Detonations three-dimensional

D.N. Williams, L. Bauwens, and E.S. Oran, Detailed structure and propagation of three-dimensional detonations. Proceedings 26th Symposium (International) on Combustion, The Combustion Institute, Pittsburg, PA, pp. 2991-2998,1996. 

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. 

However, there is now evidence that all self-sustaining detonations have a three-dimensional cellular structure. 

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 C-J 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 Three-Dimensional Wave System of Spinning Detonation , Ibid, pp 839-50 890 R. Cheret J. Brossard, "Cylindrical and Spherical Detonations in Gases , Ibid, Paper 84, p 149 (Abstracts only) 89g)... 

Macpherson (Ref 31) discussed the three-dimensional wave system of spinning detonation... 

The above considerations, although obtd from the one-dimensional case, may be correlated with the charge-diameter effect and limits of detonability in the three-dimensional explosions... 

Detonation Waves, Cylindrically Symmetric Flow Within the Steady Zone in. See under Detonation Waves Steady-State, Three-Dimensional, Axially Symmetric with Finite Reaction Rate... 

DETONATION WAVES STEADY-STATE, THREE-DIMENSIONAL, AXIALLY SYMMETRIC, WITH FINIT E REACTION RATE... 

Evans Ablow (Ref 66, p 157) in Section V, entitled Three Dimensional, Axially Symmetric, Steady-State Detonation Waves With Finite Reaction Rate stated the following ... 

The three dimensional wave system in spinning detonation was examined by Mac Pherson (Ref 105)... 

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)... 

Three-dimensional detonation waves are also described in Refs 31, 51, 59 60... 

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... 

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 ]... 

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 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... 

The problem that remains is the study of the interaction of a shock with a matrix of holes in three-dimensional geometry. The basic two-dimensional processes involved in the failure of detonation, the failure diameter of explosives, and the sputtering initiation observed for density discontinuities near the critical size have been described. The three-dimensional study of the interaction of numerous failures and reignited detonations which is necessary for a complete numerical description of these problems must await new computing hardware ... 

Detonation wave, steady state, three-dimensional, axially symmetric with finite reaction rate 4D710... 

Experiment indicates the existence of completely idiosyncratic three-dimensional regimes of propagation of so-called spin of a detonation wave in which the instantaneous distribution also depends on the angle in the cylindrical system of coordinates, coaxial with the tube, in spite of the complete symmetry of the initial conditions. 

For purposes of further analyses of detonation structure, the shock wave may be treated as a discontinuity. Both the viscous interaction between the shock and the reaction region and the molecular transport within the reaction region are small perturbations that do not appear to exert qualitatively significant influences on the wave structure. This conclusion appears to apply not only to steady, planar waves but also to unsteady, three-dimensional structures it affords one helpful simplification in the complicated analyses of transverse wave structures. It also alters the interpretation of a detonation as a deflagration-supported shock the support provided by the chemical reactions is of a nonplanar compressible gasdynamic character with negligible molecular transport. 

The experimental prevalence of multiheaded spin has prompted categorical statements to the effect that all self-sustaining detonations exhibit significant three-dimensional structure [25]. The belief that no Chapman-Jouguet detonations are planar rests on the conclusion that all such planar waves are unstable to certain nonplanar disturbances. This conclusion is difficult to substantiate in general because of the complexity of the needed... 

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