Performance Characteristics and limitations of Che ical' Propellants

ARTHUR J. STOSICK

Jet Propulsion laborafory, California lnsfitute of Technology, Pasadena 3, Calif.

The general characteristics and limitations o f chemical propellants are examined from two fundamental and general points o f view. The thermodynamic requirements are reviewed and the fact i s stressed that ultimate limits are nearly approached b y present systems. The second major consideration concerns the fact that combustion characteristics o f liquid propellants depend primarily on heat and mass transfer processes, rather than on chemical details. Logistic con- siderations are o f dominant importance in selecting liquid propellants. In the case o f solid pro- pellants many opportunities for useful chemical approaches to improved propellants are clear.

HE broad interest in matters pertaining to rocket missiles T is clear from the frequent accounts in newspapers and mag% zines. Not only do we find factual n e m releases, of present and future missiles, but various manufacturers adorn their advertise- ments with pictures of missiles which, in some instances, they may have helped to design or build. Because of this broad in- terest, a symposium dealing with propellants is timely. To provide a background for the specialized papers to follow the major performance characteristics of propellants and some of the intrinsic limitations of chemical propellants are discussed. Following the pattern of an earlier analysis the discussion is limited to propellants containing only the elements carbon, hydrogen, oxygen, and nitrogen, but the arguments are readily extended to include other elements. Horrever, the main con- clusions are not greatly altered.

Specific examples of computations of propellant performance have been omitted in order not to direct attention from the under- lying principles. The computation procedures used in these early calculations, as well as later improvements, have since been described by other authors both in journal articles and in text- books. These well known publications also contain many examples of specific numerical results, both theoretical and ex- perimental.

Thermodynamic Considerations

A rocket derives its thrust bv conducting a chemical reaction which produces hot gases inside a chamber equipped with an escape nozzle or orifice. Thrust is produced because of the ex- cess pressure inside the chamber as compared to the outside pressure. This excess pressure drops from a high value near the closed end to a zero value a t the exit of a welI-designed nozzle. Thus, a t the closed end of the combustion chamber there will be a pressure several hundred to several thousand pounds per square inch in excess of the external pressure. At the end of the nozzle, the static pressure inside the nozzle matches that of the outside atmosphere. This pressure gradient in the chamber and nozzle causes the gas to accelerate to a very high velocity.

If, in Figure 1, the force contributions arising from this pres- sure field are added, the result is the value of the thrust. At this point it becomes clear that unless gases are produced there mill be no thrust; this excludes reactions which produce no gases or only small amounts of gases. Simple physical argu-

ments based on conservation of momentum lead to a relation betn-een the thrust, the jet velocity, and the mass flom- rate of dis- charged fluid.

To calculate the thrust, the mass flom- rate and the jet velocity must be known. The flow rate is determined by the design parameters of the rocket system; the jet velocity is primarily determined by the propellant choice, and secondarily by operat- ing conditions, and is readily computed by simple thermodynamic procedures, complicated numerically only by the necessity t o consider chemical equilibria in multicomponent systems.

The basic thermodynamic equations are:

Reversible adiabatic flow Perfect gas with constant heat capacity

q = O

A S = sz - SI = 0

- A H = - ( H ~ - H , ) = A (kinetic energy) = (?$ - - "2":) u1 = 50 ft./sec. << u2 = 7,000 ft./eec.

The flow process can be properly idealized as a reversible adiabatic or constant entropy flow process preceded by an adiabatic constant pressure combustion step. In the thermo- dynamic equations the variables for the exhaust gas are related to those for the chamber gas. Also, the exhaust velocitv, commonly denoted by the letter c, is easily calculated knowing the thermodynamic characteristics of the combustion gas, in particular its heat capacity, the initial pressure and temperature, and the final pressure. The pressures are determined primarily by design considerations. The initial temperature is the adia-

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ROCKET PROPELLANTS

batic flame temperature for the selected propellant, and this parameter can also be calculated by simple thermodynamic procedures.

