KIKETICS O F PROPELL.4NTS
847
REFERENCES
S.: J. Chem. SOC.126, 250 (1921). HAENSEL, G . : German patent 688,696 (1940). HARING, H . E . : Trans. Am. Electrochem. SOC.49, 417 (1926). HEINERT, E . : Z. Elektrochem. 37, 61 (1931). International Critical Tables, Vol. 111. McGraw-Hill Book Company, Inc., Kew York (1928). (6) Abhandlungen der deut,schen Bunsengesellschaft, S o . 3 (1910), (7) SCHIMMEL, F. A. : “t’ber die elektrolytische Kupferraffination aus ammoniakalischer Kuprosalzlosung,” Dissertation, Darmstadt, 1928.
(1) (2) (3) (4) (5)
GLASSTOSE,
SYMPOSIClI O S KISETICS OF PROPELLdSTS
ISTRODUCTORY RE MARKS^ R . E. GIBSON
A p p l i e d P h y s i c s Laboratoly, T h e J o h n s H o p k i n s Unicersity, Sili’er S p r i n g , .Maryland Received J a n u a r y 5 , 1550 ORIGIN AND GENERAL SIGNIFICANCE O F STUDY O F KINETICS O F PROPELLASTS
In these introductory remarks I propose to outline the origin and general significance of the study of the kinetics of propellants and to present some of the elementary ideas which underlie the discussions that are to follow.
Propulsion This symposium deals ITith a very special aspect of a field of study which has a very \videspread appeal and importance: namely, the study of how to move massive bodies from one place to another Ti-ith ever-increasing velocities. As applied to transportation, the science and art of propulsion is basic to our presentday type of civilization; as applied to ballistics, it provides our most potent weapons in time of war. Although the various engines used for propulsion appear upon superficial examination to differ greatly, e.g., aeroplane engines, locomotives, guns, or rockets, they all depend basically on the controlled conversion of chemical energy into the elastic energy of a gas, which in turn is transformed into energy of directed motion by an engine devised to suit the particular application. Walking is the only common form of propulsion that does not depend on this principle. Furthermore, up t o the present, the chemical reactions involved in practical propulsion have all been limited to interactions in the system carbon, hydrogen, nitrogen, oxygen. Thus, although our discussions will be limited to a very restricted field, the physical-chemical results will certainly be of much wider application. Presented a t the Symposium on Kinetics of Propellants which was held under the auspices of the Division of Physical and Inorganic Chemistry a t the 112th Meeting of t h e American Chemical Society, New Tork City, September 15, 1917.
848
R. E. GIBSON
Solid propellants The chemical reactions which produce the hot compressed gases in propulsion reactions are so frequently oxidation reactions that it has become common practice to divide each propulsion chemical system into two main components: ( I ) the fuel or substance to be oxidized; (2) the oxidizer or oxidizing substance. Together these constitute a propellant. The interaction of these two components makes available the energy that is required. Generally speaking, these two components are stored separately and mixed mechanically at the time, and in the vessel, where the propulsion reaction takes place. For example, fuels such as coal, petroleum] or gas are mixed with air, the most common oxidizer, just prior to combustion. Likewise, in large rockets having a liquid propulsion system, the fuel and the oxidizer are kept in separate containers until they are mixed in the combustion chamber, where they react a t once. I n such rockets, aniline, alcohol, gasoline, or hydrazine hydrate are used as fuels, whereas concentrated nitric acid, liquid oxygen, hydrogen peroxide, etc., are used as oxidizers. However, in solid propellants, which find their chief application in rockets or guns, the fuel and oxidizer are intimately mixed a t the time of manufacture and the solid remains in a condition of thermodynamic metastability until the proper energy of activation is supplied through the mechanism of ignition. It is convenient to distinguish two classes of solid propellants. ( I ) Composite or heterogeneous propellants: In propellants of this class the fuel and oxidizer occur as separate phases, such as a mixture of finely divided crystals held together by a suitable bond. Ordinary black powder is the most common composite propellant-the fuel being sulfur and carbon, and the oxidizer potassium nitrate. During the war a number of composite propellants were developed: for example, mixtures of ammonium picrate and sodium or potassium nitrate, held together with plastic binders, gave propellants of high power and excellent burning