NUMERICAL STUDY OF DETONATION PROPAGATION IN VISCOUS TURBULENT FLOW IN A DUCT

Gasdynamics of detonation waves was widely studied within last hundred years - analytically, experimentally, and numerically. The majority of classical studies of the XX century were concentrated on inviscid aspects of detonation structure and propagation. There was a widespread opinion that detonation is such a fast phenomenon that viscous e¨ects should have insigni¦cant in§uence on its propagation. When the era of calculations based on the Reynolds-averaged Navier- Stokes (RANS) and large eddy simulation approaches came into effect, researchers pounced on practical problems with complex geometry and with the interaction of many physical effects. There is only a limited number of works studying the in§uence of viscosity on detonation propagation in supersonic §ows in ducts (i. e., in the presence of boundary layers).

A Zel’dovich–von Neumann–Döring-like detonation wave in a multi-temperature mixture

The detonation wave structure is analysed in a binary mixture undergoing a reversible chemical reaction represented by $A_{r}\rightleftharpoons A_{p}$. It is assumed that the flow satisfies the proper basic assumptions of the Zel’dovich–von Neumann–Döring (ZND) detonation model, namely the flow is one-dimensional and the shock is represented by a jump discontinuity, but the assumption of local thermodynamic equilibrium is disregarded. This allows us to deeply investigate the coupling between the detonation structure of overdriven detonations and its chemical kinetics. The thermodynamic non-equilibrium effects are taken into account in the mathematical description, using the model of a multi-temperature mixture developed within extended thermodynamics, which has been proved to be consistent with a kinetic theory approach. The reaction rate is then enriched with terms that take into account the temperatures of the constituents. The results show that the temperature difference between components within the detonation wave structure, which describes thermodynamic non-equilibrium, is driven by the chemical reaction. Numerical computations confirm the existence of non-monotonic profiles in the reaction zone of overdriven detonations which are sensitive to changes in the activation energy and reaction heat.