Steady detonation waves with losses

The Euler equations for a reacting polytropic gas with model losses, applied to unsupported steady detonation waves, lead to fast and slow detonation speeds for a given loss. The reaction rate is taken to have the Arrhenius form. The differential equations for the Mach number squared m and the reaction progress variable λ are integrated numerically using a fourth-order Runge-Kutta-Fehlberg method. The calculations are presented as plots of trajectories in the λ-log (m) plane. The main parameters that are varied are the activation temperature, the heat of reaction, the order of the reaction, and the polytropic exponent γ. The onset of detonation failure, and a continuum of solutions that appears in some parameter ranges, are explored in detail. The results are summarized in plots of the detonation Mach number squared m₀ versus the logarithm of the loss parameter.