The flow following the impact of a plane detonation front, in a condensed organic explosive, on a rigid piston is obtained by a finite difference procedure. The equation of state E = Pv/(γ−1) is used for the gaseous explosion products with γ equal to 2.5, 3.0, and 3.5. Explicit formulas for the piston motion are obtained analytically for γ = 3. The effects of the detonation parameters and the explosive-mass to piston-mass ratio on the terminal velocity of the piston and on the energy transmitted to the piston are described. For γ = 2.5 to 3.5, the terminal velocity of the piston depends almost entirely on the chemical energy released in the explosion and on the explosive-mass to piston-mass ratio; i. e., for a fixed chemical energy, the total energy transmitted to the piston is insensitive to the form of the detonation wave.
The purpose of this note is to establish Theorem A below for the two-point homogeneous vector boundary problemwhere the Pi(x) are given real m × m symmetric matrix functions of x with P0(x) positive definite and Pi(x) of class C2−i on an infinite interval [a, ∞), and where by a solution of (1.1) — (1.2) for a ≤ x1 < x2 < ∞ we understand a real m-dimensional column vector u = u(x) of class C2 on [a, ∞) which is such that Pi(x)u(2−i) is of class C2−i on [a, ∞) and which satisfies (1.1) — (1.2) with the former a vector identity on [a, ∞).
Impacts of oblique detonations in pentolite on iron are treated by the methods of plane, steady, compressible flow. Regular reflection, three-shock Mach reflection, and expansion are discussed. The maximum transmitted pressure, 452 kbar, is shown to occur at an impact angle of 63.4°, at the onset of Mach reflection. The steady double plastic wave structure in iron, which appears at impact angles between 71.3° and 90°, is calculated. Results for two colliding detonation waves are obtained as a special case.
The artificial viscosity method is used to calculate the flow following the detonation of a centrally initiated pentolite sphere in fresh water at sea level, up to the time the main shock in the water is 100 charge radii from the center. Pressure, particle velocity, and temperature versus distance at various times are obtained; also peak pressures, time constants, and pressure versus time at fixed positions. Partial steam formation in the water close to the gas bubble is shown to be possible but unimportant at the distances covered. The partition and distribution of kinetic and internal energies in the water and the gas sphere, and the energy dissipated by shock heating, are found. The calculated dissipated energy is 33% of the total energy released in the detonation when the shock front is 10 charge radii from the center, and 40.5% when the shock front is 100 charge radii from the center.
Flows following the underwater detonation of pentolite cylinders at the center of one end are calculated to times when the distances of the main shock from the center are about 15 times the radius of a sphere of the same mass. Length to diameter (L/D) ratios of 1, 2, 4, and 7 are treated. An axisymmetric Lagrangian artificial viscosity scheme is used with lateral rezoning to tracks that radiate outward from the gas–water boundary. The usable energy in the water, the internal plus the kinetic energies minus the energy dissipated by shock heating, is obtained both as a function of the angle with the charge axis and the distance from the center. The usable energy is found to be generally decreasing with increasing L/D, greatest off the detonator end of the charge, and lowest off the nondetonator end, where there is the most energy dissipation. Off the side of the charge, the peak shock pressure increases with increasing L/D and 45% to 55% of the usable energy is concentrated near the shock front. Along the charge axis the pressure waves in the water become flatter, with more of the usable energy near the gas–water boundary, as the L/D ratio increases.
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