Solving Curved Detonation Riemann Problems

It is desirable to compute accurate solutions to detonation problems without numerically solving differential equations in the thin reaction zone. For planar detonation waves, algebraic jump conditions can be used to compute the one parameter family of behind states comprising the burned Hugoniot and wave curves. For curved detonations, the state at the end of the reaction zone depends on both the detonation velocity and the curvature of the wave. Recently, curved detonation jump conditions have been derived which contain “source terms” involving front curvature, reaction zone length and integrals of physical quantities in the reaction zone. In this paper, we parameterize the source terms by the detonation velocity and curvature and show how the curved detonation jump conditions can be solved to compute the curved detonation Hugoniot. We demonstrate the method using the Forest Fire rate law with HOM equation of state for the explosive PBX-9404.