The shock dynamics of multidimensional condensed and gas-phase detonations

Detonations are comprised of broad detonation shocks supported by thin reaction zones. Approximations based on weak shock curvature, measured on the inverse reaction zone scale, and quasi-steady flow, measured on the particle passage time through the reaction zone, can be used to simplify the mathematical description of detonations that are governed the gasdynamic equations for a reacting flow. When the detonation reaction zone contains a sonic locus, it is possible to derive intrinsic (coordinate independent) partial differential equations for the lead detonation shock's motion in terms of the normal detonation shock velocity, the shock curvature, and higher normal time derivatives. We refer to this collection of theory and supporting experimental results as detonation shock dynamics (DSD) after Whitham's geometrical shock dynamics (GSD). The reduced detonation dynamics is based on the concept of an eigenvalue (sonic) detonation, an idea that goes back to the original investigations in the 1940s. We present a review of the theoretical and experimental developments and attempt to update Fickett and Davis' discussion of work prior to 1980. We give examples of the theory and applications that include (1) weakly curved, quasi-steady, near-CJ detonation, (2) critical detonation curvature, (3) quasi-steady extinction and ignition (and low-velocity detonation), (4) shock acceleration effects, and (5) cellular and pulsating detonation in gases. We also review the engineering method of DSD as it is applied to explosive systems.