One of the most difficult problems in modeling explosive reactive flows is describing the interactions of the exothermic chemical energy release and the development of compression and shock wave fronts. Such flows include: impact ignition; deflagration, deflagration-to-detonation transition (DDT); fracture- plus-recompaction detonation transition (labeled XDT for "Sunknown" T before the mechanism was identified); shock-to-detonation transition (SDT); and detonation. In the simplest case of self-sustaining, steady state detonation in a polytropic gas, the chemical energy must supply 3/8 of the energy required to sustain the leading shock wave front in the one-dimensional Zeldovich- von Neumann– Doring (ZND) model. The non-equilibrium ZND model of detonation was developed to examine the internal molecular excitation processes that precede, control the rates of, and follow chemical reactions induced by shock compression in the complex three-dimensional fronts of detonation waves. Multiphonon uppumping and internal vibrational energy redistribution (IVR) processes create transition states through which the initial endothermic bond breaking reactions occur. Then the exothermic chain reactions rapidly produce highly vibrationally excited products, which distribute vibrational energy among the reaction products via "supercollisions." The physical mechanism by which the chemical energy released well behind the individual shock fronts supports these wave fronts has been postulated to be the amplification of pressure wavelets by the relaxation of vibrationally excited products to lower levels as chemical and mechanical equilibrium is established. Several instability analyses have shown that the leading shock front of a detonation wave is unstable with respect to perturbations that propagate through the subsonic reaction zone and overtake the front. More recent analyses have shown that only certain frequencies can amplify the shock front. However, the instability frequencies have not yet been related to the vibrational relaxation frequencies in the product molecules. Thus inclusion of non-equilibrium chemistry in instability analyses is necessary.
The physical mechanism of wavelet amplification by vibration relaxation is quite general. Little theoretical research has been done on reactive flows other than detonation. The SDT process in solid explosives must also depend upon this wave amplification mechanism, because experiments have shown the initial shock front increases only slightly in strength as it propagates through the unreacted explosive mechanically creating local "hot spots" that react close behind this front. The main chemical energy release occurs well behind the shock front as the reaction grows from the "hot spot" ignition regions. The transition to detonation occurs when a high pressure wave produced by the main chemical energy release overtakes the leading shock front producing a detonation wave. Similar processes are likely to occur on larger spatial and longer time scales during the formation of compression and shock waves in reactive flows started by very low levels of input energy, such as deflagration, DDT, and XDT. Experiments have demonstrated amplification of deflagration and weak shock waves by exothermic chemical energy release. The opposite effect, shock wave damping by a non-equilibrium gas that lacks vibrational energy, is a well- known phenomena. The coupling between exothermic chemical release and wave formation can be very efficient, as in the case of primary (very sensitive) solid explosives, such as azides and fulminates, which can transition from a subsonic deflagration wave to a supersonic detonation wave without an observable buildup process. Detailed mathematical modeling of these complex reactive flow processes with non-equilibrium chemistry has not yet been attempted.