characteristics. (9) Colloidal or homogeneous propellants: In propellants of this class the fuel and oxidizer form one phase and, indeed, the fuel and oxidizer are frequently present in each molecule. The chemical constituents of a colloidal propellant are (I) a high polymer capable of self-combustion, i.e., containing 'sufficient oxygen to oxidize the carbon and hydrogen to carbon monoxide or carbon dioxide and water, e.g., nitrocellulose; (d) an explosive plasticizer which is compatible with the high polymer and also rich in oxygen, e.g., nitroglycerin or similar nitrates; (3) other nonexplosive plasticizers to permit adjustment of the fuel-oxidizer ratio; (4)inorganic salts; ( 6 ) a stabilizer to absorb decomposition products and prevent autocatalytic increases in decomposition rates. In the class of colloidal propellants, ordinary single-base smokeless povder, consisting of gelatinized nitrocellulose xith nonexplosive plasticizers, salts, and stabilizers, has been the most common type in use in this country. However, the most versatile members in this class are the double-base poTvders, which have long been used in guns by other countries and which have proved to be very valuable as rocket propellants. Double-base powders contain nitrocellulose and nitro-
KISETICS O F PROPELLSXTS
849
glycerin or other explosive plasticizers as the main constituents, with nonexplosi\-e plasticizers, salts, and stabilizers as minor constituents. A typical doublebase poxvder useful for rockets will contain approximately 50 per cent nitrocellulose, 3 0 4 0 per cent nitroglycerin, and 10-20 per cent other constituents. It forms a hard horny colloid vhich is quite tough. This symposium will be concerned mainly .ivith propellants of this composition. THE ORIGIN O F KISETIC PROBLEMS O F PROPELLASTS
It is of interest to note that all the investigations to be discussed today arose from extremely practical problems connected with the internal ballistics of guns and especially of rockets. The art of making and using solid propellants for guns has been promoted for many decades and reached a high state of perfection long ago. Although scientific principles and knowledge were applied to this art from time t o time in a spasmodic manner, it must be recognized that it was the empirical ballisticians who developed in gun propellants those qualities of reliability, reproducibility, and effectiveness that gave the high standards of safety and accuracy now required from all types of guns. When the development of rockets for military purposes was seriously considered, propellants of higher pover (Le., higher specific impulse) than black powder were required, and it was natural for the developers to turn to available gun propellants for their source of supply. Double-base powder of high nitroglycerin content was found to be most suitable. Its performance in rockets, however, raised a number of serious problems, and it soon became evident that a planned scientific attack on the physics and chemistry of rocket propellants must replace the empirical approach, if those problems were to be solved in a short enough time. Indeed, it was decided that quicker and surer progress would be possible if the planned program contained fundamental research studies designed t o lead to an understanding of the physical chemistry of propellant reactions, as well as more short-range developmental studies. Subsequent events have shown that this course was a wise one. These studies of propellants raised important research problems in all three of the recognized fields of physical chemistry. Studies of such important engineering qualities as the specific impulse, Le., the thrust produced by unit mass rate of discharge of propellant gas, the temperature of the gases, the discharge coefficient, etc., led to important applications of chemical thermodynamics to propellant gas systems under extreme conditions of pressure and temperature. Questions arising in the fabrication of rocket propellants in different sizes and shapes and their ability to withstand the peculiar stresses set up under service conditions led to work in the field of the structure and physical properties of solids-particularly plastics. Both in guns and in rockets the exact control of the rate of evolution of hot gas is a problem of prime importance in determining the thrust and the equilibrium pressure, and this leads a t once to a study of the chemical kinetics of the complex series of reactions commonly called the “burning of the propellant.” Time and the occasion permit me to speak only of this third class of problem.