When chemicals react t o produce a flame, the reactants, usually near room temperature, are changed to products a t a high temperature. For simplicity, imagine this process to occur i n two steps, which, when combined, are equivalent to the actual process. In the first step consider that the reactants in their selected initial states, and at the operating chamber pressure,

C = I E T SPEED m = MASS W = WEIGHT

l s p = SPECIFIC IMPULSE

dm Thrust = s PdA = F = c- dt

F = (;) (9%)

dw dt F = Zsp -

Figure 1. Thrust value calculated from force contributions

react at constant pressure to produce products corresponding t o aome assumed final temperature, TI for the flame. Also, imagine that the heat released in this reaction, Qf, is stored in a heat reservoir. In the second step of the process assume that this heat is returned to the combustion products and is used to heat them from the reference temperature, To, to the assumed final flame temperature, T. The heat needed for this second step is AH;, = C,(T - To) . If QTo = AH;,,, the flame tem- perature was correctly estimated; if QT" is greater than AH&:,, a higher trial flame temperature is required.

The curve for AHF0 is approvimately a straight line and its course is easily extrapolated. The curve for Qf for any representative carbon, hydrogen, oxygen, nitrogen system is essentially hori- zontal in the lower temperature region, but begins a steep de- cline near 2500" K. This is the result of the onset of several reactions which result in the dissociation or conversion of the primary combustion products into unstable or less energetic species. Some of these reactions along with the energy absorp- tion for the process are:

In Figure 2 are shown typical plots of Qf and AH;,.

AH k c a1 . /mole kcal./gram

Hz -+ 2H 103.8 51.9 HzO -+ l/zHz + OH 67.9 3 . 8 '/zNz + HzO + Hz + NO 79.4 1 . 7 COz + Hz + CO + HzO 9 . 8 0 . 2

It is significant that the first two reactions which are the strongest energy absorbers also are the first to occur to a sig- nificant extent. These numbers also take on greater significance when compared to the typical heat release value of 1 t o 1.5 kcal. per gram of conventional propellant. Thus, a relatively small amount of dissociation corresponds to a major absorption of the potential heat release. At 3500' K. hydrogen gas at 20 atm. dissociates into atoms to an extent of about 3%. This small amount of this one reaction is enough to absorb nearly all of the heat normally released by the propellant.

As seen from these arguments there is a n intrinsic limitation to the flame temperatures in chemical systems. Also, inasmuch as this limitation results from properties of combustion products rather than reactants, the problem cannot be evaded by selecting other reactants in the carbon, hydrogen, oxygen, nitrogen system.

An artifice that helps only slightly is the use of reactants with negative heats of formation in an attempt to increase QZ. The second set of dashed curves in Figure 2 shows that only slight increase in the flame temperature is achieved by large attempted changes in QZ. The flame temperature, which might have been expected to rise from A' to B', instead rises only from A to B.

The implications of the flame temperature limitation can be pursued further to show how the temperature limit imposes a limit to jet velocities. By algebraic manipulation the expression for the jet velocity, c, can be factored into two terms, the nozzle thrust coefficient, CF, and the propellant characteristic velocity, c*. This factoring is also a matter of practical convenience in- asmuch as c* can be measured experimentally more readily than can c. These terms are:

C = C F x C*

where R =

Y =

z=

universal gas constant

C P

c v average molecular weight of flame gas

-

I I , I ZOO0 3000 do00 wm 6ooo IWO

T (temp1 OK.

QZ = ZQ/ (products a t temperature T) -zQr (reactants a t temperature T o )

AHTO = JT;Cp (products corresponding to T) dT T

Figure 2. Plots of QZ and AH&

The value of CF, the nozzle thrust coefficient, depends on the operating pressures, the nozzle geometry, and only t o a very minor degree on propellant properties. The characteristic velocity does not depend on operating or design parameters, but is dependent only on propellant characteristics. In this expression, the only significant variable terms occur in the ratio (To/3T), and propellant improvement rests on achieving a maximum value for this ratio.

By the previous arguments, it is shown that T, has an intrinsic thermodynamically established upper limit. It is also noted that @ for usual propellants is in the vicinity of 20, and could a t best be reduced only to about 2 (corresponding to Hz) for normal molecules stable in the range of attainable values for To. This lower limit for 2 and the discussed upper limit for T , clearly imply an upper limit to the performance of chemical propellants. Propellants already tested are essentially a t the limit deduced by these arguments.

