Numerical calculations based on the finite element method (FEM) were performed dealing with the thermal initiation of a confined explosive charge (here: TNT confined in a steel casing). These calculations show self-intensifying heating inside the explosive as soon as the temperature reaches a critical value. The point of initiation is located slightly inside the explosive charge. At the interface explosive to metallic wall, heat conduction into the wall prevents a fast heating whereas deeper inside the explosive, less internal energy is released due to the lower local temperature. As expected, the initiation times are getting shorter with increasing laser power. In addition, the parametric studies show that the critical temperature and the distance between the initiation point and the wall are decreasing with rising laser power density. As the FEM-calculations are very time consuming, simplified analytical considerations were applied to approximate the temperature and time necessary to achieve a thermal initiation. Starting from analytical solutions of the heat equation, that describe the thermal evolution inside the metallic shell for Gaussian shaped laser beams in the multiple kw-range, an iterative algorithm has been developed to determine the critical temperature and the initiation time. An extended analytical derivation also made it possible to determine the temperature evolution for a rotating tube.
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