendiri Hingga kau lelah menanti Hingga kau lelah menangis Sally kau selalu sendiri Sampai kapanpun sendiri Hingga kau lelah menanti Hingga kau lelah menangis Sally kau selalu sendiri Sampai kapanpun sendiri Hingga kau lelah menanti Hingga kau lelah menangis Sally kau selalu sendiri Sampai kapanpun sendiri Hingga kau lelah menanti Hingga kau lelah menangis lyric Di Belakangku kau peluk aku sebelum membunuhku tersenyum melihatku merenung melihatmu kau menungguku menunggu ku terjatuh setiap langkah tertuju setia dalam menunggu reff: aku menunggumu menunggumu, menunggumu mati di depanku di depanku, di depanku kau peluk aku sebelum membunuhku tersenyum melihatku merenung melihatmu repeat reff apa yang kau lakukan di belakangku mengapa tak kau tunjukkan di hadapanku apa yang kau lakukan di belakangku di belakangku, di belakangku, di belakangku di belakangku, di belakangku repeat reff

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Chapter 1: Rocket Engines

 

1.1    Introduction

Understanding plume phenomenology requires some knowledge of rocket engines, their fundamental principles of operation, and their basic configuration. This chapter by no means constitutes a comprehensive treatment of the subject nor even an in-depth introduction. For that, the reader should refer to the classic text by George Sutton^1.1 or a comparable source. Here the subject is reviewed to the extent necessary to provide missile defense system engineers and phenomenologists the fundamental parameters characterizing engine performance, particularly their effect on the observable attributes of the plume.
This chapter is divided into two parts. First, basic concepts and ideal engines are considered. Ideal in this context refers to the processes of operation characterized by one-dimensional isentropic fluid-mechanical relations. The content is restricted to those aspects of the flow that have a direct effect on the characterization of exhaust properties. The second part is devoted to the attributes of real engines that affect the reliability of plume properties based on the assumption of ideal combustion and flow processes.

1.2    Ideal Engines

1.2.1    Principles of Operation

A chemical rocket engine is a device for generating thrust by high-pressure combustion of propellants, that is, reactants, carried aboard the vehicle. The propellants are contained either in separate tanks as liquid fuels and oxidizers or in the combustion chamber itself, combined as a solid-propellant grain.^* Thrust is consequent to the expansion of the combustion products through an exhaust nozzle. The gross thrust derives from the imbalance of pressure forces within the engine as shown schematically in Fig. 1.1. Within the combustion chamber, high pressure is produced by the reaction of the propellants. The pressure forces on the walls are balanced radially but not axially; the principal component of the thrust results from the force acting on the forward end of the chamber not balanced by an opposing force at the other end. That force acts on the gaseous combustion products that are accelerated to supersonic velocities through a converging-diverging (De Laval) nozzle.
A second increment of thrust is generated by the imbalance of the longitudinal components of the pressure forces normal to the diverging section of the nozzle. The gross thrust is invariant with altitude provided the flow in the nozzle does not separate from the walls. The net thrust is slightly less; the difference is the integral of the atmospheric pressure over the external surface of the engine. Consequently, the net thrust increases with altitude to an asymptotic limit termed the vacuum thrust. (Aerodynamic drag on the engine is treated separately as part of the drag on the vehicle that also depends on the ambient atmospheric pressure.) The mathematical basis for quantifying the various components of thrust is presented in a number of texts;^1.1 the basic relations are discussed in Subsec. 1.2.3.

Fig. 1.1. Imbalance of forces in a rocket engine.