850
R . E. GIBSON
Elementary zdeas concerning the burnzng of solid propellants It has long been k n o m that a solid propellant is satisfactory only if it obeys the law of burning in parallel layers; this is to say that the self-oxidation reaction, Le., the “burning,” takes place onlyon the exposed surfaces and that the rate at which the burning surface progresses normal to itsclf into the powder grain is the same at all points. This rate of progression is called the lznear burning rate of the powder. If these conditions hold, it is possible to calculate the geometry of the powder grain and hence the area of the burning surface a t any instant during the reaction. If r is the linear burning rate (inches per second) a t any time, S is the area of the burning surface (in square inches), and p is the density in pounds per cubic inch, then rSp is the rate of evolution of gas in pounds per second. I t has also been known for a long time that the linear burning rate as defined above depends strongly on the pressure under which the burning takes place. For practical purposes equations such as r=a+bP
(1)
or
r
=
cPn
(2)
represent the data very well over a considerable range of pressures. In these equations a , b, and care constants for a given temperature, r is the linear burning rate, P is the pressure, and n IS a constant. Investigations during the war increased enormously the variety of propellants for which good burning-rate data are available and have established the validity and utility of these equations, especially equation 2 , over a wide range of powder compositions. A typical example is given in figure 1. Although there is considerable uncertainty about the superiority of either of the above equations over the other, or even about the most suitable form of pressure equation, it has been found that equation 2 is easier to handle in some mays and does not lead to misleading results.
Simple equilzbrium equataon In order to illustrate the practical significance of kinetic problems in the design of rockets, we may consider the simple equation for the equilibrium pressure generated in a rocket when the burning-rate law (equation 2 ) is obeyed and where all other factors affecting the rate of burning are kept constant. This equation is
where S is the area of the burning surface, c and n are the constants in equation 2 , p is the density of the powder, pp is the density of the powder gas, At is the area of the nozzle, and CD is the discharge coefficient. This equation illustrates a t least one kinetic problem-the value of a search for a low-pressure exponent. If n = 1, a stable equilibrium pressure is impossible; if n = 0, the equilibrium pressure varies linearly with the various parameters inside the bracket. For
85 1
KINETICS OF PROPELLANTS
powders available in the past, n = 0.75 approximately, which means that the equilibrium pressure depended on the fourth power of these parameters, a circum-
3.0 12.0
z p
v
d
z
1.0
0.5
2 0.3 0.5 1.0 2.0 3.0 5.0 AVERAGE PRESSURE (1000 LBJINZ) FIG.1. Burning-rate d a t a for powder composition 14400 Powder composition 14400 Kitrocellulose . . . . . . . ................................ including per cent nitrogen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nitroglycerin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ethyl centralite. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Total volatiles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diphenylamine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H e a t of explosion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
59.92 13.22 38.96 0.94 1.18 0.18 1257 cal/g.
Burning-rate data TEMPERAILRE
10-1
"C
?i C'
Ti
1
0 78
1
'
3 70 3 31 2 24
0.71 0.62
0.49
2WO lb./in.a
3000 1b.fin.~
in.!sec.
in.:rec.
i".,'SCC.
0 i6 0 76
- 25
BVRNIXG RATE A I PRESSURES 01
c -
n
~
1.20 1.04 0.84
~
1.64 1.42 1.15
1
4OW l b . / i o . ~
I
in./rcc.
~
2.04 1.76
1.44 0 77 0 595 226
stance which led all too readily to uncontrollable pressures. An understanding of the effect of pressure on the linear burning rates and a knowledge of means of making it as small as possible were much to be desired.
