Detonation - Theories

Theories

The simplest theory to predict the behavior of detonations in gases is known as Chapman-Jouguet (CJ) theory, developed around the turn of the 20th century. This theory, described by a relatively simple set of algebraic equations, models the detonation as a propagating shock wave accompanied by exothermic heat release. Such a theory confines the chemistry and diffusive transport processes to an infinitely thin zone.

A more complex theory was advanced during World War II independently by Zel'dovich, von Neumann, and W. Doering. This theory, now known as ZND theory, admits finite-rate chemical reactions and thus describes a detonation as an infinitely thin shock wave followed by a zone of exothermic chemical reaction. With a reference frame of a stationary shock, the following flow is subsonic, so that an acoustic reaction zone follows immediately behind the lead front, the Chapman-Jouguet condition. There is also some evidence that the reaction zone is semi-metallic in some explosives.

Both theories describe one-dimensional and steady wave fronts. However, in the 1960s, experiments revealed that gas-phase detonations were most often characterized by unsteady, three-dimensional structures, which can only in an averaged sense be predicted by one-dimensional steady theories. Indeed, such waves are quenched as their structure is destroyed. The Wood-Kirkwood detonation theory can correct for some of these limitations.

Experimental studies have revealed some of the conditions needed for the propagation of such fronts. In confinement, the range of composition of mixes of fuel and oxidant and self-decomposing substances with inerts are slightly below the flammability limits and for spherically expanding fronts well below them. The influence of increasing the concentration of diluent on expanding individual detonation cells has been elegantly demonstrated. Similarly their size grows as the initial pressure falls. Since cell widths must be matched with minimum dimension of containment, any wave overdriven by the initiator will be quenched.

Mathematical modeling has steadily advanced to predicting the complex flow fields behind shocks inducing reactions. To date none has adequately described how structure is formed and sustained behind unconfined waves.