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A HYDRODYNAMIC THEORY FOR THE INTERACTION OF A GASEOUS DETONATION WITH A COMPRESSIBLE BOUNDARY.
MICHIGAN UNIV ANN ARBOR COLL OF ENGINEERING
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Detonations through an explosive of finite width are curved and propagate at a lower velocity than an ideal one-dimensional plane wave. A theory relating the velocity decrement and curvature of a gaseous detonation to the conditions at the explosive inert interface is developed. A two-dimensional detonation bounded on one side by a solid wall and on the other by an inert gas is considered. Approximate reaction zone equations are derived by expanding the flow variables in powers of a small parameter proportional to the ratio of reaction zone thickness to radius of curvature. Locally the reaction zone equations are the same as for onedimensional flow with increasing area and heat addition, the rate of increase depending on the local wave curvature and the density variation through a plane detonation. Using Fays result that the relative detonation velocity decrease is proportional to the fractional increase in the reaction zone streamtube area, an ordinary differential equation for variation of the wave angle is developed. Approximate solutions of the above equation yielded velocity decrements which agreed with experimental results. Author
APPROVED FOR PUBLIC RELEASE