Complex phenomena occur in a combustion chamber during a ballistic cycle. From the ignition of the black powder in the primer to the exit of the projectile through the muzzle, two-phase gas-powder mix undertakes various transfers in different forms. A detailed comprehension of these effects is fundamental to predict the behavior of the whole system, considering performances and safety. Although the ignition of the powder bed is three-dimensional due to the primer’s geometry, simulations generally only deal with one- or two-dimensional problem. In this study, we propose a method to simulate the two-phase flows in 1, 2 or 3 dimensions with the same system of partial differential equations. A one-pressure, conditionally hyperbolic model  was used and solved by a nonconservative finite volume scheme associated to a fractional step method, where each step is hyperbolic. We extend our study to a two-pressure, unconditionally hyperbolic model  in which a relaxation technique was applied in order to recover the one-pressure model by using the granular stress. The second goal of this study is also to propose an improved ignition model of the powder grains, by taking into account simplified chemical kinetics for decomposition reactions in the two phases. Here we consider a 0th-order solid decomposition and an unimolecular, 2nd-order gas reaction. Validation of the algorithm on several test cases is presented.
Multi-Dimensional Two-Phase Flow Modeling Applied to Interior Ballistics
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Nussbaum, J., Helluy, P., Herard, J., and Baschung, B. (August 5, 2011). "Multi-Dimensional Two-Phase Flow Modeling Applied to Interior Ballistics." ASME. J. Appl. Mech. September 2011; 78(5): 051016. https://doi.org/10.1115/1.4004293
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