Shock interactions

Deflagration to Detonation Transition and Shock Interaction is discussed by Cook(1958), pp 183-87... 

Mader then reprogrammed his computations, for an Eulerian code and considered the interactions of 4 cylindrical voids rather than a single void (Ref 16). He showed that shock interactions with four holes lead to much greater faster computed nitromethane decomposition than the shock interaction with a single hole for the same initial conditions... 

Detailed discussion of shock interactions between multiple underwater charges, interactions with the surface or with solid obstructions are beyond the scope of this article. Only a cursory overview of these phenomena will be presented... 

FIGURE 6.9. Schematic diagram of reactive triple-shock interaction. 

Why do we want these particular properties the Lagrangian slope and the vector qualities along the u axis The answer is that these allow us to solve interactions of shocks. In essence, when we deal with shock interactions, we will be using two different P-u Hugoniots along with the three jump relationships. Then we will have five equations in the five variables and be able to solve shock problems specifying only the initial conditions. 

In this chapter we will examine three basic types of shock interactions. These are... 

Example 18.2 Let us assume that we have a slab of 921 -T aluminum (material A) in contact with a slab of copper (material B). A long-pulse shock wave traveling through the aluminum encounters the interface. The initial shock pressure in the aluminum was 25 GPa. What pressure does this change to when the shock interacts at the interface ... 

Figure 19.9 P-u diagram for shock interaction at free surface.

When the left-going shock interacts with the rear face or free surface of the flyer, it forms a right-going rarefaction wave. This rarefaction is along the right-... 

That such an event is not an isolated example and occurs with other azides has been shown in recent work by Chaudhri and Field [28]. They obtained a sequence in which crystals of silver and jS-lead azides were mounted side by side. In both cases initiation occurred at the interface, but also later when the water shock interacts with discontinuities near the ends of the crystals. Since the reaction fronts in the crystals were subsonic it was possible for the shocks in the crystals, as well as stress waves produced by reaction, to travel ahead. The waves were capable of fracturing the crystals (by, for example, a spall-type mecha-... 

Cavitation evolution dynamics in cylindrical liquid volumes under the axial loading by an exploding wire is studied experimentally aind theoretically. The method of dynamic head registration is used to study the structure of two phase flows formed and evaluate characteristic time of cavitation liquid fracture. As a result of numerical simulation of the experiments, which was performed in a single-velocity two-phase model approximation, the energy transformation mechanism is determined at shock interaction with a free real liquid surface. A two-phase model is suggested to describe the irreversible development of a cavitation zone formed as a result of the mentioned interaction. The model is based on practically instantaneous tensile--stress relaxation in a centered rarefaction wave and further inertial evolution of the process. 

Figure 3 compares the results of the numerical simulation with pressure-time histories for a planar shock interaction with a PUR foam of average density p kg/m. Initial shock Mach number Mi=1.7 tto=0.975 Po=l bar and d=100 mm. Pressure gauges were mounted in the back wall under the material and in front of the boundary of the foam. The corresponding pressure time histories are shown by dotted lines 2 and 4. The results of computation are shown by solid lines,... 

Studies of the shock interaction with a spherical or cylindrical body (without a gas layer) were first performed experimentally by Bleakney, White, and Griffith and numerically by Colgan and Fonaijov. (Additional details are... 

The shocks interact with the walls and the explosive confinement and send reflected shocks back into the detonation products, resulting in additional heating and varying amounts of additional chemical reaction. Because the gas-analysis studies give such varied results, not the products along a C-J isentrope but rather the products many steps removed are being measured. The equation of state described in this section is inadequate to account for the additional reaction of the ammonium nitrate and detonation products that apparently occurred in the Hershkowitz experiments. 

Three-dimensional calculations of a detonation wave in HMX interacting with a matrix of particles showed the detonation wave propagating between the particles at the C-J detonation velocity with the actual velocity determined by the shortest path through the particles. This effective velocity was less than the HMX detonation velocity and greater than the one-dimensional layer model velocity discussed earlier. The explosive shock pressures were C-J or even higher from the shock interaction with the tungsten and colliding detonation waves. 

The voids or density discontinuities in a heterogeneous explosive cause irregularities of the mass flow when shocked. The heterogeneous explosive is initiated by local hot spots formed in it by shock interactions with density discontinuities. The hot spot mechanism is important in the propagation and failure of the detonation wave. As shown in Chapter 1, the density discontinuities are also a dominant feature of the heterogeneous explosive reaction zone. 

The experimental observations are that approximately the same amount of decomposition was observed for 0.1 cm of air, Krypton, methane, or vacuum. Our most favorable calculations indicate that heat conduction alone is insufficient to cause appreciable reaction in air or vacuum and that the methane filled gap should give TNT temperatures at least 300°K lower than the Krypton-filled gap. Therefore, it would appear that some phenomenon other than plane surface heat conduction dominates the initiation process of explosives when gaps are present. Some mechanism is required for heat in the gas to be concentrated in local areas of the explosive surface, or some other source of initiation energy is required such as shock interactions or internal void compression. The concentration mechanism appears to be relatively independent of the gas temperature and essentially independent of the gas. 

The shock interactions formed in nitromethane by corners of Plexiglas, Aluminum, and Gold, the resulting formation of a hot spot, and the build up to propagating detonation have been computed. The accuracy of the results was demonstrated by their agreement with the experimental induction times. 

To increase the understanding of the basic processes involved in shock initiation of inhomogeneous explosives, numerical two and three-dimensional hydrodynamics have been used to study the formation of hot spots from shocks interacting with single and multiple voids, air holes, and other density discontinuities. 

The process of heterogeneous shock initiation is described by the Hydrodynamie Hot Spot Modelf which models the hot spot formation from the shock interactions that occur at density discontinuities and describes the decomposition using the Arrhenius rate law and the temperature from the HOM equation of state described in Appendix A. 

The development of the three-dimensional Eulerian code, 3DE, described in Appendix D, allowed the Hydrodynamic Hot Spot Model of heterogeneous shock initiation to be used to investigate the shock interaction with a matrix of holes and the resulting formation of hot spots, their interaction and build up toward a propagating detonation. The Hydrodynamic Hot Spot Model has been used to evaluate the relative effect of explosive shock sensitivity as a function of composition, pressure, temperature, density, and particle size. It has also been used to understand the desensitization of explosives by preshocking. 

Another result of the Hydrodynamic Hot Spot Model is that explosives with faster Arrhenius kinetics form hot spots that decompose faster and are less affected by side rarefactions before appreciable decomposition occurs. Explosives with faster Arrhenius kinetics exhibit increasing shock sensitivity with decreasing particle size for smaller particle sizes than explosives with slower kinetics. The effect of increasing the initial temperature of an explosive in the hydrodynamic hot spot model is to increase the temperature of the hot spots resulting from shock interactions with voids. The hotter hot spots decompose more and result in faster build up to detonation. Thus increasing the initial temperature of an explosive without significantly changing the density or density discontinuities results in a more shock-sensitive explosive. 

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