Explosion adiabatic

When all the reaction heat is disposed in the heating of the mixture, i.e. when the thermal balance of an adiabatic process can be expressed with sufficient accuracy by equation 

To integrate Eq. (43.1) additional assumptions concerning the temperature and concentration dependence of the reaction rate dc/dt and an additional relation between C and T are required. In particular, introducing the maximum temperature T ax for complete combustion under adiabatic conditions and 

Variation in temperature (1, left-hand ordinate), relative concentration c/cq [2, right-hand ordinate) and reaction rate (3, arbitrary units) as a function of kgt for an adiabatic reaction 

It will be seen that the maximum reaction rate is reached at 1700 K representing 85% of the maximum temperature. As the activation energy increases, the maximum combustion rate shifts towards higher temperatures. 

---

Under these conditions, the time within which a given value of 9 is attained is proportional to the magnitude tx. Consequently, the induction period in the instance of adiabatic explosion is proportional to tx. The proportionality... 

The energy increment that is passed on has been called the enthalpy excess, but might better be called the thermal or internal energy excess, for the products at the iso-choric adiabatic explosion temperature have, by definition, exactly the same total internal energy as the original undetonated explosive... 

As an example of the usefulness of approximate solutions of Eq 1, let us consider how to compute the explosion time of a planar hot spot whose temperature and radius are given. A rough, but as will be shown, not too bad an estimate is obtained from solutions of the adiabatic explosion time equation ... 

P = Pex. If, for simplicity, we assume that the impacted sample is at Tm at t = 0, then (in accordance with Eq la) its T—t history will be given by curve I in the diagram. For each T there is a corresponding adiabatic explosion time Tad- Three typical T—Tad pl°ts (curves II, III IV) are shown in the diagram. Curve II does not intersect curve I, therefore there can be no explosion at t = 0. Curve III intersects curve I twice, therefore explosion should have occurred before it actually did, which is contrary to the assumption of explosion at f = 0. Curve IV, which has a point of tangency with curve I, is thus the only possible curve that satisfies the requirements of the problem under consideration. This condition of tan-... 

Influence of Kinetics on Adiabatic Explosion Times of PETN... 

Adiabatic Explosion. Since an expln takes place in an extremely short time, it may be considered to be adiabatic. Assuming that an explosive is heated by the decompn of part of the sample and that the rate of decompn increases with increasing temp, R. B.Parlin et al(Ref) derived the equation for the time-temp relationship in a purely thermal expln. A discussion of this equation would require undue space here Ref R.B.Parlin et al, OSRD Report 20 26 (1943)(Uncl assified)... 

The conditions of the chemical reaction are extremely close to the conditions of adiabatic explosion. 

Adiabatic Explosion. Since an exqiln takes place in an extremely short time, it may be considered to be adiabatic. Assuming that an explosive is heated by the decompo of part of the sample and that die rate of de-compn increases with increasing temp, R. 

Under these conditions, the time within which a given value of 9 is attained is proportional tothe magnitude x. Consequently, the induction period in the instance of adiabatic explosion is proportional to ri. The proportionality constant has been shown to be unity. Conceptually, this induction period can be related to the time period for the ignition of droplets for different air (or ambient) temperatures. Thus r can be the adiabatic induction time and is simply... 

Of interest are some correlations which Cook tentatively established between theoretical detonation and explosion results and the practical performance of explosives. For a group of primary and near-primary explosives (lead azide, mercury fulminate, and six CHNO explosives), he found a correlation between the probable order of ease of transition from deflagration to detonation and adiabatic explosion temperature. Moreover, he noted a rough correlation between the effectiveness of a primary explosive as a detonator (its ability to transfer detonation to a secondary explosive) and the C-J pressure [130]. 

In the constant-volume, adiabatic explosion case the entire explosive is converted instantaneously into products within the confines of the original explosive there is no shock wave propagation, and chemical energy is converted entirely into thermal energy without losses to the environment. 

Table IV. C-J Detonation and Constant-Volume Adiabatic Explosion Properties of Lead Azide Based on Cook s EOS...

Since the conversion is incomplete, at Tmax the gas consists of four components CO, O2, 0, and CO2. The calculated maximum explosion temperature for this case is Tmax = 2 880 K. Thus, the true temperature of adiabatic explosion of a stoichiometric CO/O2 mixture, Tmax is about half the value of Tmax calculated before and corresponding to the complete conversion of CO + 1/2 O2 to CO2. 

Also plotted in Figure 3.4 are adiabatic explosion times, defined by the relation... 

Physically this represents the time it would take for an infinite mass of explosive to ignite if it were initially at the uniform temperature Ti. The adiabatic explosion time is necessarily shorter than explosion times obtained by raising only the surface of the explosive to Ti. 

Explosion time data for nitromethane are available for pressures of 67 to 104 kbar. While some of the data are not one-dimensional, it is interesting to determine whether the data are consistent with an adiabatic explosion model with the same kinetics and temperature calculations as used in the numerical hydrodynamic calculations. To perform the adiabatic explosion time calculations the same nitromethane constants and a heat of decomposition of 1000 cal/g were used. 

Figure 3.7 Nitromethane time to adiabatic explosion vs. temperature profile and experimental data.

The data and the adiabatic explosion curve are plotted in Figure 3.7. The data are consistent with the adiabatic explosion model within any reasonable estimate of the experimental error and the error in the calculated temperature. 

The hot spot formed when a shock wave interacts with a spherical hole scales with the radius of the hole as long as no chemical reaction occurs. Using hot spot temperatures in the calculated range of 700 to 1300°K and calculating the adiabatic explosion is shown below. The ordering is identical to that observed experimentally. 

---