Shock waves propagation model

Detailed nucleosynthesis predictions are in general available for ID explosion models only, under the assumption that a shock wave propagates outward through most of the supernova structure, compresses the various traversed... 

Compared to uniform compression, uniaxial strain along one of the lattice vectors is more likely to lead to detonation. Dick has proposed [43] that detonation initiation in nitromethane is favored by shock-wave propagation in specific directions related to the orientation-dependent sterie hindrance to the shear flow. This proposal is based on a model according to which the sterically hindered shear process causes preferential excitation of optical phonons strongly coupled with vibrons. 

This fitting approach for 7 and e<> guarantees that both the detonation wave propagation model and the one-dimensional gasdynamics of the reflected shock wave are properly reproduced by the numerical simulations except extremely near the wave focus. Variations in specific heats, species concentrations, and molecular weight with thermodynamic state are all accounted for with this method. 

The DDT mechanism for this case Is similar but not identical to that of Case B. A convective flame front propagates ahead of the compressive waves which are necessary to form a precursor shock front. In modeling DDT the convective front (and its consequences) must be included because of its influence on dp/dt in the ignition region... 

Another particularly important topic in the modeling of strongly nonlinear phenomena is the occurrence of multiple fronts. For instance, in a supersonic reactive flow problem the position and speed of propagation of the shock wave and reaction front are different. 

Following is a resume of paper by Fickett (Ref 2) If a cylinder of explosive is suddenly heated or struck at one end, a detonation wave propagates down the length of the charge with approximately constant velocity. This phenomenon is often treated by the model of von Neumann-Zel dovich. Transport properties are neglected, and the wave consists of a plane shock followed by a short reaction zone of constant length in which the explosive material is rapidly transformed into decomposition or detonation products. 

In a stationary detonation wave, the shock front is followed by a zone of chemical reaction which can be considered as an ordinary stationary-state combustion wave propagating through the denser and hotter gases behind the shock front (Fig. XIV.7). Such a combustion wave is characterized by a pressure decrease and a temperature increase across the flame front. Because of this and because, in the stationary state, the flame front must follow the shock front at a fixed distance, the model of the moving surface is not quite adequate to describe a stationary detonation/ A further difference between the two is that, whereas in the mechanical shock the surface velocity Vb was an independent parameter at the disposal of the experimenter, in the detonation the chemical composition of the reacting gases is the collective parameter which replaces vt and is the means by which the experimenter can control the detonation velocity. 

The constraint of a collision in a given sequence in our simple chain model means that there is a shock front propagating through the system, a front which reverses its direction every time an end atom collides with the hard walls. When a perfectly ordered crystal hits a hard wall, one can understand how a dispersion-free propagation of a shock wave is possible. The new feature is that such a shock front was seen in full MD simulations of impact heated clusters, using realistic forces, and has been recently studied in more detail. ... 

Aeeording to the hydrodynamic theory of reaction waves propagating in one dimension (see references to the Introduction. Volume I) the detonation velocity is expected to be less than ideal in samples of diameter d such that the observed velocity D will approach the ideal velocity, > as J oo. Eyring et al. [25] developed a model based on a curved shock front bounded by a burned... 

We model the propagation of the shock wave using the ID Euler equations for compressible flow, which neglect thermal transport. 

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