1.2.2    Engine Types

All rocket engines generate their thrust consequent to high pressures generated by propellant combustion. The simplest engines, usually designated as motors, utilize solid fuels and oxidizers blended into a more or less homogeneous mixture, cast into the pressure-containing structure of the motor casing, as illustrated in Fig. 1.2. As the propellants are consumed, the chamber pressure and hence the thrust vary somewhat with time. Solid-propellant motors normally are not throttleable or restartable; the combustion once initiated continues until the propellant is depleted.
A comparably simple engine uses pressure-fed liquid propellants, as indicated in Fig. 1.3. In this case, the tanks must be pressurized to a level higher than that in the combustion chamber; flow and combustion are initiated by the opening of valves in the propellant lines. (For hypergolic propellants, ignition is spontaneous; otherwise, an igniter of some sort is required. Frequently, initial injection of a small amount of a hypergolic combination is used as a starter.) Obviously, the walls of the tanks of a pressure-fed engine must be strong hence relatively heavy. Consequently, such liquid-propellant engines have found application only at very low thrust levels, for example, as required for space maneuvering where the weight of the tanks can be tolerated in the interest of simplicity and reliability. A hybrid engine, Fig. 1.4, uses a solid grain with a liquid oxidizer (or vice versa). This concept to some degree combines the simplicity of a solid propellant motor with the controlled combustion of a liquid propellant. There have been a number of such engines constructed and tested, but not used to date in any space or missile application.
Large liquid propellant engines used in the older long-range missiles or space launch vehicles are configured as illustrated in Fig. 1.5. The propellants are carried in tanks at pressures only sufficient to control the flow into gas-turbine driven pumps that increase the pressure to the necessary levels for introduction into the chamber. Gas generators that provide the working fluid utilize the same propellants as the engine itself, but at a much fuel-richer mixture, hence a lower combustion temperature that can be tolerated by the turbine blades. In an open-cycle engine, these fuel-rich combustion products are exhausted in parallel with the main exhaust, obviously with an appreciable amount of unused energy. Modern liquid propellant engines are of the closed-cycle type illustrated in Fig. 1.6; the fuel-rich exhaust of the gas generator or preburner is reintroduced into the main combustion chamber where additional oxidizer is available. Thus, such engines operate with a higher overall combustion efficiency.

1.2.3    Performance Parameters

Although the flow in a real rocket engine exhibits gradients in the radial and tangential directions, it is instructive to define various parameters by which performance is characterized in terms of a one-dimensional flow of combustion products.

Fig. 1.6. Closed-cycle engine.

Accordingly, the basic expression for the thrust is derived from a simple balance of force and momentum:

(1.1)

where F is the thrust, the mass flow rate, V_e, P_e, A_e are the velocity, static pressure, and area at the nozzle exit, and P_a is the ambient pressure. Both the exhaust velocity and the exit pressure depend on the nozzle expansion ratio; optimum performance occurs when the ambient and exit pressures are the same. If the exit pressure is less than the ambient, there is a loss in thrust; if the exit pressure exceeds the ambient, the full potential in thrust is not realized. The design altitude for a rocket engine occurs where the ambient pressure equals the exit pressure. However, the optimum nozzle expansion ratio for an engine designed for an upper stage involves a trade-off in the overall performance, because increasing the nozzle length also increases the engine weight. Usually, compromise results in the optimum expansion occurring at a fairly low value in the range of altitude for each stage in the flight of a ballistic missile.
Because the second term in Eq. (1.1) is relatively small, the exit or exhaust velocity is also a fundamental indicator of engine performance for a given propellant consumption rate. Preferable for that purpose, however, is the effective exhaust velocity, V_eff, defined by

(1.2)

The customary index of performance is the specific impulse, I_sp, defined by

(1.3)

where the numerator is the total impulse during the burn time t, the denominator is the total weight of propellant consumed during that period, and g is the acceleration of gravity at sea level. I_sp is expressed either in seconds in English units (thrust in pounds and propellant consumption in pounds/second) or metric units (Newtons and kilograms/second).
For solid propellants, both thrust and propellant consumption rate vary over the period of the burn so that Eq. (1.3) must be used to express the specific impulse. However, for liquid propellants over most of the burn of a given stage, the thrust and flow rates are constant, so that Eq. (1.3) reduces to

