Hot spots models

Dymond, J. 1975. K-Ar ages of Tahiti and Moorea, Society Islands, and implications for the hot-spot model. Geology 3 236-240. 

Mader (Ref 7) called this hot spot model the hydrodynamic hot spot and the development of this model is largely due to his work. In Ref 7 Mader considered the shock initiation of nitromethane containing inhomogeneities such as voids or grit particles. To quote Mader ... 

Use of high energy radiation to create hot spots. Attempts have been made to initiate explosives by ionizing radiation such a-particles, high speed electrons, y-rays, Pions etc (Refs 8 9). No initiations were observed. Cerny Kaufman (Ref 9) take this absence of initiation to indicate failure of the hot spot model. However a crude preliminary calculation, based on the Friedman model (Ref 15), suggests that the dimensions of the Pion heated regions for Lead Azide (Fig 2 of Ref 9) and for RDX (Fig 3 of Ref 9) are smaller than the critical hot spot dimension at the corresponding temperatures... 

A detailed analysis of the hot spot model was attempted by Cemy and Kaufman (Ref 128) who irradiated several expls with if mesons (pions). High, local energy densities in roughly spherical shape can be formed from slow pion bombardment of solids... 

Subsequently an extreme test of the hot spot model as applied to microscale thermal effects of ionizing radiation was proposed by Mallay, Prask and Cemy (Ref 129). RDX, HMX, PETN and NG were irradiated with fission fragments from the spontaneous fission of californium-252 at elevated temps (160°, 215°, 125° and 180°, respectively). The californium-252 was mixed thruout the expl pellet or liq (for NG). No explns were obtained nor any signs of accelerated thermal decompn were evident at the elevated temps or when heated to ignition although the irradiated expls were exposed to 200—2000 fission fragments... 

Early explanations about the effect of mechanical energy on the reactivity of solids are the hot-spot-model [23] and the magma-plasma-model [8]. The generation of hot-spof may be used to explain the initiation of a self-sustained reaction such as explosion, deflagration, or decomposition. Temperatures of over 1000 K on surfaces of about 1 pm2 for KM to 10-3 s can be created. These temperatures can also be found near the tip of a propagating crack [24]. Typically nonequilibrium thermodynamics are used to describe these phenomena. The magma-plasma-model allows for local nonequilibrium states on the solid surface during impact however, due to the very short time scale of 1(H s of these states only statistical thermodynamics can describe the behavior. 

An analysis of the hot-spot model was attempted by Cemy and Kaufman [50], who irradiated several explosives with tt" mesons (pions). The decay of mesonic atoms formed by the capture of n mesons can result in the emission of 12-17 charged particles from a single lattice site. It was estimated that a temperature of IO" °C would be produced over a 10-A radius for 10 " sec. The calculations indicated that the temperature would decrease rapidly, but that the radius of a hot-spot site would increase to meet the criterion of Bowden. 

The hot-spot model of cavitation with the high pressures reached (1200-1500 bars) in or next to the cavitation bubble should favor reactions with strong steric demand and reactions initiated by electron transfer. An important difference between these two effects is that the first one (steric) is stoichiometric in character whereas the second (ETC) is catalytic. ETC, corresponding to a typical T) e la sonochemical... 

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. 

The interaction of a shock wave with a single air hole and a matrix of air holes in PETN, HMX, TATB, and Nitroguanidine was modeled in references 23 and 24. The basic differences between shock-sensitive explosives (PETN or HMX) and shock insensitive explosives (TATB or Nitroguanidine) were described by the Hydrodynamic Hot Spot Model. 

The Hydrodynamic Hot Spot Model has been used to describe the experimentally observed sensitivity to shock sensitivity of the heterogeneous explosives PETN, HMX, TATB, and Nitroguanidine, with PETN being the most sensitive and Nitroguanidine the least sensitive. 

A more detailed evaluation can be obtained from calculations using the Hydrodynamic Hot Spot Model. 

From the Hydrodynamic Hot Spot Model, one can postulate that the coarse particle explosives have fewer holes or voids per unit volume than the fine-particle explosives, resulting in fewer but larger hot spots. As the explosive particles become finer, the number of hot spots formed by a shock wave increases while the hot spot size decreases. 

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. 

The Hydrodynamic Hot Spot Model describes the basic differences between the shock-sensitive and shock insensitive explosives. The interaction of a shock wave with air holes in HMX, TATB and TNT, the resulting hot spot formation, interaction and the build up toward detonation or failure have been modeled. An increase in hole size results in larger hot spots that decompose more of the explosive, add their energy to the shock wave, and result in increased sensitivity to shock. An increase in number of holes also results in more hot spots that decompose more explosive and increase the sensitivity of the explosive to shock. The interaction between hole size and number of holes is complicated and requires numerical modeling for adequate evaluation of specific cases. The hole size can become sufficiently small that the hot spot is cooled by side rarefaction before appreciable decomposition can occur. 

The Hydrodynamic Hot Spot Model can be used to evaluate the relative effect of explosive shock sensitivity as a function of composition, pressure, temperature, and density (as represented by the number and sizes of the holes present for hot spot generation). 

The Hydrodynamic Hot Spot Model has resulted in an increased understanding of the effect of explosive composition, hole size, number of holes, explosive Arrhenius decomposition rate, initial temperature and shock pressure on shock initiation of heterogeneous explosives. The Hydrodynamic Hot Spot Model reproduces the observed shock initiation behavior. This indicates that the dominant features are shock heating by hydrodynamic hot spot formation, cooling by rarefactions and the Arrhenius decomposition rate as a function of temperature. 

The detailed understanding of the shock initiation process in heterogeneous explosives that has been obtained from the Hydrodynamic Hot Spot Model has been used to develop a technique for performing engineering modeling of many practical explosive vulnerability problems. The technique is called Forest Fire and will be described in Chapter 4 and Chapter 6. 

Charles L. Mader and James D. Kershner, The Three-Dimensional Hydrodynamic Hot Spot Model , Eighth Symposium (International) on Detonation, NSWC-MP 86-194, 42-51 (1985). 

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