Steady-state two-dimensional detonation

Abstract

An analytical steady-state theory of the detonation ‘diameter effect’ is presented. This theory, which includes the off-axis flow, is a generalization of the Wood-Kirkwood analysis. When the state dependence of the reaction rate is stronger than that of the product of the sound speed squared and the flow divergence, detonation failure can occur. The leading term in the extrapolation of the detonation velocity to infinite charge size is quadratic in the inverse charge size and not linear as popularly believed. When calibrated to the detonation velocity vs. charge-size data, the theory reproduces the limited amount of experimental shock loci to a high degree of accuracy.