Two-Dimensional Reaction Zones of Homogeneous Explosives

The resolved reaction zones of nitromethane, liquid TNT, and ideal gases have also been studied using the two-dimensional Lagrangian code 2DL, described in Appendix B and the two-dimensional Eulerian code 2DE described in Appendix C. 

To study the stability of detonations, one uses a piston that is as close to the steady-state piston as possible so that the one-dimensional perturbations introduced by deviations from the steady-state will be of tractable size. The magnitude of the one-dimensional perturbations depends upon the details of the piston profile, the numerical method and the mesh size. For a given mesh size, one-dimensional perturbations increase with the method in the order 2DL, SIN, 2DE. While attempts were made, by adjusting the mesh size, to obtain one-dimensional perturbations of approximately the same size in all three methods, this is unimportant to the question of whether the perturbations introduced grew or decayed. To calculate the steady-state reaction zone piston in the 2DE method, it was necessary to use for the piston s W a lower mass fraction of undecomposed explosive than the W of the cell above the piston. This was accomplished by multiplying by a constant called piston factor . 

Since the magnitude of the one-dimensional perturbation introduced into the calculation varies, the shock-front pressure vs. time is not identical for the various methods. The stability results are related not to the magnitude but only to the growth or decay of the perturbations. These results show that growth or decay of the perturbation is independent of the numerical method and, incidentially, independent of the nature of the perturbation. 

One can obtain identical stability results for two-dimensionally unperturbed flow using any of the four methods of numerically solving the reactive hydrodynamics. While this is not sufficient to guarantee that the stability results are independent of the numerical method, it is a necessary result. Encouraged by these results, we proceed to study two-dimensionally perturbed detonations. 

To study the two-dimensionally perturbed flow, a perturbation was introduced by increasing the initial density of a center cell near the piston interface. The density was increased by 1.1 and 1.3 po, without changing the stability results. Perturbations of all wavelengths are introduced by this procedure. In 2DL the viscosity constant was changed over half an order of magnitude without changing the stability results. 

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