Meyer R., Koehler J., Homburg A. Explosives. Wiley-VCH, 2002 / Explosives 5th ed by Koehler, Meyer, and Homburg (2002)

1.3 Explosion temperature.

The heat of explosion raises the reaction products to the explosion temperature. Table 35 gives the internal energies of the reaction products in relation to the temperature. The best way to calculate of the explosion temperature is to assume two temperature values and to sum up the internal energies for the reaction product multiplied by their corresponding mole number. Two calorific values are obtained, of which one may be slightly higher than the calculated heat of explosion and the other slightly lower. The explosion temperature is found by interpolation between these two values.

For the example composition at: 3600 K and 3700 K. Table 35 gives for

The interpolated temperature value for 1167 kcal/kg is 3670 K.

For industrial nitroglycerine-ammonium nitrate explosives, the following estimated temperature values can be recommended:

Table 30

1.4 Specific energy.

The concept of specific energy can be explained as follows. When we imagine the reaction of an explosive to proceed without volume expansion and without heat evolution, it is possible to calculate a theoretical thermodynamic value of the pressure, which is different from the shock wave pressure (W Detonation); if this pressure is now multiplied

by the volume of the explosive, we obtain an energy value, the “specific energy”, which is the best theoretically calculable parameter for the comparison of the W Strengths of explosives. This value for explosives is conventionally given in meter-tons per kg.

The specific energy results from the equation

f = n RTex.

f:specific energy

n:number of gaseous moles

Tex: detonation temperature in degrees Kelvin

R:universal gas constant (for ideal gases).

If f is wanted in meter-ton units, R*) has the value 8.478 V 10– 4.

The values for the considered example composition are

n = 38.19 Tex = 3670 K

f = 38.19 V8.478 V10– 4 3670 = 118.8 mt/kg.

For the significance of specific energy as a performance value,

W Strength.

1.5 Energy level.

Because higher loading densities involve higher energy concentration, the concept “energy level” was created; it means the specific energy per unit volume instead of unit weight. The energy level is

l = r · f

l: energy level mt/l r: density in g/cm3

f:specific energy mt/kg.

Since the example composition will have a gelatinous consistency, p may be assumed as 1.5 g/cm3. The energy level is then

l = 1.5 V118.8 = 178.2 mt/l.

1.6 Oxygen balance.

W oxygen balance

2. Explosive and Porpellant Composition with a Negative Oxygen Balance

Calculation of gunpowders.

The decomposition reactions of both detonation and powder combustion are assumed to be isochoric, i.e., the volume is considered to be constant, as above for the explosion of industrial explosives.

*For the values of R in different dimensions, see the conversion tables on the back fly leaf.

The first step is also the sum formula

CaHbOcNd

as described above, but now

c < 2a + 12 b

The mol numbers n1, n2, etc. cannot be directly assumed as in case the of positive balanced compositions. More different reaction products must be considered, e.g.,

CaHbOcNd = n1CO2 + n2H2O+ n3N2 + n4CO+ n5H2 + n6NO;

CH4 and elementary carbon may also be formed; if the initial composition contains Cl-, Na-, Ca-, K-, and S-atoms (e.g., in black powder), the formation of HCl, Na2O, Na2CO3, K2O, K2CO3, CaO, SO2 must be included. Further, the occurrence of dissociated atoms and radicals must be assumed.

The mole numbers n1, n2, etc., must meet a set of conditions: first, the stoichiometric relations

second, the mutual equilibrium reactions of the decomposition products: the water gas reaction

H2O+CO = CO2 +H2;

the equilibrium is influenced by temperature and is described by the equation

K1: equilibrium constant

[CO2], [H2], [H2O] and [CO]: the partial pressures of the four gases.

The total mole number n is not altered by the water gas reaction; K1, is therefore independent of the total pressure p, but depends on the temperature (W Table 37). Equation (5) can be written as

The reaction for NO formation must also be considered 1/2 N2 +CO2 = CO+NO

with the equilibrium equation

K2: equilibrium constant,

p:total pressure; p/n-n1, etc., the partial pressures

n:total number of moles

Because NO formation involves an alteration of n, the equilibrium constant K2 depends not only on the temperature, but also on the total pressure p.

For the calculation of the six unknown mol numbers n1 ... n6, there are six equations. Alteration of the mole numbers cause alteration of the values for the reaction heat, the reaction temperature, the reaction pressure, and hence the constants K1 and K2. Calculations without the aid of a computer must assume various reaction temperatures to solve the equation system, until the values for the reaction heat as a difference of the energies of formation and the internal energy of the reaction products are the same (as shown above for the detonation of industrial explosives). This is a long trial and error calculation; therefore the use of computer programs is much more convenient.

For low caloric propellants and for highly negative balanced explosives, such as TNT, the formation of element carbon must be assumed (Boudouard equilibrium):

CO2 +C = 2 CO

with the equilibrium equation

Explosion fumes with a dark color indicate the formation of carbon. The calculation becomes more complicated, if dissociation processes are taken into consideration (high caloric gunpowders; rocket propellants).

In the computer operation, the unknown mole numbers are varied by stepwise “iteration” calculations, until all equation conditions are satisfied. The following results are obtained.

heat of explosion temperature of explosion

0.37% KOH

1.50% OH

0.42% H }dissociated atoms and radicals

0.09% O

0.02% K

2. Rocket Propellants

Raketentreibstoffe; propellants de roquette

The calculation of the performance data of rocket propellants is carried out in the same manner as shown above for gunpowders, but the burning process in the rocket chamber proceeds at constant pressure instead of constant volume. For the evaluation of the heat of reaction, the difference of the enthalpies of formation instead of the energies must now be used; for the internal heat capacities, the corresponding enthalpy values are listed in Table 36 below (instead of the energy values in Table 35); they are based on the average specific heats cp at constant pressure instead of the cv values. The first step is to calculate the reaction temperature Tc and the composition of the reaction gases (mole numbers n1, etc.). The second step is to evaluate the same for the gas state at the nozzle exit (transition from the chamber pressure pc to the nozzle exit pressure pe e.g., the atmospheric pressure). The basic assumption is, that this transition is “isentropic”, i.e., that the entropy values of the state under chamber pressure and at the exit are the same. This means that the thermodynamic transition gives the maximum possible output of kinetic energy (acceleration of the rocket mass).

The calculation method begins with the assumption of the temperature of the exit gases, e.g., Te = 500 K. The transition from the thermodynamical state in the chamber into the state at the nozzle exit is assumed to be instantaneous, i.e. the composition of the gases remains unchanged (“frozen” equilibria). The entropy of the exit gases at the assumed temperature Te is assumed to be the same as the entropy of the gases in the chamber (known by calculation); the assumed value Ta is raised until both entropy values are equal. Since both states are known, the corresponding enthalpy values can be calculated. Their difference is the source of the kinetic energy of the rocket (half the mass V square root of the velocity); the W Specific Impulse (mass V velocity) can be calculated according to the following equation (the same as shown on p. 295):

I = 92.507 цддддH –H

sfroz c e

J: mechanical heat equivalent