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In this paper, an Eulerian–Lagrangian two-phase flow model for liquid-fueled detonations is constructed. The gaseous mixture is described by an Eulerian method, and liquid particles in gaseous mixture are traced by a Lagrangian method. An improved space-time conservation element and solution element (CE/SE) scheme is applied to the simulations of detonations in liquid C  10  H  22  -O  2  /air systems. Different fuel droplet sizes and equivalence ratios are considered in the present study. Interestingly, the numerical results show that liquid-fueled detonations have some difference with gaseous detonations. Especially, a deficit in the propagation velocity compared to the gaseous detonation velocity is observed in mixtures with lean fuel and larger droplet sizes, while an increase in the propagation velocity compared to the gaseous detonation velocity is observed in the mixtures with very rich fuel. The surprising phenomenon is analyzed and discussed with the aid of detailed numerical results. In addition, the formation and propagation of two-phase detonation waves are characterized by series of results and the influence of particle radii is also discussed. All numerical results show that the present model can describe the gas-particle two-phase system accurately, and can be applied to numerical simulations of liquid-fueled detonations.

Numerical Simulation of Liquid-Fueled Detonations by an Eulerian–Lagrangian Model