The study analyses the cellular reaction zone structure of unstable methane–oxygen detonations, which are characterized by large hydrodynamic fluctuations and unreacted pockets with a fine structure. Complementary series of experiments and numerical simulations are presented, which illustrate the important role of hydrodynamic instabilities and diffusive phenomena in dictating the global reaction rate in detonations. The quantitative comparison between experiment and numerics also permits identification of the current limitations of numerical simulations in capturing these effects. Simulations are also performed for parameters corresponding to weakly unstable cellular detonations, which are used for comparison and validation. The numerical and experimental results are used to guide the formulation of a stochastic steady one-dimensional representation for such detonation waves. The numerically obtained flow fields were Favre-averaged in time and space. The resulting one-dimensional profiles for the mean values and fluctuations reveal the two important length scales, the first being associated with the chemical exothermicity and the second (the ‘hydrodynamic thickness’) with the slower dissipation of the hydrodynamic fluctuations, which govern the location of the average sonic surface. This second length scale is found to be much longer than that predicted by one-dimensional reaction zone calculations.

In this paper the structure of strong transverse waves in two-dimensional numerical simulations of cellular detonations is investigated. Resolution studies are performed and it is shown that much higher resolutions than those generally used are required to ensure that the flow and burning structures are well resolved. Resolutions of less than about 20 numerical points in the characteristic reaction length of the underlying steady detonation give very poor predictions of the shock configurations and burning, with the solution quickly worsening as the resolution drops. It is very difficult and dangerous to attempt to identify the physical structure, evolution and effect on the burning of the transverse waves using such under-resolved calculations. The process of transverse wave and triple point collision and reflection is then examined in a very high-resolution simulation. During the reflection, the slip line and interior triple point associated with the double Mach configuration of strong transverse waves become detached from the front and recede from it, producing a pocket of unburnt gas. The interaction of a forward facing jet of exploding gas with the emerging Mach stem produces a new double Mach configuration. The formation of this new Mach configuration is very similar to that of double Mach reflection of an inert shock wave reflecting from a wedge.

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In this paper we describe a new normal-modes approach to the linear stability problem of an idealized detonation having an Arrhenius form of the reaction rate, with emphasis on Chapman-Jouguet detonations. We determine analytical asymptotic solutions of the ordinary differential equations for the linearized perturbations, which are used as initial conditions for the integration of these equations. A shooting method is employed to solve the eigenvalue problem. We compare with, and extend, the previous results of Lee & Stewart in the case of one-dimensional perturbations, and show that the growth rates of the unstable spectrum are dominated by a real eigenvalue for large activation temperatures. We also present the dependence of the unstable spectrum on the heat of reaction. Dispersion relations are given for multidimensional perturbations.

The structure of steady, one‐dimensional detonation waves in C–O is investigated for initial densities in the range 2×107 to 1×109 g cm−3. At these and greater densities, the self‐supporting detonation wave is of the pathological type. For such waves the detonation speed is an eigenvalue of the steady equations, and the reaction zone contains an internal frozen sonic point where the thermicity vanishes. The self‐supporting flow downstream of this singular point is supersonic, and is very different from that in supported (overdriven) detonations. A method for determining the structure of pathological detonation waves is described. These waves are examined, and the self‐sustaining wave is compared with and contrasted to the supported detonations considered previously by Khokhlov. We show that the thickness of the self‐sustaining detonation is a few times the thickness of supported detonations, and that the self‐sustaining detonation produces more of the iron‐peak and less of the intermediate mass elements than do supported detonations. Implications for the cellular detonation instability are also discussed.