(1.4)

from which it follows that

(1.5)

In other words, the effective exhaust velocity and the specific impulse are equivalent measures of engine performance.
Because thrust varies with the ambient pressure, so also does the specific impulse, which is frequently expressed in terms of the two limits: I_sp(sl) and I_sp(vac), referring to sea level and vacuum respectively. The former of course would only be applied to first stages.
The thrust of a rocket engine can also be expressed directly in terms of the imbalance in pressure forces

(1.6)

where P_c is the pressure in the chamber and A_t is the nozzle throat area. The dimensionless thrust coefficient, C_f, is defined by Eq. (1.6); in essence, it characterizes the contribution of the diverging section of the nozzle to the total thrust. Values of C_f typically range from 1.6 to 2.0 for nozzles of practical length.
Another quantity useful in characterizing rocket performance is the characteristic exhaust velocity, C*, defined by

(1.7)

and from Eqs. (1.4) and (1.6)

(1.8)

Equations (1.1) through (1.8) are the defining expressions for the performance parameters based on one-dimensional representations. All can otherwise be written in terms of fluid properties based on the assumption of isentropic flow through the nozzle:

(1.9)

where γ is the ratio of specific heats, R is the gas constant, T_c is the stagnation temperature at the nozzle inlet (i.e., the chamber temperature for a reasonable contraction ratio), and the velocity in the chamber is negligible compared to that at the exit. Isentropic flow relations can also be used to express the thrust, thrust coefficient, specific impulse, and characteristic velocity all in terms of the pressure ratio, specific heat ratio, and the combustion temperature.^1.1 It is particularly instructive to do so for the characteristic velocity:

(1.10)

or

(1.11)

where R_u is the universal gas constant and M_m is the mean molecular weight of the combustion products. From the above relations, it follows that

(1.12)

which says that the maximum I_sp is realized at a mixture ratio such that the ratio of combustion temperature to molecular weight is a maximum. This mixture ratio is generally considerably lower than stoichiometric. The above result expressed in Eq. (1.12) also follows directly from the fact that, in expanding high temperature combustion products to a high velocity, thermal energy is converted into kinetic energy, that is,

(1.13)

Figure 1.7 shows a typical variation of I_sp with oxidizer/fuel (O/F) ratio for the common propellant combination of monomethyl hydrazine and nitrogen tetroxide. The optimum value for O/F, yielding the maximum I_sp, produces significant amounts of light molecules, for example, H₂, CO, in the exhaust (see Chapter 4). It is not appropriate to characterize these products as "unburned fuel," which implies an inefficiency in combustion; they are products of the reaction of the fuel with the oxidizer even for a perfect combustion at the optimum mixture ratio. These combustion products are the primary source for the afterburning of plumes in the ambient atmosphere, a subject discussed in Chapter 3.
Note also in Fig. 1.7 that near the maximum, the specific impulse is a slowly varying function of mixture ratio and in particular does not degrade much with moderate departures from the optimum O/F. Accordingly, rocket engines are frequently designed to operate slightly fuel-richer than optimum to reduce the heat transfer to the nozzle. Another consequence of this attribute is that although inefficiency in combustion results in lower temperatures, so also mean molecular weights are lower so that changes in the ratio are not large and there is only a small penalty in specific impulse.

Fig. 1.7. Variation of specific impulse with mixture ratio.

