A ZND model of detonation wave is a steady 1D model that consists of a shock wave, propagating at a constant speed, and a reaction zone behind it which ends up in the equilibrium state. Usual macroscopic governing equations are classical Euler gas dynamics equations adjoined with an equation that tracks the progress of chemical reaction.
The aim of this talk is to give an overview of recent results in the study of ZND-like detonation waves, using the model of mixtures developed within the context of extended thermodynamics--a theory that tends to bridge the gap between macro and meso scale. First, it will be described the structure of extended thermodynamics (ET). It will be compared with the models of thermodynamics of irreversible processes (TIP) with the emphasis on the basic mathematical difference--ET models are hyperbolic, whereas TIP models are usually parabolic. Second, the modeling of mixtures will be described within ET, with an emphasis on the multi-temperature model and its relation to the models of kinetic theory of gases. Some recent results concerning the structure of shock waves in binary mixtures will also be presented.
ET provides a good framework for the study of ZND-like detonation waves, and also brings some new physical and mathematical insight. The focus will be on exothermic reversible chemical reactions and the influence of different temperatures of the constituents on the structure of reaction zone. To that end, a mathematical model is developed capturing these effects. It is shown that solutions essentially depend on three parameters: the overdrive degree, the difference of binding energies and the activation energy. It will be shown that multi-temperature assumption brings qualitatively new result. When it is taken into account, there exists a threshold in the parameters space that divides the region with monotonous solutions from the region with oscillatory solutions. Without the multi-temperature assumption, the solutions of the ZND detonation waves are only monotonous. Also, the detailed dependence of solutions upon the parameters will also be analyzed. |