Self-similar detonation waves

Abstract

New results on similarity solutions to one-dimensional reactive flow problems with strong shocks are presented. Using dimensional methods, two modelling numbers for the flow are identified and the possible equations of state, including Mie-Gruneisen forms which admit similarity solutions are characterised. In a special case the entire problem is reduced to a nonlinear eigenvalue problem in sound speed-particle velocity phase plane. In this plane the critical points are analysed and the relationship between singular points in the self-similar solution and the characteristics of the Zel'dovich-von Neumann-Doering equations is found.