Propagation dynamics of one-dimensional liquid-fuel detonation across air layers

In liquid-fuel detonation systems, such as rotating detonation engines (RDEs), the propagation of detonation waves often occurs in an inhomogeneous two-phase environment where fuel droplets and air coexist. High-resolution numerical simulations are performed to investigate the one-dimensional propagation dynamics of liquid-fuel detonation across air layers in n -heptane droplet-air mixtures. A coupled Euler-Lagrange framework is employed, in which the gaseous phase is solved using the reactive Navier-Stokes equations with a skeletal mechanism, while droplet dynamics, evaporation, and phase interactions are tracked in a Lagrangian manner. The influences of air-layer length, fuel-section length, and droplet diameter on detonation structure are systematically examined. Four distinct propagation modes are identified as the detonation wave traverses the air layer: high-intensity shock-detonation, low-intensity shock-detonation, low-intensity shock-deflagration, and low-intensity shock-delayed deflagration. The transitions between these regimes are primarily associated with the strength of the detonation wave across the air layer, the induction time and detonation initiation time of the n -heptane droplets/air mixture. A theoretical model is developed to predict the regime transitions, demonstrating that the propagation behavior is primarily controlled by the phase-velocity differential that determines the droplet evaporation rate. This study provides fundamental insights into the dynamics of liquid-fuel detonation propagation in non-uniform media and offers a framework for modelling detonation-phase interactions in multiphase reactive flows.