1.2.4    Thrust Control

The thrust of a rocket engine of given dimensions is roughly proportional to the mass flow rate of the combustion products through the nozzle. In a liquid propellant engine, that rate is controlled simply by restricting the flow in the oxidizer and fuel lines leading to the injector assembly. Thrust termination or engine cutoff is accomplished by closing the valves in those lines. Control of thrust in a solid-propellant motor is quite different; the burning rate of the propellant varies directly and rapidly with the pressure at the surface where reaction is occurring. This behavior is expressed by the relation

(1.14)

where β is the burning rate, for example, inches/second, and P_c is the pressure at the surface of the grain. The coefficient α is a function of the initial temperature of the grain and the exponent n varies with the propellant formulation, typically with values between 0.2 and 0.8. Figure 1.8 illustrates this relation for a representative ammonium perchlorate solid propellant.^1.2
This relation at first would appear to represent an unstable condition regardless of the value of the exponent; as the pressure caused by the combustion builds up, the burning rate would continue to increase with time, thus precluding control. However, that is not the case. This can be illustrated by a simple argument (see Fig. 1.9).^1.3 Assume a solid propellant motor is designed for a specified thrust at a nominal chamber pressure. The required nozzle area is then specified by means of Eq. (1.6), from which the nozzle flow rate follows as a function of chamber pressure. The design then must specify the area of propellant burning surface for the required gas production rate to maintain the chamber pressure and thrust. Nonlinear gas production rates for hypothetical propellants exhibiting burning rates characterized by n > 1 and n < 1 at the nominal combustion chamber pressure are shown in Fig 1.9, together with the linear variation of the nozzle flow rate with the chamber pressure.

Fig. 1.8. Variation in burning rate of a solid propellant.

Consider the result of a small momentary decrease in chamber pressure. For n < 1, the gas generation rate exceeds the nozzle flow rate so that the pressure will tend to be restored; on the other hand, for n > 1, the pressure will continue to decrease. Conversely, for a momentary increase in chamber pressure, for n < 1 the gas generation rate is less than the nozzle flow rate, again producing a restoring effect. However, in this case n > 1 yields a higher gas production rate, thus further amplifying the effect. Hence, propellants characterized by n < 1 can be configured for stable combustion but not so for n > 1. (It would also follow that, for a propellant exhibiting a burn rate profile such as that indicated in Fig. 1.8 by n > 1, the pressure in the chamber would not build up at all after ignition.)
In real motors, two other effects are occurring simultaneously. The burning area will vary somewhat as the propellant is consumed, and the nozzle throat area can increase, for example, as the insulating liner ablates. The design of a solid propellant motor must account for all those effects to maintain a more or less constant chamber pressure.

Fig. 1.9. Criterion for stability in solid propellant combustion.

Some earlier research studies were devoted to the development of plateau propellants, that is, with a plateau in the burning rate relation, as indicated by the dashed line in Fig. 1.8; this can be accomplished by adding certain compounds in the propellant mix.^1.3,1.4 However, such propellants have not been widely pursued. Current practice relies on the behavior of conventional propellants with a burning rate characterized by an exponent considerably less than unity. For example, for the propellant in the solid rocket motor units of the space shuttle, the exponent is about 0.31.
The design for a reasonably constant thrust level during the burn then requires consideration of the rates of change in throat area and burning surface area of the propellant grain. In regard to the latter, modern solid motors frequently are designed with rather complex cross sections for the propellant grains. A further complicating factor is the variation of the burning rate with the initial temperature of the propellant (Fig. 1.8), which is not necessarily subject to strict control.
Solid motor thrust cannot be controlled during the burn in the sense that a liquid engine can be throttled by action of valves in the propellant feed lines. Accordingly, solid motors are designed to burn essentially to propellant depletion. However, it is desirable to terminate the thrusting in a more controlled manner than that resultant to totally depleting the propellant grain. This is usually done by suddenly opening a number of ports in the chamber so that the burning rate drops rapidly.
A manifestation of this overall behavior of solid propellant combustion is a chamber pressure that never reaches an absolutely constant value as in a liquid-propellant engine. Moreover, the resultant chamber pressure is dependent to some degree on the initial temperature of the grain; burn time also would depend on that temperature. Nevertheless, the pressure in a properly designed solid motor would attain a level sufficiently constant and close enough to the nominal design value to provide a stable period of combustion and hence total impulse. A typical chamber pressure history would appear as in Fig. 1.10, which shows another characteristic feature, a much slower tailoff in thrust compared to a liquid propellant cutoff.

