UNDERSTANDING CURVED DETONATION WAVES

The reaction zone of a detonation wave is very small compared to the hydrodynamic length scale for a typical application. Consequently, it is impractical for numerical calculations to resolve the reaction zone. Yet accounting for the width of the reaction zone is critical because it affects the wave speed of a curved detonation. The curvature effect results from the interaction between the rate of energy release and geometric source terms within the reaction zone. When the reaction zone width is determined by the computational cell size rather than the physical scale, the numerics introduces an artificial curvature effect which frequently dominates the physical effect and leads to mesh dependence of simulations. Modified Hugoniot jump conditions are derived which characterize the curvature effect. They express the conservation laws and are not sensitive to the detailed reaction dynamics but instead depend only on the reaction zone width, and averages of pressure and of mass, momentum and energy densities.