Jouguet plane, Chapman

The pressure developed by decomposition of acetylene in a closed container depends not only on the initial pressure (or more precisely, density), but also on whether the flame propagates as a deflagration or a detonation, and on the length of the container. For acetylene at room temperature and pressure, the calculated explosion pressure ratio, / initial > deflagration and ca 20 for detonation (at the Chapman-Jouguet plane). At 800 kPa (7.93... 

Note 3. When the term Chapman-Jouguet (C-J) is used to denote a given pressure, particle velocity, temp, etc, it means the values of these parameters at the Chapman-Jouguet plane, which accdg to the classical NDZ (vonNeumann-Doring-Zel dovich) theory is the rear boundary of the reaction zone. 

Detonation. Chapman-Jouguet Plane and Chapman-Jouguet Layer. See under Detonation, Chapman-Jouguet Point... 

Dremin et al (Ref 12) gives values for the following parameters of RDX TNT D=detonation velocity, Uj = velocity of detonation products at the detonation-wave front, and P = Chapman-Jouguet-plane pressure at various densities... 

Furthermore, since (W) (D) are related thru the density (p ) in the original explosive, and the density (p2) at the Chapman-Jouguet plane, by the equation ... 

T = temperature in °K and W=particle velocity. Subscript 1 applies to the original explosive and subscript 2 to the conditions at the Chapman-Jouguet plane (Ref 53, p 376)... 

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-... 

A recent study of the role of Al in expl mixts is that of Cook and co-workers(Ref 42). The low relative "brisance of aluminized explosives has been attributed in the past to incomplete reaction of Al at the Chapman -Jouguet plane," and the high blast potential to after-burning of the Al. Thus, early shaped charge studies indicated that Al acts effectively as a diluent as far as the end effect is concerned. More careful studies by Cook showed, however, that Al lowers the detonation pressure and velocity even more than an ideal diluent. The effective endothermic reaction of Al in the deto n wave is shown in the following results of deton pressures measured by the shaped charge method ... 

Gas detonation at reduced initial pressures were studied by Vasil ev et al (Ref 8). They point out the errors in glibly comparing ideal lossless onedimensional computations with measurements made in 3-dimensicnal systems. We quote In an ideal lossless detonation wave, the Chapman-Jouguet plane is identified with the plane of complete chemical and thermodynamic equilibrium. As a rule, in a real detonation wave the Chapman-Jouguet state is assumed to be the gas state behind the front, where the measurable parameters are constant, within the experimental errors. It is assumed that, in the one-dimensional model of the detonation wave in the absence of loss, the conditions in the transient rarefaction wave accompanying the Chapman-Jouguet plane vary very slowly if the... 

Figure 13, which is a graphical representation of the ZND theory, shows the variation of the important physical parameters as a function of spatial distribution. Plane 1 is the shock front, plane 1 is the plane immediately after the shock, and plane 2 is the Chapman-Jouguet plane. In the previous section, the conditions for plane 2 were calculated and u was obtained. From u and the shock relationships or tables, it is possible to determine the conditions at plane 1. Typical results are shown in Table 5 for various hydrogen and propane detonation conditions. Note from this table that (/02/yOi) = 1.8. Therefore, for many situations the approximation that is 1.8 times the sound speed, 02, can be used. 

Figure 6.2 presents the dependence of the relative pressure rise Pc-jIPq in the Chapman-Jouguet plane as a function of the hydrogen volume content in a H2 -I- air/02 mixture. The totality of data for Pq-j and Ti at < 1 corresponds to lean mixtures (deficiency in hydrogen), and at 0 >1 - rich mixtures (surplus hydrogen). Based on various data, the lower detonation limit of hydrogen -i- air mixtures lies in the range of 11-13% H2 volume content in air, i.e. 4> 0.31-0.37. The upper detonation limit is close to 70% H2, i.e. 4> w 5.56. 

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... 

In the case of a freely spreading detonation wave (in a cartridge not closed with plate 2), pM is not equal to pD, which is the pressure of detonation at the Chapman-Jouguet Point (ie in the plane of completion of chemical reaction), but can be calculated. If detonation velocity, D, and its density, are known, pD may be calcd... 

The question considered is a description of the conditions which must be met by a localized initiator if a spherical detonation wave is to be formed. The first problem is a determination of the possibility of the existence of such a wave. Taylor analyzed the dynamics of spherical deton from a point, assuming a wave of zero-reaction zone thickness at which the Chapman-Jouguet condition applies. He inquired into the hydrodynamic conditions which permit the existence of a flow for which u2 +c2 = U at a sphere which expands with radial velocity U (Here U = vel of wave with respect to observer u2 = material velocity in X direction and c -= sound vel subscript 2 signifies state where fraction of reaction completed e = 1). Taylor demonstrated theoretically the existence of a spherical deton wave with constant U and pressure p2equal to the values for the plane wave, but with radial distribution of material velocity and pressure behind the wave different from plane wave... 

Theoretical estimates of ua Particle velocity (uCJ) at the Chapman-Jouguet (CJ) plane can be computed by use of the conservation equations, the C-J condition and an appropriate equation of state (EOS) for the detonation products. It is the lack of an unequivocal EOS that makes such calcns uncertain. 

If a detonation is viewed as a plane Chapman-Jouguet wave traveling steadily in a tube in a direction away from its closed end, then we may question whether the result that v o = e,oo obtained in Section 2.3.3, is consistent with the end-wall condition. From the standpoint of the method of characteristics for reacting gas mixtures (Section 4.3), the fact that the characteristics propagate at the frozen sound speed implies [59] that the upstream end of the rarefaction wave that follows the detonation (Section... 

If a detonation is viewed as a plane Chapman-Jouguet wave traveling steadily in a tube in a direction away from its closed end, then we may question whether the result that o. obtained in Section 2.3.3, is... 

Fig. 6. Detonation in a slab of energetic material, (a) The detonation shock front runs at a constant velocity, driven by fast expansion of chemical reaction products. The highest pressure is in the von Neuman spike region just behind the front. At the Chapman Jouguet (C-J) plane the reaction is Just complete, (b) Shock compression follows the indicated Rayleigh line to where it intersects the unreacted Hugoniot at the von Neumann spike. The point where this Rayleigh line is tangent to the reacted Hugoniot is the C-J state of stable detonation velocity.

The product mixture which exists in a particular plane in the reaction zone behind the detonation front obeys the Chapman-Jouguet (C-J) hypothesis. In essence, the C-J or sonic plane differentiates between the part of the reaction zone where the detonative decomposition is completed (and exothermic reactions supply energy with the local speed of sound to the detonation front) and that part in which further energy release due to reactions among the products is not supplied sufficiently rapidly to maintain steady wave propagation. 

For a plane detonation wave. Chapman and Jouguet s hypothesis states that the line (Po, Vo) (P, V) is tangent to the Hugoniot for the explosion products in this case, the point (P, V) is called the C-J point. In the case of a concave shock front, as in an implosion, the convergence effects may raise the pressure well above the C-J point (as in the case illustrated in Figure 1.1), with a corresponding increase in the detonation velocity D. The plane-wave velocity, for which the C-J condition is satisfied, is denoted by Dcj-... 

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