Fig. 1.10. Variation of chamber pressure in a solid propellant motor.

1.2.5    Thrust Vector Control

In addition to the thrust level, the thrust vector also must be controlled. There are four basic methods for achieving that control, as illustrated in Fig. 1.11. The whole engine or the nozzle assembly can be rotated by using a gimbal or swiveling mechanism. Heat-resistant vanes or other aerodynamic surfaces can be moved into the exhaust stream to deflect it. Alternatively, such deflection can be effected by injecting fluid through the wall of the diverging section of the nozzle. Otherwise, the thrust vector can be changed by rotating the entire missile by using auxiliary, for example, vernier, engines.^* The pros and cons of these various approaches are discussed in Sutton.^1.1 Most modern launch vehicles employ gimbaled nozzles for controlling the thrust vector. However, a number of current short-range missiles, descendents of the German V-2 rocket of World War II, use graphite vanes in the exhaust.

Fig. 1.11. Methods of thrust vector control.

The effect of these various methods for controlling the thrust vector on the observables of the plume of course depends on the magnitude of the change in exhaust flow direction induced. For very slight changes required to maintain a programmed flight path, the net effect on plume emission is correspondingly small. On the other hand a large change in exhaust flow direction relative to the flight path, that is, the missile velocity vector, could significantly increase the angle of attack and hence the infrared (IR) emission from the plume.

1.3    Real Engines

1.3.1    Three-Dimensional Flow

Fig. 1.12. Nozzle shapes.

The assumption of a one-dimensional flow is useful for providing a basic understanding of the functioning of a rocket engine and for defining standard performance parameters. However, the flow in a real rocket engine departs from that ideal concept in three ways. First, the flow through a nozzle cannot be represented as one-dimensional. Consider a simple nozzle with a conical divergent section, as illustrated in Fig. 1.12(a). The flow at the exit plane is divergent hence inherently nonuniform. This divergence represents a loss in thrust, the radial components not contributing to the total. A closer approximation to an ideal one-dimensional nozzle would be one contoured to produce a uniform parallel flow at the exit plane, as indicated in Fig. 1.12(b). The shape of such a nozzle can actually be determined using a standard procedure for characterizing a supersonic flow, for example, the method of characteristics. However, for a real engine, such a nozzle would be very long hence unacceptably heavy. In engineering practice, the trade-off in nozzle weight versus increased thrust for an overall optimization results in a bell-shaped nozzle, Figure 1.12(c), in which the exit flow is nearly parallel but necessarily nonuniform in velocity and other properties. Methodology for the optimization of the nozzle wall contour was developed by G.V.R. Rao at Rocketdyne;^1.5 it involves the matching of the expansion waves generated just downstream of the throat with the compression waves created as the flow is turned further downstream, thus to minimize the losses.^1.1
Up to this point, the term ideal flow has referred to one-dimensional isentropic representation, in which properties at any station along the flow in the chamber and nozzle are considered to be uniform and in both thermal and chemical equilibrium. It is convenient now to extend that definition of ideal to include representations in which various two-dimensional (axisymmetric) nonequilibrium effects can be treated by well-developed methodology, such as that described in Chapter 5. This permits definitions of efficiency in terms of the ratios of measured performance to theoretical performance. Thus, a combustion efficiency η_c can be defined as

(1.15)

and a nozzle efficiency as

(1.16)

where the theoretical values are those predicted by the Joint Army-Navy-NASA-Air Force one-dimensional equilibrium (JANNAF ODE) code (see Chapter 4).

