Analytical study on detonation pressure and velocity deficit

Abstract

Steady detonation is studied analytically from the viewpoints of conservation laws and entropy change. The mechanisms affecting the pressure at the end of the rarefaction wave and the velocity deficit are examined. Mass, energy, and momentum conservation are applied in the one-dimensional flow based on the Zeldovich–von Neumann–Doering model. The impulse function is found to be larger at the end of the rarefaction wave than in the region from the detonation front to the Chapman–Jouguet (CJ) sonic point. The extra force propels the detonation gas and is consumed by friction under the moving gas. The friction works in the boundary layer, which changes from laminar to turbulent. The detonated gas expands isentropically from the CJ point to the end of the rarefaction wave. The two-position heat release reaction and friction affect the entropy change during the expansion process. The calculated pressure at the end of the rarefaction wave is in reasonable agreement with past experimental results. The velocity deficits reach several percent and are also in reasonable agreement with previous experiments.