Detonation velocity ideal

Cook, Detonation Velocities of Ideal Explosives With Inert Additives , UnivUtah, Salt Lake, TechRept No 18, AD 16380 (1953)... 

Eyring et al (Refs 1 3) first investigated the effect of curvature of the wave front on the detonation velocity. They obtd a relation betw the ratio of the actual to the ideal wave velocities (D/Dq) on the one hand and the ratio of the reaction zone length to the radius of curvature of the front (X/r) on the other. The reaction zone was defined as the zone betw the Cj (Chapman-Jouguet)-layer. If the wave front is assumed to maintain its... 

Accdg to remarks of Dunkle (Ref 8), an ideal detonation can be visualized as a steady-state process, in a frame of reference in which the detonation zone is stationary and time-invariant, with the undetonated explosive being "fed into the front at the detonation velocity D and with laminar flow of the products away from the C-J plane the rear boundary of the reaction zone is at velocity (D-u), where u is the particle velocity of the products in stationary coordinates. By the Chapman-Jouguet rule, D-u = c, the local sonic velocity at the C-J plane. That is, the velocity of the products with respect to the detonation front is sonic at the C-J temperature and pressure. Thus, even if the products were expanding into a vacuum, the rarefaction wave would never overtake the detonation front as long as any undetonated explosive remains... 

Dunkle (Ref 7) stated that accdg to the NDZ theory the first part of the deton wave, sometimes called the von Neumann spike, is an almost ideal shock wave in which very little chem reaction takes place. While the pressure at the spike is ca twice the C-J pressure, the temperature is ca half the C-J temp. This initial pressure and temp rise occurs entirely within ca 10 5cm thickness of the deton front. The 2nd phase of the deton wave is a gradual decrease in the pressure and an increase in the temp concurrent with the completion of the chem reactions. The length of the reaction zone can be detd experimentally from the minimum diam of a rod of explosive which propagates a steady-state detonation also from the changes in the deton velocity when this rod is surrounded by an inert casing material of varying thickness or from the decrease in the deton velocity when the deton wave is made to go around a bend of known radius of curvature... 

There were two steps in Jones determination of equations of his theory. He first solved the perturbed hydrodynamic equations for D, using a constant covolume equation of state. Then, using an expression for the ideal deton velocity D, he obtd the equation ... 

Lewis 8c Friauf (Ref 11) have compared experimental values of the deton velocities for the expln of H2-O2 mixts, both with and without the addn of an inert gas, with the predictions of theory, employing the ideal gas eq of state. When account was taken of dissociation equilibria of the product gases, good agreement betw theory and experiment was obtd. A study of deton velocities of solid expls has been made by Schmidt (Ref 17), who employed the Abel eq of state. His work was criticized in Ref 39, p 85-L... 

Detonation and deflagration) 110) J. Herschkowitz, "The Chapman-Jouguet Plane for a Granular Explosive , PATM 1474(1964) (Based on the deton vel of a granular mixt of K perchlorate and powdered A1 confined in a Lucite tube and an ideal deton velocity calcd by the Ruby computer, H. found that the C-J plane is ca 0.9cm behind the plane at which the expln reaction begins) 111) W.H. Rinken-bach, formerly of PicArsn, Private communication, Oct 1964) 112) F.J, Cheselske, "In-... 

Fig 3-2, p 47 gives velocity versus density of the above expls, while Fig 3.3 deals with velocity vs diameter for the same expls. Both of these Figs are reproduced here as Figs 1 2 under DETONATION VELOCITY-CHARGE DIAMETER AND DENSITY RELATIONSHIPS. These curves were obtd at large enough.diameters to ensure ideal deton... 

Baum et al (Ref 8, pp 242-44) showed how the above equation is derived from Abel equation of state, thermodynamic laws 8t Hugoniot equation for ideal gases. They also presented a curve of density-deton velocity relationship for firedamp gas. The curve is nearly a straight line... 

In diameters within the range between dc and djjj, the velocity is highly sensitive to diameter at lower densities and/or coarser granulations. The latter increase dm but, unlike lower densities, do not lower the ideal detonation velocity. Decrease in particle size, increase in confinement, and rise in charge density, decrease both dm and dc for TNT of high density and fine granulation, djjj can be as small as 3 0 cm and dc as small as 0.7 cm (See Fig 3.4 on p 48 of Cook s book )... 

Detonation Velocity, Influence of Inert Components and Inert Additives. Cook (Ref 1, p 211), under the heading Influence of Inert Additives on the Detonation Velocity of Ideal Explosives , gives a formula for determination of detonation velocity of an explosive contg an inert additive if velocity of pure expl is known. 