1.3.2    Nozzle Expansion Ratio

The flow in the supersonic section of the nozzle will expand to a pressure dependent on the ratio of the exit plane area to the throat area. If the exit pressure is greater than the ambient pressure, the exhaust will immediately expand until the static pressure in the stream adjusts to its surroundings. In this case the thrust coefficient is somewhat less than that for a longer nozzle. Conversely, if the exit plane pressure is less than ambient, the exhaust stream will contract. In this case there is a decrement of thrust in accordance with Eq. (1.1). The condition of equal pressure is encountered at the design altitude. These three conditions are illustrated in Fig 1.13 along with a fourth, in which the exit pressure is so much lower than the ambient pressure that the flow within the nozzle separates from the wall.
The nozzle of a particular stage of a ballistic missile is configured to maximize total impulse as the vehicle rises and passes through the design altitude. Obviously, an upper-stage engine will incorporate a nozzle of greater expansion ratio, with the limiting factor being the burden of additional weight. Of course, a long-range missile will rise far above the design altitude of its uppermost stage. The behavior of the exhaust expanding into ever-diminishing pressure is discussed in Chapter 2.
If a rocket engine is statically tested on the ground, the nozzle exit pressure will invariably be less than the one atmosphere of the surroundings, and the plume will necessarily contract. If the design exit pressure is not too much less than an atmosphere, the nozzle will flow full and the gases will overexpand and then contract outside the nozzle. This characteristic permits diagnostic measurements of exit plane properties during such testing that are then applicable to the plume of the missile in flight. However, if the nozzle expansion ratio is too great, as for an upper-stage engine in a sea-level test, the flow will separate from the nozzle wall, and a recirculation region will form inside the nozzle along with a system of oblique shock waves. This condition is also illustrated in Fig 1.13. In this case the nozzle exit properties would differ considerably from those at or above the design altitude.

Fig. 1.13. Nozzle flow in static testing.

1.3.3    Unmixedness

The combustion and flow processes in real rocket engines are only approximated by the one-dimensional relations defined above. In addition to the three-dimensional aspects of the flow (the divergence losses), there are other sources of inefficiency. These include viscous boundary layer losses, kinetic losses in the chemical reactions themselves, particulate drag losses, and losses in energy release caused by nonideal vaporization and mixing on a small scale. However, the most significant departure from the idealized flow as described above is consequent to two effects: the unmixedness of the reactants in the combustion chamber and, in the case of liquid propellants, incomplete vaporization. The latter effect is discussed in Subsec. 1.3.4.
In a real liquid-propellant engine, the fuel and oxidizer are introduced separately into the chamber through a large array of small impinging jets to form fine mists that quickly mix and react. (Commonly, the injector is designed to produce a uniform mixture ratio in the central region of the combustion chamber but a richer mixture near the wall to facilitate cooling.) In addition, throughout the chamber, there are local regions of nonoptimum O/F that result in gradients in temperature and variations in the mole fractions of the products. This effect, which persists through the chamber and nozzle, can produce striations in the exhaust that in some cases can be related to the pattern of holes in the injector. Figure 1.14 is a photograph of the exhaust of an Atlas booster engine showing such streakiness. Figure 1.15 is a better example of that effect, an image produced by an infrared camera (3–5 µm) of a Delta liquid-propellant core stage at about 96 km altitude, viewed from the ground. The radial streaks, attributable to the injector pattern, are more or less stationary; the tangential pattern is nonstationary and consequent to fluctuations in the flow. These effects can yield conditions in the exhaust leading to significant departures of the predicted radiative properties of plumes based on assumptions of well-mixed gas-phase reactions.

Fig. 1.14. Striations in the exhaust from an Atlas booster engine. (Courtesy Boeing Rocketdyne.)

