Hydrodynamic detonation velocity

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

From the magnitude of the pressures (Table XII) it appears that the velocities (Table XI) are likely to be the hydrodynamic detonation velocities for the confined samples. No pressure measurements were taken with the unconfined pellets and so the reported velocities of 2-3 km/sec may not be true detonation. 

Extension of the hydrodynamic theory to explain the variation of detonation velocity with cartridge diameter takes place in two stages. First, the structure of the reaction zone is studied to allow for the fact that the chemical reaction takes place in a finite time secondly, the effect of lateral losses on these reactions is studied. A simplified case neglecting the effects of heat conduction or diffusion and of viscosity is shown in Fig. 2.5. The Rankine-Hugoniot curves for the unreacted explosive and for the detonation products are shown, together with the Raleigh line. In the reaction zone the explosive is suddenly compressed from its initial state at... 

Thus DpJ is the theoretical maximum or hydrodynamic value of the detonation velocity when the initial density and pressure are respectively pdetonation velocity for any other initial density and pressure p and p. respectively /3 is the increase in the hydro-dynamic detonation velocity for a tenfold increase in density or pressure... 

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 ... 

Accdg to Schmidt (Ref 1, as quoted from rdsumd in CA) "That the detonation velocity (D) of explosives increases regularly with the density (d) follows directly from hydrodynamic relations when the thermodynamic.behavior of very dense gases is considered. D increases in proportion as the gas vol (v) is decreased by the covol (a) ... 

Accdg to Dunkle (Ref 8, p 206), confinement and obturation of expls in rigid tubes leads to an increase in deton velocity and this has been explained by various investigators on the basis of the hydrodynamic theory of detonation... 

The propagation velocity of the TM does not exceed 85-87% of the theoretical detonation velocity DT. Calculation of DT is carried out under the assumption of a chemical reaction which runs after compression by the shock wave without any thermal or hydrodynamic losses. In the case of the TM, meanwhile, the very possibility of propagation of a fast flame with the velocity of the shock wave depends on a velocity redistribution as a result of braking of the layers adjacent to the wall. In constructing the equations for the motion as a whole, braking plays the role of a loss which reduces the velocity. In fact, the velocity will be even smaller than the value cited besides the losses in the hydrodynamic preparation zone (the zone of velocity redistribution between the shock wave front and the forward point of the flame front, zone I-II in Fig. 19) we must add the losses in the combustion zone (from the forward point of the flame front to the cross-section in which combustion has ended, zone II-III in Fig. 19). 

This also characterizes the very style of the experimental studies. Even until recently the hydrodynamic theory of the detonation velocity, which was excellently confirmed in experiments, created a sense of contentedness and did not inspire the search for the chemical reaction mechanism or investigation of the conditions at the detonation wave front. If our paper brings about new experimental studies which penetrate deeper into the essence of the phenomenon, then our task will have been accomplished. 

Density is an important characteristic of explosives. Raising the density (e.g. by pressing or casting) improves -> Brisance and Detonation Velocity (- Detonation, Hydrodynamic Theory of Detonation). Low-density explosives, in contrast, produce a milder thrust effect (- also Loading Density - Cartridge Density). 

The change in detonation velocity at the low impurity levels is unexpected based on hydrodynamic theory. Impact sensitivity and detonation velocity tend to vary inversely. 

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... 

On the basis of hydrodynamic theory, detonation velocity can be related approximately to the detonation pressure by the equation ... 

The normal detonation velocity Dq is then computed from the perturbed hydrodynamic equations. With an expression for the ideal detonation velocity D, it is then possible to relate the ratio D jDg to the reaction-zone length and the charge radius. The final formulation of this theory by Parlin and Robinson employed the a(v) equation of state. The final results of this formulation were as follows ... 

A recent review of detonation theory is given elsewhere [12]. Models of the phenomenon envisage a detonation wave propagating into unreacted material with a sharp discontinuity in temperature and pressure at the detonation front. A reaction zone of a millimeter or smaller dimensions and yielding the equilibrium quantities of reaction products at high temperature and pressure abuts the up-stream side of the front. Using macroscopic hydrodynamic-thermodynamic theory, the energy released, and an equation of state for the assumed products, detonation velocities, pressures, and temperatures may be calculated in certain cases. 

