Chapman-Jouguet model, detonation

The effective "Chapman-Jouguet (CJ) point" on the cylindrical charge axis always coincides with the beginning of the sharp rarefaction region outlined by the heavy line in Fig 5.2 (Ref 8, p 94). If aQ is less than or equal to the distance from the wave front to this point on the charge axis, detonation will be ideal. But if it is greater than the distance h, detonation will be nonideal In this model nonideal detonation is restricted to effective reaction-zone length of a =3/8(Dt) for L [Pg.364]

Reynolds number, p 46), etc 61-72 (Shock relationships and formulas) 73-98 (Shock wave interactions formulas) 99-102 (The Rayleigh and Fanno lines) Ibid (1958) 159-6l(Thermal theory of initiation) 168-69 (One-dimensional steady-state process) 169-72 (The Chapman-Jouguet condition) 172-76 (The von Neumann spike) 181-84 (Equations of state and covolume) 184-87 (Polytropic law) 188, 210 212 (Curved front theory of Eyring) 191-94 (The Rayleigh transformation in deton) 210-12 (Nozzle thepry of H. Jones) 285-88 (The deton head model) ... 

The Zel dovich- van Neumann-Doering Model The Chapman- Jouguet Hypothesis and Pathological Weak Detonations... 

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... 

A critical characteristic of energetic materials is the Chapman-Jouguet (CJ) state. This describes the chemical equilibrium of the products at the end of the reaction zone of the detonation wave before the isentropic expansion. In the classical ZePdovich-Neumann-Doring (ZND) detonation model, the detonation wave propagates at constant velocity. This velocity is the same as at the CJ point which characterizes the state of reaction products in which the local speed of sound decreases to the detonation velocity as the product gases expand. 

This same qualitative argument cannot be used to rule out weak detonations. Brinkley and Kirkwood [50] have formalized the dynamic argument by analyzing a model in which the detonation is of infinitesimal thickness and the pressure behind the wave initially decreases monotonically (with finite slope) toward the closed end of the tube. They find that the time rate of increase of the pressure immediately behind the detonation wave is negative for strong detonations, positive for weak detonations, and zero for Chapman-Jouguet waves. Hence (compare Figure 2.5) weak detonations... 

The next section deals with the calculation of the detonation velocity based on Chapman-Jouguet theory. The subsequent section discusses the ZND model in detail, and the last deals with the dynamic detonation parameters. 

We thus see that the motion of a real detonation front is far from the steady and one-dimensional motion given by the ZND model. Instead, it proceeds in a cyclic manner in which the shock velocity fluctuates within a cell about the equilibrium Chapman-Jouguet value. Chemical reactions are essentially complete within a cycle or a cell length. However, the gas dynamic flow structure is highly three-dimensional and full equilibration of the transverse shocks, so that the flow becomes essentially one-dimensional, will probably take an additional distance of the order of a few more cell lengths. 

The d = 13 X law led the author to develop a simple model whereby the critical energy for initiation can be predicted when the cell size and the equilibrium Chapman-Jouguet detonation states are known. This simple so-called surface energy model of Lee (34) gave predictions for the critical initiation charge weight for various hydrocarbon fuel-air mixtures in close accord with the experimental data obtained by Elsworth (39). 

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. 

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