In a solid-propellant engine, the effects of unmixedness are coupled to a characteristic temporal unsteadiness. For one thing, there are small-scale inhomogeneities in the propellant mix, and the burning rate is not perfectly constant, influenced by variations in the local pressure along the length of the chamber. Not only are there spatial inhomogeneities in the resultant combustion products, but also finite-sized chunks of unburned grain can be intermittently ripped off the surface and carried in the flow. Some of these chunks are large enough that on occasion their burning extends into the exhaust. In addition, liquid alumina, produced in the combustion, can accumulate in nooks and crannies in the motor and be blown out intermittently, likewise producing momentary flashes. The latter effect is considered by some analysts to be the dominant source of nonuniformity in a solid-propellant exhaust.

Fig. 1.15. Image of Delta core stage viewed from the rear. (Courtesy ISTEF.)

1.3.4    Incomplete Vaporization

A comparable source of inefficiency in the performance of a real engine is that of incomplete vaporization of one or both propellants. In general, vaporization of droplets, usually the fuel, is the rate-limiting factor in the combustion of liquid propellants; a theoretical representation of this effect was provided many years ago by Richard Priem and his associates at the NASA Lewis Laboratory.^1.6 Figure 1.16 illustrates the process of a burning in a liquid-propellant rocket chamber. Droplets of fuel and oxidizer are produced by the impingement of liquid streams, usually like-on-like, from the injector. These droplets, surrounded by gaseous products of prior combustion, initially moving at higher velocity than the gas close to the injector face, at first are accelerated by drag to the gas velocity, and then lag the rapidly expanding gaseous products. In general the droplets are heated convectively, evaporate, and react with the vapor of the other propellant. For simplicity, Fig. 1.16 represents the place where the velocities are matched so that the flame front is approximately spherical. Thus, heat is transported inward while fuel vapor moves radially outward from the droplet, there to encounter an oxidizer-rich local environment. The droplet essentially remains at the boiling point until it is finally consumed; the downstream point of disappearance will depend on droplet size. The rate of droplet vaporization has been established to be the rate-controlling process in liquid-propellant combustion.^1.7
There are, of course, steep radial gradients in temperature and composition from the droplet to the free stream. Consequently, hydrocarbon fuel vapor can be heated to the cracking point before the reaction, thus producing carbon as a product not predicted for the overall mixture ratio and persisting as soot particles through the subsequent mixing and acceleration. This process is discussed further in Chapter 9.

Fig. 1.16. Flame front of a burning droplet. 1.8

As a further departure from ideal well-mixed gaseous combustion, the spray from impinging streams of hypergolic propellants can be interrupted by the highly unsteady reactions occurring near the injector face, resulting in substantial numbers of relatively large droplets. The liquid vaporization rate diminishes with the reduction in convective heat transfer as the droplets are accelerated by the gaseous products in their motion toward the nozzle. Thus, a fraction of the mass flow entering the nozzle could be unevaporated and of course unreacted. However, the particles are unlikely to survive the highly turbulent shearing forces through the nozzle. (Although propellant droplets are sometimes seen in the exhaust of small, relatively inefficient thrusters used for attitude control or orbital maneuvering, they are not evident in the exhaust of large booster engines.) The net effect of this unevaporated liquid is an effective O/F ratio for the gaseous phase reaction closer to stoichiometric than the nominal O/F for the chamber. This can result in considerably higher temperatures at the nozzle exit than predicted by the standard performance codes for the nominal mixture ratio; this is discussed in Chapters 5 and 10.