April 1956 I N D U S T R I A L A N D E N G I N E E R I N G C H E M I S T R Y 723

Kinetic Considerations

As noted, detailed chemical differences in the propellant re- actants become obscured by high temperature thermodynamic limitations characteristic of the combustion products. In a similar way, the dominant control of the course of the com- bustion reactions by physical processes in typical jet devices obscures and minimizes rather large differences between pro- pellant systems contrary to the expectations based on purely chemical considerations. It therefore happens that rather large changes in the chemical nature of the propellant system, es- pecially for liquid propellants, can be made with little observable change in the rate of the combustion process. This comment is rather generally true, but it is most strikingly displayed by liquid bipropellant (fuel + oxidizer) systems.

Air view of CalTech Jet Propulsion Laboratory

Liquid bipropellant systems have been tested n-hich involve a substantially complete selection of the possible fuel-oxidizer combinations possible by selecting any of the fuels and any of the oxidizers listed.

Fuels Oxidizers Saturated hydrocarbons P\-itric acid Unsaturated hydrocarbons Oxides of Nitrogen Aromatic hydrocarbone Liquid oxygen Aliphatic alcohols Hydrogen peroxide Heterocyclics Tetranitromethane iiliphatic amines Aromatic amines Ammonia Hydrazine Hydrogen

At a given operating pressure level regardless of the choice made for the propellant, the required combustion chamber volume per unit of propellant mass flow rate is about the same to within about 25%. The residence time required for any of these bipropellants to coni- plete their energy release varies from a common value by only about 25%, regardless of the choice of chemicals. It is almost inconceivable that the course and the time scale for chemical kinetic processes for so wide and unrelated an array of chemical choices could be so closely alike. Accordingly, it must be con-

This can be stated in another way.

cluded that the close similarity in the combustion course among these systems must be the result of some common limiting physi- cal process. Chemical kinetic data available support this view since they predict required residence times shorter by several orders of magnitude than the times which are observed to be necessary.

The physical processes common to all these systems are the evaporation and the mixing of two liquids, the fuel and oxidizer. Evidence to support the dominant role of these processes is easy to obtain. Relatively reliable calculations can be made of the time required to evaporate fuel and oxidizer droplets of the size produced by rocket injectors when the drops are in the environ- ment characteristic of rocket Combustion chambers. The cal- culated time agrees very well Kith the observed time scale. -4 second piece of evidence may be found in the fact that the

necessary combustion chamber column can be greatly reduced if the propellants are vaporized prior to injection. This elimi- nates the vaporization step and leaves only the mixing of the gases and their burning to be completed in the combustion chamber.

Another bit of evidence may be derived from the fact that significant differences between combustion chamber efficiencies, for a given propellant system, can be obtained by deliberate attempts to alter the physical processes of evaporation and mixing.

A fourth and final bit of evidence comes from surveys made of the temperature and gas composition in active rocket combustion chambers. These studies lead to the conclusion that the gases which fill most of the combustion chamber, except for a region very near the injector or in regions of known poor mixing, are combustion products very near their ultimate maximum tem- perature. Near the injector end there are also large numbers of liquid drops which have not yet evaporated or reacted. If mixing and evaporation proceeded much faster than the chemical step, it would be expected that cool gases containing large amounts of unreacted chemicals would be found in most of the injector end of the motor. This pattern is not observed.

Conclusions The origins of two kinds of limitations on propellant systems

have been examined. The examples were selected from com- monly known liquid bipropellants, but the conclusions are not conditioned in a major way by this limitation. Simple thermo- dynamic limitations based on properties of combustion products, rather than on the choice of reactants, limit the maximum jet velocity obtained from chemical propellants. Also physical processes of evaporation and mixing are the dominant factors in determining the course of the combustion reactions and the necessary size of the combustion chamber. Chemists who wish to make valuable contributions to the ar t of propellantry should recognize these limitations and direct their ingenuity toward means of circumventing them. These limitations are less strin- gent in the field of solid propellants, and it is likely that this is t,he area in which chemists can most easily make their valuable con- tributions. There are great opport,unities for chemists to devise controls over the course and rate of solid propellant combustion both by chemical and by physical means, as well as great op- portunities to improve the properties and processing of t'his im- portant group of propellants. RECEIVED for review September 23, 1955. ACCEPTED February 10, 1956. This paper presents the results of one phase of research carried out a t the Je t Propulsion Laboratory, California. Insti tute of Technology, under con - tract No. DA-04-495-0rd 18, sponsored by the Department of t h o Army Ordnance Corps.

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