Ideal deton velocities correspond to a composition of the products of deton which depend only on the contents C - H - N - O and the temp pressure of deton all the parameters of the ideal deton wave of a mixed HE can be calcd exactly the same way as is done for individual HE s. It should only account for the peculiarity of the progress of the reaction in a deton wave of mixed HE s, associated with.the fact that at the start the expl components are decompd in a specific volume and then a prereaction takes place in the deton products. In the case when the decomposition of the deton products in the first stage is energetically more favorable than after the subreaction, the first stage of the reaction is responsible for the ideal velocity. This applies to mixtures of the type such as Pentolite... 

Hydrodynamic Detonation Velocity. Same as Ideal Detonation Velocity, briefly described in Vol 4 of Encycl, p D630-R... 

Included in this section are the steady state detonation properties of Tetryl. Initiation behavior will be treated in Section VII Detonation Velocity and L VD According to Cook (Ref 17) the ideal detonation velocity of Tetryl is given by ... 

Cook also showed that ideal detonation velocity in coarse Tetryl at 1.05g/cc is achieved at charge diameters above 3cm (Ref 17, p 53), provided adequate initiation is used... 

Above the critical diameter, the dependence of the detonation velocity (/)) on the charge diameter (d) is characteristic for many explosives, particularly at lower densities and for explosives which exhibit non-ideal behavior. The reason for this is due to the fact that radial loses of energy are higher at lower charge diameters. Fig. 3.2a shows the dependence of the detonation velocity on the charge diameter of various high (secondary) explosives at low densities. 

As previously stated, this discussion is valid for homogeneous explosives, such as the ones used in the military, since their reactions are predominantly intramolecular. Such explosives are often referred to as ideal explosives, in particular when they can be described using the steady state model of Chapman and Jouguet. In heterogeneous explosives (non-ideal), which are currently used in civil applications, intermolecular (diffusion controlled) mechanisms are predominant for the air bubbles, cavities or cracks (etc.). As a general rule detonation velocities increase proportional to the diameter. 

The thermodynamic data as well as the detonation parameters can nowadays be very reliably obtained by using quantum-mechanical computer calculations. On the one hand it is important to check experimental results, and on the other hand and even more importantly - it is important to predict the properties of potential new energetic materials without any prior experimental parameters, for example during the planning of synthetic work. Moreover, such computational methods are ideal for the estimation of the detonation parameters of newly synthesized compounds, which have not been obtained in the 50 100 g quantities which are necessary for the experimental determination of such detonation parameters (e.g. detonation velocity). 

We will review the basic quantities of thermodynamics energy, temperature, heat, work, and the ideal gas law. These quantities will be used to explain the principles of thermophysics and thermochemistry, which will be applied to the specific reactions of combustion and detonation. Using the thermochemical data of heats of detonation or explosion, we will see how to calculate adiabatic reaction temperatures. These data in turn will be used to analyze or predict pressures of explosions in closed vessels. We shall also see how, using thermochemical data, to predict detonation velocities and detonation pressures. 

This veolcity is called the ideal detonation velocity or the infinite diameter detonation velocity, and is designated as either Dj or Z) . Knowing D, we can plot the same data in reduced (or relative) terms in the form of D/ZJj versus d, as seen in Figure 21.5. 

From the previous chapter on ideal detonation, we know that both Pq, the detonation pressure, and D, the detonation velocity, are dependent upon the initial density of the unreacted explosive. We will recall that at the CJ point, the product... 

In this chapter we investigated some of the real effects in explosives. These included, in the nonideal region of detonation, the effects of diameter in lowering the detonation velocity and eventually causing failure in detonation. In ideal detonation we examined the effects of temperature, density, and geometry. 

Aeeording to the hydrodynamic theory of reaction waves propagating in one dimension (see references to the Introduction. Volume I) the detonation velocity is expected to be less than ideal in samples of diameter d such that the observed velocity D will approach the ideal velocity, > as J oo. Eyring et al. [25] developed a model based on a curved shock front bounded by a burned... 

Explosive Behavior. The behavior of the explosive must be accurately described, since the explosive is the source of energy in blasting. Numerical methods for modeling explosives and the properties of many common explosives have been discussed in a book by Mader (3). An ideal detonation is one in which the chemical energy of the explosive is released nearly instantaneously at the detonation front. Many military explosives are ideal in this sense, while commercial explosives, such as ANFO, are non-ideal. In non-ideal explosives, the chemical energy is released over some distance behind the detonation front. The behavior of such explosives, including the detonation velocity,... 

What this generalization implies is that one can estimate the impulse from an idealized PDE knowing the plateau pressure, P3, and the detonation velocity. That is, the impulse per unit area is given by... 

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