1.3.5    Cooling

Another source of departure from the ideal is the cooling of the chamber walls, which introduces strong gradients in gas temperature through the boundary layer. Cooling of course is necessary; the combustion temperatures greater than 3000 K and chamber pressures of more than 130 atmospheres introduce an enormous heat transfer load. Three methods, frequently in combination, are used for the chambers and nozzles of liquid-propellant engines: regenerative, film, and radiative cooling, as illustrated schematically in Fig. 1.17. Combustion efficiency loss in regenerative cooling is minimized because some of the energy loss is recaptured in the coolant propellant (which is then introduced into the chamber at a higher temperature). In film cooling some engines, fuel is sprayed on the chamber wall through an annular array of nonimpinging streams from the injector. In others, the outermost sets of impinging jets are configured to produce a relatively rich mixture. In either case, a much lower combustion temperature results in the peripheral zone of the chamber, thus reducing the heat transfer. In radiative cooling, the chamber walls are constructed of materials capable of maintaining their structural integrity and strength at very high temperatures. This method is usually restricted to engines of very low thrust. In solid-propellant motors, the chamber walls are protected by a layer of insulation. Furthermore, they are thick enough to keep their strength at considerably elevated temperatures.
Rocket engine nozzles also require cooling. Although the gas temperature and pressure drop rapidly through the nozzle, the heat transfer varies directly with the product of the density and flow velocity. Moreover, as a consequence of viscous effects in real gases, the recovery temperature in the boundary layer is closer to the stagnation temperature than to the static temperature of the free stream. The net effect is that the maximum heat transfer rate occurs at the nozzle throat. Nozzles are cooled by one or more of the methods outlined above, frequently in combination with a fourth method, ablative cooling. In this method, the nozzle wall is lined with a high-temperature insulating material that gradually erodes, thus carrying off much of the heat transferred to the wall. In some liquid-propellant engine nozzles, a regeneratively cooled section is joined to a downstream section that is ablatively or radiatively cooled. Nozzles of solid-propellant motors are usually constructed with a high-temperature material such as graphite forming the throat, frequently in combination with ablative materials lining the converging and diverging sections.

Fig. 1.17. Methods of nozzle cooling.

1.3.6    Exit Plane Properties

An important consequence of these attributes of real engines lies in the departure of nozzle exit flow properties from the ideal or theoretically calculated values. Inefficiencies in the combustion process tend to produce significantly different temperatures and molecular weights in the products; this results in a small and tolerable reduction in specific impulse (Fig. 1.17). However, there can be substantial impact on the properties of plumes calculated using theoretically derived nozzle exit properties as input.
Where possible, actual nozzle exit properties should be determined experimentally. The usual method involves multispectral measurements of the IR emission and absorption in their variation with offset from the plume axis. By one of several inversion techniques, the radial profiles in temperature and partial pressures of the emitting species can be extracted. This subject is elaborated in Chapter 10. Alternatively, real engine effects ought to be included in theoretical methods for defining exit conditions as input to plume models, as indicated in Chapter 5.

1.4    References

^1.1G. P. Sutton, Rocket Propulsion Elements, 6th ed. (John Wiley and Sons, Inc., New York, 1992).
^1.2M. Shorr and A.J. Zaehringer, Solid Rocket Technology (John Wiley and Sons, New York, 1967).
^1.3N. Kubota, "Survey of Rocket Propellants and Their Combustion Characteristics," in Fundamentals of Solid-Propellant Combustion, K. Kuo and M. Summerfeld, eds., Vol. 90 of Progress in Astronautics and Aeronautics (AIAA, New York, 1984).
^1.4E. K. Bastress, "Modification of the Burning Rates of Ammonium Perchlorate Solid Propellants by Particle Size Control," Ph.D. thesis, Princeton University, 1961.
^1.5G.V.R. Rao, "Exhaust Nozzle Contour for Optimum Thrust," Jet Propulsion 28, 377 (1958).
^1.6R. J. Priem and M. F. Heidmann, "Propellant Vaporization as a Design Criterion for Rocket Engine Combustion Chambers," NASA Technical Report R-67, 1960.
^1.7W. T. Olsen, "Problems of High-Energy Propellants for Rockets," Rocket and Missile Technology, Chemical Engineering Progress Symposium Series, Vol. 57, No. 33, American Institute of Chemical Engineers, 1961.
^1.8R. S. Levine, "Some Considerations of Liquid Propellant Combustion and Stability," Rocket and Missile Technology, Chemical Engineering Progress Symposium Series, Vol. 57, No. 33, American Institute of Chemical Engineers, 1961.