852
R. E. GIBSON
Effect of chemical composition The linear rate of burning of powders also depends on their chemical composition, a dependence vhich seems to work through the adiabatic flame temperature of the propellant gas. In general, the hotter the powder, the faster its rate of burning under a given pressure. Studies of the effect of composition on the rates of burning have proved to be very fruitful in suggesting or verifying hypotheses used in theoretical descriptions of the process. Figure 2 shows the burning rates of a few powders as a function of their heat of explosion. The relationship depicted is valuable but should not be overrated. You will notice the general order of magnitude of the linear burning rates of powders in the nitrocellulosenitroglycerin double-base family. Effect of temperature At constant pressure, the linear burning rate of a given powder increases Jyith its initial temperature, a circumstance which can be compensated for by a slight
1 000
I
wo
1000
,
1100
MEAT OF EXPLOSION
1200
I Iyx)
CAUGM
FIG.2 . Burning rates of various double-base powders at 2 5 T . and 2500 lh,/in,* as functions of the heat of explosion.
correction in guns but iyhich created a profoundly disturbing effect in rockets. The constant in equation 2 is not much affected by temperature, so that the whole effect of temperature on the equilibrium pressure may be followed through its influence on the constant c. Relations such as
where c’ and T , are constants, have been used successfully to express this variation. If the exponent n is close to 1, it n-ill be seen that variations in c with temperature can cause profound changes in the equilibrium pressure. The temperature coefficient of the linear burning rate is, therefore, a quantity which must be understood and controlled, if successful practical applications in rockets are to be made. Effect of radiation The radiation falling on a burning grain of powder from the enveloping hot gases also affects the linear rate of burning. The hotter the adiabatic flame tem-
KINETICS OF PROPELLANTS
853
perature, the greater is this effect. The effect of radiation on the burning rate may be treated by the hypothesis that the radiation penetrates into the powder beyond the burning surface and upon absorption raises the temperature of the solid with consequent increase in its burning rate. By the addition of suitable absorbing material into the propellant, the penetration of the radiation can be controlled and even used t o advantage.
Effect of gas velocity Under comparable conditions of pressure and temperature the burning rate of a powder of given composition increases as the velocity of the propellant gas parallel t o the burning surface increases. The contribution of this effect to the overall burning is called “erosiue burning” and becomes especially significant in rockets, where the channel available for the movement of the hot gases is narrower and where the gases flow over a considerable length of burning surface. Especially the effect of erosive burning may be described by an equation of the form
r
=
cPn(1
+ kv)
(5)
where the symbols are the same as in equation 2 with the addition of k (a constant) and v (the velocity of the gas over the powder).
Summary of factors influencing gas evolution I t will be seen from the foregoing that control of the rate of generation of hot gases by a solid propellant is definitely a complicated problem. Basically the principal factors involved are pSr, the product of the density, the burning surface, and the linear burning rate. The burning surface S is controlled by the geometry of each single grain of the propellant charge and must be known a t every instant of the reaction. The linear burning rate depends on the following factors and is under control only when all these factors are under control: (1) chemical composition; ( 2 ) chamber pressure; (3) initial powder temperature; (4) radiation from environment; and (5) tangential velocity of propellant gases. I t is only recently that the significance of these last three variables has been recognized and investigated. Generally speaking, the empirical understanding of these factors has advanced to a point where an equation similar to equation 3 but taking all effects into account, can be set up to give quite accurately the equilibrium pressure in a rocket from a knowledge of properties of the propellant. On the basis of this work, it has been possible to design successful rockets in which gas is generated at rates of the order of 500 lb./sec.-a very brisk reaction. Theoretical and experimental studies of the physical-chemical mechanism of the burning of propellants are the ultimate source of a basic understanding of this complex process. As the symposium proceeds, we shall see what progress has been made in this direction. I should like to emphasize this work as a field which presents challenging and interesting problems to the serious student of kinetics. The problems are difficult and the phenomena too susceptible to practical test to permit oversimplification masquerading as basic knowledge. However, the applications of the result are far-reaching, and the interest and discipline of the investigation cannot fail t o inspire the enthusiastic physical chemist.
