On the hydrodynamic thickness of cellular detonations

The characterization of the detonation dynamic parameters (detonability limits, direct initiation energy, critical tube diameter, etc.) requires a characteristic length scale for the detonation wave in the direction of propagation. However, most detonations are unstable, their reaction zones are turbulent, and their structure departs significantly from the idealized one-dimensional Zel'dovich–Von Neumann–Doring model. It is argued that the most suitable length scale to characterize a turbulent detonation wave is the location of the sonic surface, which separates the statistically stationary flow of the reaction zone structure from the unsteady expansions behind the wave. Previous real and numerical experiments are reviewed in order to determine the relation between the global location of the mean sonic surface and the chemical, mechanical, and thermodynamic relaxation processes occurring in the detonation wave structure. Based on the experimental evidence, we postulate that the structure of turbulent detonations can be modeled in the one-dimensional Zel'dovich–Neumann–Doring framework, with the turbulence effects as source terms in the momentum and energy equations. These source terms involve the relaxation rates for the mechanical fluctuations, thermal fluctuations and the chemical exothermicity towards equilibrium. In the framework of the idealized one-dimensional structure with source terms, the sonic surface location is governed by the balance between the competing source terms satisfying the generalized Chapman–Jouguet criterion. We recommend that future work in detonation research should be focused at: 1) acquiring a large experimental database for the mean detonation properties (detonation velocity, location of sonic surface and mean reaction zone profiles); 2) the development of the appropriate source terms involving the turbulent fluctuations in the averaged equations of motion.