Pulsating one-dimensional detonations in hydrogen–air mixtures

Abstract

The propagation of one-dimensional detonations in hydrogen–air mixtures is investigated numerically by solving the one-dimensional Euler equations with detailed finite-rate chemistry. The numerical method is based on a second-order spatially accurate total-variation-diminishing scheme and a point implicit time marching algorithm. The hydrogen–air combustion is modelled with a 9-species, 19-step reaction mechanism. A multi-level, dynamically adaptive grid is utilized, in order to resolve the structure of the detonation. Parametric studies for an equivalence ratio range of 0.4–2.0, initial pressure range of 0.2–0.8 bar and different degrees of detonation overdrive demonstrate that the detonation is unstable for low degrees of overdrive, but the dynamics of wave propagation varies with fuel–air equivalence ratio and pressure. For equivalence ratios less than approximately 1.2 and for all pressures, the detonation exhibits a short-period oscillatory mode, characterized by high-frequency, low-amplitude waves. Richer mixtures exhibit a period-doubled bifurcation that depends on the initial pressure. Parametric studies over a degree of overdrive range of 1.0–1.2 for stoichiometric mixtures at 0.42 bar initial pressure indicate that stable detonation wave propagation is obtained at the high end of this range. For degrees of overdrive close to one, the detonation wave exhibits a low-frequency mode characterized by large fluctuations in the detonation wave speed. The McVey–Toong short-period wave-interaction theory is in qualitative agreement with the numerical simulations; however, the frequencies obtained from their theory are much higher, especially for near-stoichiometric mixtures at high pressure. Modification of this theory to account for the finite heat-release time significantly improves agreement with the numerically computed frequency over the entire equivalence ratio and pressure ranges.