Transient, Three-Dimensional Detonation Waves

Accdg to Evans Ablow (Ref 66, Section Vir, p 173), two aspects of three dimensional transient detonation waves have received attention (1) the initiation of detonation by a point or localized source (2) oscillating detonation. 

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 

Following this discussion is the mathematical treatment (which includes equations 7.1.1 to 7.14 ind), demonstrating that three- 

On p 174 are examined requirements upon the initiator for such waves. An initiating shock must be of sufficient pressure and duration to permit complete reaction before a terminating rarefaction wave intervenes. 

The quantitative requirements as in the onedimensional case, are determined by the reaction kinetics, the physical state, and the equations of stat e of the material or of its components if the chge is heterogeneous. The shock- terminating rarefaction is here provided by the three- dimensional geometry and does not need a pressure-relieving rear boundary condition as in the one-dimensional case. If the shock wave is inadequate for detonation initiation, a deflagration frequently occurs instead. In Section VI,B of Ref 66, it was shown that for the correct boundary conditions a deflgrn can create a shock wave which can initiate a deton 

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Ref A.K. Oppenheim, 4thSympCombstn (1952XPub 1953), PP 471-80 Ibid, JAppl Mechanics 20 115(1953) and Ref 66,pp 171-73 [See also Detonation Waves Transients in Propagation of Transient, Anomalous and Metastable (Unstable) Detonation Waves and "Detonation Wave Transient, Three - Dimensional ]... 

Calculation of the dynamic parameters using a ZND wave structure model do not agree with experimental measurements, mainly because the ZND structure is unstable and is never observed experimentally except under transient conditions. This disagreement is not surprising, as numerous experimental observations show that all self-sustained detonations have a three-dimensional cell structure that comes about because reacting blast wavelets collide with each other to form a series of waves which transverse to the direction of propagation. Currently, there are no suitable theories that define this three-dimensional cell structure. 

Under this term ate known waves which ate generated by condensed expls developing such high pressures (10s to l05atm) iQ the detonation reaction that the flow behind the front has a component radially outward Evans Ablow (Ref 66) described three-dimensional waves under the titles "Three-Dimensional, Axially Symmetric, Steady-State Detonation Waves With Finite Reaction Rate (pp 157-67), and Three-Dimensional, Transient Detonation Waves (pp 173-75)... 

The theories of transient processes leading to steady detonation waves have been concerned on the one hand with the prediction of the shape of pressure waves which will initiate, described in Section VI, A of Ref 66, and on the other hand with the pressure leading to the formation of such.an initiating pulse, described in Section VI, B. In Section V it was shown that the time-independent side boundary conditions are important in determining the characteristics of steady, three-dimensional waves. It now becomes necessary to take into consideration time-dependent rear boundary conditions. For one-dimensional waves, the side boundary conditions are not involved... 

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