The hydrodynamic approaches assume instantaneous reaction, and apart from a dependence on density, the simplest theories assume detonation parameters to be invariant for a substance and applicable to propagation in infinite, homogeneous (isotropic) media. They give no information on the effect of size or crystal orientation, or on the detailed mechanism by which a detonation propagates. Several theories developed by Jones in the United Kingdom and by Eyring, Wood, and Cook in the United States related detonation velocity to reaction-zone length and explosive diameter, but experimental problems severely limited their validation and application to azides. 

While the fast regime occurred in crystals at close to sonic velocities, they remained substantially (" 50%) below those obtainable with larger-diameter, polycrystalline compacts and suggested the existence of low-velocity detonation as well as full, hydrodynamic detonation in the substances. However, the propagation mechanism at low velocity appeared to be different in compacts than in crystals. Voids and fragments absent in single crystals were postulated to play an important role in the propagation of low-velocity detonation in compacts. 

Thus, in summary, early work showed that, although detonation and defla- gration can be described in macroscopic thermodynamic terms, it was not possible to determine without trial-and-error experiments whether a substance will detonate. Furthermore, among the azides which were known to detonate, available hydrodynamic theory was unable to predict a detonation velocity to better than 20% unless the sample density was so low as to be of little practical interest. The transition from initial reaction to detonation had been little studied, and it was not clear whether deflagration should to be viewed as a transient process in the development of a detonation or solely as a distinct phenomenon. 

Figure 26. Detonation velocity vs. thickness for compressed layers of lead azide of density 3.1 X 10 kg/m. The experimental points lie on the continuous curve calculated from hydrodynamic theory [127J.

As was covered earlier under deflagration and detona Vion, the detonation velocity of an explosive is the speed at which the detonation wave moves through the explosive. For most of today s (x>nimercial explosives, detonation velocity ranges from about 5,000 fps for ANFO to more than 22,000 fps for high explosives such as cast 50/50 Pentolite. It should also be noted that eveiy explosive compound v/ill have a maxxmuin or ideal detonation velocity, which is referred to as its hydrodynamic velocity. 

The close agreement between the calculated and measured detonation velocities is in favour of the basic prerequisite of the hydrodynamic detonation theory which implies that the chemical reaction rate is sufficiently high to ensure the onset of thermodynamic equilibrium in the detonation wave front. Rich mixtures display the greatest discrepancy between calculated and measured velocities. This is probably due to the insufficient rate of the chemical reaction preventing completion of the latter in the detonation wave. In reality, under the assumption of a completed reaction, the detonation velocity is lower than the calculated one. This indicates that at high detonation velocities the chemical reaction is the limiting factor. 

The BKW code is described in detail in Appendix E and the personal computer executable code is included on the CD-ROM along with the USERBKW code, which assists in assembling the required input files for BKW. If the explosive or propellant elemental composition, density and heat of formation are known, the BKW code can be used to compute the C-J equilibrium detonation product composition, the C-J pressure, detonation velocity, temperature, the single shock Hugoniot and the isentrope. The HOM equation of state constants are generated for use in hydrodynamic codes. 

I) O.A. Gurton, PrRoySoc 204A, 31-2(1950) (Fading of deton in solid expls) J) A. LeRoux, MP 33, 283-321(1951) (Deton of solid expls by impact with solid shots at high velocities) K) M.A. Cook et al, "Reaction Kinetics and Thermo-Hydrodynamics of 80/20 Tritonal , Univ of Utah, Tech Rept XXIX(1954), Contract N7-onr-45107 (Conf) (Not used by us) L) M.A. Cook, JPhysChem 58, 1114(1954) (A study of the equation of state for EDNA) M) H. Sudo, JlndExplsSocJapan 15, 277-81(1954) (Photographic study of deton of solid expls)... 

Detonation, Ideal and Nonideal. Accdg to Cook (Ref 2, p 44), an ideal detonation corresponds to the theoretical maximum or hydrodynamic value D. This maximum velocity D is subject to direct experimental determination it is the steady value attained at a sufficiently long distance from the initiator in a tube or charge of diameter sufficiently large that further in-... 

On the basis of the hydrodynamic theory, the characteristics of detonation have been calculated and values for temperature of detonation, pressure of detonation and velocity of detonation are given for four explosives in Table 5... 

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