Flat detonation wave

An explosive lens is used to generate a flat detonation wave. The explosive lens consists of two cone-shaped segments of explosives, an inner cone and an outer cone, which are fitted together as shown in Fig. 9.2. When detonation is initiated by an electric detonator, a booster charge positioned at the top-center of the inner-cone explosive detonates. Then, the inner cone detonates and the detonation wave propa-... 

Fig. 9.2 Formation of a flat detonation wave by an explosive lens.

If the velocity of the flat detonation wave formed at the bottom of the outer-cone explosive is not sufficient for some objectives, a cylindrical-shaped high-explosive is attached to the bottom of the outer-cone explosive, as shown in Fig. 9.3. The detonation velocity of the attached high-explosive is higher than that of the outer-cone explosive. The flat detonation wave of the outer-cone explosive then initiates the detonation of the high-explosive and forms a reinforced flat detonation wave therein. 

Next to the - Chapman-Jouget theory, during the last 50 years, the principal methods of calculating detonation pressure and the velocity of flat detonation waves have been the Becker-Kistiakowsky-Wilson (BKW), the Lennard-Jones-Devonshire (LJD) and the Jacobs-Cow-perthwaite-Zwisler (JCZ) equations of state. 

The induction time data and density profiles pf detonations in oxy-hydrogen and oxy-methane mixtures were analyzed on the basis of the kinetic data obtained by the reflected-wave technique and similar methods. A plot of the ignition delay vs 1/T in oxy-ammonia mixtures gave a straight line with a slope corresponding to an activation energy of 42.5 kcal/mole. In these mixtures the induction zone is not uniform, but the shock front is flat and end of the reaction zone is clearly discernible. Onedimensional detonation waves of low Mach number but relatively stable were obtained in a gas preheated to 600-1800°K ahead of the shock front... 

Detonation Wave, Plane. This is a detonation wave in which.the front is flat. See under Detonation, Spherical-and Plane-Fronts, p D708... 

For a cylindrical pellet of an explosive composition the velocity of detonation will increase as the diameter of the explosive composition increases up to a limiting value. The detonation wave front for a cylindrical pellet at steady state conditions is not flat but convex as shown in Figure 3.6, where D is the axial detonation velocity and Dt is the detonation velocity close to the surface of the composition. 

Flat metal plates and cylinders driven by tangentially incident detonation waves were examined by Hoskin et al (Ref 5) using a 2-D steady state characteristic code. Their computations for plates or cylinders indicate that metal compressibility has little effect on the terminal velocity imparted to the metal by the expl. Thus the Gurney treatment is found to give essentially the same terminal states as their more sophisticated characteristics computation. This... 

Above, the special detonation of liquid explosives is discussed. In the detonation wave range of under-pressure detonation, there is constant flow area— the flat-form of pressure. After the feature is proved, there will be potential applications in explosion industry. 

The above classical detonation theory was proposed by Zebdovich [529, 530, 534] (see also [334]), Doring [113] and Grib [169] on the basis of a unidimensional model of a stationary detonation wave. Further studies showed (for references see Strehlow s review [458, 535]) that the real gas-kinetic and the chemical-kinetic pattern of a detonation wave are much more complicated than the idealized plane shock wave. Moreover, the flat chemical reaction fronts which follow from the classical theory are non-stationary, thus leading to distortions and discontinuities in the flame front resulting in the violation of the idealized detonation wave pattern. 

Such shock matching is useful for plane, one-dimensional systems with flat-topped detonation waves. The CD-ROM has a shock matching code called MATCH. Numerical studies are necessary to determine the effect of multidimensional geometries and of explosives with steep Taylor waves. 

To further test the weak detonation model, S. Goldstein measured the water shock velocity in the aquarium test after the detonation wave interacted with the water above the top of the X0233 cylinder. Her experimental water shock velocities, as a function of distance above the top of the explosive cylinder, are shown in Figure 2.28 along with the calculated water shock velocities. They are consistent with a flat top Taylor wave characteristic of a weak detonation and a detonation front pressure of 160 kbars. The initial water shock velocities exhibit behavior characteristic of irregular decomposition of the explosive near the shock front. The 2DL calculated aquarium pressure contours are shown in Figure 2.29. 

If the wave is sufficiently curved, the detonation proceeds like a diverging detonation wave and little or no explosive remains undecomposed. If the wave is flat, or nearly so, when it arrives at the corner, then much more partially decomposed explosive will remain after shock passage. Because the actual experiment was performed with air in the corner, the Lagrangian calculation required that some low-density material corner (Plexiglas was used). The calculation slightly underestimates the amount of explosive that remains undecomposed. 

To study this system in a more realistic geometry, the Eulerian code, 2DE, described in Appendix C, was used because it can describe large distortion problems such as an explosive-air interface. The results calculated using the Forest Fire burn are shown in 4.19. Again, the results depend upon the detonation wave profile before it reaches the corner. If the wave started out flat, the explosive region near the explosive-air interface remained partially decomposed and the detonation wave never completely burned across the front until the wave became sufficiently curved at the front and near the interface. The failure process of a heterogeneous explosive is a complicated interaction of the effective reaction zone thickness which determines how flat the wave should be and the curvature required for decomposition to occur near the surface of the charge. 

Numerical reactive hydrodynamic codes such as SIN, TDL or 2DE include the Forest Fire decomposition rate. For unresolved burns, it is necessary for the decomposition front of a detonation wave to occur over several computer meshes or cells so that the physics of the flow, the shock jump conditions, are properly described. Historically this was accomplished by adjusting the artificial viscosity so that the burn occurred over about 3 cells. If the mesh size changed, a new viscosity coefficient was determined empirically that would result in a realistic burn. As shown in the movie on the CD-ROM at /MOVIE/VISC.MVH, if there is insufficient viscosity, one obtains a reactive front with a peak that oscillates. If there was too much viscosity, a flat pressure profile occurs at the front. The problem is not unique to Forest Fire as other burn rates such as Arrhenius have the same numerical problems when numerically unresolved in reactive hydrodynamic codes. 

Reflected Pressure. Reflected pressure increases the pressure on a rigid surface if the shock wave impinges on the surface at an angle to the direction of the propagation of the wave. The maximum ratio of reflected pressure to incident (side-on) pressure when a strong shock wave strikes a flat surface head-on is 8 1. Furthermore, acceleration from a suddenly applied force of the detonation wave can double the load that a structure feels. Table 5.3 shows overpressure that can be expected from typical detonations. ... 

The parting of material that is, cutting results from the interaction of shock waves induced by detonation. The width of the flat explosive strip should be twice the thickness of the metal to be cut in order to get better results. This method is not accurate and can be employed where high cutting accuracy is not required. Flexible linear shaped charges (FLSCs) are usually employed for this purpose. 

Characterization of the explosive requires experimental determination of the detonation pressure and velocity. If the experimental state is near the ideal BKW detonation product Hugoniot, the isentrope of the detonation products can be determined by displacing the isentrope through the experimental state. Otherwise, the ideal detonation product Hugoniot must be displaced so that it intersects the observed detonation pressure and velocity by decreasing the energy available to the detonation products. This results in a weak detonation with a flat top Taylor wave. 

The addition of inert metal (or other inerts) particles to explosives results in weak detonations with flat topped Taylor waves. The nonideal behavior is caused by failure of some of the individual detonation wavelets between the metal particles. Subsequent decomposition of the partially decomposed explosive occurs behind the detonation front. 

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