The motion of shock waves and products of detonation confined between a wall and a rigid piston

In a previous paper, Aziz et al. [1] considered the motion of a rigid piston under the impact of a detonation wave. In their one-dimensional model the back-end of the "pipe" was open, allowing the products of detonation to escape. The present research considers the case when the detonation products cannot escape because the pipe is closed in the rear. The numerical results verify the conjecture that there is a critical value of the mass ratio, r, (ratio of the mass of the undetonated explosive to the piston mass) above which the trajectory of the piston is the same regardless of whether the pipe end is closed or open. A detailed examination of the piston motion indicates an apparent anomaly-the piston speed is increased above the "open-pipe" value before the shock wave rebounding off the closed end reaches the piston again. In order to explain this phenomenon a detailed analytical solution of the piston motion and flow field is carried out, for the case of polytropic detonation products γ = 3.