On the energy evolution in gaseous detonation waves

There is a definite inconsistency between the classical ZND theory of detonation and contemporary experimental observations and attempts to model real detonation waves. Nevertheless, the classical onedimensional model of detonation is still extensively used in interpreting measurements because of its simplicity and physical clarity. This naturally raises the questions, what does actually the classical model represent and how one can relate the real multidimensional wave structure to an effective onedimensional detonation? The answer to these questions is extremely important from the practical point of view, because it defines how simple the solution of the criticality problems in detonation could be (i.e. whether one has to solve the very cumbersome three-dimensional nonsteady gasdynamic problem with detailed kinetics of the chemical reaction comprising a few hundreds of elementary steps to predict such parameters as critical initiation energy, critical distances, and concentrations, or the solution of a simplified onedimensional gasdynamic problem with global chemical kinetic equations would suffice?). The present communication discusses the following topics with the aim of answering partly the above questions. (1) An analysis of the detailed kinetic calculations of the heat evolution rate in some fuel-air mixtures and comparison of these results with experiments reveals that (a) in the majority of detonable mixtures heat release can be described by global equations with an accuracy quite sufficient for assessing the critical detonation parameters, (b) chemical kinetics shows no so-called recombination zones with an appreciable heat evolution that follow the main reaction zone, (c) the ratio between the induction and the explosion (within which the major fraction of the stored energy is evolved) times exceeds unity under the conditions corresponding to detonation waves in fuel-air mixtures, which contradicts the shock tube measurements. All these results can be reasonably explained by the fact that the chemical reaction in detonation waves (in shock waves as well) proceeds in a gas with a highly inhomogeneous distribution of the parameters (temperatures, pressures, and particle velocity) which gives rise to the so-called hot-spot mechanism of chemical reactions in gaseous and two-phase media. It is shown that the hot spot ignition is the main reason of instability of detonation waves. Nonsynchronous mixture ignition at different points produces the effect of extended heat evolution zone and reduces the effective induction zone. Results of measurements of averaged and local parameters behind detonation waves in gases support the idea that the effective heat evolution rate in the onedimensional representation of the wave is much more complicated than that inherent in the chemical reaction alone, because it contains also a significant contribution of the kinetic and thermodynamic energy redistribution within the major reaction zone and downstream of it, which makes the onedimensional structure of detonation waves deviate significantly from the classical pattern leading to nonmonotonic heat release behind the shock front (the possibility of appearance of two or more effective sonic planes and heat rlease maxima). However, a onedimensional analysis of marginal detonation waves has demonstrated that critical parameters can be estimated quite accurately within simplified models, which is attributable to the fact that the criticality is associated with local termination of the reaction within narrow stream tubes where the flow pattern resembles closely the ZND non-CJ detonation wave structure. Unlike the chemical reaction zone in detonations far away from the limit, which is shorter than the detonation cell size, the reaction zone in marginal detonations is comparable with the cell size. The results of onedimensional calculations of critical diameters and minimal energies of direct initiation of detonation are compared with experim