ChapmanJouguet

The Chapman–Jouguet condition is a fundamental concept in detonation theory. It describes a self-sustaining detonation wave in which the flow immediately behind the detonation front is sonic with respect to the front. In this Chapman–Jouguet detonation, the chemical reaction heat release and the shock jump conditions combine so that information cannot travel upstream from the reaction zone, making the detonation speed determined by the properties of the unreacted gas and the reaction itself rather than by boundary conditions.

The condition is named after Sydney Chapman, a British mathematician, and Gustaf Jouguet, a Swedish-French physicist, who developed its idea in the early 20th century. The Chapman–Jouguet framework is a cornerstone of the Zeldovich–von Neumann–Döring (ZND) model of detonations and underpins much of the theoretical and applied understanding of gaseous explosions.

The CJ condition arises from applying the Rankine–Hugoniot jump relations to a reacting flow and enforcing a sonic point within the reaction zone. Concretely, it identifies a unique detonation velocity, D_CJ, at which the flow immediately behind the detonation front is sonic relative to the front. This makes D_CJ an eigenvalue of the problem: it cannot be obtained by simply specifying boundary conditions at the far field but must satisfy the internal balance of shock compression, energy release, and chemical kinetics. In practice, the CJ velocity depends on the initial state of the gas, the heat release of the reaction, and the effective equation of state; real systems may deviate due to multi-step chemistry, non-ideal effects, or boundary influences.

Applications of the CJ concept include estimating detonation velocities in gas mixtures, informing safety and performance analyses, and guiding numerical simulations of reactive flows. Limitations arise from its idealizations, as real detonations can be overdriven or underdriven and may involve complex kinetics.