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Research Papers

Multi-Dimensional Two-Phase Flow Modeling Applied to Interior Ballistics

[+] Author and Article Information
Julien Nussbaum

 ISL - French-German Research Institute of Saint-Louis, 5 rue du Général Cassagnou, BP 70034, 68301 Saint-Louis Cedex, Francejulien.nussbaum@isl.eu

Philippe Helluy

 IRMA, Université de Strasbourg, 7 rue Descartes, 67084 Strasbourg Cedex, Francehelluy@math.unistra.fr

Jean-Marc Herard

EDF, Research Branch, MFEE, 6 quai Watier, 78400 Chatou, Francejean-marc.herard@edf.fr

Barbara Baschung

 ISL - French-German Research Institute of Saint-Louis, 5 rue du Général Cassagnou, BP 70034, 68301 Saint-Louis Cedex, Francebarbara.baschung@isl.eu

J. Appl. Mech 78(5), 051016 (Aug 05, 2011) (9 pages) doi:10.1115/1.4004293 History: Received November 25, 2010; Revised May 23, 2011; Published August 05, 2011; Online August 05, 2011

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 [1] 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 [2] 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.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 2

1-D configuration at interface between solid and gas during heating

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Figure 3

1-D configuration at interface between solid and gas during combustion

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Figure 4

Evolution of surface temperature and combustion rate with a constant heat flux

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Figure 5

Evolution of surface temperature, combustion rate and total external heat flux when the ignition flux is suddenly switched off

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Figure 6

Steady combustion rate in function of pressure: compatibility with classical burning law

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Figure 7

Configuration in the combustion chamber at initial time

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Figure 1

Sketch of an initial configuration at firing

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